E.
Bartolomé
*^{a},
A.
Arauzo
^{bc},
J.
Luzón
^{bd},
S.
Melnic
^{e},
S.
Shova
^{f},
D.
Prodius
^{g},
I. C.
Nlebedim
^{g},
F.
Bartolomé
^{b} and
J.
Bartolomé
^{b}
^{a}Escola Universitària Salesiana de Sarrià (EUSS), Passeig Sant Joan Bosco 74, 08017-Barcelona, Spain. E-mail: ebartolome@euss.es
^{b}Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
^{c}Servicio de Medidas Físicas. Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
^{d}Centro Universitario de la Defensa. Academia General Militar, Zaragoza, Spain
^{e}Institute of Chemistry, Academy of Sciences of Moldova, Academiei 3, MD-2028, Chisinau, Republic of Moldova
^{f}“Petru Poni” Institute of Macromolecular Chemistry, Alea Gr. Ghica Voda 41A, 700487 Iasi, Romania
^{g}Ames Laboratory, US Department of Energy and Critical Materials Institute, Ames, IA-50011-3020, USA
First published on 24th June 2019
Two new neodymium molecular magnets of formula {[Nd(α-fur)_{3}(H_{2}O)_{2}]·DMF}_{n} (1) and {[Nd_{0.065}La_{0.935}(α-fur)_{3}(H_{2}O)_{2}]}_{n} (2), α-fur = C_{4}H_{3}OCOO, have been synthesized. In (1) the furoate ligands, in bidentate bridging mode, consolidate zig-zag chains running along the a-direction. Compound (2) is a magnetically diluted complex of a polymeric chain along the b-axis. Heat capacity, dc magnetization and ac susceptibility measurements have been performed from 1.8 K up to room temperature. Ab initio calculations yielded the gyromagnetic factors g_{x}* = 0.52, g_{y}* = 1.03, g_{z}* = 4.41 for (1) and g_{x}* = 1.35, g_{y}* = 1.98, g_{z}* = 3.88 for (2), and predicted energy gaps of Δ/k_{B} = 125.5 K (1) and Δ/k_{B} = 58.8 K (2). Heat capacity and magnetometry measurements agree with these predictions, and confirm the non-negligible transversal anisotropy of the Kramers doublet ground state. A weak intrachain antiferromagnetic interaction J′/k_{B} = −3.15 × 10^{−3} K was found for (1). No slow relaxation is observed at H = 0, attributed to the sizable transverse anisotropy component, and/or dipolar or exchange interactions enhancing the quantum tunnelling probability. Under an external applied field as small as 80 Oe, two slow relaxation processes appear: above 3 K the first relaxation mechanism is associated to a combination of Orbach process, with a sizeable activation energy U/k_{B} = 121 K at 1.2 kOe for (1), Raman and direct processes; the second, slowest relaxation mechanism is associated to a direct process, affected by phonon-bottleneck effect. For complex (2) a smaller U/k_{B} = 61 K at 1.2 kOe is found, together with larger g*-transversal terms, and the low-frequency process is quenched. The reported complexes represent rare polymeric Nd single-ion magnets exhibiting high activation energies among the scarce Nd(III) family.
Some heavy lanthanide(III) ions are especially well suited for the design of molecular magnets because of their large magnetic moment (Gd, Tb, Dy, Ho, Er, Tm and Yb), on one hand, and the unquenched orbital moment, which leads to a strong magnetic anisotropy (Tb, Dy, Ho), on the other, when the ions are placed in an anisotropic ligand field.^{1} The light rare earth are less likely to present SMM behavior since their magnetic moment is lower, although anisotropy may also be present in Pr, Nd and Sm. The quantum number J is L + S for heavy-Ln(III) ions and L–S for light-Ln(III) ions. Therefore, research of Ln-SMMs has hitherto focused on complexes based on heavy lanthanide ions, mainly Dy^{3+} (L = 5, S = 5/2, J = 15/2), Tb^{3+} (L = 3, S = 3, J = 6) and Er^{3+} (L = 6, S = 3/2, J = 15/2).
Work on light Ln-SMMs is still rare.^{2} However, they are receiving growing attention given that earlier lanthanide ions are substantially more abundant, cheaper and thus more interesting for the sustainable development of applications^{3} (e.g. they are used in the production of most commercial permanent magnets like Nd_{2}Fe_{14}B and SmCo_{5}).
In particular, Nd(III) Kramers ion, with an oblate electron density and a ^{4}I_{9/2} (L = 6, S = 3/2, J = 9/2) free ion ground state, may introduce a significant anisotropy, if the crystal field is designed such that the ground ±M_{J} doublet is stabilized well below the first-excited one.^{4,5} Neodymium single molecule magnets are however relatively rare (see review in Table 1). The first Nd-SIM reported in 2012, [NdTp_{3}], exhibited field-induced relaxation with a small thermal activation energy of U/k_{B} = 4.1 K (100 Oe).^{6} Eight field-induced Nd-SIMs^{3,7–12} and three dimeric {Nd_{2}} complexes^{13–15} with higher barrier energies have been reported ever since, with POM derivative [Na_{9}Nd(W_{5}O_{18})_{2}]_{9}^{−} holding at present the record U/k_{B} = 73.9 K (1 kOe).^{16}
Complex | g _{ x }* | g _{ y }* | g _{ z }* | H (kOe) | U/k_{B} (K) | τ _{0} (s) | C (s^{−1} K^{−n}) | n | τ _{QT} ^{−1} (s^{−1}) | A (s^{−1} K^{−1}) | Ref. | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
0-D | ||||||||||||
Na_{9}[Nd(W_{5}O_{18})_{2}] | 1 | 73.9 | 3.55 × 10^{−10} | 16 | ||||||||
C_{p}*_{2}Nd(BPh_{4}) | 1 | 41.7 | 1.4(4) × 10^{−6} | 0.0286 | 5.2 | 1.1 | 3 | |||||
[L_{2}Nd(H_{2}O_{5}]-[I]_{3}·L_{2}(H_{2}O) | 0 | 16.08 | 2.64 × 10^{−4} | 7 | ||||||||
24.69 | 5.03 × 10^{−6} | |||||||||||
Ab initio | 0.02 | 0.02 | 6.3 | 302 | ||||||||
2 | 39.21 | 8.98 × 10^{−7} | ||||||||||
(NH_{2}Me_{2})_{3}{[Nd(Mo_{4}O_{13})(DMF)_{4}]_{3}(BTC)_{2}}_{8}·(DMF) | 0.5 | 34.06 | 4.69 × 10^{−8} | 8 | ||||||||
[NdL(NO_{3})_{2}]PF_{6}·MeCN | 1 | 34(1) | 1.1(4) × 10^{−8} | 2.8(2) | 5 | 9 | ||||||
10(2) | 2.0(6) × 10^{−4} | 0.081(2) | 9 | |||||||||
[Nd(NO_{3})_{3}(18-crown-6)] | 1 | 30.9(4) | 2.2(3) × 10^{−9} | 4.1(3) | 5 | 10 | ||||||
Nd(fdh)_{3}(bpy) | Exp. | 1.04 | 1.43 | 4.31 | 2 | 28.7 | 9.2 × 10^{−8} | 11 | ||||
Ab initio | 0.56 | 1.06 | 4.78 | 106.42 | ||||||||
[Li(DME)_{3}][Nd(COT′′)_{2}] | 1 | 21 | 5.5 × 10^{−5} | 12 | ||||||||
[NdTp_{3}] | 0.1 | 4.1 (100%) | 4.2(2) × 10^{−5} | 6 | ||||||||
5.46 (3.8%) | 2.6(2) × 10^{−4} | |||||||||||
Nd _{ 2 } | ||||||||||||
[Nd_{2} (2-FBz)4-(NO_{3})_{2}(phen)_{2}] | 13.67 | 7.4 × 10^{−6} | 0.02 | 9 | 265.21 | 13 | ||||||
[Nd_{2}(L)_{4}(H_{2}O)_{6}](L)_{2}(H_{2}O)_{14} | 6.2 | 2.2 × 10^{−5} | 15 | |||||||||
[Nd_{2}(μ_{2}-9-AC)_{4}(9-AC)_{2}(bpy)_{2}] | — | — | 1.03 | 6 | 823.60 | 14 | ||||||
1-D | ||||||||||||
{[Nd(pzdo)(H_{2}O)_{4}][Co(CN)_{6}]}·0.5(pzdo)·4H_{2}O | 1 | 51(2) | 4.5(9) × 10^{−8} | 0.09(6) | 5.6(9) | 2.2(9) | — | 20 | ||||
[Nd(NO_{3}){Zn(L)(SCN)}_{2}] | 1 | 38.5(5) | 2.07(1) × 10^{−7} | 4 | ||||||||
[Nd_{2}(CNCH_{2}COO)_{6}(H_{2}O)_{4}]·2H_{2}O | 1.5 | 26.6 | 1.75 × 10^{−7} | 17 | ||||||||
{[Nd(μ_{2}-L1)_{3}(H_{2}O)_{2}]·MeCN}_{n} | 1.021 | 2.012 | 3.514 | 2 | 27 | 4.1 × 10^{−7} | 18 | |||||
[Nd(μ_{2}-L2)(L2)(CH_{3}COO)(H_{2}O)_{2}]_{n} | 0.622 | 1.730 | 4.122 | 3.5 | 29 | 3.1 × 10^{−7} | 18 | |||||
[Nd(μ_{2}-L1)_{3}(H_{2}O)_{2}]·H_{2}O | 2.0 | 28(2) | 7.29(3) × 10^{−7} | 0.014(2) | 19 | |||||||
[Nd(μ_{2}-L_{2})_{2}(CH_{3}COO)(H_{2}O)_{2}]_{n} | 2.0 | 19.7(2) | 3.43(2) × 10^{−6} | 0.0026(2) | ||||||||
{Nd(α-fur)_{3}(H_{2}O)_{2}} (1) | Exp. | 1.2 | 121(2) | 1.04 × 10^{−13} | 1.41 × 10^{2} | 3.7 | 3.5 × 10^{2} | 1.9 × 10^{3} | This work | |||
Ab initio | 0.52 | 1.03 | 4.41 | 125.0 | ||||||||
{Nd_{0.065}La_{0.935}(α-fur)_{3}(H_{2}O)_{2}}_{n} (2) | Exp | 1.2 | 61(2) | 3.63 × 10^{−11} | 2.89 × 10^{−3} | 9.9 | 7.82 | 0.247 | This work | |||
Ab initio | 1.35 | 1.98 | 3.88 | 58.8 |
On the other hand, our group reported in 2014 the first polymeric Nd complex, based on cyanoacetate ligands, [Nd_{2}(CNCH_{2}COO)_{6}(H_{2}O)_{4}]·2H_{2}O, showing field-induced slow relaxation with U/k_{B} = 26 K (1.5 kOe).^{17} In recent years a few more 1D nanomagnets have been reported,^{4,18,19} the complex {[Nd(pzdo)(H_{2}O)_{4}][Co(CN)_{6}]}·0.5(pzdo)·4H_{2}O showing the highest U/k_{B} = 51.2 K (1 kOe) to date.^{20}
There are also a few examples of heterometallic SMMs, combining [Mn/Nd],^{21–23} [Ni/Nd],^{24} [Co/Nd],^{25} [Zn/Nd],^{4} in which the neodymium atom plays a secondary role, increasing the anisotropy. Notably, slow relaxation under zero dc bias field has been observed only in one case.^{7} This may be explained in terms of the large transversal components of the Nd g*-factor, favoring fast relaxation through quantum tunneling at H = 0.^{17}
Herein we present the synthesis, structural and magneto-thermal characterization of two new Nd-based polymeric complexes, {[Nd(α-fur)_{3}(H_{2}O)_{2}]·DMF}_{n} (1), and the non-isostructural, magnetically diluted {[Nd_{0.065}La_{0.935}(α-fur)_{3}(H_{2}O)_{2}]}_{n} (2), where α-fur = C_{4}H_{3}OCOO. Compound (2) is designed to determine single-ion relaxation in absence of Nd–Nd interaction, in contrast to (1) where Nd–Nd interaction may play a role.
In previous works we demonstrated that furoate ligand, in bridging mode, can be successfully used to form 1D polymeric chains of rare earths. This allowed us to synthesize different isostructural homonuclear {Ln(α-fur)_{3}(H_{2}O)_{3}}_{n} complexes with either Kramers (Dy)^{29} or non-Kramers (Tb)^{30} ions, and heteronuclear complexes, such as {[Dy_{2}Sr(α-fur)_{8}(H_{2}O)_{4}]}_{n}·2H_{2}O^{26} and {Ln_{2}Ba(α-fur)_{8}(H_{2}O)_{4}}_{n} (Ln = Dy,^{27} Tb^{28}). As a result, we were able to elucidate their different dynamic behavior depending on the Kramers or non-Kramers character of the magnetic Ln and the Ln–Ln interactions.
In this work, the crystal structure, static and dynamic magnetic properties of the two new Nd molecular magnets (1) and (2) are determined and discussed under the light of ab initio calculations of the energy level distribution.
Single crystal X-ray analysis was performed on the crystal with a size of 100 μm specimens selected from the bulk. Sets of single-crystal X-ray intensity data were collected at room temperature (∼298 K) with Mo-Kα radiation (APEX CCD diffractometer Bruker Inc., Madison, USA, λ = 0.71073 Å) in φ- and ω-scan modes with at least 700 frames and exposures of 20 s per frame. The reflection intensities were integrated with the aid of the SAINT program of the SMART^{31} software package over the entire reciprocal space. Empirical absorption corrections were accomplished using the program SADABS.^{32} The structure was solved by direct methods using Olex2^{33} software with the SHELXS^{34} structure solution program and refined by full-matrix least-squares based on and refined by full-matrix least-squares on F^{2} with SHELXL-97^{34} using an anisotropic model for non-hydrogen, atoms. All H atoms attached to carbon were introduced in idealized positions (d_{CH} = 0.96 Å) using the riding model with their isotropic displacement parameters fixed at 120% of their riding atom. Positional parameters of the H (water) atoms were obtained from difference Fourier syntheses and verified by the geometric parameters of the corresponding hydrogen bonds.
The magnetization, dc and ac susceptibility of powdered samples were measured, above 1.8 K, using a Quantum Design superconducting quantum interference device (SQUID) magnetometer. Ac measurements were done at an excitation field of 4 Oe, and under dc fields between 0–30 kOe, while sweeping the frequency between 0.1 and 1000 Hz. Additional ac measurements at 1.2 kOe, at temperatures in the range 2.2 K < T > 5.6 K in an extended frequency range, 90 < f < 10000 Hz, were performed in a Quantum Design PPMS ACMS magnetometer. Measurements on powdered samples were done with the addition of Daphne oil, introduced to fix the grains at low temperatures.
Heat capacity C(T) under different applied fields (0–30 kOe) was measured on a powder pressed pellet fixed with Apiezon N grease, using the same PPMS.
a R _{1} = ∑||F_{o}| − |F_{c}||/∑|F_{o}|. b wR_{2} = {∑[w(F_{o}^{2} − F_{c}^{2})^{2}]/∑[w(F_{o}^{2})^{2}]}^{1/2}. c GOF = {∑[w(F_{o}^{2} − F_{c}^{2})^{2}]/(n − p)}^{1/2}, where n is the number of reflections and p is the total number of parameters refined. | ||
---|---|---|
Compound | 1 | 2 |
CCDC | 1914212 | 1914213 |
Empirical formula | C_{18}H_{20}NNdO_{12} | C_{15}H_{13}La_{0.935}Nd_{0.065}O_{11} |
Molecular weight | 586.59 | 508.51 |
Temperature (K) | 298 | 296 |
Wavelength (Å) | 0.71073 | 0.71073 |
Crystal system | Triclinic | Monoclinic |
Space group | P | P2_{1}/c |
a (Å) | 9.8094(6) | 10.3803(5) |
b (Å) | 11.1662(6) | 16.8316(9) |
c (Å) | 11.2979(6) | 9.4569(5) |
α (°) | 76.439(3) | 90 |
β (°) | 69.609(3) | 92.7144(15) |
γ (°) | 75.440(3) | 90 |
V (Å^{3}) | 1107.89(11) | 1650.43(15) |
Z, Z′ | 2 | 4 |
D _{calc} (g cm^{−3}) | 1.758 | 2.047 |
μ (mm^{−1}) | 2.406 | 2.687 |
Reflections collected | 38486 | 26563 |
Independent | 8697 (R_{int} = 0.0425) | 2879 (R_{int} = 0.0147) |
Crystal size (mm) | 0.12 × 0.10 × 0.10 | 0.15 × 0.10 × 0.10 |
R _{1}^{a} | 0.0322 | 0.0140 |
wR_{2}^{b} | 0.0692 | 0.0380 |
GOF^{c} | 0.995 | 1.014 |
Δρ_{max} and Δρ_{min} (e Å^{−3}) | 1.24/−0.74 | 0.32/−0.39 |
Fig. 1 (left) shows the structure of complex (1). The distorted square-antiprism coordination environment of each Nd(III) ion is shown in Fig. 1a. Each Nd is coordinated to 8 oxygen atoms, supporting five α-furoates in different coordination modes: one furoate is a bidentate-chelating ligand coordinating O4,O5, while two pairs of furoates in bridging mode, coordinated with O1,O2 and O7,O8, consolidate the Nd ions into a chain, running along the a-direction (Fig. 1b).
The Nd–Nd distance between O1,O2-bridged and O7,O8-bridged Nd pairs is slightly different, 5.0453(9) Å and 4.8401(9) Å. The coordination sphere is completed by two O1w,O2w; these water molecules are linked through H bridges to a C_{3}H_{7}NO moiety. The structure of the complex unit cell is shown in Fig. 1c. The 1D polymeric chains running along the a-direction are contained within the ab-planes, separated by an inter-chain distance of 11.292 Å. It is noted that the structure of this polymeric complex is slightly different from that of our previously reported linear Dy^{29} and Tb^{30} furoates, and that in complex (1) all Nd sites are equivalent.
The diluted furoate complex of neodymium (6.5%)–lanthanum (93.5%), complex (2) shown in Fig. 1 (right), is isostructural to previously described [Ln(α-fur)_{3}(H_{2}O)_{2}]_{n}, for large lanthanide ions Ln = Pr,^{38,39} Ce^{39} and La.^{39} Each Nd is nine-coordinated to 9 oxygen atoms: the pairs (O4,O5) and (O1,O2) support two α-furoates in bidentate mode, while O7 and O8C support each an α-furoate in bridging mode coordinating with a neighbor Ln atom; O2, O2B provide coordination with the closest Ln ion, and O10, O11 are free (Fig. 1d). The resulting structure of complex (2) is a polymeric chain running along the b-axis, where two Ln–Ln atoms are coupled through two branches to the next two Ln–Ln atoms, where Ln = La or Nd (see Fig. 1e).
Ab initio calculations yield an energy multiplet structure composed by five Kramers doublets in a range of 500 K for the two complexes, as shown in Fig. 2. The calculated eigenstates of Nd(III) in the two complexes, in terms of the weighted contribution of the free ion ±M_{J} states, is given in Table S1.†
The Hamiltonian of the polymers, consisting of a Nd chain of identical ions is:
(1) |
(2) |
Although the ab initio calculations and their predictions have been done using the full J, M_{J} states, the calculated values for the ground state anisotropic g* factors, are expressed in terms of an effective spin S* = 1/2 restricted basis. The interaction constant expressed in terms of the S* = 1/2 model is related to the J = 9/2 basis by the relation J′* = 81J′. In terms of the effective S* = 1/2 description, the first term of eqn (2) for a given isotope transforms into:
(3) |
The results in terms of S* = 1/2 model are: for complex (1) the first excited doublet is at Δ/k_{B} = 125.5 K, and the g* factors are g_{x}* = 0.52, g_{y}* = 1.03, g_{z}* = 4.41. For complex (2) the energy gap is smaller, Δ/k_{B} = 58.8 K, as a result of a less anisotropic ground state: g_{x}* = 1.35, g_{y}* = 1.98, g_{z}* = 3.88. The EAM of magnetization in the two compounds are depicted in Fig. 2.
Besides, the Nd–Nd dipolar interaction for complex (1) is calculated with the Nd moment as a classical vector oriented along the predicted direction (see Fig. 2a). The calculation predicts the value J′_{dip}/k_{B} = −6.5 × 10^{−4} K or −1.3 × 10^{−3} K, for the Nd–Nd distances 5.045 Å and 4.840 Å, respectively, when the dipolar interaction contribution to the Hamiltonian is expressed as . For complex (2), the Nd–Nd interaction is neglected because of the strong magnetic dilution.
Fig. 3 Field-dependence of the magnetization per formula unit M(H) measured for complexes (1) and (2) at T = 1.8 K. Red line: ab initio fits. |
The equilibrium dc susceptibility as a function of the temperature for complex (1) from T = 1.8 K to 300 K is shown in Fig. 4. The room temperature saturation value, χT(300 K) = g_{J}^{2}J(J + 1)/8 = 1.289 emu K mol^{−1}, with J = 9/2, yields an experimental gyromagnetic factor g_{J} = 0.65 smaller than the value for a free Nd(III) ion, g_{J} = 0.727.^{40}χT decreases as the temperature is reduced, as a result of the thermal depopulation of the excited doublets, and reaches 0.59 emu K mol^{−1} at 1.8 K. A good fit of the χT data is achieved using the ab initio calculated wavefunctions and intrachain interaction J′/k_{B} = −3.15 × 10^{−3} K (J′*/k_{B} = −0.255 K in S* = 1/2). For the highly diluted complex (2), χT(T) was measured with low accuracy due to the difficulty in subtracting accurately the sample holder signal (Fig. S1†).
Fig. 4 Temperature dependence of χT for complex (1). The dotted line marks the predicted χT (300 K) value for a Nd(III) free ion with gyromagnetic value g_{J} = 0.727.^{40} Red line: fit within a chain model of Nd ions, with ab initio calculated wavefunctions and intrachain interaction J′/k_{B} = −3.15 × 10^{−3} K. |
For complex (1) at H = 0, the magnetic contribution to the low temperature HC is just a high temperature tail, C_{m}/R ≈ BT^{−2} (B = 3.37 × 10^{−3} R K^{−2}), with an electronic contribution caused by the interaction with other Nd nearest neighbors, and a spin-nucleus hyperfine contribution, C_{hyp}/R ≈ b_{n}T^{−2}. An estimate of the constant b_{n} ≈ 9.37 × 10^{−4} R K^{−2} was obtained from: , with S* = 1/2, and values of , for ^{143}Nd, and , for ^{145}Nd, corresponding to diluted Nd ethylsulphate, used as reference,^{40} and natural abundancies of ^{143}Nd, ^{145}Nd (see section 4). The estimated hyperfine contribution is represented by the dashed line in Fig. 5b.
For the 6.5%Nd complex (2), where Nd–Nd interactions are negligible, the observed HC at H = 0 is indeed compatible with the existence of such a hyperfine contribution, as shown in Fig. 5c.
The electronic contribution associated to Nd–Nd coupling in complex (1) after subtracting the hyperfine contribution is C_{elec}/R ≈ 2.46 × 10^{−3}T^{−2}, depicted in Fig. 5b.
At H ≠ 0, Schottky type anomalies show up. The in-field heat capacity data could be well fit under the model described by eqn (1), with the ab initio-calculated gyromagnetic values, neglectable hyperfine term, and intrachain interaction of J′/k_{B} = −3.15 × 10^{−3} K (J′*/k_{B} = −0.255 K in S* = 1/2) for complex (1) and J′/k_{B} = 0 K for the diluted complex (2), see Fig. 5b, c. According to the ab initio calculations, about 30% of the J′ Nd–Nd interaction in (1) is caused by the dipolar one.
For the two complexes, at H = 0, no contribution to χ′′ could be observed above 1.8 K, implying that there exists a relaxation process, related to Quantum Tunneling (QT) with τ_{QT} < 10^{−5} s faster than the frequency window of our experiment (0.01 < f < 10 kHz). In a Kramers Nd(III)-based complex, QT would be in principle forbidden, however, it can be enabled by the existence of a non-zero dipolar field that splits the Kramers degeneracy, and/or by the transverse components of the g* tensor. The application of an external field H ≠ 0 detunes the QT process, and allows the observation of slow relaxation dynamics.
Fig. 6 (top panel) summarizes the ac results for complex (1). Fig. 6c shows the imaginary susceptibility χ′′(f) data measured at T = 2.0 K and different fields. The application of a field as small as 50–80 Oe sets on a slow relaxation process at high frequencies (τ_{HF}), whose associated peak χ′′ grows in intensity till reaching a maximum at 1.2 kOe, and then decreases again for higher fields. At H > 2.5 kOe a second relaxation process (τ_{LF}) with smaller intensity at lower frequencies appears. The double-peaked χ′′(f) data observed at constant field H = 10 kOe and varying temperatures, Fig. 6b, evidence the existence of two different slow relaxation paths above 1.8 K, (τ_{HF}) and (τ_{LF}). At H = 1.2 kOe, however, only one χ′′(f) peak appears, corresponding to the higher frequency process (τ_{HF}), see Fig. 6a.
Fig. 6 (bottom panel) shows the ac results for complex (2). The χ′′(f, T) data at constant field H = 1.2 kOe (Fig. 6d) and H = 10 kOe (Fig. 6f) evidence that in the 6.5% Nd-diluted sample the τ_{HF} peak appears at lower frequencies, whereas the τ_{LF} peak is not observed.
Fig. 7 shows the dependence of the relaxation time with the inverse temperature, τ(1/T), and the magnetic field, τ(H), for the different observed processes, determined from the position of the χ′′(f) peaks, for the two complexes.
Fig. 7 (a) Relaxation time vs. inverse of the temperature, at H = 1.2 kOe and H = 10 kOe, and fits with eqn (4); (b) relaxation time as a function of the applied field, at constant T = 2 K, and fits with eqn (4), for complex (1) (bold symbols) and complex (2) (open symbols). |
The high frequency relaxation process, τ_{HF}(1/T), in the 6–8 K temperature range follows an Arrhenius law, τ = τ_{0}exp(U/k_{B}T), indicative of thermally activated spin-reversal over an energy barrier, with an estimated value U/k_{B} = 74.6 K (τ_{0} = 5.19 × 10^{−11} s) for (1) and U/k_{B} = 52.1 K (τ_{0} = 1.90 × 10^{−10} s) and for (2). However, a pronounced curvature in τ_{HF} with decreasing temperature is observed, revealing the presence of additional relaxation pathways, also facilitated by phonons. Besides, the fast decay of the relaxation time observed for growing fields, especially for (2), points towards a relevance of direct processes. Therefore, we analysed altogether the field and temperature dependence of the relaxation data using the equation:
(4) |
To avoid over parametrization, we first fit the τ_{HF}(H) data to determine B_{1}, B_{2}, D_{1}, D_{2}; then fit the τ_{HF}(1/T) curves at two fixed fields (H = 1.2 kOe and 10 kOe) to obtain the Raman (C, n) and Orbach (τ_{0}, U) parameters.^{41} The τ(H,T) curves could be well reproduced, see Fig. 7, using the fitting parameters summarized in Table 3. For both compounds, the determined Orbach activation energies, U/k_{B} = 121 K (1) and U/k_{B} = 61 K (2), are close to the ab initio calculations. The Raman exponent for the two compounds was n ≈ 5 (1) and n ≈ 9 for (2), within the range of values usually reported for Nd ions.^{3,10,13,20}
# | Dependence | B _{1} (s^{−1}) | B _{2} (Oe^{−2}) | D _{1} (s^{−1}K^{−1}Oe^{−4}) | D _{2} (s^{−1}K^{−1}Oe^{−2}) | C (s^{−1} K^{−n}) | n | τ _{0} (s) | U/k_{B} (K) |
---|---|---|---|---|---|---|---|---|---|
(1) | τ _{HF} ^{−1}(H) | (11 ± 1) × 10^{+3} | (21 ± 1) × 10^{−6} | 0 | (2.7 ± 0.2) × 10^{−4} | (1.57 ± 0.05) × 10^{+2} | 5.0 ± 0.2 | (2.56 ± 0.01) × 10^{−13} | 121 ± 2 |
τ _{HF} ^{−1}(1/T),1.2 kOe | (11 ± 1) × 10^{+3} | (21 ± 1) × 10^{−6} | 0 | (13.7 ± 0.4) × 10^{−4} | (1.41 ± 0.05) × 10^{+2} | 3.7 ± 0.5 | (1.04 ± 0.01) × 10^{−13} | 121 ± 2 | |
τ _{HF} ^{−1}(1/T), 10 kOe | (11 ± 1) × 10^{+3} | (21 ± 1) × 10^{−6} | 0 | (1.67 ± 0.2) × 10^{−4} | 9.9 ± 0.5 | 5.3 ± 0.2 | (2.56 ± 0.01) × 10^{−13} | 121 ± 2 | |
(2) | τ _{HF} ^{−1}(H, 1/T) | 8.0 ± 0.5 | (1.6 ± 0.2) × 10^{−8} | (1.19 ± 0.06) × 10^{−13} | 0 | (2.89 ± 0.01) × 10^{−3} | 9.9 ± 0.5 | (3.63 ± 0.01) × 10^{−11} | 61 ± 2 |
Regarding the τ(H) dependence, some distinct differences are found for the two complexes: the τ_{QT} term is much smaller for the diluted compound (2) than for (1), as a result of the reduced interactions. Yet, even for (2) it is necessary to apply a small field to suppress completely QT, which is still favored by the transversal component of the ground state. The field strength at which slow processes appear allows us to estimate the internal dipolar field. Indeed, the tunneling time depends on the distribution of dipolar (or exchange) energy bias P(ξ_{dip}) and on the quantum tunnel splitting Δ_{T}:^{42}
(5) |
The energy bias distribution may be approximated to a Gaussian, with , where the width σ_{ξdip} can be estimated from the condition σ_{ξdip} ≈ k_{B}T_{N}. At H ≠ 0, the QT probability decreases as the Zeeman energy bias moves the tunneling energy window out of the dipolar energy bias distribution. We may consider that for an external field given by H ≈ 2σ_{dip,z}, QT is suppressed. In complex (1), the slow relaxation process appears at about 50–80 Oe. Therefore, the width of the bias field is estimated to be σ_{dip,z} = H_{dip,z} ≈ 25–40 Oe Note that this dipolar field would imply that magnetic ordering transition, if present, would occur at k_{B}T_{N} = σ_{ξdip =}σ_{dip,z}/g_{z}*μ_{B} ≈ 0.01 K, i.e. below the range of our measurements. Indeed, no ordering was observed in the C_{m}(T) curves down to the smallest measured temperature, 0.3 K.
At high fields the QT is effectively suppressed and the direct process becomes dominant. For compound (2), it is found that eqn (4) is nicely verified in both H and T dependences. Indeed, τ_{HF} decreases as H^{−4}, as predicted for a Kramers doublet with a negligible effect due to hyperfine interaction (D_{1} ≠ 0, D_{2} = 0).
In contrast, for compound (1), either the τ_{HF}(H) or the τ_{HF}(1/T) dependencies with (D_{1} = 0, D_{2} ≠ 0) could be fit, but not with the same set of parameters (Table 3). We note that also in previously reported Nd compounds the relaxation field dependence was not well explained by eqn (4).^{4,10} Since from compound (2) we may conclude that hyperfine effects are weak or negligible, the τ_{HF} decrease with H^{−2} cannot be caused by this effect. The discrepancy in the H and T parameters for compound (1) is probably caused by the effect of Nd–Nd interactions, which are completely neglected in the approximations implicit in eqn (4). For example, considering interactions as an additional effective internal field, its effect, according to eqn (4), would be the decrease of τ_{HF}(H) of (1) compared to the diluted (2), as is qualitatively found.
On the other hand, the τ_{LF}(1/T) and τ_{LF}(H) dependencies of the very slow process observed for complex (1) are characteristic of a direct process affected by phonon-bottleneck (PB) effect, a mechanism that we have commonly encountered in polymeric furoate complexes.^{27–30,43} The PB effect was indeed demonstrated through relaxation measurements performed under different pressure conditions of the bath on complex (1) (S3): the χ′′(f) peak shifted to higher frequencies by increasing the pressure, and moved back reversibly by lowering the pressure (Fig. S2†). However the very slow process τ_{LF} is not observed in (2). This fact is in agreement with previously reported results showing that PB processes are released upon magnetic dilution.^{29,43}
In this work we have reported the synthesis of two new Nd-based complexes, coordinated by furoate ligands, displaying field-induced relaxation behavior. The application of a small field of ca. 80 Oe is enough to quench QT and allow relaxation through slower paths. The temperature and field dependencies of the relaxation rates indicate that relaxation proceeds not only through an Orbach process, but also through Raman and direct processes. In the polymeric complex (1), a sizeable energy barrier of energy U/k_{B} = 121 K at 1.2 kOe was measured, close to the ab initio predicted difference between the ground and first excited doublet Δ/k_{B} = 125.5 K. In (2), despite magnetic dilution was introduced so as to reduce dipolar interactions, which favour QT, a factor of two smaller relaxation barrier of U/k_{B} = 61 K at 1.2 kOe was found. The larger SIM energy barrier for (1) than for (2) is a reflect of the different Nd(III) coordination environment and symmetry: indeed, although in both compounds transversal components g_{x}*, g_{y}* appear, preventing the observation of slow relaxation under H = 0, (1) presents a more anisotropic ground-state than (2): g_{z}*^{2}/(g_{x}*^{2} + g_{y}*^{2}) = 14.6 (1), 2.6 (2). The stronger relaxation time τ_{HF}(H) field dependence and higher values, by at least two orders of magnitude at H = 10 kOe, in compound (2) with respect to (1) is most probably caused by the absence of Nd–Nd interactions.
The two new furoate-based complexes enlarge the still scarce family of Nd(III) based compounds. The energy barrier of compound (1) is the highest ever reported for a Nd complex.
Footnote |
† Electronic supplementary information (ESI) available. CCDC 1914212 and 1914213. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c9dt02047k |
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