The importance of second sphere interactions on single molecule magnet performance

Abstract

Owing to their potential applications in areas such as information storage, molecular spintronics, and quantum computing among others; the field of single molecule magnets (SMMs) has experienced a surge of interest and advances. One aspect of these systems that is often overlooked is the effect that second-sphere interactions can have on the magnetic performance and viability of SMMs. This review focuses on SMMs that display significant secondary interactions which influence magnetic performance, and highlights the importance of considering these interactions in the design of future SMMs.

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Introduction

The discovery that single molecules were capable of retaining magnetisation outside of an applied magnetic field resulted in a burst of interest in the wider field of molecular magnetism. The first reported single molecule magnet (SMM) was the Mn₁₂ cluster [Mn^III₈Mn^IV₄(OAc)₁₆ (H₂O)₄O₁₂]·2AcOH·4H₂O reported by Sessoli et al.,¹ the structure of which was first reported in 1980 by Lis et al.² Over the next 30 years, researchers have developed SMMs that featured a variety of different transition metals, lanthanides, and a combination of the two. One of the major factors driving research into SMMs and similar materials is their potential technological applications. Owing to their magnetic properties, researchers have proposed that SMMs can be utilised where traditional bulk ferromagnetic materials are currently being used, such as in information storage or processing. Furthermore, since SMMs are discrete molecular species, they have potential applications in advanced technologies such as molecular spintronics and quantum computing.^3,4 However, several major hurdles must be overcome before these technological innovations can be implemented. The most significant being that the vast majority of SMMs only work at low temperatures, below the temperature of liquid nitrogen. This limits their viability in information storage or processing technologies as traditional components are able to operate in ambient conditions. Thus, a key focus for researchers is developing SMMs that can retain their magnetisation at ever higher temperatures.

SMMs are often defined by two main parameters: the blocking temperature (T_B) and the effective energy barrier for reversal of magnetisation (U_eff).^5–7 The blocking temperature T_B, being the temperature below which magnetisation is retained, would be the most sensible parameter for determining SMM performance. However, the exact definition of T_B often varies between groups with the more commonly utilised definitions being; the maximum temperature at which magnetic hysteresis is observed,^8,9 (the temperature corresponding to the maximum zero-field AC susceptibility),^10–13 and the temperature at which the relaxation time is equal to 100 seconds.^14–16 Furthermore, the exact definition used for T_B is not always present in publications, making comparisons of T_B between studies difficult.¹⁷U_eff is typically an easier to measure parameter and, with respect to the studies covered within this minireview, is the more popular parameter for defining and comparing SMMs.^18–20U_eff represents the minimum amount of energy required to overcome the barrier for reversal of magnetisation, and as such is the parameter most directly related to SMM performance. U_eff is obtained by fitting the temperature dependence of the relaxation time to an Arrhenius law.^21–23 Thus, U_eff provides information about the exponential relaxation regime, which is dominated by the Orbach process.^24,25 However, at lower temperatures significant deviation from the Arrhenius law can be observed, which is often attributed to direct processes and quantum tunnelling of magnetisation (QTM).^26,27 Additionally, Raman relaxation and thermally-assisted QTM can operate over a wide temperature range. All this means that simply achieving a high U_eff will not necessarily lead to improved SMM performance.^28–32

In conjunction with the typical magnetic analyses, DFT and other computational calculations are popular for interpreting and rationalising SMM behaviour.^33,34 These computational methods tend to agree well with the experimental results whilst providing researchers a way to probe how small structural differences between SMMs can affect their magnetic properties.³⁵

Initial attempts to enhance SMM performance were focused on maximising the total ‘spin’ of the system.^36,37 However, it was later found that U_eff was independent of the total spin, but instead reliant on the magnetic anisotropy of the magnetic centre,³⁶ thus, researchers focused their efforts on maximising the magnetic anisotropy. Lanthanide ions have large intrinsic single ion magnetic anisotropy, thus are excellent candidates as SMMs.³⁸ The first lanthanide SMM was reported in 2003 by Ishikawa et al. and utilised a sandwich-type coordination where two phthalocyanine ligands are bonded to a central Tb^III or Dy^III.³⁹ Fitting the experimental data to the Arrhenius law showed energy barriers of 230 K and 28 K respectively.

All elements possess an intrinsic electron distribution that is unique, for lanthanide ions these can be either oblate or prolate.^40,41 Matching the ligand field to the type of ion (axial ligand field for oblate ions and equatorial ligand field for prolate anions) reduces electrostatic interactions between the lanthanide ion and the ligand, which maximises the anisotropy thereby enhancing SMM performance.¹⁹

A major factor limiting the performance of SMMs is the presence of through-barrier relaxation processes which remove the magnetisation without having to fully overcome the energy barrier, therefore minimising these processes is essential for developing high-end SMMs.^42,43 One of the key routes in reducing QTM is by utilising exchange pathways to couple adjacent metal centres together. This can effectively reduce the probability of QTM by requiring the coupled metal centres to both simultaneously lose their magnetisation.⁴⁴ Lanthanide ions do not possess strong pathways for this exchange coupling, but transition metal ions do. Thus, exchange coupled 3d–4f complexes are an attractive prospect for designing SMMs as this combines the intrinsic magnetism of lanthanide ions with the exchange pathways present in transition metal ions.^45–50 Another route to reducing QTM is by controlling the symmetry of the complex. One of the major factors behind QTM in SMMs is the magnitude of transverse crystal fields (CFs). Designing SMMs with a strong ligand field and high symmetry coordination environments (such as C_5h, D_4hD_5h, D_4d and D_6d) the CFs can be minimised, which in turn suppresses QTM.^51–54

Second sphere interactions, or secondary interactions consist of interactions that are not directly involved in the primary coordination sphere. The two most common types of secondary interactions are steric effects and hydrogen bonding. Steric effects are due to electrostatic repulsion which results in molecules and atoms pushing neighbouring species away. Effective use of sterically bulky macrocyclic ligands has been explored by Tang et al., in their quest to elucidate the relaxation mechanisms of SMMs.^55–58 These bulky ligands helped isolate the magnetic centres and reduce the CFs. With the addition of electron withdrawing substituents to the macrocycles Tang et al. were able to further weaken the equatorial crystal field, dramatically increasing SMM performance.⁵⁹ Hydrogen bonding interactions result in an attraction between hydrogen bond donor and acceptor species. This effect is shared by similar interactions such as weaker halogen bonding and π–π stacking interactions.

Effects of secondary interactions

The effects of secondary interactions on SMMs are numerous and varied often involving the interplay of multiple types of interactions. Perhaps the most often mentioned secondary effect in the context of SMMs is the physical isolation of magnetic centres, which prevents interactions between adjacent magnetic centres, resulting in a reduction of the number of relaxation pathways present. This is most easily achieved by electrostatically driven processes where sterically bulky ligands push neighbouring molecules apart and is represented in Fig. 1(A). Similarly to this, utilising secondary interactions to impose rigidity on a complex can result in a decrease in molecular vibrations, which then decreases the number of relaxation pathways.⁶⁰ Another subcategory of this involves magnetic dilution where the majority of magnetically active ions in a sample are replaced with diamagnetic ions.⁶¹ An effect utilising hydrogen bonding is shown in Fig. 1(B), where hydrogen bonds mediate exchange between adjacent metal centres. This can result in an increase or decrease in QTM or even the presence of SMM behaviour. An effect that is often the result of multiple secondary interactions is the reorientation of the magnetic axis of the complex as represented in Fig. 1(C). This is often, but not exclusively, a negative effect and is a result of secondary interactions altering the orientation of the anisotropy axes and the symmetry axis of a molecule. This phenomenon has been thoroughly explored by Sessoli et al., in their work on a series of Ln-DOTA complexes.^62–65 The nuclearity of SMMs is a sterically dominated effect. By utilising ligands with similar coordination sites, but differing steric bulk, it is possible to control the number and orientation of magnetic ions present in the complex, as shown in Fig. 1(D). Finally, the electron density of the magnetic centres can be affected by secondary interactions. This effect is the broadest as it often involves the interplay of several secondary interactions and can be either positive or negative, as represented in Fig. 1(E) and (F) respectively, depending on whether the electron density is altered to enhance the intrinsic anisotropy of the magnetic centre or not.

Fig. 1 Representations of secondary effects (dashed lines represent the secondary interactions). (A) Isolation of adjacent magnetic centres. (B) Magnetic exchange mediated by hydrogen bonds. (C) Reorientation of the magnetic axis away from the ideal orientation. (D) Nuclearity of complexes can be determined by secondary interactions, predominantly electrostatic repulsion. (E) Alteration of electron density by secondary interactions into a more favourable distribution. (F) Alteration of electron density by secondary interactions into a less favourable distribution.

This mini-review provides a brief overview of cases where the effects of secondary interactions directly influence the magnetic properties of ligand metal systems and are a major focus of the study. The effects are divided into sections depending on how they affect SMM performance. Examples of SMMs displaying significant secondary interactions are highlighted and discussed with regard to the relevant secondary effects. A table listing the reported complexes and their magnetic properties is presented at the end of this article (Table 1).

Table 1 Table containing all the reported complexes in this review

No.	Formula	T B (K)	U eff (K)	Ref.
	Positive effects
1	[Dy^III2(DMOMP)2(TFNB)4]·Et2O	—	38.9	66
2	[Dy^III2(DMOAP)2(TFNB)4]	—	74.7
3	[Dy^III2(DMOEP)2(TTA)4]	—	20.0
4	[Dy^III2(DMOEP)2(BTFA)4]	—	33.6
5	[Dy^III2(DMOEP)2(TFNB)4]	—	97.3
6	[Co^II2(calix)2]·(Et3NH)2	—	—	67
7	[Co^II (Himl)2]·CH3OH	—	—	70
8	[Co^II (Himn)2]	—	—
9	[Co^II (Hthp)2]	—	—
10	[Mn^III3O(Me-salox)3(MeOH)3(ClO4)]·MeOH	—	58	69
11	[Mn^III3O(Ph-salox)3(MeOH)3(ClO4)]·2MeOH	—	42
12	[Mn12O12(O2C(C6H4-p-F))16(H2O)4]	—	59.3	72
13	[Ni^II(4-Clbpy)2][(pzTp)Fe^III(CN)3]2·4H2O	—	—	73
14	[Ni^II(4-Clbpy)2][(Tp*)Fe^III(CN)3]2·4CH3OH·2H2O	1.8	62.31
15	[Dy^III(L1R)(4-Me-PhO)2](BPh4)	—	800	74
16	[Dy^III(L1S)(4-Me-PhO)2](BPh4)	—	766.9
17	[Dy^III2(L2R)2(4-Me-PhO)2(OH)2](BPh4)2	—	198.6
18	[Dy^III2(L2S)2(4-Me-PhO)2(OH)2](BPh4)2	—	230.2
19	[LCu^IIGd^III(NO3)3]·3.5THF	—	—	75
20	[LCu^IITb^III(NO3)3]·3.5THF	—	—
21	[LCu^IIDy^III(NO3)3]·3.5THF	—	—
22	[(μ3-C9H3O6)(LCu^IIGd^III-(NO3)2)3]·3THF	—	—
23	[(μ3-C9H3O6)(LCu^IITb^III-(NO3)2)3]·3THF	—	—
24	[(μ3-C9H3O6)(LCu^IIDy^III-(NO3)2)3]·3THF	—	—
25	[Dy^III(tmpd)3(4,4′-dmpy)]	—	66	79
26	[Dy^III(tffb)3(4,4′-dmpy)]	—	189
27	[Dy^III(tffb)3(5,5′-dmpy)]	—	115
28	[Dy^III(tmpd)3(5,5′-dmpy)]	—	205
29	[Cu^IIL(H2O)Gd(NO3)2(H2O)2]·NO3	—	—	80
30	[Cu^IIL(MeOH)Tb(NO3)3]	—	24.6
31	[Cu^IIL(MeOH)Dy(NO3)3]	—	—
32	[Cu^IIL(H2O)Dy(NO3)3]	—	—
	Negative effects
33	[Dy^III(H2O)5(HMPA)2]Cl3·HMPA·H2O	∼7	460	81
34	[Dy^III(H2O)5(HMPA)2]I3·2HMPA	∼7	600
35	([Dy^III(L)2(H2O)4]·(6Br))n	—	—	84
36	([Gd^III(L)2(H2O)4]·(6Br))n	—	—
37	([La^III(L)2(H2O)4]·(6Br))n	—	—
38	[((PyPz3)Co^II)2(DHBQ)](PF6)2	—	117	85
39	[((PyPz3)Co^II)2(CA)](PF6)2	—	40.3
40	[((PyPz3)Co^II)2(BA)](PF6)2	—	33.1
41	[Dy^III((−)/(+)hfc)3(L)]2·C7H16	4	—	86
42	[[Dy^III((−)/(+)hfc)2(L)][BarF]]n·nCH3NO2	—	—
43	[Dy^III(N-NCS)3(H2O)5]·0.45(KSCN)·(18-crown-6)	—	47	87
44	[Dy^III(NO3)2(N-NCS)3(H2O)]·(H2O)(NH4)2·2(18-crown-6)	—	65.9
45	[Dy^III(NO3)3(H2O)3]·(18-crown-6)	—	66–71
46	[Er^III(NO3)3(H2O)3]·(18-crown-6)	—	21–24
	Other effects
47	[Nd^IIIL12][Et3NH]·THF	—	—	90
48	[Tb^IIIL12][Et3NH]·THF	—	—
49	[Dy^IIIL12][Et3NH]·THF	—	13.45
50	[Nd^IIIL22][Et3NH]·THF/H2O	—	—
51	[Tb^IIIL22][Et3NH]·THF/H2O	—	—
52	([Dy(OAc)3(H2O)3][Dy(H2O)3(prop·SMe)3][H2O⊂Cr3Dy6(OAc)12(bda)3(gly)3(ox)3(prop·SMe)3]2(H2O))·12H2O·1.5MeCN	—	11.9	91
53	([Tb(OAc)3(H2O)3][Tb(H2O)3(prop·SMe)3][H2O⊂Cr3Tb6(OAc)12(bda)3(gly)3(ox)3(prop·SMe)3]2(H2O))·11.25H2O·1.5MeCN	—	4.9

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Positive effects

There have been numerous cases where secondary interactions have been reported to enhance or even cause SMM behaviour.

Magnetic isolation

The most noted benefit of secondary interactions with regards to SMMs, is their ability to isolate the magnetic core, resulting in a decrease of the potential pathways for the relaxation of magnetisation. A prime demonstration of this is presented by Liu and co-workers who reported on a series of five binuclear dysprosium complexes featuring substituents with differing electronic and steric environments.⁶⁶ They synthesised the complexes, [Dy₂(DMOMP)₂(TFNB)₄]·Et₂O (1), [Dy₂(DMOAP)₂(TFNB)₄] (2), [Dy₂(DMOEP)₂(TTA)₄] (3), [Dy₂(DMOEP)₂(BTFA)₄] (4) and [Dy₂(DMOEP)₂(TFNB)₄] (5), where H-DMOMP = 2,6-dimethoxy-4-methylphenol, H-DMOAP = 3,5-dimethoxy-4-hydroxybenzaldehyde, H-DMOEP = methyl 3,5-dimethoxy-4-hydroxybenzoate, TTA = 2-thenoyltrifluoro-acetone, BTFA = benzoyltrifluoroacetone, and TFNB = 4,4,4-trifluoro-1-(2-naphthyl)-1,3-butane-dione. The reported U_eff values of the complexes under the optimal applied field are 38.9 K, 74.7 K, 20.0 K, 33.6 K and 97.3 K for complexes (1), (2), (3), (4) and (5) respectively. The structures of complexes (3), (4) and (5) are identical except for the terminal substituents of the β-diketonate. Liu et al. deduced that the vast difference in U_eff was due to the amount of conjugation and steric hindrance increasing from thiophene (3) to benzene (4) to naphthalene (5) in (Fig. 2).

Fig. 2 General structure of complexes reported by Liu et al. (1), R¹ = CH₃ R² = naphthalene, (2), R¹ = CHO R² = naphthalene, (3), R¹ = COOCH₃ R² = thiophene, (4), R¹ = COOCH₃ R² = benzene, (5), R¹ = COOCH₃ R² = naphthalene.

A similar phenomenon of magnetic isolation was explored by Petit et al. who synthesised the dinuclear cobalt complex [Co^II₂(calix)₂]·(Et₃NH)₂ (6), where calix = p-tert-butylcalix[8]arene (Fig. 3).⁶⁷ This study focused on identifying the role the second coordination sphere plays in quantifying the zero-field splitting (ZFS) on the cobalt sites. Through ab initio calculations the authors deduced that the effect of the second coordination sphere on the ZFS of the Co^II ions was twice that of the first coordination sphere. Additionally, it was discovered that half of the magnetic anisotropy of the Co^II ions is a result of the symmetry lowering effects of the calix[8]arene in the second coordination sphere.

Fig. 3 Structure of the complex (6) reported by Petit et al. Counterions and non-interacting hydrogen atoms have been omitted for clarity. Colour code: Co, O, C and H are purple, red, grey and white respectively. Thermal ellipsoids of metal atoms shown at 30%.

Magnetic exchange mediation

The most direct way that secondary interactions can impact SMM performance is by mediating exchange coupling adjacent metal ions. This is most commonly achieved through hydrogen-bonding which is used to couple adjacent metal centres in a manner similar to magnetic superexchange.⁶⁸ This can create an exchange bias which can alter QTM.⁶⁹

The direct implications of hydrogen bonding on the magnetic relaxation dynamics of SMMs was investigated by Mitsuhashi et al.^70,71 who synthesised a series of three tetracoordinated mononuclear cobalt complexes, [Co(iml)₂]·CH₃OH (7), [Co(imn)₂] (8) and [Co(thp)₂] (9), where H-iml = 2-(2-imidazolyl)phenol, H-imn = 2-(2-imidazolinyl)phenol, and H-thp = 2-(1,4,5,6-tetrahydropyrimidin-2-yl)phenol.⁷⁰ These three complexes differ by slight alterations in the conformation of the N–H groups. They found that the static magnetic properties of the complexes were comparable with axial zero field splitting parameters (D) of −42(11), −38(3), and −35(24) cm⁻¹ for (7), (8), and (9), respectively. The dynamic magnetic properties revealed that only two of the complexes displayed frequency dependent in phase (χ′) and out of phase (χ′′) signals between 1.9–8 K and 1.9–3.5 K for (8) and (9), respectively. Mitsuhashi et al. identified two reasons for this, firstly, (7) formed a two-dimensional hydrogen bonding network whilst (8) and (9) formed one-dimensional chains. The inter-sheet Co–Co distance in (7) (7.51 Å) is much shorter than the interchain distances in (8) and (9) (≥ca. 9 Å). Mitsuhashi et al. surmised that since each Co^II ion is surrounded by more magnetic ions, dipolar interactions can enhance the QTM resulting in reduced SMM performance. Secondly the closest Co⋯Co distance between two adjacent molecules for (7) is 7.03 Å whilst it is 6.05 Å and 6.36 Å for (8) and (9), respectively. Thus, the hydrogen-bonded chains of (8) and (9) can be regarded as a chain of dimers, in which the magnetic exchange coupling between SMMs works to suppress QTM.

This same phenomenon was explored by Yang et al. who synthesised two trinuclear manganese complexes [Mn₃O(Me-salox)₃(MeOH)₃(ClO₄)]·MeOH (10) and [Mn₃O(Ph-salox)₃(MeOH)₃(ClO₄)]·2MeOH (11) where HMe-salox = 2-hydroxyphenylethanone oxime and HPh-salox = (2-hydroxyphenyl)(phenyl)methanone oxime.⁶⁹ Magnetic measurements revealed that both complexes displayed frequency dependent in phase (χ′) and out of phase (χ′′) signals between 2 K and 7 K, with (10) showing an effective energy barrier of 58 K, whilst complex (11) had an effective energy barrier of 42 K. An interesting difference was found in the stepwise magnetisation hysteresis loops of the complexes where the QTM steps of (11) were observed at fields of −0.52 T, −0.17 T, 0.16 T, 0.52 T, 0.87 T, 1.21 T, and 1.67 T, whereas those for complex (12) were observed at fields of 0 T and 0.7 T. This difference was attributed to the supramolecular environments each individual complex resides in. The less bulky complex (10) conforms to a ‘tail to tail’ arrangement of adjacent units which provides strong hydrogen bonding interactions between the binding ligand and a terminal MeOH ligand of neighbouring units (Fig. 4). Complex (11) meanwhile, adopts a ‘head to tail’ arrangement providing a single hydrogen bonding interaction between an uncoordinated perchlorate anion and a terminal MeOH ligand. The presence of the strong hydrogen bonding interaction in complex (10) mediated a pathway for the exchange bias effect which in turn caused the QTM steps in the hysteresis loop.

Fig. 4 Structure of the two complexes reported by Yang et al. With the tail–tail arrangement (A) and the head to tail arrangement (B). Intermolecular interactions are shown by dashed cyan lines. Solvent molecules and non-interacting hydrogens have been omitted for clarity. Colour code: Mn, O, N, C, Cl, and H are lilac, red, blue, grey, green, and white, respectively. Thermal ellipsoids shown at 15%.

Fournet et al. investigated the hydrogen bond mediated magnetic coupling of a new member of the Mn₁₂ family [Mn₁₂O₁₂(O₂C(C₆H₄-p-F))₁₆(H₂O)₄] (12) which was the first of its family to display a three-dimensional ferromagnetic network.⁷² Magnetic measurements of the complex revealed a U_eff of 59.3 K which is typical for the Mn₁₂ family. There are two main types of intermolecular hydrogen bonds, one involving ortho-C–H⋯F units the other involving meta-C–H⋯F units. Fournet et al. further explained that due to the symmetry and spins in the relevant manganese and fluorine orbitals, exchange interactions mediated by the hydrogen bonds were predominantly ferromagnetic for the ortho units and antiferromagnetic for the meta units. The overall result is a net ferromagnetic interaction due to the greater localisation of spin onto the ortho position.

Control over complex nuclearity

A less direct way that second sphere interactions can impact SMM performance is by controlling the nuclearity of resulting complexes. This is often achieved by utilising ligands that provide identical metal binding sites but different steric bulk. In this vein, Jiao et al. reported two complexes in 2018 which showed intramolecular ferromagnetic interactions.⁷³ A trinuclear [Ni^II(4-Clbpy)₂][(pzTp)Fe^III(CN)₃]₂·4H₂O complex (13) and a tetranuclear [Ni^II(4-Clbpy)₂][(Tp*)Fe^III(CN)₃]₂·4CH₃OH·2H₂O (14) where Clbpy = 4,4′-dichloro-2,2′-bipyridine, pzTp = tetrakis(pyrazolyl)borate, and Tp* = hydrotris-(3,5-dimethylpyrazol-1-yl)borate. They proposed that the interaction between the bulky Tp* units and the 4-Clbpy ligand resulted in the formation of a tetranuclear square complex. Magnetic studies performed on these two complexes revealed that the trinuclear complex (13) showed no SMM behaviour, however, the tetranuclear complex (14) displayed frequency dependent in phase (χ′) and out of phase (χ′′) signals between 1.9 K and 5 K, and an effective energy barrier of 62.31 K. This difference was put down to three factors: the larger ground spin state owing to the addition of an extra Ni^II ion, weaker intermolecular interactions removing pathways for magnetic relaxation, and stronger intermolecular ferromagnetic interactions due to the difference in Ni–N–C bond angles.

Zhao and co-workers utilised two chiral pairs of weakly coordinating hexaazamacrocycles, one based on (1R,2R/1S,2S)-1,2-diphenylethylenediamine, and the other, on (1R,2R/1S,2S)-1,2-diaminocyclohexane in their report investigating the effects of steric hindrance on the performance of dysprosium single molecule magnets (Fig. 5).⁷⁴ The mononuclear complexes were synthesised by using the bulkier 1,2-diphenylethylenediamine based hexaazamacrocycle which resulted in two complexes (15) and (16) displaying SMM behaviour with U_eff values of 800.0 K and 766.9 K, respectively. Two dinuclear complexes (17) and (18) which displayed SMM behaviour were synthesised using the less sterically bulky 1,2-diaminocyclohexane based macrocycle. These complexes gave U_eff values of 198.6 K and 230.2 K, respectively. The reason for the large difference between energy barriers was put down to the geometry of the magnetic cores. The mononuclear Dy^III ions possess an almost perfect local D_6h geometry which enhances the axial crystal field. In contrast, the dinuclear Dy^III ions possess a ‘hula-hoop’ geometry which weakens the axial crystal field, thereby reducing U_eff.

Fig. 5 Structures of the mononuclear (A, 15/16) and dinuclear (B, 17/18) complexes reported by Zhao et al. Hydrogen atoms have been omitted for clarity. Colour code: Dy, O, N, and C are cyan, red, blue, and grey, respectively. Thermal ellipsoids shown at 15%.

Reorientation of magnetic axis

An interesting way that secondary interactions have been shown to affect the magnetic properties of SMMs is by reorienting the magnetic axes. An example where this was beneficial is reported by Novitchi et al. The group developed two series of 3d–4f SMMs [L4CuGd(NO₃)₃]·3.5THF (19), [L4CuTb(NO₃)₃]·3.5THF (20), and [L4CuDy(NO₃)₃]·3.5THF (21) [(μ₃-C₉H₃O₆)(L4CuGd-(NO₃)₂)₃]·3THF (22), [(μ₃-C₉H₃O₆)(L4CuTb-(NO₃)₂)₃]·3THF (23), and [(μ₃-C₉H₃O₆)(LCuDy-(NO₃)₂)₃]·3THF (24). Where H₂L4 = N,N′-bis(3-hydroxymethyl-5-methylsalicylidene)-1,3-diaminopropane.⁷⁵ The magnetic properties of the dysprosium complexes, (21) and (24), showed that the dinuclear complex (21) displayed magnetic hysteresis curves of low coercivity, whilst the hexanuclear cluster (24) was much larger; coercivity being a measure of how resistant the complex is to becoming demagnetised by an external magnetic field. Furthermore, the hysteresis curves of (21) were only open at 0.04 K whilst for (24) the hysteresis curves were open at temperatures up to 1.1 K. Previous research done on similar complexes suggested that this difference was not a result of intramolecular magnetic interactions, since these were expected to be negligible.^76–78 Novitchi and co-workers deduced that intermolecular π–π stacking and hydrogen bonding interactions between two hexanuclear clusters resulted in a reorientation of the anisotropy axes of the lanthanide ions (Fig. 6). This in turn caused the large change in SMM behaviour.

Fig. 6 Structures of two molecules of the dinuclear (A) and hexanuclear (B and C) dysprosium complexes reported by Novitchi et al. Solvent molecules and non-interacting hydrogen atoms have been omitted for clarity. Hydrogen bonding interactions are shown by dashed cyan lines. Colour code: Dy, Cu, O, N, C, and H are cyan, orange, red, blue, grey, and white, respectively. Thermal ellipsoids shown at 15%.

Changing electron density

Recent advances in SMM research have revealed that matching the electron density of the magnetic ion with an appropriate ligand field is essential to enhancing the magnetic properties of SMMs, especially those that are lanthanide based. A key example of this was shown by Zhang et al. who developed a series of four mononuclear dysprosium complexes [Dy(tmpd)₃(4,4′-dmpy)] (25), [Dy(tffb)₃(4,4′-dmpy)] (26), [Dy(tffb)₃(5,5′-dmpy)] (27), and [Dy(tmpd)₃(5,5′-dmpy)] (28), where tmpd = 4,4,4-trifluoro-1-(4-methoxyphenyl)-1,3-butanedione, tffb = 4,4,4-trifluoro-1-(4-fluorophenyl)-1,3-butanedione, 4,4′-dmpy = 4,4′-dimethyl-2,2′-bipyridyl, and 5,5′-dmpy = 5,5′-dimethyl-2,2′-bipyridyl.⁷⁹ Magnetic measurements on these complexes revealed U_eff values of 66 K (25), 189 K (26), 115 K (27), and 205 K (28). Experimental and theoretical investigations revealed that the symmetry of the electron density distribution surrounding the central Dy^III ion is critical in regulating the slow relaxation of magnetisation. It was found that complex (28) had the strongest axial ligand field, which when coupled with the Dy^III ion's naturally oblate electron density resulted in the complex with the highest energy barrier to reversal of magnetisation. Furthermore, the lowest energy barrier was displayed by complex (25), which was found to have the shortest intermolecular Dy⋯Dy separation because of the presence of strong π–π stacking interactions. This resulted in stronger dipolar interactions between the molecules which, in this case, increased QTM and thus a lower energy barrier for reversal of magnetisation.

Fellah et al. investigated the effects a non-coordinating alcohol group had on the magnetic properties of a series of four binuclear CuLn complexes, [CuL1(H₂O)Gd(NO₃)₂(H₂O)₂]·NO₃ (29), [CuL1(MeOH)Tb(NO₃)₃] (30), [CuL1(MeOH)Dy(NO₃)₃] (31), and [CuL1(H₂O)Dy(NO₃)₃] (32) where H₂L1 = 1,3-bis(2-hydroxy-3-methoxybenzylidene)propan-2-ol.⁸⁰ Of these complexes, only (30) displayed SMM properties with an U_eff barrier of 24.6 K. In all complexes, the alcohol group acts as a hydrogen bond donor for intermolecular interactions and a hydrogen bond acceptor for intramolecular interactions (Fig. 7). The researchers noted that only complexes (30) and (31), which contained a methanol molecule bound to the copper, displayed slow relaxation of magnetisation. Furthermore, they postulated that the intramolecular hydrogen bonding between the non-coordinated alcohol group and the apical ligand (H₂O or MeOH) could help stabilise the coordination with respect to the lability of this ligand. This in turn directly affected the magnetic properties of the reported complexes.

Fig. 7 Structure of the terbium complex (30) reported by Fellah et al. Hydrogen bonding interactions are shown by dashed cyan lines. Non-interacting hydrogen atoms have been omitted for clarity. Colour code: Tb, Cu, O, N, C, and H are cyan, orange, red, blue, grey, and white respectively. Thermal ellipsoids shown at 15%.

Negative effects

In this section the impact secondary interactions can have to diminish or prevent SMM behaviour will be discussed. As one might expect, the negative effects of secondary interactions are far less commonly reported, with even fewer being the focus of the reported research.

Changing electron density

Secondary interactions which alter electron density on the magnetic centre can also quench the potential magnetic properties. This happens by either providing various relaxation pathways for the reversal of magnetisation, most notably QTM; or, by reducing the magnetic anisotropy of the metal ion, reducing SMM performance. This effect was thoroughly investigated by Canaj and co-workers who synthesised two dysprosium SMMs [Dy(H₂O)₅(HMPA)₂]3Cl·HMPA·H₂O (33) and [Dy(H₂O)₅(HMPA)₂]3I·2HMPA (34), HMPA = hexamethylphosphoramide (Fig. 8).⁸¹ Magnetic studies revealed that the energy barrier for the reversal of magnetisation was 460 K (33) and 600 K (34). This difference was attributed to the large computed LoProp (local properties)⁸² charge of the chloride anion compared to the iodide anion. In practice, this resulted in a larger equatorial electron density for (33) which for a Dy^III ion results in a larger transverse ligand field and a resultant increase in QTM. Furthermore, they performed ab initio calculations to identify what effect removing anions/molecules in the second coordination sphere had on the magnetic properties of the complex. The result was an increase in the calculated energy barrier for reversal of magnetisation U_cal to a maximum of approximately 3100 K for the two-coordinate [Dy(HMPA)₂]³⁺ model. This drastic increase was a result of the decreasing equatorial electron density and the increase in the axial crystal field as they moved to lower coordinate models.

Fig. 8 Diagram of the chlorine containing complex (A) and the iodine containing complex (B) reported by Canaj et al. Solvent molecules and non-interacting hydrogens have been omitted for clarity. Hydrogen bonding interactions are shown as dashed red lines. Colour code: Dy, O, N, C, P, Cl, I, and H are cyan, red, blue, grey, orange, green, violet, and white, respectively. Thermal ellipsoids shown at 15%.

A more conclusive example of the detrimental effects of changing the electron density was studied by Ramakant et al. who developed a series of lanthanide based 1D polymers ([Dy(L2)₂(H₂O)₄]·6Br)_n (35), ([Gd(L2)₂(H₂O)₄]·6Br)_n (36), and ([La(L2)₂(H₂O)₄]·6Br)_n (37), where L2 = 3,3′,3′′-((2,4,6-trimethylbenzene-1,3,5-triyl)tris(methylene))tris(1-(carboxymethyl)-benzimidazolium).⁸³ They found that (35) displayed some SMM behaviours whilst (36) and (37) did not, which is not unreasonable since La^III is diamagnetic and Gd^III is typically magnetically isotropic. The observed out-of-phase ac magnetic susceptibility (χ′′) measurements on (35) showed frequency dependence between 1.9 K and 4.2 K however, there was no clear (χ′′) maxima within the experimental temperature and frequency ranges. This absence was a result of fast QTM bypassing the energy barrier. Through theoretical calculations they reasoned that hydrogen bonding interactions between bound water molecules and the bromine anions resulted in an increase in equatorial electron density, which resulted in an unfavourable crystal field and thus negatively affected the slow relaxation of magnetisation.

A case where the magnetic anisotropy of the metal centres was altered is reported by Yao et al. who investigated the effect of substituent size in a series of three dinuclear cobalt(II) SMMs: [((PyPz₃)Co)₂(DHBQ)](PF₆)₂ (38), [((PyPz₃)Co)₂(CA)](PF₆)₂ (39) and [((PyPz₃)Co)₂(BA)](PF₆)₂ (40) (Fig. 9) where PyPz₃ = 2-(di(1H-pyrazol-1-yl)methyl)-6-(1H-pyrazol-1-yl)pyridine, dhbq = 2,5-dioxo-1,4-benzoquinone, CA = chloranilate and BA = bromanilate.⁸⁴ Magnetic measurements revealed the energy barriers for reversal of magnetization to be 117 K (38), 40.3 K (39), and 33.1 K (40). Analysis of the X-ray data revealed that the cobalt centres adopted a distorted trigonal prismatic geometry with this distortion becoming more pronounced with the larger substituents, (38) → (39) → (40) in ascending order. The corresponding magnetic analysis revealed that the more structurally distorted the complex, the lower the effective energy barrier. This was ascribed to the greater distortions increasing the rhombic anisotropy, which promoted QTM mechanisms.

Fig. 9 Structures of the three complexes reported by Yao et al. Counterions and hydrogen atoms have been omitted for clarity. Colour code: Co, O, N, C, Cl, and Br are purple, red, blue, grey, green, and orange, respectively. Thermal ellipsoids shown at 15%.

Douib et al. recently reported an investigation on the influence that bulky anions had on the magnetic properties of a pair of chiral dysprosium SMMs.⁸⁵ The chiral pair of complexes [Dy((∓)hfc)₃(L3)]₂·C₇H₁₆ (41) where hfc = 3-(heptafluoropropylhydroxymethylene)-(±)-camphorate and L3 = 4′-(4′′′-pyridyl-N-oxide)-1,2′:6′,1′′-bis-(pyrazolyl)pyridine, were dinuclear M₂L₂ type complexes, and possessed eight oxygens occupying the primary coordination sphere of the lanthanide ions. Six oxygens were provided by the coordinated hfc anions and one each by the two bound ligands. Addition of the bulky BarF anion (BarF = tetrakis[3,5-bis(trifluoromethyl)phenyl]borate) resulted in the formation of the chiral pair of 1D coordination polymers [[Dy((∓)hfc)₂(L3)][BarF]]_n·nCH₃NO₂ (42). The presence of the bulky anion caused partial dissociation of the hfc anions from the metal centre, which resulted in the lanthanide ion having five oxygen and three nitrogen atoms occupying its coordination sites (Fig. 10). They reported that the dinuclear complex (41) acts as a SMM with a blocking temperature of 4 K whilst the polymeric complex (42) acts as a one-dimensional assembly of field induced SMMs where the magnetic relaxation occurs through Raman processes. They attributed the enhanced SMM properties in the dinuclear complexes to the electronic distribution of the first coordination sphere better matching the oblate DyIII ion when compared to the polymer complex.

Fig. 10 Structures of the dinuclear complex (A) and polymer complex (B) reported by Douib et al. Solvent molecules and hydrogen atoms have been omitted for clarity. Colour code: Dy, O, N, C, F, and B are cyan, red, blue, grey, lime, and pink, respectively. Thermal ellipsoids shown at 15%.

Reorientation of magnetic axis

A combination of secondary interactions can result in the symmetry of the complex no longer aligning with the easy axis of magnetisation, hindering SMM behaviour. Alternatively, secondary effects can also reorient the magnetisation axis itself away from the principal symmetry axis of the molecule. Both result in a lowering of the energy barrier.

An example of the former was presented by Gil et al. who investigated how the secondary interactions caused by 18-crown-6 affected the SMM performance of two mononuclear dysprosium based complexes [Dy(NCS)₃(H₂O)₅]·0.45(KSCN) (18-crown-6) (43) and [Dy(NO₃)₂(NCS)₃(H₂O)]·(H₂O)(NH₄)₂·2(18-crown-6) (44).⁸⁶ The effective energy barriers for reversal of magnetisation were determined to be 47 K for (43) and 65.9 K for (44). They went further and performed a series of theoretical calculations to identify the effects of all secondary interactions resulting from the encapsulation by the crown ether. They found that hydrogen bonding interactions between bound water molecules and the crown ether had a detrimental effect on the magnetic anisotropy due to the water molecules being bound on the equatorial plane of the dysprosium anion. Furthermore, through ab initio calculations they found that by altering the electrostatic potential exerted by the crown ethers to align with the magnetic easy axis, they were able to enhance the magnetic properties. However, the mismatched symmetry axis of the crown ether molecules and the magnetic easy axis of the recorded complexes resulted in less optimal SMM performance.

Exploring the same phenomenon Herchel and co-workers investigated the effect of the second coordination sphere, specifically, the effect that 18-crown-6 had on the magnetic properties of two mononuclear lanthanide complexes [Dy(NO₃)₃(H₂O)₃]·(18-crown-6) (45) and [Er(NO₃)₃(H₂O)₃]·(18-crown-6) (46).⁸⁷ Due to the complicated relaxation pathways present, the experimentally determined energy barriers lie in the ranges 66–71 K (45) and 21–24 K (46). Theoretical calculations of each complex with and without the presence of the crown ethers (Fig. 11) indicated that the calculated energy barriers for the complexes without crown ethers present were 143 K (45′) and 42 K (46′) whilst with the crown ethers they were 57 K (45) and 16 K (46). This was attributed to the reorientation of the magnetisation axis, demonstrating that the second coordination sphere has the capability to drastically reduce the magnetic performance of SMMs.

Fig. 11 Effect of 18-crown-6 on the magnetic axis as reported by Herchel et al. blue line represents the magnetic axis.

Other effects

Secondary interactions can influence SMMs through ways that don't directly impact the magnetic properties. For example, secondary interactions are the dominant forces behind crystal packing and the formation of supramolecular architectures, where control of these could prove beneficial in the development of future SMMs.^88,89

Exploring this, Sushila et al. synthesised five mononuclear lanthanide complexes (NdL5₂)(Et₃NH)·THF (47), (TbL5₂)(Et₃NH)·THF (48), (DyL5₂)(Et₃NH)·THF (49), (NdL6₂)(Et₃NH)·THF/H₂O (50), and (TbL6₂)(Et₃NH)·THF/H₂O (51). Where H₂L5 = 2-[N,N-bis(2-hydroxy-3,5-dichlorobenzyl)aminomethyl]pyridine and H₂L6 = 2-[N,N-bis(2-hydroxy-3,5-dibromobenzyl)aminomethyl]pyridine.⁹⁰ The complexes are essentially isostructural however, only the dysprosium containing complex (49) showed SMM behaviour with U_eff of 13.45 K. A notable trend of this series is that the overall coordination environment of the magnetic centre was invariant to the halogen used. This is a result of the hydrogen/halogen bonding interplay, which controls the overall crystal packing, being largely independent of the halogen present. However, the individual molecules do show subtle variations in order to cope with the stereo-electronic requirements when different halides are present.

Schmitz et al. reported the magnetic properties of two self-assembling supramolecular architectures ([Dy(OAc)₃(H₂O)₃][Dy(H₂O)₃(prop·SMe)₃][H₂O⊂Cr₃Dy₆(OAc)₁₂(H₂bda)₃(gly)₃(ox)₃(prop·SM)₃]₂(H₂O))·12H₂O·1.5MeCN (52) and ([Tb(OAc)₃(H₂O)₃][Tb(H₂O)₃(prop·SMe)₃] [H₂O⊂Cr₃Tb₆ (OAc)₁₂(H₂bda)₃(gly)₃(ox)₃(prop·SMe)₃]₂(H₂O))·11.25H₂O·1.5MeCN (53) where H-prop·SMe = 3-(methylthio)propionic acid; H₂-bda = N-butyldiethanolamine; H₂-ox = oxalic acid; H₂-gly = glycolic acid.⁹¹ The recorded energy barriers were 11.9 K (52) and 4.9 K (53). The overall structures of each complex have dimensions of ca. 17 × 12 Å, which is comprised of distinct molecules which self-assembled and are maintained by purely intramolecular hydrogen bonds. They postulated that the formation of the supramolecular architecture was likely templated by cooperative hydrogen bonds of a central trio of water molecules in a manner which resembles polyoxovanadate chemistry.⁹²

Conclusions

The biggest challenge facing researchers into SMMs is raising the temperature at which SMMs can retain their magnetisation. Two key routes to achieving this is through raising the effective energy barrier, U_eff, for the reversal of magnetisation or by reducing the number of pathways for through barrier relaxation to occur. In this context we have identified several areas where consideration of the effects of secondary interactions is necessary for the development of high-performance SMMs:

(1) By utilising secondary interactions to control the bond angles and physical positioning of metal centres in 3d–4f SMMs. This would provide a way to modulate the superexchange pathways and identify the ideal conditions to maximise SMM performance.

(2) Intermolecular hydrogen bonding interactions have been reported to facilitate magnetic exchange between adjacent metal centres. Designing SMMs with these interactions present can provide a way to suppress QTM through the exchange bias effect.

(3) Symmetry factors of the secondary coordination sphere can have a significant impact on the magnetic properties of SMMs, notably the use of sterically bulky units to modify the symmetry axis of the complex. Thus, utilising secondary interactions to impose higher order symmetry on metal complexes provides another effective way to suppress QTM.

In summary, we believe that an increased focus on secondary interaction provides an attractive avenue for the development of high-performance SMMs. On the other hand, failing to account for the effects secondary interactions can result in vastly diminished SMM performance.

Author contributions

BEM preparation and writing of the initial draft; ideas and evolution of overarching research goals and aims; PGP initial ideas of research goals and aims; oversight and leadership responsibility for the research activity, revision of the work; GJR and TND supervisory responsibility for the research activity, revision of the work; MED revision of the work.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

BEM and MED would like to acknowledge the Massey University Doctoral Scholarship for financial support. TND would like to acknowledge the Massey University College of Sciences Māori academic staff development programme.

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