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Molecular magnetic hysteresis at 60 kelvin in dysprosocenium

Nature volume 548, pages 439442 (24 August 2017) | Download Citation


Lanthanides have been investigated extensively for potential applications in quantum information processing and high-density data storage at the molecular and atomic scale. Experimental achievements include reading and manipulating single nuclear spins1,2, exploiting atomic clock transitions for robust qubits3 and, most recently, magnetic data storage in single atoms4,5. Single-molecule magnets exhibit magnetic hysteresis of molecular origin6—a magnetic memory effect and a prerequisite of data storage—and so far lanthanide examples have exhibited this phenomenon at the highest temperatures. However, in the nearly 25 years since the discovery of single-molecule magnets7, hysteresis temperatures have increased from 4 kelvin to only about 14 kelvin8,9,10 using a consistent magnetic field sweep rate of about 20 oersted per second, although higher temperatures have been achieved by using very fast sweep rates11,12 (for example, 30 kelvin with 200 oersted per second)12. Here we report a hexa-tert-butyldysprosocenium complex—[Dy(Cpttt)2][B(C6F5)4], with Cpttt = {C5H2tBu3-1,2,4} and tBu = C(CH3)3—which exhibits magnetic hysteresis at temperatures of up to 60 kelvin at a sweep rate of 22 oersted per second. We observe a clear change in the relaxation dynamics at this temperature, which persists in magnetically diluted samples, suggesting that the origin of the hysteresis is the localized metal–ligand vibrational modes that are unique to dysprosocenium. Ab initio calculations of spin dynamics demonstrate that magnetic relaxation at high temperatures is due to local molecular vibrations. These results indicate that, with judicious molecular design, magnetic data storage in single molecules at temperatures above liquid nitrogen should be possible.


Metallocenium cations are positively charged species that contain a metal ion sandwiched between two aromatic π ligands; the bis-cyclopentadienyl (Cp) family is the classical example. The isolation of [Ln(CpR)2]+ (Ln = lanthanide; CpR = C5R5; R = H, alkyl or silyl) has proved problematic because lanthanide bonding is predominantly ionic and Ln(iii) cations are relatively large, so additional ligands tend to coordinate equatorially. The most similar structurally characterized lanthanide and rare-earth examples reported so far, [Sm{C5Me4(SiMe2CH2CH = CH2)}2][BPh4] (Me = CH3, Ph = C6H5)13, [Sc(Cp*)2{μ-(C6F5)2B(C6F5)2}] (Cp* = C5Me5)14, [{Ln(Cp*)2}2{μ-(C6F5)2B(C6F5)2}2] (Ln = Pr, Nd)15 and [Dy(Cp*)2{μ-(Ph)2BPh2}]16,17, all feature weak equatorial ligand interactions. Recently, the elusive dysprosocenium cation has become a key synthetic target18 because the near-cylindrical symmetry and axial concentration of negative charge of the Cp ligands should give a very high energy barrier to magnetic relaxation for Dy(iii)19,20 and hence possibly allow magnetic hysteresis at relatively high temperatures. However, some ligand fields are better suited to Ln(iii) cations for which the most magnetic states are prolate in nature; for example, [Er(C8H8)(Cp*)] exhibits hysteresis up to 5 K (ref. 21), but for [Dy(C8H8)(Cp*)]22 and [Dy{C8H6(SiMe3)2-1,4}2Li(THF)(DME)]23 hysteresis is not observed above 1.8 K (all with sweep rates of about 20 Oe s−1), and [Er{N(SiMe3)2}3] shows hysteresis whereas [Dy{N(SiMe3)2}3] does not24.

Complex 1 ([Dy(Cpttt)2][B(C6F5)4], with Cpttt = {C5H2tBu3-1,2,4} and tBu = C(CH3)3) was synthesized by the reaction of [Dy(Cpttt)2(Cl)] with the silylium reagent [H(SiEt3)2][B(C6F5)4] (Et = CH2CH3) in benzene at room temperature (Fig. 1)25. Guo et al.26 have simultaneously reported the synthesis and magnetic data for 1. Bright yellow crystals of 1 were obtained in 60% yield by layering a saturated dichloromethane solution of crude material with hexane at 4 °C, followed by storage at −25 °C. Detailed synthetic information and full characterization of all compounds is given in Supplementary Information. Single-crystal X-ray diffraction studies show no appreciable interactions of the {B(C6F5)4} anion with the cation in 1 (shortest equatorial Dy···F distance, 5.996(3) Å; estimated standard deviations in parentheses calculated from least-squares refinement), owing to the steric demands of the six tBu groups, although two short intramolecular Dy···Cmethyl distances (mean, 2.964(5) Å) produce an approximately linear H···Dy···H motif (174.96°; mean Dy···H distance, 2.499 Å). The bent dysprosocenium cation exhibits a Cpcentroid1···Dy···Cpcentroid2 angle of 152.56(7)° with the two C5 rings approximately eclipsed, in contrast to [Dy(Cp*)2{μ-(Ph)2BPh2}] (Cpcentroid1···Dy···Cpcentroid2 angle of 134.00(4)°), which adopts a staggered conformation16. The mean Dy···Cpcentroid distance in 1 is relatively short (2.316(3) Å), as expected from electrostatic considerations for the isolated cation, compared to [Dy(Cp*)2{μ-(Ph)2BPh2}] (2.373(2) Å)16. Complete active space self-consistent field spin–orbit (CASSCF-SO) calculations on the X-ray structure of 1 show that it has large easy-axis magnetic anisotropy (Supplementary Table 13), and so should exhibit single-molecule-magnet behaviour. Further calculations show that the close equatorial H atoms, the bent geometry and the eclipsed disposition of the rings do not make substantial contributions to the electronic structure of 1 (Supplementary Tables 14–16).

Figure 1: Synthesis and structure of [Dy(Cpttt)2][B(C6F5)4] (1).
Figure 1

a, Synthesis of 1. b, Molecular structure of 1 with selective atom labelling (B, yellow; C, grey; Dy, cyan; F, green). Displacement ellipsoids set at the 30% probability level and hydrogen atoms are omitted for clarity. Selected distances and angles: Dy···Cpcentroid1, 2.318(2) Å; Dy···Cpcentroid2, 2.314(2) Å; Dy···C7, 2.971(5) Å; Dy···C24, 2.956(5) Å; Cpcentroid1···Dy···Cpcentroid2, 152.56(7)°.

Magnetic measurements reveal that 1 exhibits open hysteresis at and below 60 K using a sweep rate of 22 Oe s−1, with 83% remanent magnetization and a coercive field of 20–25 kOe at 2 K (Fig. 2). The low-temperature hysteresis data show a step at zero-field, probably due to enhanced relaxation by quantum tunnelling of the magnetization, a common feature in single-molecule magnets6. To confirm that the magnetic hysteresis is of molecular origin and not a result of long-range ordering, we measured a structurally analogous doped sample, [Y(Cpttt)2][B(C6F5)4] doped with 8% Dy (2), and two frozen dichloromethane solutions of 1 with concentrations of about 21 mM (3) and 170 mM (4) (Supplementary Figs 32–35, Supplementary Table 3). These samples also exhibit hysteretic behaviour, confirming that these properties are intrinsic to the [Dy(Cpttt)2]+ cation. Although the zero-field step is reduced for 2 (Supplementary Figs 32 and 35), suggesting that dipolar interactions are partially responsible for this feature in 1, the step is more pronounced for the dichloromethane solution samples 3 and 4 (Supplementary Figs 33–35), implying that the local environment of the molecule plays a crucial part in the zero-field dynamics. Similar results are found for a solution sample with an alternative solvent, 1,2-difluorobenzene (Supplementary Fig. 35), indicating that this step is not due to coordination of dichloromethane. Despite the faster zero-field relaxation, hysteresis still persists up to at least 54 K for 4 (Supplementary Fig. 34). Field-cooled (FC) and zero-field-cooled (ZFC) magnetic susceptibilities χ for 14 coincide with the theoretical equilibrium trace until 61 K, below which they bifurcate and are out of equilibrium (Fig. 3a and Supplementary Figs 36–39).

Figure 2: Magnetic hysteresis of 1.
Figure 2

Hysteresis was measured with a mean field sweep rate of 22(9) Oe s−1 (numbers in parentheses here are standard deviations) for field strength |H| < 10 kOe, 54(15) Oe s−1 for 10 kOe < |H| < 20 kOe and 91(17) Oe s−1 for 20 kOe < |H| < 70 kOe, giving an overall mean sweep rate of 50(33) Oe s−1. The sweep rate was slow (22 Oe s−1) around zero-field, where the relaxation dynamics of single-molecule magnets are crucially dependent on the sweep rate. a, Hysteresis loops recorded at temperatures of 2 K (purple) to 30 K (black) in steps of 4 K. b, Hysteresis loops recorded at temperatures of 52 K (light blue) to 62 K (black) in steps of 2 K, with truncated x and y axes, showing open hysteresis at 60 K (red) but closed at 62 K (black). NA, Avogadro’s number; μB, Bohr magneton.

Figure 3: Relaxation dynamics of 1.
Figure 3

a, Field-cooled (FC) and zero-field-cooled (ZFC) magnetic susceptibilities (shown as the product χT) at 1 kOe FC (purple), 500 Oe FC (green), 1 kOe ZFC (light blue) and 500 Oe ZFC (orange), with the CASSCF-SO-calculated curve (black line) scaled by 1.08. The vertical line shows the bifurcation point at 61 K. b, Temperature dependence of the magnetic relaxation rate τ−1. Solid purple points are the relaxation rates extracted from a.c. susceptibility data (Supplementary Table 5) and solid green points from d.c. magnetization decay data (Supplementary Table 8). The dashed black line shows , with Ueff = 1,223 cm−1 (1,760 K) and τ0 = 1.986 × 10−11 s, the dotted black line shows , with C = 1.664 × 10−6 s−1 Kn and n = 2.151, and the solid red line shows their sum, .

To probe the origin of the magnetic hysteresis, we measured the magnetic relaxation rate using alternating-current (a.c.) magnetic susceptibility and direct-current (d.c.) magnetization decay. The out-of-phase component of the a.c. susceptibility χ″ of 1 exhibits frequency-dependent peaks between 72 K and 112 K (Supplementary Fig. 40). Fitting these data with the Debye model6 shows that the relaxation rate τ−1 follows an Arrhenius law: , with effective energy barrier Ueff = 1,223 cm−1 (1,760 K), pre-factor τ0 = 1.986 × 10−11 s, T the temperature and k the Boltzmann constant (Fig. 3b and Supplementary Fig. 56). This finding is consistent with an Orbach relaxation mechanism over an effective energy barrier Ueff. To extend investigation of the relaxation dynamics to lower temperatures, we measured the d.c. magnetization decay between 26 K and 62 K. Fitting these data with single exponentials6 yields the magnetic relaxation rates (Supplementary Figs 43–46, Supplementary Table 8). Between 26 K and 50 K the relaxation rate has a power-law dependence on temperature and is well modelled by τ−1 = CTn, with C = 1.664 × 10−6 s−1 Kn and n = 2.151 (Fig. 3b and Supplementary Fig. 57). Whereas this value of n is close to that expected for a phonon bottleneck (n = 2)27, the relaxation rates for the doped and solution samples 24 follow almost exactly the same temperature dependence as 1 (Supplementary Figs 58–61). Consequently, these dynamics are intrinsic to the [Dy(Cpttt)2]+ cation and not the result of inefficient heat flow between the lattice and the bath. Intriguingly, the intersection of the exponential and power-law dynamics occurs at 60.4 K for 1, coincident with the temperature at which magnetic hysteresis appears and the FC/ZFC susceptibilities bifurcate.

The computational and magnetic data for 1 are generally in excellent agreement with those reported in ref. 26. Slight differences are observed in the FC/ZFC behaviour, probably due to different temperature sweep rates having a profound effect on the relaxation dynamics below 61 K. The origin of the discrepancy between the power-law relaxation exponents (n = 2.151 here versus n = 3.92 in ref. 26) is not obvious. However, we find consistent behaviour for samples of different concentrations and phases, and at lower temperatures (Supplementary Fig. 61); we therefore suggest that our results demonstrate the intrinsic properties of 1.

To investigate the mechanism of magnetic relaxation, we undertook an ab initio study of the spin dynamics; such approaches have only recently become viable28,29. Magnetic relaxation in single-molecule magnets is effected by the coupling of the electronic states to the quantized vibrational modes of the lattice (phonons). However, because the relaxation dynamics for [Dy(Cpttt)2]+ are consistent between the crystalline phase and amorphous frozen solution, we hypothesize that magnetic relaxation is moderated by localized molecular vibrations (optical phonons). Therefore, as a first approximation we consider only the gas-phase vibrational modes of the [Dy(Cpttt)2]+ cation. Our approach consists of four stages: (i) calculation and (ii) calibration of vibrational modes; (iii) calculation of spin–phonon coupling; and (iv) simulation of dynamics. We calculate the vibrational modes using density functional theory, and calibrate the vibrational energies and atomic displacements by comparing them to the experimental vibrational spectra (Supplementary Fig. 63, Supplementary Table 19) and to the thermal displacement parameters from X-ray diffraction data, respectively. We determine the spin–phonon coupling by performing a CASSCF-SO calculation for each vibrational mode on molecular geometries distorted from equilibrium along the relevant normal mode vector, followed by a crystal field decomposition of the electronic structure; thus, we define the electronic part of the spin–phonon coupling from the change in the crystal field potential; see Supplementary Information for details. We then calculate the transition rates between each electronic state by allowing a finite Gaussian linewidth σ for each vibrational mode, and finally simulate the spin dynamics by solving the master equation6.

Considering single-phonon transitions (Supplementary Table 22), we find one slow relaxation rate (Supplementary Table 23) corresponding to the Orbach mechanism; this result echoes the archetypal case of Mn12 (ref. 6). As a function of temperature, the calculated relaxation rate reproduces the slope of the a.c. data well (Fig. 4a and Supplementary Fig. 65), demonstrating that the Orbach mechanism is moderated by local molecular vibrations. Varying σ affects the effective pre-factor τ0 of the Orbach mechanism slightly (Supplementary Fig. 65), but we fix σ = 10 cm−1 to be consistent with the full-width at half-maximum linewidth of the experimental vibrational spectra. Given our approximations, the agreement between our ab initio spin dynamics and experimental measurements is remarkable. The calculated transition rates reveal a heterogeneous relaxation pathway that does not proceed through all states sequentially; the most probable pathway for Orbach relaxation is |±15/2〉 → |±13/2〉 → |±11/2〉 → |±9/2〉 → |±5/2〉 → |3/2〉 → |7/2〉 → |11/2〉 → |13/2〉 → |15/2〉 (Fig. 4b, Supplementary Table 24). Decomposing the transition rates further, it is the vibrational motion of the C–H groups on the Cpttt ligands that facilitates the initial |±15/2〉 → |±13/2〉 relaxation step (Supplementary Fig. 66, Supplementary Table 25). Therefore, we propose that substitution of these groups would greatly affect the relaxation dynamics and possibly lead to magnetic hysteresis at higher temperatures.

Figure 4: Ab initio spin dynamics.
Figure 4

a, Temperature dependence of the magnetic relaxation rate τ−1. Solid purple points are the relaxation rates extracted from a.c. susceptibility data (Supplementary Table 5) and solid green points from d.c. magnetization decay data (Supplementary Table 8). The dashed and dotted black lines show the Orbach and Raman relaxation rates, respectively, determined from ab initio calculations. b, Energy barrier to magnetic relaxation for 1. The electronic states from CASSCF-SO calculations are labelled with their dominant mJ composition in the J = 15/2 basis (Supplementary Table 20); only the main components of the two most energetic doublets are shown. Arrows represent the Orbach relaxation pathway at 150 K with σ = 10 cm−1, with the opacity of the arrows proportional to the single-phonon transition probability normalized from each departing state and commencing with unit population in |−15/2〉; only relaxation pathways towards |+15/2〉 are shown (Supplementary Table 24). 〈Jz〉 is the expectation value of the operator along the quantization axis.

Considering the two-phonon second-order Raman process (Supplementary Table 26), we find three slow relaxation rates (Supplementary Table 27); however, only one contributes to the relaxation dynamics. Although we have shown that the low-temperature τ−1 T2 region is not due to a phonon bottleneck, the temperature dependence of the calculated Raman mechanism deviates considerably from the experiment, a feature that is not improved by altering σ (Fig. 4a and Supplementary Fig. 67). This could be due to our gas-phase approximation, which lacks the true dispersion of the optical modes and their coupling to the acoustic modes30, or to the neglect of explicit anharmonicity28.

Simple electrostatic models have predicted that the quintessential Ln single-molecule magnet should be a Dy(iii) complex with negatively charged ligands along a single axis19,20, and considerable magnetic anisotropy has been achieved for such complexes9,10,11,12,31. However, until now, an increase in the largest Ueff by a factor of 30 (about 42 cm−1 (ref. 7) to 1,261 cm−1 (ref. 10)) had been accompanied by an increase by a factor of only 4 in the highest temperature at which magnetic hysteresis was observed (4 K (ref. 7) to 14 K (ref. 8) at a sweep rate of about 20 Oe s−1). The Ueff value for 1 is similar to that for [Dy(tBuO)2(pyridine)5][BPh4] (1,261 cm−1; ref. 10); however, the highest temperature at which magnetic hysteresis is observed is substantially larger (60 K versus 4 K) and there is much more remanent magnetization at 2 K (83% versus about 11%). Furthermore, the zero-field step that we observe is much smaller than for other Dy(iii) single-molecule magnets9,10,11,12,31, suggesting that such steps, which plague single-molecule magnets, are not solely due to hyperfine coupling or local dipolar fields as is routinely suggested. We theorize that the lack of a severe zero-field step and the notably improved relaxation dynamics for 1 are due to the unique spin–phonon coupling of the constrained metal–ligand vibrational modes that are intrinsic to the bis-η5-Cpttt coordination geometry. This is in contrast to other molecules with large Ueff that do not exhibit hysteresis at comparably high temperatures, such as [Dy(tBuO)2(pyridine)5][BPh4]10, in which the first coordination sphere is constructed from mono-atomic donors that have greater metal–ligand flexibility.

Data Availability

The supplementary crystal data can be obtained free of charge from the Cambridge Crystallographic Data Centre (www.ccdc.cam.ac.uk/data_request/cif) using identifiers CCDC 1542354–1542357. Research data files supporting this publication are available from Mendeley Data (http://dx.doi.org/10.17632/sj5t9dy53s.1). Source Data for Figs 2, 3, 4 are available in the online version of the paper. All other datasets generated and analysed during this study are available from the corresponding authors on reasonable request.


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We acknowledge funding from the Engineering and Physical Sciences Research Council (studentship to C.A.P.G. and EP/P002560/1 for F.O. and D.R.), the Ramsay Memorial Fellowships Trust (fellowship to N.F.C.) and the University of Manchester. We thank the University of Manchester for access to the SQUID magnetometer and Computational Shared Facility and R. E. P. Winpenny, E. J. L. McInnes and D. Collison for comments.

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  1. School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

    • Conrad A. P. Goodwin
    • , Fabrizio Ortu
    • , Daniel Reta
    • , Nicholas F. Chilton
    •  & David P. Mills


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C.A.P.G. and D.P.M. provided the original concept. C.A.P.G. synthesized and characterized the compounds. F.O. carried out the single-crystal X-ray diffraction analysis and supporting synthetic/characterization work. N.F.C. collected and interpreted magnetic data. N.F.C. devised the relaxation dynamics model and wrote computer programs to perform these calculations. D.R. and N.F.C. performed the calculations. D.P.M. and N.F.C. wrote the manuscript with contributions from all authors. D.P.M. and N.F.C. supervised the project.

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The authors declare no competing financial interests.

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Correspondence to Nicholas F. Chilton or David P. Mills.

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    This file contains Supplementary Methods, Discussion, Data and Equations, Supplementary Tables 1-21, Supplementary Figures 1-64. It includes details of synthesis methods, crystallography, NMR, UV-Vis-NIR, vibrational spectra, magnetic data, theoretical analysis and additional references. This file was replaced on 4 September 2017 to correct a file corruption in the equations.

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