Magnetic materials based on heterometallic Cr^II/III–Ln^III complexes

Abstract

Accommodating disparate spin centres within a single ensemble is a valuable synthetic strategy to obtain interesting molecular magnetic materials. 3d–4f heterometallic complexes are one such subclass that has been extensively explored for the last three decades owing to their interesting magnetic properties. The primary reason is that the bridging ligand mediates magnetic super-exchange between 3d and 4f ions to considerably reduce the prevalent quantum tunnelling of magnetisation (QTM) in such complexes. Among the 3d–4f family, Cr^III–Ln^III assemblies nicely demonstrate the pivotal role played by strong exchange interactions between these two individual spin carriers to engender interesting single-molecule magnet (SMM) properties. In fact, this part of heterometallic chemistry has flourished greatly in the last decade despite its late development. In this review we provide an extensive synthetic, structural, magnetic, and magnetocaloric description of various Cr^III–Ln^III complexes along with their fundamental mechanisms of exchange interaction. Finally, we provide some possible solutions to improve the SMM properties of the Cr^III–Ln^III and other heterometallic complexes.

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1. Introduction

In the last few decades, the single-molecule magnet (SMM) field has drawn increasing attention and started blossoming since the seminal discovery by Christou and co-workers in 1993 that magnetic memory can be entangled within a discrete mixed-valence complex [Mn^III₈Mn^IV₄O₁₂(OAc)₁₆(H₂O)₄]·2AcOH·4H₂O (1), famously known as Mn₁₂ac.^1,2 This example launched an entirely new research direction in the molecular magnetism field, which soon turned from a solely coordination chemistry context into the centrepiece theme of a multidisciplinary research field.^3–5 The SMM can be defined as a discrete coordination or organometallic molecular entity that can retain its magnetization even in the absence of an external dc magnetic field below a certain temperature. Unlike conventional bulk magnets, they behave as quantized systems, and their magnetization dynamics are solely of molecular origin instead of a collective phenomenon.^6,7 These molecules are characterized by two important parameters: the first is the energy barrier for magnetization reversal (U_eff), which is related to the axial zero-field splitting parameter (ZFS), D and total ground-state spin, S through the equation U_eff = S²|D| for integer and for half-integer spin systems (Fig. 1). The second is the blocking temperature (T_B) below which these complexes show open hysteresis in the magnetization (M) vs. field (H) plot, a direct signature of permanent magnet behaviour. Moreover, these nanomagnets also exhibit interesting physics, such as quantum tunnelling of magnetization (QTM), quantum phase interference (QIP), etc.,^8–10 which endows them with the potential to be promising candidates for numerous potential technological applications such as high-density data storage device fabrication, quantum computation, and molecular spintronic materials.^4,11–13 Therefore, harnessing a system with T_B above room temperature is the holy grail of the molecular magnetism field. Based on these backgrounds, varieties of molecular complexes have been synthesized; depending upon composition, they can be divided into three major subcategories: mono or polynuclear 3d transition metal complexes,^14–21 mononuclear or polynuclear rare earth 4f complexes^22–31 and heterometallic 3d–4f^32–40 or 4d–4f complexes.^41,42 Initially, the main quest in this field was to harness high nuclearity complexes composed of paramagnetic first-row transition metal ions (Mn^II/III, Fe^II/III, Co^II, and Ni^II),^15,43 inspired by some of the groundbreaking works reported earlier in the literature such as {Mn^III₈Mn^IV₄},¹ {Mn^IIMn^III₇Mn^IV₄},⁴⁴ {Fe^III₈},⁴⁵ {Fe^III₁₉},⁴⁶ {Fe^III₉},⁴⁷ and {V^III₄}.^{46,48,49–52} The main objective was to maximize the total ground state spin (S) as the formula for the thermal energy barrier (U_eff) to magnetization-reversal has quadratic dependence on S, mentioned earlier (vide supra). However, later it was conceived from the combination of various systematic experimental investigations and multi-reference ab initio calculations that the incorporation of a large number of paramagnetic metal ions in a single molecule to maximize the thermal energy barrier by enhancing the total ground state S might be counterproductive. This is because the uniaxial magneto-anisotropy parameter (D) usually shares an inverse relationship with S², making U_eff virtually invariant to S.^53–55 As a proof of principle, a Mn₁₉ complex [Mn^III₁₂Mn^II₇(μ₄-O)₈(μ₃,η₁-N₃)₈(HL¹)₁₂(MeCN)₆]Cl₂ (2) possesses a remarkably large ground state spin of 83/2, but surprisingly did not show any SMM behaviour due to its overall negligible anisotropy.⁵⁶ On the contrary, interesting SMM behaviour can be retrieved successfully just by invoking a highly anisotropic Dy^III ion through the replacement of the central isotropic Mn^II centre in the resultant complex [Mn^III₁₂Mn^II₆Dy^III(μ₄-O)₈(μ₃-Cl)_6.5(μ₃-N₃)_1.5(HL¹)₁₂(MeOH)₆]Cl₃ (3) [L¹H₃ = 2,6-bis(hydroxymethyl)-4-methylphenol].⁵⁷ Subsequently, the Ln^III-based SMM field has started blooming since the seminal discovery of double-decker mononuclear phthalocyanine (Pc) lanthanide complexes [Ln^IIIPc₂]ⁿ (Ln^III = Tb, Dy, Ho; H₂Pc = phthalocyanine; n = −1, 0, +1) (4), by the Ishikawa group, portraying interesting SMM behaviour.⁵⁸ The heterometallic 3d–4f-based SMM chemistry began with the report of the tetranuclear {Cu^II₂Tb^III₂} (U_eff = 14.7 cm⁻¹; T_B = 1.2 K) complex by Osa and co-workers in 2004.⁵⁹ From then, a plethora of such complexes appeared in the literature, mainly composed of first-row transition metals such as Co^II, Mn^III, Ni^II and Cu^II ions, primarily due to the significant molecular anisotropy in their various coordination geometries, either through first (Co^II ion), second-order spin orbit coupling (Ni^II ion) or via Jahn–Teller distortion (Mn^III octahedral).^{19,21,60–66} In fact, the chemistry of such a mixed 3d–4f class of complexes had been further extended to earlier transition metals such as Cr^III ion, and Cr^III–Ln^III-based SMM chemistry witnessed considerable growth in the last decade. Up to now, using various multidentate chelating or open-arm flexible ligand systems, more than forty Cr–Ln heterometallic complexes of varying nuclearities (between 2–16) have been isolated.

Fig. 1 Double-well energy diagram for a SMM system where spin is a good quantum number to define the system.¹⁹ Reprinted with permission from ref. 19. Copyright 2016 Royal Society of Chemistry.

The typical examples are {CrLn₂},^67,68{Cr₂-Ln₂},^69,70{Cr₂Ln₃},^71,72{Cr₄Ln},⁷³ {Cr₂Ln₄},^74,75 {Cr₃Ln₃},^76,77 {Cr₄Ln₄},^78–80 {Cr₃Ln₆},⁸¹ {Cr₆Ln₆}⁸² and {Cr₈Ln₈}.⁸³ All these compounds unveiled interesting magnetic properties, and some even turned out to have excellent SMMs. Despite such a significant number of reports of Cr^III–Ln^III-based complexes with intriguing magnetic properties, to date not a single review has been dedicated to this particular field of coordination chemistry. Therefore, it is high time to deliver a meaningful comprehensive literature review based on these heterometallic assemblies, which eventually will help the readers to have a clear understanding regarding the various aspects of the magnetic properties of these complexes. We strongly believe that this kind of account will set the tone for further augmenting this interesting subcategory of heterometallic SMM chemistry with its full potential in forthcoming days. To do so, we describe this review in three parts: (i) the importance of 3d–4f magnetic exchange interaction in articulating the SMM behaviour with particular emphasis on the mechanism of Cr^III–Ln^III exchange coupling; (ii) the origin of magnetic anisotropy and role played by both Cr^II and Cr^III ions in the synthesis of SMMs; and finally (iii) detailed synthetic and structural aspects of different heterometallic Cr–Ln-based complexes of varying structural topologies reported to date, with a major focus on elaborative discussion of magneto-structural correlations including the SMM behaviour and magnetocaloric effect.

2. General mechanism of Cr^III-4f magnetic exchange interactions

In general, 3d–4f magnetic exchange plays a vital role in mitigating the low-temperature QTM (quantum tunnelling of magnetization) process by which a molecule demagnetizes fast upon penetrating through the imposed energy barrier via ground or low-lying excited states (thermal-assisted tunnelling).^23,84 Therefore, it is necessary to have a discussion on the mechanism of magnetic exchange and its overwhelming influence in augmenting the SMM performance of various 3d–4f coordination complexes. From the experimental point of view, appropriate calculation and analysis of intramolecular magnetic exchange coupling constants is tremendously difficult for systems containing 4f ions due to the presence of large magnetic anisotropy and weak exchange interactions arising from the high degree of localization of 4f orbitals. However, the magnetically isotropic Gd^III ion (f⁷) provides a much easier way to evaluate the exchange interactions in 3d-Gd systems, which do not have many complications from overparameterization, and finally to extend the conclusion to other isostructural 3d–4f complexes containing highly anisotropic Ln^III ions. In 1985, the synthesis of the seminal heterometallic trinuclear complex {Cu^II₂Gd} by Gatteschi and co-workers, employing a multidentate chelating Schiff base ligand N,N′-ethylene- bis (o-hydroxyacetophenoneiminato), showed strong Cu^II–Gd^III ferromagnetic exchange interactions [J_Cu–Gd = 5.32(5) and 7.38(7) cm⁻¹].⁸⁵ In fact, the further assertion that the ferromagnetic interaction between Cu^II and Gd^III ion is independent of the topology and nuclearity of the final complex opens the avenue to explore the magnetic properties of various other 3d–4f-based heterometallic complexes.^{32,60,65,66,86} Although the ferromagnetic interactions between {3d–4f} pairs are not intrinsic, several factors such as the nature of both 3d and 4f ions, coordination geometry and hence local symmetry around these ions, the nature and number of bridging ligands between the metal ions, and the dihedral angle etc., control the magnitude and sign of overall magnetic interaction.^{62,69,87–95} In fact, the sign of magnetic exchange interaction is crucial, since a ferromagnetic coupling surmounts a large ground state total spin (S) which is very important for constructing interesting SMMs and magnetic refrigerators. To understand the actual mechanism of such dominant ferromagnetic exchange interactions in the {Cu^II–Gd^III} pair, several qualitative explanations have been proposed. Gatteschi suggested transfer of electron density from the 3d_x²–y² orbital of Cu^II to the 5d orbital of Gd^III, while Kahn proposed the spin polarization mechanism where interaction takes place between the tails of the Cu 3d orbital with the empty Gd 6s orbital.^96,97 They explained that the diffuse nature of 5d orbitals makes them likely to be delocalized on the bridging atoms and thereby mediates the exchange interactions. In order to get further insight into the general mechanism of exchange coupling in {Cu^II–4f}as well as other{3d–4f} pairs, Ruiz and Rajaraman's group independently documented a series of extensive CASSCF and DFT calculations on various heterometallic complexes.^87,94,98,99 From their calculations, it is apparent that the overall magnetic exchange interactions (J_3d−4f) can be considered as a cumulative effect of both ferro (J_F) and antiferromagnetic (J_AF) interactions involving both types of metal ions, i.e. J_T = J_F + J_AF (Fig. 2). The antiferromagnetic (AFM) part (J_AF) of J_T arises from the direct non-vanishing overlap of magnetic orbitals between 4f and 3d ions of suitable symmetry, while the ferromagnetic (FM) contributions (J_F) come from the combined effect of interactions between remaining orthogonal 4f and the magnetic 3d orbitals, and charge transfer (CT) transition from the σ-type d orbitals (d_x²–y² & d_z²) of 3d metal ion to the empty 5d/6s/6p orbitals of lanthanides. Moreover, the 5d orbitals also get electronic contribution from the local 4f → 5d orbital excitation (Fig. 2). However, no CT takes place from π-type d orbitals such as d_xy, d_xz or d_yz containing unpaired electrons. It is important to note that the level of electronic occupation of 5d orbitals plays a pivotal role in controlling the sign of the coupling constant, with larger occupancies leading to more ferromagnetic interaction in structurally related compounds. To get more information regarding the Cu–Ln magnetic interactions which are outside of the scope of this review, readers are recommended to go through the recent comprehensive review published by Chandrasekhar and co-workers.³²

Fig. 2 Schematic representation of probable general 3d–4f magnetic exchange interactions in heterometallic complexes.⁹⁴ Reprinted with permission from ref. 94. Copyright 2016 American Chemical Society.

With this brief background, we shall consider the nature of {Cr^III–Ln^III} interactions, which is the focus of this review. Literature precedents showed that generally J_{Cr(III)–Ln(III)} interactions are antiferromagnetic, which is contrary to {Cu^II–Ln/Gd^III} interactions (Table 2). In this regard, Rajaraman and co-workers provided a deeper understanding regarding the mechanism of coupling involved in {Cr–Gd} systems through their extensive calculation published in a couple of papers.^71,100 From their calculations, it was very evident that unlike the late 3d transition metal ions, the lack of unpaired electron(s) in σ-type orbitals (d_x²–y² & d_z²) completely attenuates the charge transfer from 3d orbital of Cr^III to the 5d orbitals of Gd^III ion, resulting in a significant reduction in the J_F contribution. On the other hand, substantial J_AF contributions come from the relatively strong direct overlap between the two sets of Cr^III-3d and Gd^III-4f magnetic orbitals. This agrees well with the overall Cr^III–Gd^III AFM interactions found in most of the Cr^III–Ln^III complexes. Furthermore, magnetostructural correlation had been developed by variation of ∠Cr–F–Gd bridging angle (130–180°) as a quality check parameter on a series of complexes to gain insight into the nature of magnetic exchange, which revealed that the magnitude of ferromagnetic J_{Cr(III)–Gd(III)} interaction decreases with increase in ∠Cr–F–Gd angle (Fig. 3), and in fact a switch from ferro- to antiferromagnetic interaction is predicted at a critical bridging angle of 138°.¹⁰⁰

Fig. 3 Angular dependence of J parameter on varying ∠Cr–F–Gd bridging angle.^71,100 Reprinted with permission from ref. 117. Copyright 2013 Royal Society of Chemistry.

Such increase in antiferromagnetic interactions at a larger ∠Cr–F–Gd bridging angle was interpreted as follows: at a lower angle, there is a significant decrease in the Cr^III–Gd^III orbital direct overlap leading to less J_AF contribution, whereas a moderate increase in spin densities on metal ions and concomitant proportional decrease in spin densities on bridging fluoride ions through charge transfer leads to predicted overall ferromagnetic coupling. On the other hand, at a larger angle, the orthogonal arrangement of the spin-bearing 3d orbitals of Cr^III and the Gd^III 5d-orbitals leads to a reduction in the ferromagnetic interaction and a concomitant increase in the antiferromagnetic coupling, resulting in an overall increase in J_AF contribution.^71,100 From the magnetostructural data in Table 1, it is also evident that the magnitude of {Cr^III–Ln^III} interaction in hydroxide or methoxide bridge complexes is somewhat stronger compared to the fluoride bridge complexes, presumably due to the short Cr^III–Ln^III distance or the low <Cr–O–Ln bridging angle.¹⁰¹

Table 1 Representative magneto-structural correlation data of some important Cr^III–Ln^III-based complexes

Complex	Cr⋯Ln distance (Å)	Bridging angle (°)	J Cr(III)–Ln(III) (cm^−1)	U eff (cm^−1) & TB(K)	Ref.
a Theoretically calculated value. b Corresponding structural data for gadolinium are missing.
trans-CrF2(py)4Gd(hfac)4 (5) py = pyridine, hfac = hexafluroacetyalacetonatao	Cr⋯Gd 4.253(6)	<Cr−F−Gd = 178.32(39)	J Cr(III)–Gd(III) = −0.84(4)(−0.80)^a	—	100
Cyclo-{mer-[CrF(μ-F)2 (py)3]Gd(hfac)3}2(6b)	Cr⋯Tb^b 4.154(8), 4.099(6)	<Cr−F−Tb^b = 156.21(5)° and 165.32(5)	J Cr(III)–Gd(III) = −0.57(7)	—	102
{fac-[Cr(μ-F)3(Me3tame)]2Gd3(hfac)6 (μ-F)3} (7) tame = 1,1,1-tris-((methylamino)methylethane)	Cr⋯Gd 3.989(2) & 4.050(2)	<Cr−F−Gd = 142.8(3)−146.6(3)	J Cr(III)–Gd(III) = −0.14(0)	—	103
[{CrF3(Me3tacn)}2Gd3F2(NO3)7(OH2)(CH3CN)] (8) Me3tacn = N,N′,N′′-trimethyl-1,4,7-triazacyclononane	3.8895, 3.9815 & 4.0234	<Cr−F−Gd = 142.028,137.148 & 144.318	JCrIII–GdIII = +0.046 and +0.036	—	71
[Cr2Dy2(OMe)2(O2CPh)4(mdea)2(NO3)2] (9) mdeaH2 = N-methyldiethanolamine	Cr⋯Dy 3.3025	<Cr−O−Dy = 103.3010 & 95.809	JCrIII–DyIII = −20.5–26.0a	54 & 3.5	70
[Cr4Dy4(μ3-OH)4 (μ-N3)4(mdea)4(piv)4] (10)	Cr⋯Dy 3.3334	<Cr−O−Dy = 98.709	JCrIII–DyIII = −4.5	10.5 & 0.04	80
[Cr4Dy4(μ-F4)(μ3-OMe)1.25(μ3-OH)2.75(O2CPh)8(mdea)4] (11)	Cr⋯Dy 3.30111	<Cr−O−Dy = 103.2716 & 96.6615	JCrIII–DyIII = −1.8 &−0.8b	55 &3.5	78
{Et3NH[Cr2Gd3(OH)6(piv)10 (H2O)2]} (12)pivH = pivalic acid	Cr⋯Gd 3.4537(15) & 3.4502(18)	<Cr−O−Gd = 103.35(22), & 104.10(1)	J Cr(III)–Gd(III) = +0.215	—	104

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3. Origin of magnetic anisotropy and importance of Cr^II/III ion in fabricating Cr–Ln-based SMMs

Knowledge regarding the uniaxial magnetic anisotropy, which has a direct relationship with the ground state electronic structure of any paramagnetic metal ion under various ligand/crystal field environments, is very crucial and fundamental to fine tune the nature of SMMs. As far as heterometallic SMMs are concerned, literature precedents highlight that the initial development of Cr–Ln-based combinations was quite sluggish and sparse compared to other 3d metal counterparts such as Mn^III,^105–107 Co^II,^108–111 Ni^II,³⁸ Fe^II/III,^112–115 and Cu^II ion.^32,86,116 In fact, the use of chromium as a constituent ion is more often than not overlooked despite the added advantage that the majority of chromium isotopes (⁵⁰Cr, ⁵²Cr, ⁵⁴Cr, natural abundance more than 90.0%) are devoid of nuclear spin (I = 0), which contributes significantly to the electron–nucleus hyperfine interaction-mediated fast QTM efficiency.^117,118 The various reasons for such sluggish and late development of Cr–Ln-based systems are: (i) the inert nature and rigid coordination characteristics of the Cr³⁺ion;⁷⁹ (ii) this ion also shows weak anisotropy (the |D| values usually lie in the range of 0.2 to 0.5 cm⁻¹)¹¹⁹ compared with late transition metal ions such as Fe^II, Ni^II, Co^II ions due to isotropic electronic distribution; and (iii) the lack of unpaired electron in the σ-bonding d_x²–y² or d_z²-orbital under various crystal field environments enables Cr^III to be involved in intramolecular antiferromagnetic exchange interactions with the Ln^III ions. Nonetheless, in 2010 Powell and co-workers successfully isolated heterometallic octanuclear complex [Cr₄Dy₄(μ₃-OH)₄(μ-N₃)₄(mdea)₄(piv)₄]·3CH₂Cl₂ (10) (H₂mdea = methyldiethanolamine, PivH = pivalic acid) featuring a 4f-square in a 3d-square structural topology, which revealed interesting SMM behaviour with effective energy barrier (U_eff) = 10.5 cm⁻¹ and open hysteresis loop up to ∼1 K (sweep rate 0.035 Ts⁻¹).⁸⁰ A couple of years later, a seminal report of the tetranuclear complex [Cr^III₂Dy^III₂(OMe)₂(O₂CPh)₄(mdea)₂(NO₃)₂] (9) by Murray and co-workers showed U_eff = 54 cm⁻¹ and T_B = 3.5 K (sweep rate 0.035 Ts⁻¹). Detailed analysis of magnetic data revealed that strong antiferromagnetic interactions (J_{Cr(III)–Dy(III)} = −16.7 to −20.3 cm⁻¹) exist between the Dy^III and Cr^III ions in 9 which are mainly of the collinear ising-type, i.e. the chromium spins are always aligned along the Z axis. The utmost importance of strong Cr^III–Ln^III exchange interaction was further nicely illustrated by the Rajaraman and Murray group together through the isolation of a couple of structurally similar complexes [Co^III₄Dy^III₄(μ-F)₄(μ₃-OH)₄(o-tol)₈(mdea)₄]·3H₂O (13) and [Cr^III₄Dy^III₄(μ-F₄)(μ₃-OMe)_1.25(μ₃-OH)_2.75(O₂CPh)₈(mdea)₄] (11), where they have shown that purposeful replacement of the diamagnetic Co^III ion in 13 by a paramagnetic Cr^III ion in 11 (J_{Cr(III)–Dy(III)} = −1.8 cm⁻¹ by POLY_ANISO) has led to an increase in U_eff from 39.0 to 55.0 cm⁻¹ along with the significant suppression of QTM at low temperature in the chromium analogue, with the observation of highly coercive magnetic hysteresis loops up to ∼2 K.⁷⁸ These examples clearly highlight that the Cr^III–Ln^III magnetic exchange interaction alone is sufficient to engender interesting magnetic properties in Cr–Ln-based systems despite the isotropic/weakly anisotropic nature of the Cr^III ion. Moreover, Long's group's seminal work on a series of mononuclear complexes of general formula [Cr(dmpe)₂(CN)X](PF₆) (X = Cl (14a), Br (14b), I (14c)), possessing Cr^III ion in a pseudo-octahedral geometry, has shown that a considerable amount of axial ZFS (|D| = 0.11–2.30 cm⁻¹) can be installed even within the Cr^III ion through the spin–orbit coupling imparted by varying the coordinated ligands from lighter chlorine to heavier iodine atom.¹²⁰ Based on those landmark reports, SMM chemists were enticed enough to embark on the voyage of exploring heterometallic assemblies based on the combination of a highly anisotropic 4f ion with Cr^III in the quest for molecular systems possessing fascinating SMM properties. Consequently, to date, more than forty Cr^III–Ln^III-based complexes have been reported in the literature, and their synthetic methods, including their detailed magnetic properties, will be discussed in the subsequent sections. As far as the nature of bridging ligands is concerned, these complexes can be divided into two major subcategories: either single or doubly fluoride-bridged complexes of the general formula {Cr^III–F–Ln^III};⁷¹ or based on the oxygen atom-bridged complexes {Cr^III–X–Ln^III} (X = O, OH or OR),^78,80 of which the latter group arguably contributes the most in this specific family of heterometallic assemblies.

On the other hand, literature precedents lend support that Cr^II ions often could be a good source of easy-axis anisotropy (D < 0) under various geometries such as octahedral, tetragonal pyramidal, seesaw and square planar¹²¹ (see also other references in Table 1), and hence could be a potential component for developing Cr^II–Ln^III-based SMM systems. A qualitative d orbital splitting diagram along with the electron distribution of Cr^II ion in various geometries is shown in Fig. 4. A close inspection of the octahedral ligand field splitting of the free Cr^II ion revealed that a low-lying orbital ground doublet ⁵E_g and a high-lying orbital triplet ⁵T_2g arise from the electronic configuration due to the promotion of an electron from t_2g to e_g. The ⁵E_g, being highly unstable towards Jahn–Teller distortion, undergoes tetragonal elongation and significantly contributes to the ZFS akin to the isoelectronic Mn^III ion. In other geometries, the axial anisotropy arises presumably from ligand field symmetry-induced mixing of non-degenerate levels through second-order spin orbit coupling (SOC).⁶² A high-frequency/field electron paramagnetic resonance (HFEPR) spectroscopy measurement has been used to investigate the ZFS parameters of the Cr^II ion which divulged significant negative values of D in the range of −1.5 to −3.7 cm⁻¹ (Table 2). Moreover, the presence of an unpaired electron in the σ-bonding d_z² orbital under various ligand field environments paves the way for ferromagnetic interaction with the Ln^III ions through the spin-delocalization mechanism.⁸⁷ Therefore, combining the Cr^II ion with highly anisotropic 4f metal ions such as Dy^III and Tb^III could be helpful to isolate heterometallic complexes with interesting SMM properties. Nonetheless, to date not a single Cr^II–Ln^III-based system has been isolated, presumably due to the strong redox-unstable nature of the Cr^II with respect to oxidation towards Cr^III under open atmospheric condition and the lack of an appropriate synthetic design.¹²²

Fig. 4 Qualitative d-orbital splitting energy diagram of Cr^II ion under various geometries reported in the literature.

Table 2 Axial (D) and rhombic (E) ZFS parameters of Cr^II ion in some representative complexes under different coordination number and geometries from HF-EPR data

Complex	Coordination number	Geometry (valence electronic configuration)	D exp (cm^−1)	E exp (cm^−1)	Ref.
a Theoretical value from CASSCF/NEVPT2 calculations.
[K(18-crown-6) (Et2O)2] [Cr{N-(SiMe3)2}3] (15)	3	Trigonal planar (e′′^2a1′^1e′^1)	−15.10^a	0.0453^a	123
[Cr(N(TMS)2)2(X)2] TMS = SiMe3, X = pyridine (16a) X = THF (16b)	4	Square planar (eg^2a1g^1b2g^1)	−2.01 for 16a	0.02	117
			−2.54 for 16b	0.01
Cr(RNC(CH3)NR)2	4	Square planar	−1.74	0.07	124
R = ^iPr (17a) = Cy (17b)		Square planar	−1.82	0.09
(Cyclohexyl) = Dipp (17c)		Seesaw	−1.71	0.06
(2,6-Diisopropylphenyl) = ^tBu (17d)			−1.94	0.03
[Cr5(tpda)4Cl2] (18) (H2tpda = N^2,N^6-di(pyridin-2-yl)-pyridine-2,6-diamine)	5	Square-pyramidal (e^2b2^1a1^1)	−1.53 (SMM)	0.0092	125
[Cr3(dpa)4Cl2] (19) Hdpa = dipyridin-2-ylamine	5	Square-pyramidal	−1.643 (SMM)	0.034	126
Mo2Cr(dpa)4Cl2 (20)	5	Square-pyramidal	−2.187 (SMM)	0.024	127
W2Cr(dpa)4Cl2 (21)	5	Square-pyramidal	−3.617 (SMM)	0.0385	127
(NH4)2Cr(H2O)6(SO4)2 (22)	6	Octahedral (t2g^3eg^1)	−2.43	0.089	128
Cr(dmpe)2-(CN)X X = Cl (14a), I (14c)	6	Pseudo-octahedral (t2g^4)	−3.97 (14a) and −6.26 (14c)	—	120

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4. Cr^III–Ln^III complexes as magnetic refrigerants

In addition to their exciting magnetic properties, heterometallic Cr^III–Ln^III complexes have gained tremendous interest owing to the magnetocaloric effect (MCE), which forms the basis of molecular magnetic coolers.^129–132 Molecular magnetic cooling is a kind of magneto-thermodynamic phenomenon that denotes the change in entropy (−ΔS^max_m) of a magnetically active substrate under a variable temperature and magnetic field. They have great application in refrigeration under ultralow temperature environments, and have great environmentally friendly advantages. For a large MCE value, complexes must possess a combination of a large-spin ground state, insignificant anisotropy (D = 0), high magnetic density, and weak ferromagnetic interaction.⁹⁸ Recently, cryogenic magneto-refrigerants based on 3d-Gd^III complexes formed with the rational incorporation of an isotropic 3d ion and Gd^III ion (isotropic with the highest possible spin state of S = 7/2) have emerged as a promising candidate for enhancing the MCE value.^133,134 Among the 3d metal ions, one of the best candidates may be the isotropic Cr^III ion, with a maximum entropy of 222 J kg⁻¹ K⁻¹.¹³⁵ However, due to the inert nature of the Cr^III ion it becomes challenging to stitch it with Ln^III ions to synthesize polynuclear complexes with a high MCE value. Thus, Cr^III–Ln^III complexes as magneto-refrigerants are seldom explored and need more investigation to harness the effective potential of these complexes.

Pedersen and group have demonstrated a few examples of the magnetocaloric effect through the use of fluoride-bridged Cr^III–Ln^III complexes, which lead to weak exchange interactions and show relevant magnetic entropy changes.^71,100,102 Recently, Zhao and group have displayed a significant magnetocaloric effect in a ferromagnetic {Cr^III₂Gd^III₃} cluster having large magnetic entropy change of 27.0 J kg⁻¹ K⁻¹ at 4.0 K.¹⁰⁴ Zhai and group have synthesized a 3-dimensional sulphate framework-based unit having a large MCE of −ΔS^max_m = 38.33 J kg⁻¹ K⁻¹ at 2 K.¹³⁶ Shao and group have employed a building block strategy to generate a neutrally layered 2-dimensional metal coordination polymer consisting of an octanuclear {Cr^III₄Gd^III₄} metal cluster core and an organic ligand as a linker. The complex exhibits a large magnetic entropy of 28.8 J kg⁻¹ K⁻¹ at 3.5 K.¹³⁷ Xu and group have constructed a {Ln^III₈Cr^III₄} motif with a one-dimensional chain structure displaying a magnetic entropy change of −ΔS^max_m = 23.40 J kg⁻¹ K⁻¹ at 3 K.¹³⁸ Wen and group have reported the first example of an isolated 3D two-fold interpenetrating Cr^III–Gd^III framework using a carboxylate ligand having a large magnetocaloric effect of 39.86 J kg⁻¹ K⁻¹ at T = 2 K.¹³⁵ There are substantially fewer polynuclear Cr^III–Ln^III compounds with giant MCE, such as {Cr₄Ln},⁷³ {Cr₆Ln₂},¹³⁹ {Cr₂Ln₄},¹⁴⁰ {Cr₄Ln₄},¹⁴¹ {Cr₃Ln₇},¹⁴² {Cr₁₂Ln₄},¹³⁹ {Cr₂Ln₅},¹⁴⁰ {Cr₄Ln₈}.¹⁴⁰ Thus, Cr^III–Ln^III compounds could be a potential candidate for magnetic refrigerants with large magnetic entropy change; however, Cr^III–Ln^III compounds are rarely investigated, and thorough and detailed study is needed to establish their fruitfulness as magnetic coolers.

5. Cr^III–Ln^III heterometallic complexes of varying nuclearities

5.1 Dinuclear Cr^III–Ln^III complexes

The use of 2,2′-bipyridine ligand afforded two hydroxo-bridged iso-structural discrete dinuclear heterometallic Cr^III/Ln^III complexes [LnCr(bipy)₂(μ-OH)₂(H₂O)₆](ClO₄)₄·2H₂O {Ln = Gd (23a) or Dy (23b)} by heating an aqueous solution of 2,2′-bipyridine and CrCl₃ with a molar ratio of 1 : 1 followed by the addition of Ln(ClO₄)₃.¹⁴³ Interestingly, it was found that the stoichiometry of the added lanthanide perchlorate salt had an impact on the nuclearity of the final outcome. The use of 24 equivalents of Ln(ClO₄)₃ yielded dinuclear [Cr^IIILn^III] (Ln = Gd (23a) and Dy (23b)) complexes, whereas 12 equivalents of Ln(ClO₄)₃ led to the formation of trinuclear [Cr^III₂Ln^III] (Ln = Gd (24a), Dy (24b), and Tb (24c)) species (discussed in the next section).

Structural inspection showed two 2,2′-bipyridine ligand chelated with Cr^III ion, two μ-OH anions bridges between Gd^III and Cr^III ions with a Gd⋯Cr distance of 3.417(1) Å and six terminal aqua ligands bound with Gd^III to fulfill the distorted square antiprism geometry (Fig. 5). Magnetic data analysis revealed antiferromagnetic interaction between metal centers (Ln = Gd^III (23a) and Dy^III (23b)) with J_Cr–Gd = –0.102 cm⁻¹.¹⁴³

Fig. 5 Molecular structure for the cationic core of 23.

The reaction of CrO₃ and Gd₂O₃ in the presence of iminodiacetic acid (H₂IDA) under hydrothermal conditions constructed a three-dimensional (3D) two-fold interpenetrated coordination polymer [Cr^IIIGd(IDA)₂(C₂O₄)]_∞ (25). Here the oxalate anion was generated in situ from the dicarboxylate ligand under hydrothermal conditions in the presence of an oxidant like CrO₃.^144,145

The dinuclear asymmetric unit consists of one Gd^III ion and Cr^III ion held together by two IDA²⁻ anions and one oxalate anion (ox²⁻) anion. The Gd^III ion is eight coordinated, surrounded by four O atoms from two ox²⁻ anions and four O atoms of IDA²⁻ anions, while the Cr^III ion, six coordinated, forms a tetradentate metalloligand by the chelation of two IDA²⁻ anions.

An interpenetrating 3D network is obtained by {Gd(ox)}_∞ chains connected to metalloligands formed by adjacent Gd^III ion and Cr^III ions bridged by syn, anti carboxylate groups. Magnetic data analysis revealed the presence of antiferromagnetic interaction between the Gd^III ion and Cr^III ion. A large magnetocaloric value −ΔS^max_m = 39.86 J kg⁻¹ K⁻¹ suggests that the Cr–Gd complex could be a promising cryogenic magneto-refrigerant candidate.¹³⁵

5.2 Trinuclear complexes

Trinuclear isostructural [Cr^III₂Ln] (Ln = Gd (24a), Dy (24b), or Tb (24c)) species consist of a CrLnCr core formed by linkage of each Cr^III ion to Ln^III ion with the aid of two μ-OH⁻ groups. Similar to the complexes 23a and 23b, Ln^III ions in all the complexes are eight coordinated, in a distorted square antiprism geometry and Cr^III ions, six coordinated, distorted octahedral geometry (Fig. 6).¹⁴³ The [Cr₂Ln] core is not linear and angle ∠Cr–Gd–Cr is 111.27(4)° with an average Gd⋯Cr separation of 3.449(7) Å.

Fig. 6 Molecular structure for the cationic core of 24.

Antiferromagnetic interaction predominates between Cr^III and Gd^III ions in complex 24a. AC susceptibility data reveal no frequency-dependent out-of-phase maxima for all the complexes.

Another example of a linear trinuclear complex is the fluoride-bridged asymmetric [Dy(hfac)₃(H₂O)–CrF₂(py)₄–Dy(hfac)₃(NO₃)] (26) cluster (Fig. 7).⁶⁷ The structural parameters reveal that the angles ∠Cr–F–Dy and ∠Dy–Cr–Dy are 177.74(7)° and 177.80(5)°, respectively, with a Cr–Dy separation of 4.223(5) Å. The bond lengths associated with Cr–F and Dy–F of the bridging fluorides are as follows: bridging Cr–F lengths are significantly elongated [1.915(1) Å and 1.905(1) Å] compared to the non-bridging fluorides [1.844(2) Å and 1.845(2) Å] as in {Cr^IIIF₂(py)₄}⁺. The Dy–F distances (2.347(2) Å and 2.325(1) Å) are shorter compared to the Dy–O bond lengths ∼2.369(2) Å to 2.45(2) Å.

Fig. 7 Molecular structure of 26.

Interestingly, a ferrimagnetic to a ferromagnetic arrangement of magnetic moments of both metal ions were recorded by X-ray magnetic circular dichroism (XMCD). Fitting XMCD data to a spin-Hamiltonian mode, a weak antiferromagnetic interaction of J = −0.18 cm⁻¹ between both metal ions was obtained. In this context, it is important to mention that XMCD is a fantastic tool for the exact determination of exchange parameters even when the interaction is weak and strong anisotropy effects of the 4f ion are present.¹⁴⁶ Detailed magnetic analysis reveals the SMM behavior of 26 with effective energy barrier of 3 cm⁻¹. DFT calculations demonstrate the antiferromagnetic interaction between Dy^III–Cr^III ions originates from a superexchange mechanism via the fluoride bridge.⁶⁷

A trinuclear methoxo-bridged complex [Cr^IIIDy₂(OCH₃)₄(dpm)₅(CH₃OH)]·CH₃OH (27) was synthesized from the reaction of CrCl₃·(THF)₃, DyCl₃·CH₃OH, (1,1,1-tris(hydroxymethyl)-ethane (H₃L) and dipivaloymethane (dpm) ligand. The complex 27 has an overall star-shaped topology involving bridging methanol-methoxide units and beta-diketonates where a central Cr^III ion is coordinated to three Dy^III ion with the help of two tripodal trianionic ligand L³⁻ (Fig. 8).

Fig. 8 Molecular structure of complex 27.

The core consists of two μ₃-methoxy bridges above and below the plane of metal ions, while the edges of the triangle are connected by μ-bridged two methoxide ligands that link between Cr^III and Dy^III ions. Another neutral methanol molecule participates in bridging two Dy^III ions. To gain insight into the dynamics of magnetization, ac susceptibility measurements were performed revealing SMM behavior in zero dc field with effective energy barrier of 13.8 cm⁻¹ and τ₀ = 8.4 × 10⁻⁹ s.⁶⁸

5.3 Tetranuclear complexes

Bendix and co-workers reported a series of isostructural tetranuclear molecular square complexes, [{Cr^IIIF₂(NN)₂}₂{Ln(NO₃)₄}₂] (Ln = Ce–Nd, Sm–Ho (28a–28i)) by the 1 : 1 reaction of Ln(NO₃)₃(aq.) with difluorido complex cis-[Cr^IIIF₂(NN)₂](NO₃) [NN = 1,10-phenanthroline (phen) or 2,2′-bipyridine (bpy)]¹⁴⁷ as building blocks in methanol (Scheme 1). In these complexes, cis-coordination by the two fluoride ions from cis-[Cr^IIIF₂(NN)₂]⁺ facilitates the formation of the square motif through an almost linear fluoride-bridge between Cr^III and Ln^III (∠Ln–F–Cr ∼ 169°).

Scheme 1 Line draw structure for complexes 28a–28i.

This is the first example of unsupported fluoride-bridges between a paramagnetic transition metal ion and lanthanide ion which have exhibited interesting magnetic properties. The structural simplicity allowed the theoretical modelling and quantification of magnetic properties of fluoride-mediated gadolinium analogue which displays overall antiferromagnetic Gd–Cr exchange interactions with J_Gd–Cr∼ between −0.14 cm⁻¹ and −0.71 cm⁻¹. However, for some compounds, the temperature dependencies of the χ_T value drop slightly with decreasing temperature because of the progressive depopulations of Stark sublevels of Ln^III ions which basically mask the weak ferromagnetic Ln–Cr (Ln = Nd, Sm) interactions. The lack of any out-of-phase (χ′′) signal in ac susceptibility measurements with and/or without static field precludes the possibility of SMM behaviour in these complexes.¹⁰³

With the aim of expanding the family of fluoride-bridged Cr^III–Ln^III clusters, Bendix and co-workers utilized trifluorido complex mer-[CrF₃(py)₃] (py = pyridine) as synthon. This upon reaction with [Ln(hfac)₃(H₂O)₂] in the presence of different solvents has led different tetranuclear complexes, [Cr₂Ln₂(μ-F)₄(μ-OH)₂(py)₄(hfac)₆], (Ln = Y(29a), Gd(29b), Tb(29c), Dy(29d), Ho(29e), and Er(29f); hfacH = 1,1,1,5,5,5-hexafluoroacetylacetone), and [Cr₂Ln₂(μ-F)₄F₂(py)₆(hfac)₆], ((Ln = Y(6a), Gd(6b), Tb(6c), Dy(6d), Ho(6e), and Er(6f); hfacH = 1,1,1,5,5,5-hexafluoroacetylacetone), in acetonitrile and 1,2-dichloroethane, respectively (Scheme 2). The structural analysis of 29 revealed two octahedrally coordinated Cr^III ions bridged by two hydroxide ions (<Cr–O–Cr ∼ 96°). Other positions of the octahedron were occupied by two pyridine (trans to hydroxide group) and two trans fluoride ions. Each fluoride ion forms a bridge to the Ln^III ion (<Cr–F–Ln ∼ 140°). Ln^III displayed eight coordination which is fulfilled by two bridging fluoride ions and three bidentate [hfac]⁻ ligands. Here it is important to mention that partial hydrolysis of less robust mer-[CrF₃(py)₃] complexes assisted in the construction of the aforementioned structures of complexes 29. On the other hand, complexes 6 contain two mer-[CrF₃(py)₃] moieties where two cis-fluoride ions coordinated to Ln^III ions forming a fluoride-bridged square of alternating Cr^III and Ln^III metal centres. The bridging angles for the fluoride ions vary in the range of 156° to 166°.

Scheme 2 Line draw structure for complexes 29a–f and 6a–f.

Analysis of the magnetic data for 29b and 6b revealed that fluoride-mediated Cr^III–Gd^III exchange interactions were 0.43(5) cm⁻¹ and 0.57(7) cm⁻¹, respectively, which is consistent with the earlier reports.¹⁰⁰ Variable-temperature and frequency dependent ac susceptibility measurements in the presence of a static field showed that 29a is a typical SMM with U_eff = 4.59(18) cm⁻¹ as the thermal barrier for relaxation with τ₀ = 2.8(3) × 10⁻⁵ s (Fig. 9). On the other hand, the temperature variation of χ′′ for 6a, obtained in a 1000 Oe static field without peak maxima, is indicative of a slow relaxation phenomenon without measurable energy barrier. Interestingly, 6b displayed a moderate cooling power with maximum magnetic entropy change −ΔS^max_m of 11.4 J kg⁻¹ K⁻¹ for ΔH = 9 T at T = 4.1 K.¹⁰²

Fig. 9 Out-of-phase (χ′′(T)) component of the ac susceptibility obtained on 29a in a dc field of H_dc = 1200 Oe (H_ac = 3.8 Oe). Inset: χ′′(ν_ac) of 29a at selected temperatures from 1.85 K to 3.40 K at H_dc = 1600.¹⁰² Reprinted with permission from ref. 102. Copyright 2012 Royal Society of Chemistry.

Apart from the aforementioned structural motifs in the tetranuclear Cr–Ln system, other well-studied motifs are “diamond”, “butterfly” or “defective dicubane” arrangements. In general, there are two possible variances for the abovementioned 3d/4f cores: in Type I arrangement, two 4f metal ions present in the body positions and the 3d transition metal ions occupy the outer wingtip sites; in Type II exactly the opposite situation prevails, where 3d metal ions occupy the body positions and 4f metal ions are at the wingtips (Scheme 3). Murray and co-workers have reported extensive magnetic studies for complexes consisting of Type I core based {M^III₂Ln^III₂}, (M = Co, Cr and Ln = Dy, Tb, Ho).^{69,70,148–155}

Scheme 3 Schematic diagram of Type I and Type II compound.

Systematic study has revealed that the Type I complexes can be subdivided into three families depending on the metal and co-ligands used in that particular system. The first type of such family assembled with benzoate and amine-polyalcohol co-ligands and resulted in {Co^III₂Dy^III₂}-benzoate butterfly complexes; [Co^III₂Dy^III₂(OMe)₂(O₂CPh)₄(RN{(CH₂)₂O}₂)₂(L)₂][X]₂ (R = H (30a), Me (30b), Bu (30c), (CH₂)₂OH) (30d), L = MeOH or NO₃ and X = NO₃.^154,155 This class of compounds displays magnetic behaviour analogous to Dy₂ derivative as Co^III is a diamagnetic substance. It was found that all the complexes displayed SMM behaviour and a thermal energy barrier ranging from 54 to 80 cm⁻¹.¹⁵⁵ This wide range of thermal energy barrier for the spin reversal is due to the use of electronically different N-substituted diethanolamine ligands in the formation of different complexes. Another example of this category consists of double cluster compounds [Co^III₂Dy^III₂(OMe)₂(teaH)₂(O₂CPh)₄(MeOH)₄](NO₃)₂·MeOH·H₂O (31a) and [Co^III₂Dy^III₂(OMe)₂(teaH)₂(O₂CPh)₄(MeOH)₂(NO₃)₂]·MeOH·H₂O.(31b).¹⁵⁴ The magnetization relaxation for this category of complexes exhibits temperature dependency below 2.5 K, suggesting quantum tunnelling of magnetization (QTM) below this temperature. Importantly, the extent of QTM has been reduced in these classes of complexes compared to the analogous Dy SMMs (binuclear Dy2 SMMs) due to the presence of nonmagnetic exchange ground state that arises from the antiferromagnetic dipolar coupling. This observed phenomenon was corroborated using ab initio calculations. Theoretical calculations explain the suppressed QTM due to the following reasons: the ground doublet has a small splitting (10⁻⁶ cm⁻¹), due to the non-Kramer's state resulting from two coupled Dy^III ions, which reduces QT. A second reason is the non-magnetic ground state, as the dipolar coupling is much stronger than the exchange interaction and antiferromagnetic in nature, which reduces the transverse influence from the neighbouring molecules. The ground state being non-magnetic, the magnetic field from the neighbouring complexes will vanish on lowering temperature, and thereby only the ground of each molecule remains populated at T ∼ 0 K, decreasing the possibility for QTM. This was further supported by the experimental magnetic dilution technique for the analogous [Co^III₂Y^III₂] analogue. The relaxation mechanism was dominated by a single-ion character and overall weak dipolar antiferromagnetic interactions for these complexes, and these phenomena play a pivotal role in the suppression of QTM at zero-field.

In the follow-up work, the investigators were able to isolate a structurally nearly similar second set of {Co^III₂Dy^III₂}-acac butterfly complexes, [Co^III₂Dy^III₂(OR)₂(R′N{(CH₂)₂O}₂)₂(acac)₄(NO₃)₂] (R = H, Me and R′ = Me, (CH₂)₂OH) (32), utilizing acetylacetone (acacH) instead of benzoate. Both types of complex displayed square anti-prismatic (SAP) geometry with a near similar primary coordination sphere around Dy^III ions, although, as terminal substituents around the Dy^III ions differ, consequently the low-temperature spin dynamics are also different in these complexes.^152,153

A third set of compounds was isolated by substituting Co^III with Cr^III in the aforementioned families to construct structurally related {Cr^III₂Dy^III₂}-benzoate and {Cr^III₂Dy^III₂}-acac complexes.^{69,70,148–151} In 2013, Murray and co-workers reported the isolation of [Cr^III₂Dy^III₂(OMe)₂(O₂CPh)₄(mdea)₂(NO₃)₂] (9) (mdeaH₂ = N-methyldiethanolamine)⁷⁰ (Fig. 10) which showed different and distinct low-temperature spin dynamics compared to the analogous Co^III counterpart; although both have comparable relaxation energy barriers of 77 K, the activation barriers in 31b and 9 are of different origins.

Fig. 10 Molecular structure of 9 (left) and hysteresis plot for 9, with an average sweep rate of 0.003 Ts⁻¹, at different temperatures indicated (right).⁷⁰ Reprinted with permission from ref. 70. Copyright 2013 John Wiley and Sons.

As a result, at very low temperature a significant increase in relaxation time was observed for 9 compared to 31b.

Ab initio calculations corroborate that the magnetic properties in 9 arise as a consequence of the magnetic interactions between the Dy^III and Cr^III ions (J_Dy–Cr = |8|−|10| cm⁻¹). Therefore, the energy barrier in 9 is of a multilevel exchange type (Fig. 11), with significantly reduced QTM and considerably longer relaxation times. On the contrary, in 31b, the barrier originates from one excited state of individual Dy^III ions, and therefore shorter relaxation times are observed. As a result of reduced efficiency of QTM, the Cr^III analogue displayed magnetic hysteresis up to 3.5 K with a large coercive field (coercive field of ca. 2.8 T at 1.8 K), whereas for the Co^III analogue (31b) no hysteresis was observed above 1.8 K using a conventional SQUID magnetometer. The comparison of the {M^III₂Ln^III₂}, (M = Co, Cr) cores for 31b and 9 is displayed in Fig. 12.

Fig. 11 Ab initio calculated exchange spin states and the plausible relaxation dynamics in 9, plausible anisotropy energy barrier (dashed green line), QTM (blue line), spin–phonon transitions (red and dark-green).⁷⁰ Reprinted with permission from ref. 70. Copyright 2013 John Wiley and Sons.

Fig. 12 Comparison of {M^III₂Ln^III₂} cores, (M = Co, Cr) for 31b and 9.

In their subsequent efforts, the authors prepared several iso-structural [Cr^III₂Dy^III₂] analogues containing a similar tetranuclear metallic core by varying the amine–diolate ligands.¹⁵¹ By utilizing diethanolamine (deaH₂), N-ethyldiethanolamine (edeaH₂), butyldiethanolamine (bdeaH₂), and triethanolamine (teaH₃) they have reported four new 3d/4f complexes of formulae [Cr^III₂Dy^III₂(OMe)₂(O₂CPh)₄(dea)₂(MeOH)₄](NO₃)₂ (33a), [Cr^III₂Dy^III₂(OMe)(OH)(O₂CPh)₄(edea)₂(NO₃)₂]·MeOH·Et₂O (33b) [Cr^III₂Dy^III₂(OMe)₂(O₂CPh)₄(bdea)₂(NO₃)₂] (33c), and [Cr^III₂Dy^III₂(OMe)₂(O₂CPh)₄(teaH)₂(NO₃)₂(MeOH)₂] (33d). All the compounds 33a–d distinctly displayed SMM behaviour as characterized by ac susceptibility and variable field magnetization/hysteresis measurements. Ac susceptibility analysis yields anisotropy barriers of 43.2, 55, 42.8, and 44 cm⁻¹ for 33a, 33b, 33c, and 33d, respectively. These values are comparable to the value obtained for the analogous {Cr^III₂Dy^III₂}-mdea complex 9, of 53.5 cm⁻¹. This indicates that replacement of amine–diolate ligands around the Dy ions in 33a–d has trivial influence on the energy barrier. Nonetheless, the strength of the magnetic exchange interaction determines the energy barrier for the magnetization reversal in these tetranuclear complexes, as corroborated theoretically in analogous {Cr^III₂Dy^III₂}-mdea complex.⁷⁰

As well as the Dy^III analogue (9), the author also prepared isostructural [Cr^III₂Ln^III₂(OMe)₂(O₂CPh)₄(mdea)₂(NO₃)₂]⁶⁹ where Ln = Gd (34a), Er (34b),Tb (34c) and Ho (34d) by replacing Dy^III in 9 to compare the role played by Ln^III ions in magnetic behavior. Additionally, [Cr^III₂Ln^III₂(OMe)₂(O₂CPh)₄(teaH)₂(NO₃)₂(MeOH)₂] [Ln = Pr (34e) and Nd (34f)] were also synthesized using triethanolamine and benzoic acid. The Gd derivative (34a) did not respond to the ac measurement owing to the isotropic nature of the Gd^III ion. Erbium derivative (34b) displayed only tails without any maxima in the frequency-dependent out-of-phase ac susceptibility measurement, which confirmed the occurrence of very fast QTM in ground exchange states, clearly indicating the system's inability to generate single-ion bistability. The Tb (34c) and Ho (34d) analogues responded to ac susceptibility at zero dc field with anisotropy barriers of 45 and 36 cm⁻¹, respectively, which are relatively small compared with 31b (54 cm⁻¹), indicating fast QTM in 34c and 34d with respect to 31b. Moreover, 31b opens up a hysteresis loop up to 3.5 K with a large coercive field (sweep rate of 0.003 Ts⁻¹), whereas Tb (34c) and Ho (34d) analogues display a magnetic hysteresis loop up to 2.5 (34c) and 1.8 K (34d), respectively, (sweep rate of 0.003 Ts⁻¹) with a large loss of magnetization at zero-field due to strong ground state tunnelling of magnetization (Fig. 13). These differences might be due to the following reasons: Dy^III, Tb^III and Ho^III possess oblate-spheroidal electron densities in their ground state. So, the ligand field from the axial/pseudo-axial direction may stabilize the largest angular momentum projections of the ground spin–orbit multiplet, which results in magnetic bistability and U_eff to magnetic reorientation in these complexes. Although all the systems have magnetic bistability the non-Kramers nature of Tb^III and Ho^III leads to greater tendency for QTM at the ground state and also causes inferior hysteresis for 34c and 34d analogues compared with 31b.

Fig. 13 Hysteresis plots for 34c (left) and 34d (right) with a sweep rate of 0.003 Ts⁻¹, at the temperatures indicated.⁶⁹ Reprinted with permission from ref. 69. Copyright 2015 American Chemical Society.

The same group reported a series of tetranuclear 3d–4f complexes with the general formula of [Cr^III₂Dy^III₂(OMe)₂(RN{(CH₂)₂O}₂)₂(acac)₄(NO₃)₂] [R = Me (35a), Et (35b), nBu (35c)]¹⁵⁰ (Fig. 14) with a Type 1 butterfly core arrangement. These complexes possess anisotropy barriers of [23.6 (35a), 25.7 (35b) and 28.5 (35c) cm⁻¹] with open hysteresis loops up to 1.8 K for 35a, 2.2 K for 35b and 35c. From the previous discussion it is very much evident that the energy barrier and the relaxation time for the Cr^III–Ln^III complexes are better compared to the Co^III–Ln^III analogues due to the significant magnetic exchange interaction between Cr^III and Ln^III ions to suppress the QTM.¹⁵⁴

Fig. 14 The molecular structure of compound 35a.

Importantly, in spite of nearly similar core structures, the energy barrier for 35a–c was approximately half of that of 31b. The above phenomenon was explained with the help of theoretical calculations which showed a weaker magnetic exchange interaction in 35a–c which is roughly half in magnitude to that of 31b. This result demonstrated that the strength of the Cr–Dy interaction directly played a crucial role in determining the effective energy barrier. Here it is noteworthy to mention that although the local environments around the Dy^III centre in complexes 31b and 35a–c are significantly different, this plays a only minor role in manipulating the low-temperature dynamic behaviour in these complexes (Fig. 15). The exchange interactions between the metal ions are more important than the coordination environment around the Dy^III ion as long as the change in local geometry does not drastically alter the ground state, g_z ∼ 20, of the Dy^III ion and the exchange pathways are not significantly weakened.

Fig. 15 Comparison of coordination environments for core structures of 35a and 31b.^150,154

In another work the authors synthesized butterfly-cored {Cr^III₂Dy^III₂}-hfacac (Hhfacac = hexafluoroacetoacetone), i.e [Cr^III₂Dy^III₂(OMe)₂(mdea)₂(hfacac)₆] (36).¹⁴⁹ This complex displayed a barrier of 27.8 cm⁻¹ which was slightly larger than the analogous complex, [Cr^III₂Dy^III₂(OMe)₂(mdea)₂(acac)₄(NO₃)₂] (35a). A plausible reason might be the consequence of replacing [acac]⁻ and nitrate ligands with strongly electron-withdrawing [hfacac]⁻ ligands that imposed stronger exchange interactions among the ions in 36 compared with 35a. As a result, the blocking temperature increases from 1.8 to 2.2 K for 36 compared with 35a, which is not observed in the corresponding [Co^III₂Dy^III₂] case due to weaker exchange interaction. This work represents an example in which the incorporation of an electron-withdrawing group in a complex can enhance the effective energy barrier either by stabilizing the ground Kramers doublet or by manipulating the exchange interaction. Utilizing this concept, Murray and co-workers have shown significant improvements in magnetic relaxation time, magnetic hysteresis blocking temperature and magnetic coercivity of {Cr^III₂Dy^III₂}-benzoate complexes via replacing bridging benzoate ligands with substituted benzoate ligand. Varying the benzoate ligand from electron-withdrawing (halogen) to electron-donating groups (tert-butyl), they have synthesized a variety of complexes, [Cr^III₂Ln^III₂(OMe)_2–x(OH)_x(2-Cl-4,5-F-benz)₄(mdea)₂(NO₃)₂]·xMeOH [Ln = Tb (37a), Dy (37b) and Ho (37c)] (2-Cl-4,5-F-benzH = 2-chloro-4,5-fluorobenzoic acid) and [Cr^III₂Dy^III₂(OMe)(OH)(4-^tBu-benz)₄(^tBudea)₂(NO₃)₂]·MeOH·2Et₂O (38) (^tBudeaH₂ = N-tert-butyldiethanolamine, 4-tert-benzoic acid = 4-^tBu-benzH).¹⁴⁸ All these complexes display SMM behaviour. Most importantly, the observed magnetic hysteresis loops of all samples are temperature dependent, with open loops observed up to 3.5, 4.7 and 2.6 K, for 37a, 37b and 37c, respectively. Alternatively, the benzoate analogue showed hysteresis loops up to 2.5 (34c), 3.5 (9) and 1.8 (34d). Comparison of the hysteresis loops also indicates a substantial increase in the coercive field observed for 37a, 37b and 37c compared with 34c, 9 and 34d (Fig. 16). Most importantly, 9, 34a and 34d show large loss of magnetization at zero field in M vs. H hysteresis plot, whereas complexes 37a–c display a considerable reduction of magnetization indicating significant suppression of zero-field QTM. Notably, there is no loss of magnetization at zero field for 37b compared with 9.

Fig. 16 Comparison of the hysteresis curves of (at sweep rate of 0.003 Ts⁻¹) (34c and 37a), (9 and 37b) and (34d and 37c).¹⁴⁸ Reprinted with permission from ref. 148. Copyright 2016 Royal Society of Chemistry.

Powell and co-workers reported Type II butterfly-cored complexes: [M^III₂Ln^III₂(μ₃-OH)₂(pMe-PhCO₂)₆(L)₂] [H₂L = 2,2′-((pyridin-2-ylmethyl)azanediyl)bis(ethan-1-ol), M = Cr, Ln = Dy (39a) or Y (39b); M = Mn, Ln = Dy (40a) or Y (40b); M = Fe, Ln = Dy (41); M = Al, Ln = Dy (42)] and the diluted complex [Al^III₂Dy^III₂]: [Al^III₂Dy^III_0.18Y_1.82] (43) (Fig. 17).^88,156 No out-of-phase signal was observed even after using a static dc field, indicating the absence of SMM behaviour for Cr^III analogue (39a). 40a {Mn₂Dy₂} displayed an anisotropy barrier U_eff of 13.35 cm⁻¹ at zero dc field. For 41 {Fe₂Dy₂}, 42 {Al₂Dy₂} and 43 {Al^III₂Dy^III_0.18Y_1.82} the anisotropic energy barrier was found to be 11.23, 28.84 and 44.41 cm⁻¹ under 1000 Oe applied dc field. The SMM behaviour for the four complexes follows the trend: {Al₂Dy₂} > {Mn₂Dy₂} > {Fe₂Dy₂} > {Cr₂Dy₂}. The combined experimental and theoretical calculations suggested that altering the 3d^III ions can affect the single-ion properties, the nature and the magnitude of the 3d^III–3d^III, 3d^III–Dy^III and Dy^III–Dy^III magnetic coupling, thus quenching the quantum tunnelling of magnetization (QTM) significantly, thereby improving the SMM properties within these motifs (Fig. 18).

Fig. 17 Molecular structure of 39a.

Fig. 18 Comparison of the core structures in complexes 39a, 40a, 41 and 42.^88,156

It has been noted that the tetranuclear [Cr₂Ln₂] of diverse structures represent most of the literature precedents in the family of Cr–Ln-based heterometallic complexes. We have provided the detailed magnetic properties of these analogues in Table 3.

Table 3 Representative examples of tetranuclear Cr^III–Ln^III complexes

Compounds	Bridging ligand	J CrGd [cm^−1]	Energy barrier (Ueff) time constant (τ0)	Magnetocaloric effect (−ΔSm)	Ref.
[Cr^III2Ln^III2(μ-F)4(μ-OH)2(py)4 (hfac)6] (Ln^III = Y, Gd, Tb, Dy, Ho, Er) hfacH = 1,1,1,5,5,5-hexafluoroacetylacetone, py = pyridine (29a–f)	Ln⋯F⋯Cr	J CrGd = 0.43	U eff = 4.59 cm^−1 and τ0 = 2.8 × 10^−5 s for Ln^III = Dy	—	119
[Cr^III2Ln^III2(μ-F)4F2(py)6(hfac)6] (Ln^III = Y, Gd, Tb, Dy, Ho, Er); hfacH = 1,1,1,5,5,5-hexafluoroacetylacetone, py = pyridine (6a–f)	Ln⋯F⋯Cr	J CrGd = 0.57	—	−ΔSm = 11.4 J kg^−1 K^−1	119
[Cr^III2Ln^III2(OMe)2(O2CPh)4(mdea)2(NO3)2] (Ln^III = Dy); mdeaH2 = N-methyldiethanolamine (9)	Ln⋯O⋯Cr (O from mdea)	J CrDy = |8|−|10|	U eff = 53.5 cm^−1 and τ0 = 5.1 × 10^−8 s for Ln^III = Dy	—	55
[Cr^III2Dy2(OMe)2(O2CPh)4(dea)2(MeOH)4](NO3)2 (Ln^III = Dy); deaH2 = diethanolamine (33a)	Ln⋯O⋯Cr (O from dea)	—	U eff = 43.2 cm^−1 and τ0 = 2.3 × 10^−7 s for Ln^III = Dy	—	167
[Cr^III2Dy2(OMe)(OH)(O2CPh)4(edea)2(NO3)2]·MeOH·Et2O (33b) (Ln^III = Dy); edeaH2 = N-ethyldiethanolamine	Ln⋯O⋯Cr (O from edea)	—	U eff = 55 cm^−1 and τ0 = 3.4 × 10^−8 s for Ln^III = Dy	—	167
[Cr^III2Dy2(OMe)2(O2CPh)4(bdea)2(NO3)2] (33c) (Ln^III = Dy); bdeaH2 = N-n-butyldiethanolamine	Ln⋯O⋯Cr (O from bdea)	—	U eff = 42.8 cm^−1 and τ0 = 1.1 × 10^−7 s for Ln^III = Dy	—	167
[Cr^III2Dy2(OMe)2(O2CPh)4(teaH)2(NO3)2(MeOH)2] (33d)(Ln^III = Dy); teaH2 = triethanolamine	Ln⋯O⋯Cr (O from teaH)	—	U eff = 44 cm^−1 and τ0 = 8.3 × 10^−7 s for Ln^III = Dy	—	167
[Cr^III2Ln^III2(OMe)2−x(OH)x(O2CPh)4 (mdea)2(NO3)2] (34a–d) (Ln^III = Gd, Tb, Ho, Er); mdeaH2 = N-methyldiethanolamine	Ln⋯O⋯Cr (O from mdea)	J CrGd = −0.960	U eff = 44.5 cm^−1 and τ0 = 1.7 × 10^−9 s for Tb; Ueff = 36.1 cm^−1 and τ0 = 1.1 × 10^−9 s for Ho	—	54
[Cr^III2Ln^III2−(OMe)2(O2CPh)4(teaH)2 (NO3)2(MeOH)2] (Ln^III = Pr, Nd); tea = triethanolamine (34e–f)	Ln⋯O⋯Cr (O from teaH)	—	—	—	54
[Cr^III2Ln^III2(OMe)2(MeN{(CH2)2OH}2)2(acac)4(NO3)2] (35a) (Ln^III = Dy); acacH = acetylacetone	Ln⋯O⋯Cr (O from acac)		U eff = 23.6 cm^−1 and τ0 = 1.2 × 10^−7 s for Ln^III = Dy	—	166
[Cr^III2Ln^III2(OMe)2(EtN{(CH2)2OH}2)2(acac)4(NO3)2] (35b) (Ln^III = Dy); acacH = acetylacetone	Ln⋯O⋯Cr (O from acac)		U eff = 25.7 cm^−1 and τ0 = 9.2 × 10^−8 s for Ln^III = Dy	—	166
[Cr^III2Ln^III2(OMe)2(nBuN{(CH2)2OH}2)2(acac)4(NO3)2] (35c) (Ln^III = Dy) acacH = acetylacetone	Ln⋯O⋯Cr (O from acac)		U eff = 28.5 cm^−1 and τ0 = 3.1 × 10^−7 s for Ln^III = Dy	—	166
[Cr^III2Ln^III2(OMe)2−(mdea)2 (hfacac)6] (Ln^III = Dy) (36); mdeaH2 = N-methyldiethanolamine, hfacacH = hexafluoroacetylacetone	Ln⋯O⋯Cr (O from mdea)		U eff = 28.6 cm^−1 and τ0 = 1.6 × 10^−7 s for Ln^III = Dy	—	165
[Cr^III2Ln^III2(OMe)2−x(OH)x(2-Cl-4,5-F-benz)4(mdea)2(NO3)2] ·xMeOH (Ln^III = Tb, Dy and Ho) (37a–c); mdeaH2 = N-methyldiethanolamine, 2-Cl-4,5-F-benz = 2-chloro-4,5-fluorobenzoic acid	Ln⋯O⋯Cr (O from mdea and Ln⋯O⋯Cr) from 2-Cl-4,5-F-benz		U eff = 44 cm^−1 and τ0 = 7.7 × 10^−9 s for Ln^III = Tb; Ueff = 61 cm^−1 and τ0 = 2.1 × 10^−7 s for Ln^III = Dy; Ueff = 36 cm^−1 and τ0 = 6.8 × 10^−9 s for Ln^III = Ho		164
[Cr^III2Dy2(OMe)(OH)(4-^tBu-benz)4(^tBudea)2(NO3)2]·MeOH·2Et2O (Ln^III = Dy) (38); (^tBudeaH2 = N-tert-butyldiethanolamine), 4-^tBu-benz = 4-tert-benzoic acid	Ln⋯O⋯Cr (O from mdea and bridging ligand from 4-^tBu-benz		U eff = 45 cm^−1 and τ0 = 7.7 × 10^−8 s		164
[Cr^III2Ln^III2(μ3-OH)2(p-Me-PhCO2)6(L)2] (Ln^III = Dy, Y) (39a–b); H2L = 2,2′-((pyridin-2-ylmethyl)azanediyl)bis(ethan-1-ol), p-Me-PhCO2 = 4-methylbenzoic acid	Ln⋯O⋯Cr (O from L and bridging O atom from p-Me-PhCO2		—		105
[Cr^III2Dy^III2(teaH)2(OCH3)2(piv)6] (44); teaH = triethanolamine, piv = pivalic acid	Ln⋯O⋯Cr (O from tea and bridging ligand from piv	J CrDy = −1.5	U eff = 50 cm^−1 and τ0 = 1.2 × 10^−7 s		157
[Cr^III2Tb^III2(OH)2(FcCO2)4(NO3)2(Htea)2] (45a) Fc = (η^5-C5H4)(η^5-C5H5)Fe and tea = triethanolamine	Ln⋯O⋯Cr (O from tea)		U eff = 37.5 cm^−1 and τ0 = 21 × 10^−9 s		158
[Cr^III2Dy^III2(OH)2(FcCO2)4(NO3)2(Htea)2] (45b) Fc = (η^5-C5H4)(η^5-C5H5)Fe and tea = triethanolamine	Ln⋯O⋯Cr (O from tea)		U eff = 52.1 cm^−1 and τ0 = 26 × 10^−9 s		158
[Cr^III2Ho^III2(OH)2(FcCO2)4(NO3)2(Htea)2] (45c) Fc = (η^5-C5H4)(η^5-C5H5)Fe and tea = triethanolamine	Ln⋯O⋯Cr (O from tea)		U eff = 32.6 cm^−1 and τ0 = 2 × 10^−9 s		158

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5.4 Pentanuclear complexes

Bendix and co-workers utilized synthons fac-[CrF₃(Me₃tame)] and fac-[CrF₃(Me₃tacn)], where Me₃tame = 1,1,1-tris-((methylamino)methylethane, Me₃tacn = N,N′,N′′-trimethyl-1,4,7 triazacyclononane (Me₃tacn), as building blocks to synthesize pentanuclear [Cr₂Ln₃] complexes [Ln = Gd (7a), Ho (7b), Yb (7c), Nd (7d)]. The pentanuclear complexes are in trigonal bipyramidal geometry where the equatorial plane consists of Ln^III ions which are bridged by bidentate/bridging nitrate (μ-nitrato-1,2 κO:1 κO) ligands or fluoride ligands. Cr^III ions are placed in the apical position. The Nd^III derivative consisted of the most unusual μ₃-fluorido ligand bridging in all three metal centres of the equatorial plane symmetrically. The structural simplicity allowed the modelling of the magnetic properties and quantification of magnetic coupling in 7a. Gd–Cr exchange interaction was found to be antiferromagnetic with J_Cr–Gd = −0.14 cm⁻¹ and negligible J_Gd–Gd = 0.06 cm⁻¹. The weak intra cluster interactions, large net magnetic moment and negligible ZFS in 7 indicates a large number of electronic states that are almost degenerate with the ground state. This phenomenon made them suitable candidates for evaluating the magneto-caloric effect. Experimentally 7a displayed large magneto-caloric effect with maximum value of 28.7 J kg⁻¹ K⁻¹ at 2.2 K for an applied field of 90 kOe.¹⁰³

The authors further extended this work for the other 3d analogues. Similar synthetic protocols with the precursor fac-[M^IIIF₃(Me₃-tacn)₃]·4H₂O [M = Cr, Fe, Ga] led to the isostructural [{MF₃(Me_3⁻tacn)}₂Gd₃F₂(NO₃)₇(H₂O)(CH₃CN)] complexes [M = Cr (8a), Fe (8b), Ga (8c)] (Fig. 19). Weak exchange interactions in these complexes were rationalized computationally. Cr and Fe analogues reveal large magnetic entropy changes of 38.3 J kg⁻¹ K⁻¹ for 8a at 2.0 K and 33.1 J kg⁻¹ K⁻¹ for 8b at 4.2 K with ΔH = 7 T. Interestingly, the larger spin ground state was present in 8b through intramolecular Fe–Gd ferromagnetic interactions. However, the presence of close-lying excited states through weaker coupling in 8a makes them more prominent in achieving high magneto-caloric value.⁷¹ This complementary exchange interaction (J) in 8a and 8b can nicely be correlated in terms of the d electronic configuration of the corresponding 3d metals. The Cr^III ion with (t_2g)³ electronic configuration induces relatively smaller interaction with the Gd^III 5d orbitals compared to the Fe^III ion in (t_2g)³(e_g)² configuration. The d_z² orbital of Fe^III accelerates the stronger overlap with the Gd^III 5d orbitals generating stronger ferromagnetic coupling. Theoretically it has been postulated that the extent of J_M–Gd interaction depends on the {M^III–F–Gd^III} angle. The extent of ferromagnetic J_Fe–Gd interaction increases with the increase in {Fe^III–F–Gd^III} bridging angle, whereas an opposite trend was found for {Cr^III–F–Gd^III} angles.

Fig. 19 Molecular structure of complex 8a.⁷¹

Wang and co-workers synthesized pentanuclear trigonal bipyramidal {Cr₂Ln₃} complexes Na₃[Dy₃Cr₂(HGly)₆(μ₃-OH)₆(H₂O)₉]·(ClO₄)₈·Cl₄·14H₂O (46a) and Na₃[Tb₃Cr₂(HGly)₆(μ₃-OH)₆(H₂O)₉]·(ClO₄)₆·Cl₆·6H₂O (46b) using glycine (HGly).⁷² Subsequently the reaction of 46a with a ditopic linker 4,4′-dipyridyl N,N′-dioxide (dpyo) afforded [Dy₃Cr₂(HGly)₆(dpyo)₂(μ₃-OH)₆(H₂O)₇]·(ClO₄)₉·15H₂O (47). From the structural point of view, {Cr₂Ln₃} adopted a trigonal–bipyramidal configuration where the triangular equatorial plane defined by the three Ln^III ions and Cr^III ion occupied axial positions. Each Ln₂Cr triangular face in trigonal–bipyramidal geometry was capped by one μ₃-OH⁻ group forming the [Cr^III₂(OH)₆Ln^III₂]⁹⁺ core, and furthermore adjacent Ln^III and Cr^III were connected by acid groups of glycinato ligand in syn–syn mode. Compound 47 has the core structure similar to that of 46a where two terminal water molecules of two Dy^III ions are replaced by two mono-coordinated dpyo ligands. In the quest for a polymeric network, the authors ended with a zero-dimensional molecular complex. A 3D supramolecular cds network was formed through hydrogen-bonding and π–π stacking interactions. All the three analogues displayed SMM behaviour with the following characteristics: U_eff ≈ 9.8 cm⁻¹ and τ₀ = 4.2 × 10⁻⁸ s for 46a; U_eff ≈ 9.0 cm⁻¹ and τ₀ = 6.4 × 10⁻⁷ s for 46b; and U_eff ≈ 9.2 cm⁻¹ and τ₀ = 9.16 × 10⁻⁸ s for 47. These results indicated that there is no significant impact of lanthanide ion or ligation by the dpyo ligands on the SMM behaviour in these complexes.

Zhao and co-workers reported trigonal bipyramidal {Cr₂Ln₃} complexes with the formula of [{Cr^III₂Ln^III₃L₁₀(OH)₆(H₂O)₂}(Et₃NH)] [Ln = Tb (12a), Dy (12b), Y(12c); Gd (12d) HL = pivalic acid, Et₃N = triethylamine]. The metal core of each complex is analogous to 12a, consisting of trigonal bipyramidal topology with three Ln^III ions (equatorial plane) and two Cr^III ions (axial position) held together by six μ₃-OH bridges. Around the periphery ten L⁻ ligands and two terminal water molecules further strengthen the [Cr^III₂(OH)₆Ln^III₂]⁹⁺ core where six pivalate ligands adopt a syn–syn mode to bridge adjacent Cr^III and Ln^III ions, two bidentately stitch two Ln^III centers, and two act as monodentate ligands to coordinate with one Ln^III ion.

In order to understand the nature of the Cr^III–Ln^III magnetic interaction the authors prepared an analogous Al^III–Ln^III derivative with the formula [{Al^III₂Ln^III₃L₁₀(OH)₆(H₂O)₂}Et₃NH·H₂O] [Ln = Tb (48a), Dy (48b)].¹⁵⁹ Predominant ferromagnetic interactions were found to prevail between Cr^III and Ln^III ions. AC magnetic susceptibility confirmed SMM behavior for [Cr^III₂Tb^III₃] (12a), [Cr^III₂Dy^III₃] (12b), and [Al^III₂Dy^III₃] (48b) without expected maxima until 1.8 K, mainly due to fast QTM. The authors were able to extract the parameters as follows: U_eff ≈ 11.8 cm⁻¹, τ₀ = 7 × 10⁻⁹ s for 12a and U_eff ≈ 7 cm⁻¹, τ₀ = 1.3 × 10⁻⁹ s for 12b.¹⁶⁰ The single-ion behavior of Ln^III ions and/or the Cr^III–Ln^III ferromagnetic interactions are the origin of slow relaxation of the magnetization behaviour in the abovementioned complexes. Due to isotropic Cr^III and Gd^III ions, large magnetization value, and dominant ferromagnetic exchange interaction between Cr^III and Gd^III ions, 12d showed large MCE with −ΔS^max_m of 27.0 J kg⁻¹ K⁻¹ at 4.0 K and ΔH = 7 T.¹⁰⁴

Very recently, Rajaraman and co-workers reported similar pentanuclear trigonal bipyramidal {Cr₂Ln₃} complexes, [Cr^III₂Ln^III₃(PhCO₂)₇(OH)₆(ⁱPrO)(NO₃)(H₂O)₃] (ⁱPrO = isopropoxide) [where Ln = Dy (49a), Gd (49b)] (Fig. 20).¹⁶¹ It has been well demonstrated with the aid of theoretical investigations that the stronger ferromagnetic {Cr^III–Dy^III} exchange interaction with J_{Cr^III–Dy^III} = +1.20 cm⁻¹ facilitates reducing the ground state QTM to generate the SMM behaviour in the Dy analogue, with U_eff value of 30.9 K (21.4 cm⁻¹) and τ₀ = 4.09 × 10⁻¹⁰ s.

Fig. 20 Molecular structure for 49a.¹⁶¹

Car and co-workers prepared {Cr^III₄Ln} complexes [Cr₄Ln(CH₃COO)(pyCOO)((py)₂COO)₄]·(NO₃)₂ (Ln^III = Gd (50a), Tb (50b) and Dy (50c) through hydrothermal reactions involving di-(2-pyridyl)ketone ligand. In the reaction condition di-(2-pyridyl)ketone gets reduced to gem-diol dianion (Py₂COO²⁻) and decomposed to simplified anion of pyridine 2-carboxylic acid. Collective coordination modes of these ligands led to a diamond-shaped type topology of the central metal {Cr^III₄Ln} core. The presence of competing ferro- and antiferromagnetic exchange coupling between Cr^III–Ln^III and Ln^III–Ln^III centers, respectively, below 50 K was predominant (J_Gd–Cr = 0.25 cm⁻¹ and J_Cr–Cr = −0.55 cm⁻¹). None of the compounds responded towards ac susceptibility signals, but the gadolinium derivative exhibited interesting magnetocaloric properties with −ΔS^max_m of 18.31 J kg⁻¹ K⁻¹ at 4.0 K with ΔH = 8 T.⁷³

5.5 Hexanuclear complexes

Sequential reaction of 1,3-diamino-2-hydroxy-propane-N,N,N′,N′′-tetraacetic acid (H₅hdpta), sodium acetate and CrCl₃ yielded Na[Cr^III₂(hdpta)(AcO)₂]. It is a connected ion framework containing Na⁺ nodes and dinuclear [Cr₂(hdpta)(Ac)₂]⁻ complex ligands where two Cr^III ions are chelated by one hdpta⁵⁻ and connected simultaneously by two acetate auxiliary ligands. Further reaction of Na[Cr₂(hdpta)(AcO)₂] with Gd(NO₃)₃·6H₂O afforded complex [Gd(NO₃)₃(H₂O)₄][Cr₄Gd(hdpta)₂(OH)₄(H₂O)₅]·(NO₃)·32H₂O (51). The cationic part [Cr₄Gd(hdpta)₂(OH)₄(H₂O)₅]⁺ forms a 1D chain based on Gd^III nodes and [Cr₄(hdpta)₂(OH)₄] complex ligands. Cr^III ions are anti-ferromagnetically coupled in this complex.¹⁶²

As already discussed in the tetranuclear section (vide supra), N-substituted diethanolamine ligand N-n-butyldiethanolamine (H₂bdea) in the presence of different co-ligands yielded three different types of coordination cluster ranging from octanuclear “square-in-square” (Ln = La–Tb), hexanuclear “triangle-in-triangle” (Ln = Dy, Ho, Y) and tetranuclear “butterfly” or “defect dicubane” (Ln = Er–Lu) core topologies. In this section we will discuss the hexanuclear “triangle-in-triangle”-based complexes [Cr^III₃Dy^III₃(μ₃-N₃)_0.36(μ₃-OH)_3.64(bdea)₃(μ-piv)₆(η¹-piv)₂(OH₂)] (52a), [Cr^III₃Ho^III₃(μ₃-OH)₄(bdea)₃(μ-piv)₆(OH₂)₃]Cl₂ (52b), and [Cr^III₃Y^III₃(μ₃-OH)₄(bdea)₃(μ-piv)₆(η¹-piv)₂(OH₂)] (52c). The core structure in 52a (Fig. 21) consisted of a disordered mixture of azide and hydroxide present in the centre with μ₃-bridging mode. Similarly, reaction with Ho^III also forms a similar hexanuclear “triangle-in-triangle” topology. But the structure is not iso-structural to the Dy^III analogue. This is due to the presence of charge-balancing pivalate moieties taking part in direct coordination with the Dy^III ion in 52a, whereas in Ho^III analogue (52b) chloride ions act as charge-balancing counter ions to generate a more symmetrical core for {Cr₃Dy₃} complex compared to the {Cr₃Ho₃} complex. Unfortunately, none of these complexes display SMM behavior.⁷⁷ Furthermore, changing the ligand from more sterically bulky N-n-butyldiethanolamine (H₂bdea) to less sterically encumbered N-methyldiethanolamine (H₂mdea) generated a couple of analogous hexanuclear complexes [Cr^III₃Ln^III₃(mdea)₃(piv)₈(OH)₄(H₂O)], [Ln^III = Gd (53a) and Dy (53b)] (Fig. 21). Surprisingly, unlike 52a, the Dy^III analogue 53b displayed SMM behaviour at zero dc field below 4 K. This example nicely showcased that subtle changes in the peripheral ligand backbone create a major impact in altering the magnetic properties.⁷⁶

Fig. 21 Molecular structure of complex 52a (left; N-n-butyl) and 53b (right; N-methyl).

Another unique compressed octahedral complex [(pipzH₂){Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄(H₂O)₁₀(μ₃-SO₄)₄(SO₄)₂}]·2H₂O (54) was formed by hydrothermal reaction of Dy(NO₃)₃·6H₂O, Cr(NO₃)₃·9H₂O, Na₂SO₄ and piperazine. The {Cr^III₂Dy^III₄}¹⁸⁺ core consisted of an octahedral skeleton having four Dy ions in the equatorial plane and two Cr ions present at axial positions held together by two μ₄-O²⁻ atoms (Fig. 22). Also, it was noted that Dy⋯··Dy separations are ∼4.0 Å while Cr⋯··Dy separations range from 3.30 to 3.37 Å, and the Cr⋯Cr distance is 2.91 Å, indicating a compressed octahedron {Cr₂Dy₄} core. Ac magnetic studies revealed SMM behavior in complex 54 with U_eff = 27.6 cm⁻¹ and τ₀ = 2.9 × 10⁻⁹ s. Interestingly, 54 represented the first sulphate-based SMM.⁷⁵

Fig. 22 Molecular structure of 54.

To further investigate, iso-structural analogues (pipzH₂)[Cr^III₂Ln^III₄(μ₄-O)₂(μ₃-OH)₄(H₂O)₁₀(μ₃-SO₄)₄(SO₄)₂]·2H₂O [Ln = Tb (55a), Ho (55b), Er (55c), Yb (55d), and Y (55e)] were synthesized utilizing similar synthetic protocols. The core [Cr^III₂Tb^III₄(μ₄-O²⁻)₂(μ₃-OH)₄]¹⁰⁺ is a double cubane composed of two Cr ions and four Tb ions which are bridged by two μ₄-O²⁻ atoms and four individual hydroxido μ₃-OH⁻ groups. Magnetic analysis revealed the antiferromagnetic interaction between metal centers for Tb, Ho, Er analogues. The Cr–Cr exchange interaction obtained for 55e analogue was found to be ferromagnetic with the value of 3.61(11) cm⁻¹; however, Cr–Ln interactions were antiferromagnetic. Dynamic magnetic measurements revealed slow magnetic relaxation in the Cr₂Tb₄ and Cr₂Er₄ analogues, indicating SMM behavior. However, the energy barrier (16.75 cm⁻¹) and pre-exponential factor τ₀ (4.0 × 10⁻⁹ s) could be only retrieved for the Cr₂Tb₄ analogue.⁷⁴

With the help of a sulfate framework, three [Ln₄Cr₂] cluster-based 3D complexes [Ln₄Cr₂(μ₄-O)₂(μ₃-OH)₄(H₂O)₉(SO₄)₅]·3H₂O [Ln^III = Gd^III (56a), Tb^III (56b), and Dy^III (56c)] were synthesized. The asymmetric unit of 56a consisted of two Gd metal ions, and one Cr ion along with two and half sulfate anions, two μ₃-OH⁻ groups, and one μ₄-O²⁻. The hexanuclear [Gd₄Cr₂] cluster moiety was formed with two such symmetry-linked units to generate a bi-cubic Gd₄Cr₂O₆ core (Fig. 23). 56a analogue displayed MCE of −ΔS^max_m = 38.33 J kg⁻¹ K⁻¹ under ΔH = 7 T at 2.0 K. Tb and Dy analogues exhibited slow relaxation of magnetization.¹³⁶

Fig. 23 Three-dimensional view of 56a.

Other examples of sulfate-bridged 3D inorganic polymers containing {Cr₂Dy₄} core were described as [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄(H₂O)₅(μ₄-SO₄)₄(μ₃-SO₄)]·9H₂O (57a) and [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄(H₂O)₈(μ₄-SO₄)₂(μ₃-SO₄)(ter-η³-SO₄)₂]·2H₂O (57b).¹⁶³ Despite having similar chemical components, the two compounds displayed structural divergence due to a difference in the binding modes of sulfate anions. With two Cr^III ions at axial positions and four other Dy^III ions at equatorial positions bonded together by two μ₄-O²⁻ and four μ₃-OH⁻ anions, a remarkable {Cr₂Dy₄} metallic octahedron is formed. In 57a, two types of sulfate bridging are present: firstly μ₄-SO₄²⁻ anion bridges two Dy^III and Cr^III ions from the [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄]¹⁰⁺ core by three oxygens along with a Dy^III ion from the neighboring [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄]¹⁰⁺ motif by the fourth oxygen atom. Secondly, μ₃-SO₄²⁻ anion binds three Dy atoms from two adjacent [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄]¹⁰⁺ motifs by three oxygen atoms. Thus, each [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄]¹⁰⁺ core is connected to six adjacent neighbors and each layer parallel to ab plane, forming a 3D extended network. In complex 57b the same type of bridging is present; however, along with it another bridging mode is also present. The new sulfate bridging ligand, ter-η³-SO₄²⁻ binds two Dy^III and one Cr^III from the same [Cr₂Dy₄(μ₄-O)₂(μ₃-OH)₄]¹⁰⁺ core with three oxygen atoms. Structural inspection of 57b shows that the individual units of this complex are analogous to 57a. However, the 3D network in 57b is formed by connecting the individual units of 57a through sulphate bridges (Fig. 24). SMM behavior is observed for both 57a (U_eff of 26 cm⁻¹ and τ₀ of 6.7 × 10⁻⁸ s) and 57b (U_eff of 18 cm⁻¹ and τ₀ = 7.3 × 10⁻⁹ s). It was noted that the SMM performance of 57a was better than 57b due to the orientation of the clusters, which are closely linked with permutation of magnetic moment among SMM-like clusters, thereby influencing the spin dynamics.

Fig. 24 Molecular structure of complex 57a (simplified view; left) and 3-dimensional view (right).

5.6 Heptanuclear complexes

Reaction of 2,2-dimethylolpropionic acid (H₃L), Ln(ClO₄)₃ and chromium salts utilizing different anions reacted under high pH conditions yielded a series of Ln–Cr clusters with formula [Ln₅Cr₂(H₂L)₂(OAc)₆(μ₃-OH)₆(H₂O)₁₅](ClO₄)₇ (Ln = Gd 58a and Ln = Dy 58b) and [Ln₈Cr₄(H₂L)₄(OAc)₈(μ₃-OH)₁₆(μ₄-O)(H₂O)₈](Cl)(ClO₄)₅·10H₂O (Ln = Gd for 59a and Ln = Dy for 59b) (Fig. 25). This is a unique example of anion-dependent assembly, templated by mixed anions.

Fig. 25 Molecular structure of complex 58a.

Furthermore, the cationic cluster comprises a unit [Gd(H₂L)]²⁺ and another pentanuclear cationic cluster [Gd₃Cr₂(μ₃-OH)₆]⁹⁺ which is surrounded by fifteen water molecules and six acetate ligands. Mononuclear cationic cluster [Gd(H₂L)]²⁺ is formed by one Gd(III) ion and chelating ligand H₂L⁻, while pentanuclear cationic unit [Gd₃Cr₂(μ₃-OH)₆]⁹⁺ is formed by three Gd^III ions and two Cr^III ions linked together by six μ₃-OH groups. Overall, the cationic core of [Gd₅Cr₂(H₂L)₂(μ₃-OH)₆]⁷⁺ is formed by the cumulative action of both the mononuclear cationic core [Gd(H₂L)]²⁺ and the pentanuclear core [Gd₃Cr₂(μ₃-OH)₆]⁹⁺ joined by a carboxyl group from H₂L⁻. Gd⋯Cr and Gd⋯Gd interactions are weak antiferromagnetic and ferromagnetic, respectively. 58a displayed the magnetocaloric effect with −ΔS^max_m value of 25.2 J kg⁻¹ K⁻¹ at 5 K and 7 T.¹⁴⁰

Vignesh et al. reported the heptanuclear complex [Cr^IIIDy^III₆(OH)₈(o-tol)₁₂(NO₃)(MeOH)₅]·3MeOH (60a), (o-tol = ortho-toluate).¹⁶⁴ The metal core is formed by two triangular Dy^III motifs lying above and below a single Cr^III ion producing a common vertex sharing a trigonal pyramidal structure. It is further stabilized by eight μ₃-OH, twelve ortho-tol, nitrate ions and methanol ligands. Cr^III ions are six coordinated to form octahedral geometry, and Dy^III ions are eight coordinated and in triangular dodecahedron geometry (Fig. 26). Antiferromagnetic interaction was dominant between the metal centers. M vs. H plots based on the single crystals in micro-SQUID revealed steps in the hysteresis curve analogous to the first Dy₃-based triangular toroidal system. In fact, complex 60a displayed better coercivity compared with the Dy₃ analogue, which was due to the coupling between the two {Dy^III₃} triangles.^165,166 Interestingly, it was found that the Cr^III ion did not play any role in the coupling of the two toroidal wheels and the coupling was due to the dipolar interactions between the two Dy^III₃ wheels. This phenomenon was supported by theoretical investigations.

Fig. 26 Molecular structure of complex 60a (left) and orientation of the individual magnetic anisotropy axes. Black arrows denote the rotation of the toroidal magnetic moment and the yellow arrow depicts S₆ symmetry axis (right).¹⁶⁴ Reprinted with permission from ref. 164. Copyright 2017 Nature.

For further analysis, toroidal and ferrotoroidal systems consisting of different Ln^III centers, [Cr^IIILn^III₆(OH)₈(o-tol)₁₂(NO₃)(MeOH)₅]·2MeOH (Ln = Tb (60b), Ho (60c) and Er (60d), o-tol = o-toluate) were synthesized and studied. Structural parameters were analogous to the 60a analogue, where a heptanuclear complex comprising two Ln₃ triangular motifs was joined together by a common Cr^III ion. {CrTb₆} and {CrEr₆} analogues revealed slow relaxation of magnetization under 3000 Oe static magnetic field. Magnetization measurements based on single crystals using μ-SQUID showed a hysteresis loop below 0.03 K for {CrTb₆} and {CrHo₆} analogues (sweep rate = 0.14 Ts⁻¹). Ab initio calculations confirmed toroidal magnetic moments for Tb and Ho analogues. The two Ln₃ triangles coupled together to stabilize the con-rotating ferrotoroidal ground state in these complexes. Interestingly, this represented the first toroidal behavior in non-Dy^III complexes.¹⁶⁷

Under solvothermal conditions, four isostructural Ln^III₆Cr^III complexes {(Ln₆Cr)(C8A)₂} compounds [Ln = Gd (61a), Tb (61b), Dy (61c) and Tm (61d)] (H₈C8A = p-tert-butylcalix[8]arene) were synthesized. A sandwich-like structure was formed where the Gd^III₆Cr^III core was capped between two tail-to-tail calix[8]arene molecules. This double-cone arrangement binds a Gd^III ion utilizing the four phenolic oxygen atoms at the lower rim such that a secondary building unit (SBU) of Gd₂-C8A is formed. An additional Gd^III ion placed at the joint of two conic units and coordinated by two phenolic oxygen atoms of both conic units forms a Gd₃-C8A unit. One Cr^III ion shares the common vertex of these two Gd₃-C8A entities, forming a Gd₃Cr-C8A motif. Overall, the heptanuclear core (Gd₆Cr)-(C8A)₂ is formed with the collective action of the two water molecules and two μ₄-O²⁻ bridging the Gd₃-C8A and Gd₃Cr-C8A motif. 61b shows SMM behavior due to the presence of temperature-dependent and frequency-dependent out-of-phase ac signals, with U_eff of 12.6 cm⁻¹ and τ₀ being 7.52 × 10⁻⁸ s.¹⁶⁸

Representative examples of the heterometallic heptanuclear complexes and their magnetic responses are depicted in Fig. 27.^169–172

Fig. 27 Representative examples of heterometallic heptanuclear complexes and their magnetic properties.^169–171

Utilizing maleic acid as a ligand, a heterometallic complex [{Na(H₂O)][Na₂Cr₂Tb₃(μ₃-OH)₆(L)₆(H₂O)₁₇}]·16H₂O (where H₂L = maleic acid) (62) was synthesized. The maleic ligand adopted two coordination modes: μ₃–κ¹:κ¹:κ¹ and μ₄–κ¹:κ¹:κ¹:κ¹ which coordinates to three and four metal ions, respectively. In μ₃-mode, one carboxylate group binds to Tb^III, Cr^III and Na^I ions while the other carboxylate group remains free. In μ₄-mode, the same coordination mode as that of μ₃ is present except the second carboxylate group coordinates to one mononuclear half-occupied Na^I ion. It was found that each [Na₂Cr₂Tb₃(μ₃-OH)₆(L)₆(H₂O)₁₇]⁻ anion moiety acts as linker and connects to three mononuclear Na^I nodes. Dc magnetic studies revealed ferromagnetic interaction between the metal ions. Slow magnetic relaxation for this analogue was observed below 3 K without achieving any maxima in out-of-phase signals.¹⁷³

5.7 Octanuclear complexes

In 2010, Powell and coworkers reported the first Cr^III-containing 3d–4f SMM, [Cr^III₄Dy^III₄(μ₃-OH)₄(μ-N₃)₄(mdea)₄(piv)₄]·3CH₂Cl₂ (10) (H₂mdea = N-methyl diethanolamine, HPiv = pivalic acid). This was synthesized by a one-pot reaction involving H₂mdea and NaN₃ with CrCl₂ in CH₃CN under an inert atmosphere, followed by addition of Dy(NO₃)₃·6H₂O, pivalic acid, and CH₂Cl₂. The basic structural motif was composed of a Dy₄-square within-a-Cr₄-square, where the central core consisted of four Dy^III ions to form an approximate square. Each pair of adjacent Dy^III cations was bridged by a hydroxo ligand, which also coordinated with a Cr^III ion on each edge of the Dy₄ square. The opposite face of μ₃-OH bridge was occupied by an azide ligand with end-on bridging mode to connect each Dy⋯Dy edge. Each Cr^III was chelated by a doubly deprotonated (mdea)²⁻, the oxygen atoms of which bridged to the adjacent Dy^III cations. Peripheral ligation was provided by the eight syn,syn-bridging pivalate ligands, which linked adjacent pairs of Cr^III and Dy^III cations (Fig. 28).

Fig. 28 Molecular structure of 10 (left) and hysteresis plot at different temperatures with a sweep rate of 0.035 Ts⁻¹ (right).⁸⁰ Reprinted with permission from ref. 80. Copyright 2010 John Wiley and Sons.

The complex 10 displayed SMM behaviour with the energy barrier of 15 K and pre-exponential factor τ₀ = 1.9 × 10⁻⁷ s. The hysteresis loops for 10 were obtained in micro-SQUID analysis for single crystals in the range of 0.04–1.1 K (Fig. 28). Cole–Cole plot indicated (α ≈ 0.5) more than one relaxation process in the range of 1.9–2.2 K. However, the relaxation dynamics remains almost unchanged with the application of a small dc field, indicating the relaxation processes are not influenced by QTM above 1.8 K. Ab initio calculations suggested that axial-type strong magnetic anisotropy was present on four Dy^III ions, responsible for SMM behaviour of 10 (Cr^III ions are almost isotropic). The calculations also demonstrated that the steps in the hysteresis loops in this molecule were due to the crossing of low-lying energy spectrum arising from the exchange multiplets involving Dy–Cr, Dy–Dy, and Cr–Cr exchange interactions. These low-lying energy states allowed the QTM among them to feature steps in the hysteresis curve.^80,174 Powell and co-workers carried out a detailed analysis based on single-crystal SQUID and torque magnetometry to locate the anisotropy axes for this complex in 2019. These experiments allowed them to find the easy axis anisotropy on Dy^III sites.¹⁷⁴

The same group has extended their work replacing the N-methyldiethanolamine (H₂mdea) ligand with N-n-butyldiethanolamine (H₂bdea) to produce the analogous square-in-square topologies, [Cr^III₄Ln^III₄(bdea)₄(μ₃-N₃)_x(μ₃-OH)_4−x(μ-NO₃)₂(μ,η²-piv)₂(piv)₈]; Ln = La, x = 0.9, (63a); Ln = Ce, x = 1, (63b); Ln = Pr, (63c); Ln = Nd, x = 0.9, (63d); Ln = Sm, x = 0.7, (63e); Ln = Eu, x = 0.6, (63f); Ln = Gd, (63g). Here it is noteworthy to mention that size of the Ln^III ions can direct the self-assembly of Cr^III_nLn^III_n complexes. It is evident that 63a–g were obtained for the light to middleweight lanthanides with comparatively large radius. The smaller radius Ln^III ions such as Dy, Y, Ho, and Er, lead to {Cr₃Ln₃} hexanuclear “triangle-in-triangle” complexes, which has been discussed in hexanuclear section. Moreover, the smallest lanthanides such as Tm^III and Yb^III led to tetranuclear {Cr₂Ln₂} butterfly complexes. DC magnetic measurements exhibited ferromagnetic behaviour below 10 K for 63b, 63d and 63e, while antiferromagnetic interaction prevailed for 63c at low temperature. For 63aχT drops below 5 K, indicating weak antiferromagnetic exchange interaction among the Cr^III ions as La is diamagnetic. The authors have speculated that for late lanthanides the Cr^III–Ln^III interaction is antiferromagnetic, whereas for the early lanthanides it is ferromagnetic irrespective of their arrangements (square, triangular or dimeric).⁷⁷

Murray and co-workers reported another octanuclear “square-in-square” motif containing a heterometallic {Cr₄Dy₄} core (64) analogous to 10 through the reaction of CrCl₃·6H₂O, Dy(NO₃)₃·6H₂O, benzoic acid, mdeaH₂ (N-methyldiethanolamine), NaF and NEt₃ in MeCN.¹⁷⁵ The basic structural motif of [Cr^III₄Dy^III₄F₄(OMe)_1.12(OH)_2.88(O₂CPh)₈(mdea)₄] (64) is analogous to that of [Cr^III₄Dy^III₄(μ₃-OH)₄(N₃)₄(mdea)₄(piv)₄] (10) with some minor changes in the coordinating ligand (Fig. 29). The μ₃-bridged anions throughout the crystal are disordered and modelled as MeO⁻ and HO⁻ in the ratio of 0.28 (MeO⁻):0.72(HO⁻). Here it is important to mention that the structural differences in 64 were due to the coordination of benzoic acid and F⁻ anions, whereas in 10 it was pivalic acid and N₃⁻ anions. It is noteworthy that the authors attempted to replace the μ₃-OH bridges with F⁻ anions in their butterfly {Cr^III₂Dy^III₂} families in order to study the effect of anions on the magnetic relaxation, but during the self-assembly process they ended up with the octanuclear {Cr^III₄Dy^III₄} cluster.

Fig. 29 Comparison of bond lengths and magnetic properties in complexes 64 and 10.^77,175

The anions played a pivotal role in modulating the magnetic properties of 64 compared with 10. The magnetic properties were altered in the following ways: (i) Cr^III⋯Dy^III exchange interaction was found to be stronger in 64, and as a consequence the effect of QTM was less effective in 64; (ii) these combined effects essentially led to the larger thermal barrier for the magnetization reversal in 64 (U_eff = 54.9 cm⁻¹ with τ₀ = 6.1 × 10⁻⁸ s) over 39 (U_eff = 10.4 cm⁻¹ and τ₀ = 1.9 × 10⁻⁷ s); (iii) the hysteresis loop opening for 64 was up to 3.5 K using a conventional magnetometer (scan rate 0.003 Ts⁻¹), whereas for 10 it was up to 1.1 K in micro-SQUID (scan rate 0.035 Ts⁻¹); (iv) complex 64 displayed a blocking temperature (relaxation of 100 s) of 3.8 K, which is greater than that of complex 10 (∼1 K). From these instances, it is evident that electronegative bridging fluoride ions have significant influence on the anisotropy barrier and as well as magnetization relaxation. This phenomenon has also been reflected in other fluoride-bridged lanthanide analogues.^{101,176–180}

With extension of their previous work, Murray and co-workers reported isostructural “square-in-square” topology with different co-ligands; [Co^III₄Dy^III₄(μ-OH)₄(μ₃-OMe)₄(O₂CC(CH₃)₃)₄(tea)₄(H₂O)₄]·4H₂O (65) and [Co^III₄Dy^III₄(μ-F)₄(μ₃-OH)₄(o-tol)₈(mdea)₄]3H₂O·EtOH·MeOH (13), [Cr^III₄Dy^III₄(μ-F₄)(μ₃-OMe)_1.25(μ₃-OH)_2.75(O₂CPh)₈(mdea)₄] (11) [Cr^III₄Dy^III₄(μ₃-OH)₄(μ-N₃)₄(mdea)₄(piv)₄] (10) (tea³⁻ = triply deprotonated triethanolamine; mdea²⁻ = doubly deprotonated N-methyldiethanolamine; o-tol = o-toluate).⁷⁸ Apart from 65, the other three compounds 13, 11 and 10 displayed SMM behaviour with an energy barrier U_eff of 39.0 cm⁻¹, 55.0 cm⁻¹ and 10.4 cm⁻¹, respectively. In order to understand the differences observed in the energy barrier the authors performed CASSCF/RASSI-SO/POLY_ANISO calculations on the complexes to understand the role played by exchange interaction as well as the mechanism of the magnetic relaxation phenomenon. The calculations revealed that the exchange interaction (J_Dy–Dy) is −0.16, 1.6 and 2.8 cm⁻¹ for 65, 13 and 11, respectively, whereas the J_Dy–Cr interaction is 1.8 cm⁻¹ for complex 11. The substitution of the hydroxide ion by fluoride ion quenches the QTM significantly, leading to better-quality SMM properties for 13 in comparison with 65. Additionally, the incorporation of paramagnetic Cr^III instead of diamagnetic Co^III leads to strengthening of the Cr^III⋯Dy^III coupling, resulting in quenching of QTM at low temperatures for complexes 11 and 10. Complex 11 exhibited the best SMM behavior due to the presence of highly electronegative F⁻ ions and stronger Cr^III⋯Dy^III exchange interaction to quench the QTM. The presence of the most electronegative F⁻ ions pushes the excited states higher in energy due to prominent electrostatic repulsion, and therefore the relaxation of magnetization occurs through the higher energy barrier.¹⁰⁰ As a consequence, magnetic hysteresis loops above 2 K (sweep rate 0.003 Ts⁻¹) were observed for 11.

Analogous “Dy₄-square inscribed in a M₄-square” topology can be observed with other 3d metal ions i.e. [Mn^III₄Dy^III₄(μ₃-OH)₄(μ-X)₄(O₂CBut)₈(^tBu-dea)₄], X = N₃⁻ (66a), OCN⁻ (66b), NO₃⁻ (66c);¹⁸¹ [Fe^III₄Dy^III₄(μ₃-OH)₄(O₂CC₆H₄CH₃)₁₂(n-bdea)₄] (67).¹⁸² The Mn^III₄Dy^III₄ analogue displayed frequency-dependent in-phase and out-of-phase signals below 4 K without maxima, indicating slow relaxation of the magnetization. On the contrary, complex 67 did not display any ac susceptibility responses either in zero or nonzero (500–3000 Oe) dc field, indicating the non-SMM nature of the same. In fact, the change of bridging ligand X⁻ (N₃⁻ → OCN⁻ → NO₃⁻) also did not significantly affect the magnetic properties of the [Fe^III₄Dy^III₄] analogue. Chandrasekhar and co-workers reported analogous topology for a series of Ni^II–Ln^III complexes [Ln₄Ni₄(H₃L)₄(μ₃-OH)₄(μ₂-OH)₄](Cl)₄ using N₁,N₃-bis(6-formyl-2-(hydroxymethyl)-4-methylphenol)diethylenetriamine (H₅L).¹⁸³ Similar “square-in-square”-based structures have also been found in a series of complexes [Mn^III₄Ln^III₄(OH)₄(Calix)₄(NO₃)₂(DMF)₆(H₂O)₆], Ln = Gd (68a), Tb (68b), Dy (68c) by using methylene-bridged calix[4]arenes.^184,185

Apart from the aforementioned “square-in-square” structural topology, Xu and co-workers reported two couples of chiral “tower-like” Ln₄Cr₄ complexes formulated as L- and D-[Gd₄Cr₄(IN)₁₀(μ₃-OH)₄(μ₄-O)₄(H₂O)₁₂]·[IN]₂·8H₂O (69a and 69b), L- and D-[Dy₄Cr₄(IN)₁₁(μ₃-OH)₄(μ₄-O)₄(H₂O)₈]·[IN]·1.5H₂O (70a and 70b) (HIN = isonicotinic acid). Four μ₃-OH and four μ₄-O connect four Ln^III ions and four Cr^III ions to form a “tower-like” [Ln₄Cr₄] (Ln = Gd, Dy) metal skeleton. The Gd analogue (the mixture of 69a and 69b) showed the magnetocaloric effect with −ΔS_m = 18.08 J kg⁻¹ K⁻¹ at 3 K with ΔH = 7 T.¹⁴¹

To explore the effect of nicotinic acid (HNA) instead of isonicotinic acid (HIN) as ligand, Xu and co-workers reported three-dimensional 3d–4f heterometallic cluster-based coordination polymers, [Ln₄Cr₄(μ₃-O)₄(μ₄-O)₄(NA)₈(H₂O)₁₂], [Ln = Gd (71a), Tb (71b), Er (71c)] through hydrothermal synthesis. Structural analysis showed that the basic unit of 71a was composed of butterfly-shaped Gd₄Cr₄ clusters where four Gd atoms and four Cr atoms were interconnected by four μ₃-O²⁻ and four μ₄-O²⁻to generate a Gd₄Cr₄O₈ metal skeleton. Further analysis of the core structure revealed that the cubane-like core Cr₄O₄ connects with two distorted cubane-like subunits Cr₂Gd₂O₄via a shared face. The adjacent Gd₄Cr₄ units are interconnected through NA⁻ ligands to generate a 3D structure. The Gd analogue displayed the magnetic entropy change (−ΔS^max_m) value of 22.05 J K⁻¹ kg⁻¹ at 2.5 K for the applied field of 70 kOe.¹⁸⁶

Zheng and co-workers utilized trilacunary Keggin-type polyoxometalate Na₁₀[α-SiW₉O₃₄]·16H₂O to assemble a series of {Cr₄Ln₄} heterometallic clusters with the formula of Cs₂[Cr₄Ln₄(μ₄-O)₄(μ₃-O)₄(C₈H₄O₄)₄(H₂O)₁₂](H₃SiW₁₂O₄₀)Cl·23H₂O [Ln = Ce (72a), Pr (72b), Nd (72c)] and [Cr₄Ln₄(μ₄-O)₄(μ₃-O)₄(C₈H₄O₄)₄(H₂O)₁₀](H₆SiW₁₂O₄₀)Cl₂·18H₂O, (C₈H₄O₄ = dianion of phthalic acid), [Ln = Sm (73a), Eu (73b), Gd (73c), Tb (73d), Dy (73e), Ho (73f), Er (73g)].⁷⁹ These compounds were composed of four-layered prismatic[Cr₄Ln₄] cores where Cr–Ln heterometallic clusters were stabilized by both organic ligands (phthalic acid) and inorganic POM species like Na₁₀[α-SiW₉O₃₄]·16H₂O. It is notable that Xu and co-workers also reported Cr^III–Ln^III discrete as well as 3-D polymeric clusters containing similar four-layered [Cr₄Ln₄(μ₄-O)₄(μ₃-O)₄] (Ln = Gd, Dy) cores. The authors selectively measured the magnetic properties of the Tb (73d) and Dy (73e) analogue. Only analogue 73e showed a signature of slow relaxation of magnetization behaviour without peak maxima in variable-temperature ac susceptibility measurements.

5.8 Dodecanuclear complexes

As mentioned in the heptanuclear section (vide supra), [Gd₈Cr₄(H₂L)₄(OAc)₈(μ₃-OH)₁₆(μ₄-O)₁(H₂O)₈](Cl)(ClO₄)₅·10H₂O (59a) and [Dy₈Cr₄(H₂L)₄(OAc)₈(μ₃-OH)₁₆(μ₄-O)₁(H₂O)₈](Cl)(ClO₄)₅·10H₂O (59b) were formed utilizing a procedure similar to complexes 58a–b but using CrCl₃ instead of Cr(OAc)₃.¹⁴⁰ Incorporation of Cl⁻ ions in combination with ClO₄⁻ ions as a mixed anion template led to the high-nuclearity Ln₈Cr₄ clusters. Complex 59a consisted of one quadrangular cationic core of [Gd₈Cr₄(H₂L)₄(OAc)₈(μ₃-OH)₁₆(μ₄-O)₁(H₂O)₈]⁶⁺ which can be described as four cubane-like units [Gd₃Cr(μ₃-OH)₄]⁸⁺ templated by Cl⁻ and ClO₄⁻ anion through the sharing of the Gd^III vertex center with a central μ₄-O group (Fig. 30). Weak antiferromagnetic interaction for both Gd⋯Cr and Gd⋯Gd was found for complex 59a. Magnetothermal analysis revealed magnetic entropy changes of 33.8 J kg⁻¹ K⁻¹ at 2 K and ΔH = 7 T for this complex 59a.

Fig. 30 Molecular structure of complex 59a.¹⁴⁰

Solvothermal conditions using N-substituted diethanolamine ligand yielded dodecanuclear Cr^III–Ln^III-based coordination clusters, [Cr^III₆Ln^III₆(μ₃-OH)₈(tbdea)₆(C₆H₅COO)₁₆]·2H₂O [Ln = Dy (74a), Y (74b)].⁸² To rationalize the role of the diamagnetic metal ion in the vicinity of Ln^III centers on the magnetic properties, the analogous cobalt complex [Co^III₆Dy^III₆(μ₃-OH)₈(nbdea)₆(m-CH₃C₆H₄COO)₁₆]·2H₂O·2CH₃CN (75) was synthesized. All three compounds have an analogous dodecanuclear {M^III₆Ln^III₆} core (M = Cr, Co; Ln = Dy, Y), differing only in the ligand and coligand. For 74a, the {Cr^III₆Dy^III₆} core was formed by two {Cr^III₃Dy^III₃} sub-units in the form of a “Dy₃ triangle within a Cr₃ triangle” geometry where Cr1 and Cr2 are placed on one side of the Dy₃ triangle with Cr₃ on the other side. In the {Cr^III₃Dy^III₃} subunit, three Dy atoms are bridged by μ₃-hydroxide in the central position. Each Cr^III ion is chelated with a doubly deprotonated ligand along with two alkoxide oxygens, forming an alkoxo bridge to an adjacent Dy^III ion. Six syn–syn bridging benzoate ligands connect the adjacent Dy^III and Cr^III centers around the edge of the subunits (Fig. 31). Weak ferromagnetic Cr^III⋯Dy^III interaction dominates in the [Cr^III₆Dy^III₆] complex, whereas an intramolecular antiferromagnetic interaction between the adjacent Dy^III centers is found in the [Co^III₆Dy^III₆] analogue. The ac magnetic susceptibilities for [Cr^III₆Dy^III₆] (74a) and [Co^III₆Dy^III₆] (75) exhibited slow relaxation of magnetization with the energy gap of 8.9 cm⁻¹ and 14.46 cm⁻¹, respectively, which indicated that the replacement of paramagnetic 3d ions with diamagnetic Co^III ion led to quenching of the QTM and enhanced the energy barrier. A similar improvement of SMM behavior by incorporating diamagnetic metal ions adjacent to lanthanide ions was also found in other 3d–4f heterometallic complexes.^37,187–189

Fig. 31 Molecular structure of complexes with [Cr^III₆Dy^III₆] (left) and [Co^III₆Dy^III₆] (right) cores.⁸²

In the category of [M₆Ln₆]-based complexes, literature reports show two reports, [Zn₆Dy₆] (76)-based core using 2-(hydroxy-N-(2-(2-hydroxybenzylidene)amino)ethyl)benzamide (H₃L) and [Ni₆Gd₆] complex (77) using phosphonic acid (Fig. 32). Complex [Zn₆Dy₆] (76) exhibited SMM behaviour without reaching peak maxima in dynamic magnetic measurements,¹⁹⁰ whereas [Ni₆Gd₆] complex (77) displayed MCE with −ΔS^max_m is 26.5 J kg⁻¹ K⁻¹ at 3 K and ΔH = 7 T.¹⁹¹

Fig. 32 Simplified view of structural cores for [Zn₆Dy₆] (left) and [Ni₆Gd₆] (right).^190,191

Hydrothermal conditions afforded two isomorphic heterometallic {Ln₈Cr₄} complexes formulated as [Gd₈Cr₄(IN)₁₈(μ₃-O)₂(μ₃-OH)₆(μ₃-O)₄(H₂O)₁₀]·13H₂O (78a) and [Tb₈Cr₄(IN)₁₈(μ₃-O)₂(μ₃-OH)₆(μ₃-O)₄(H₂O)₁₀]·13H₂O (78b); (HIN = isonicotinic acid). The structural unit of {Gd₈Cr₄} is composed of two {Ln₄Cr₂} “drumlike” cores linked by ligand HIN. Even though the two building blocks {Ln₄Cr₂} share the same metallic framework, they differ in the coordination mode provided by the ligand (Fig. 33). Each unit {Gd₈Cr₄} is linked by ligand HIN, forming a rare one-dimensional wave-like structure. Antiferromagnetic interaction is dominant between the Ln^III ion and Cr^III ion. Also, the entropy change for 78a was found to be −ΔS^max_m = 23.40 J kg⁻¹ K⁻¹ at 3 K and ΔH = 7 T.¹³⁸

Fig. 33 Molecular structure of complex 78a.

Representative examples in the family of heterometallic dodecanuclear complexes and the magnetic properties are listed in Fig. 34.^192,193

Fig. 34 Representative examples of heterometallic dodecanuclear complexes and their magnetic properties.^192,193

5.9 Hexadecanuclear complexes

The largest Cr^III–Ln^III complex [Cr₈Ln₈(mdea)₁₆(CH₃COO)₈(NO₃)₈] (mdeaH₂ = N-methyldiethanolamine, Ln^III = Gd (79a), Dy (79b), and Y (79c), respectively) consists of sixteen alternating Cr and Ln metal centers. The solvothermal conditions involving N-methyldiethnanolamine, Cr(acac)₃, Ln(NO₃)₃ in actonitrile at 130 °C allowed the formation of hexadecanculear complexes. All eight Cr ions and eight Gd ions are arranged alternately to form a sixteen-membered ring (Fig. 35). Dc magnetic studies showed dominant antiferromagnetic interaction in Gd and Dy analogues and weak ferromagnetic interaction in the Y analogue. The presence of a large ground spin state (S_T = 16) as well as the antiferromagnetic exchange interaction ∼1.5 cm⁻¹ for the [Cr₈Gd₈] analogue is confirmed by Quantum Monte Carlo (QMC) simulation. Moreover, ac magnetic studies show slow relaxation of magnetization for 79b with U_eff of 13.2 cm⁻¹ and τ₀ = 3.5 × 10⁻⁸ s.⁸³

Fig. 35 Molecular structure of complex 79b.

In the family of heterometallic hexadecanuclear 3d–4f complexes, Winpenny and coworkers reported [Co^II₈Gd^III₈] complexes, [Co^II₈Gd^III₈(μ₃-OH)₄(NO₃)₄(O₃P^tBu)₈(O₂C^tBu)₁₆] (80) using both phosphonic acid and carboxylic acid ligands.^194,195 This complex displayed the MCE value of −ΔS^max_m as 20.40 J kg⁻¹ K⁻¹ at 3 K and ΔH = 7 T.

5.10 Heterotrimetallic complexes

Cyano-bridged hetero-di/trimetllic complexes have been reported using [Cr(CN)₆]³⁻ as the connector to generate the multi-dimensional coordination networks.¹⁹⁶ Ohba and coworkers have reported trimetallic 3-dimensional pillared-layered complexes [Co₂Ln(L)₂(H₂O)₄][Cr(CN)₆] [La^III (81a) and Gd^III (81b)] by connecting preformed Co^II–Ln^III complexes with K₃[Cr(CN)₆] (Fig. 36). Complex La^III (81a) shows metamagnetic (T_c = 7.4 K) and complex Gd^III (81b) shows ferromagnetic (T_c = 15.4 K) interaction.¹⁹⁷

Fig. 36 Three-dimensional coordination network for complex 81b along crystallographic c-axis.

6. Conclusion and outlook

In this review, we have attempted to demonstrate the magnetic and magnetocaloric aspects of Cr^III–Ln^III-based heterometallic complexes. To do so, we have categorically presented the importance of Cr^II and Cr^III ions as sources of anisotropy and their coupling mechanism with Ln^III ions. Moreover, we have also demonstrated the detailed synthetic, structural and SMM behaviour for most of the complexes. From the synthesis and structural discussion part, it is very obvious that all the Cr^III–Ln^III heterometallic assemblies were isolated using a serendipity-based approach where the multidentate ligands (Chart 1) have been employed to bridge the Cr^III and Ln^III centers to generate the multimetallic architectures. Furthermore, the magnetic property analysis divulged how the exchange interaction between Cr^III and Ln^III ions, through either the fluoride or oxide/hydroxide bridge, played a pivotal role in shaping the interesting SMM behaviour of those heterometallic complexes by minimizing the effect of QTM. In fact, the tetranuclear complex [Cr^III₂Dy^III₂(OMe)₂(O₂CPh)₄(mdea)₂(NO₃)₂]⁷⁰ turns out to be an excellent SMM, having the strongest exchange interactions of −16.7 to −20.3 cm⁻¹ and the highest blocking temperature (T_B) of 3.7 K among the 3d–4f family of complexes reported to date. Despite the fact that some of the complexes exhibit impressive magnetic dynamics, it should be noted that the blocking barrier as well as temperature are still much lower than for the lanthanide-based single-ion magnets. Therefore, the main challenge remains in this field is to develop systems with a considerably higher blocking temperature (T_B) and U_eff. We believe that these problems can be countered through strong exchange interactions between 3d and 4f metal ions as well as by preserving the high symmetry such as C_∞, C_n (n ≥ 7), S₈, D_4d, D_5h, D_6hetc. around Ln^III ions to lower the effect of problematic QTM.^23,198 This essence and art of coupling between Cr^III as well as other paramagnetic transition metals with Ln^III spin centers can be modulated through the selection of specific coordination compartments ligands along with the preferential choice of coordinating entities such as more polarizable sulfur or selenium rather than hard fluoride or oxides (hydroxides).

Chart 1 Library of ligands used to synthesize Cr^III–Ln^III complexes.

The higher extent of polarizability associated with sulphur/selenium leads to larger degree of covalency in the bond. This essentially leads to more overlap between transition- and lanthanide-metal ions and leads to better exchange interactions between them. Moreover, the use of a radical ligand system as bridge could also mediate stronger exchange coupling between chromium and lanthanides, and hence a higher blocking barrier.¹⁹⁹ Additionally, the judicious choice of ligands with specific coordination pockets for Cr^III as well as Ln^III centres could lead to the synthesis of interesting dinuclear/trinuclear heterometallic complexes which would provide a better platform to understand and manipulate the magnetization dynamics, rather than aesthetically pleasing bigger complexes often characterized by low U_eff values.^{109,200–206} In fact, to date, the SMM properties of the Cr^II–Ln^III-based systems and surface-grafted Cr^III–Ln^III-based systems are yet to be explored. Therefore, stabilization of such systems through chemical modification also could unleash numerous potential avenues in heterometallic SMM chemistry.^207–214 So, with all sorts of possibilities, we are expecting more exciting developments in the near future from the chemical community to address some of those unsolved problems regarding both chromium-containing and other transition metal–lanthanide heterometallic assemblies.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

A. D and P. B are grateful to the Gandhi Institute of Technology and Management (GITAM) and Panskura Banamali College (Autonomous), respectively. S. D acknowledges the financial support from the SERB-DST Early Career Research Award (ECR) with Project Number ECR/2016/001746.

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