Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnet

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Science  21 Dec 2018:
Vol. 362, Issue 6421, pp. 1400-1403
DOI: 10.1126/science.aav0652

Breaking through the nitrogen ceiling

Single-molecule magnets could prove useful in miniaturizing a wide variety of devices. However, their application has been severely hindered by the need to cool them to extremely low temperature using liquid helium. Guo et al. now report a dysprosium compound that manifests magnetic hysteresis at temperatures up to 80 kelvin. The principles applied to tuning the ligands in this complex could point the way toward future architectures with even higher temperature performance.

Science, this issue p. 1400


Single-molecule magnets (SMMs) containing only one metal center may represent the lower size limit for molecule-based magnetic information storage materials. Their current drawback is that all SMMs require liquid-helium cooling to show magnetic memory effects. We now report a chemical strategy to access the dysprosium metallocene cation [(CpiPr5)Dy(Cp*)]+ (CpiPr5, penta-iso-propylcyclopentadienyl; Cp*, pentamethylcyclopentadienyl), which displays magnetic hysteresis above liquid-nitrogen temperatures. An effective energy barrier to reversal of the magnetization of Ueff = 1541 wave number is also measured. The magnetic blocking temperature of TB = 80 kelvin for this cation overcomes an essential barrier toward the development of nanomagnet devices that function at practical temperatures.

The observation of slow magnetic relaxation in coordination compounds that contain a single lanthanide ion stimulated considerable interest in monometallic single-molecule magnets (SMMs) (1). This family of materials shows magnetic hysteresis properties that arise from the electronic structure at the molecular level rather than interactions across comparatively large magnetic domains (24). In addition to the considerable fundamental interest in SMMs and related magnetic molecules, their magnetic memory properties have inspired proposals for applications as spin qubits (5) and in nanoscale spintronic devices (6). A key performance parameter of an SMM is the magnetic blocking temperature, TB, one description of which refers to the maximum temperature at which it is possible to observe hysteresis in the field dependence of the magnetization, subject to the field sweep rate. The blocking temperature provides a means of comparing different SMMs and, to date, the vast majority that show any hysteresis at all require liquid-helium cooling to do so (7, 8). A few notable examples have emerged from the extreme cold to set record blocking temperatures above the liquid-helium regime (912), including the dysprosium metallocene [(Cpttt)2Dy][B(C6F5)4] (Cpttt, 1,2,4-tri-tert-butylcyclopentadienyl), which showed magnetic hysteresis with coercivity up to 60 K (1315); however, this threshold still falls markedly short of the more practically accessible 77 K temperature at which nitrogen liquefies. We now show that by designing the ligand framework so that two key structural parameters—that is, the Dy-Cpcent distances (cent refers to the centroid of the Cp ligand) and the Cp-Dy-Cp bending angle—are rendered short and wide, respectively, we achieve an axial crystal field of sufficient strength to furnish an SMM that shows hysteresis above 77 K.

A dysprosium metallocene cation was targeted with cyclopentadienyl substituents of sufficient bulk to produce a wide Cp-Dy-Cp angle, but not too bulky to preclude close approach of the ligands. Thus, the borohydride precursor complex [(η5-CpiPr5)Dy(η5-Cp*)(BH4)] (2) (CpiPr5, penta-iso-propylcyclopentadienyl; Cp*, pentamethylcyclopentadienyl) was synthesized by treating [Dy(η5-CpiPr5)(BH4)2(THF)] (1) with KCp* (Fig. 1). The molecular structures of 1 and 2 were determined by x-ray crystallography (figs. S4 and S5 and tables S1 to S3). The target compound [(η5-Cp*)Dy(η5-CpiPr5)][B(C6F5)4] (3), hereafter abbreviated [Dy-5*][B(C6F5)4], was then isolated in 60% yield by treating 2 with the superelectrophile [(Et3Si)2(μ-H][B(C6F5)4] (Et, ethyl) (16). An x-ray crystallographic analysis of the molecular structure of 3 at 150 K (Fig. 1, figs. S6 and S7, and tables S1 and S4) revealed that the Dy-5* cation features Dy-Cp* and Dy-CpiPr5 distances of 2.296(1) and 2.284(1) Å, respectively, which are, on average, 0.026 Å shorter than the analogous distances of 2.32380(8) and 2.30923(8) Å determined for [(Cpttt)2Dy]+ (13). Furthermore, the Cp-Dy-Cp angle in Dy-5* is 162.507(1)° and hence almost 9.7° wider than the angle of 152.845(2)° found in [(Cpttt)2Dy]+. On the basis of these structural parameters, the crystal field in Dy-5* should be stronger and more axial than in [(Cpttt)2Dy]+, and hence, an improvement in the SMM properties can be expected.

Fig. 1 Synthesis and molecular structures.

(A) Reaction scheme for the synthesis of 3. (B) Thermal ellipsoid representation (50% probability) of the molecular structure of the Dy-5* cation in 3, as determined by x-ray crystallography {for clarity, the hydrogen atoms and [B(C6F5)4] counter anion are omitted}.

The dc molar magnetic susceptibility (χM) was measured for compounds 1 to 3 in the temperature range of 2 to 300 K using an applied field of 1000 Oe, and the field dependence of the magnetization for 1 and 2 was measured at T = 2 and 5 K using fields up to 70 kOe (figs. S8 to S12). A description of the properties of 1 and 2 is provided in the supplementary materials. For 3, the χMT value was measured to be 13.75 cm3 K mol–1 at 300 K and then manifested a steady decrease down to 75 K. At lower temperatures, a sharp drop in χMT was observed, indicating the onset of magnetic blocking, with a value of 0.94 cm3 K mol–1 reached at 2 K. Overall, the dc magnetic properties of compounds 1 to 3 are typical for a monometallic complex of Dy3+ with a 6H15/2 ground multiplet (17). The SMM properties of compounds 1 to 3 were then established through measurements of the in-phase (the real component, χ′) and the out-of-phase (the imaginary component, χ′′) ac susceptibilities as functions of the ac frequency (ν) and temperature, using an oscillating field of 5 Oe and zero applied dc field (figs. S13 to S28 and tables S5 to S7). Focusing again on 3, the χ′′(ν) isotherms show well-defined maxima up to 130 K (Fig. 2). The χ′(ν) and χ′′(ν) data were then used to derive Cole-Cole plots of χ′′(χ′) for relaxation in the temperature range of 82 to 138 K in intervals of 2 K, with each plot adopting a parabolic shape (figs. S26 to S28). Accurate fits of the ac susceptibility plots were obtained using equations describing χ′ and χ′′ in terms of frequency, the isothermal susceptibility (χT), adiabatic susceptibility (χS), the relaxation time (τ), and the fitting parameter α to represent the distribution of relaxation times (eqs. S1 and S2) (18).

Fig. 2 Dynamic magnetic properties.

(A) Frequency dependence of the out-of-phase χ′′M molar magnetic susceptibility for 3, collected in zero dc field at ac frequencies of ν = 0.1 to 1488 Hz from 82 K (green trace) to 138 K (purple trace) in 2 K intervals. Solid lines represent fits to the data using eqs. S1 and S2, with adjusted R2 = 0.99823 to 0.99988. (B) Temperature dependence of the relaxation time for 3. The red points are from the ac susceptibility data, and the blue points are from measurements of the dc magnetic relaxation time. The solid green line is the best fit to Embedded Image, using the parameters stated in the text.

The resulting values of α = 0 to 0.027 indicate a very narrow range of relaxation times in the high-temperature regime. The relaxation times at temperatures in the range of 2 to 83 K were determined in intervals of about 5 K from plots of the magnetization decay versus time (figs. S29 to S48 and table S8). These data show, for example, that the magnetization in 3 decays almost to zero over a 50-s time period at 77 K, increasing to about 500 min at 15 K. The temperature at which τ = 100 s is 65 K. The relaxation times determined from the ac and dc measurements were then combined to obtain further insight into the magnetic relaxation by plotting τ as a function of T–1 (Fig. 2), which revealed a strong, linear dependence of the relaxation time on temperature in the range of 55 to 138 K. The τ(T–1) plot in the range of 10 to 55 K is curved in nature and represents an intermediate regime before purely temperature-independent relaxation is observed below 10 K. The relaxation time can be expressed as Embedded Image, in which the first term represents Orbach relaxation with Ueff as the effective energy barrier to relaxation of the magnetization (kB, Boltzmann constant), the second term represents the contribution from Raman processes (C, the Raman coefficient; n, the Raman exponent), and the third term represents the rate of quantum tunneling of the magnetization (QTM). Using this equation, an excellent fit [adjusted coefficient of determination (R2) = 0.99958] of the data was obtained with τ0 = 4.2(6) × 10−12 s; Ueff = 1541(11) cm–1; C = 3.1(1) × 10−8 s−1 Kn and n = 3.0(1); and τQTM = 2.5(2) × 104 s. The Ueff value determined for 3 exceeds the value of 1277 cm–1 determined for [(Cpttt)2Dy][B(C6F5)4] by about 20% (13).

Potential applications of SMMs in information storage devices rely on the occurrence of magnetic remanence and coercivity; therefore, the hysteresis is a critical consideration (19). For 3, using a relatively fast field sweep rate of 200 Oe s–1 revealed M(H) hysteresis from 2 up to 85 K, with the loops gradually closing as the temperature increased (Fig. 3, A and B). At these temperature limits, coercive fields (Hc) of 50 kOe and 210 Oe (5.0 T and 21 mT), respectively, were measured (Fig. 3C, fig. S49, and table S9). Fixing the temperature at 77 K, a reduction in the sweep rate resulted in the coercive field approximately halving with the rate, that is, Hc = 5802 Oe at 700 Oe s–1, 2946 Oe at 350 Oe s–1, 1688 Oe at 200 Oe s–1, 825 Oe at 100 Oe s–1, 398 Oe at 50 Oe s–1, and 191 Oe at 25 Oe s–1 (fig. S50 and table S10). The observation of coercivity in 3 at 25 Oe s–1 is notable because this sweep rate is slower than the 39 Oe s–1 used to determine the blocking temperature of 60 K for [(Cpttt)2Dy][B(C6F5)4] (13). At 80 K and 25 Oe s–1, a coercive field of 63 Oe was measured (Fig. 3D), and the loops were completely closed at higher temperatures. Consistent with this finding, the field-cooled and zero-field-cooled magnetic susceptibilities for 3 diverged at 78 K (fig. S51). By analogy with the development of high-temperature (high-TC) superconductors, we propose to designate the Dy-5* cation in 3 as a high-temperature, or high-TB, SMM.

Fig. 3 Magnetic hysteresis properties of 3.

(A and B) Magnetization versus field hysteresis loops in the temperature ranges of 2 to 75 K (A) and 75 to 85 K (B) using a field sweep rate of 200 Oe s–1. (C) Expansion of the hysteresis loops at 77 K showing the coercive fields. (D) Hysteresis loops at 80 K using a field sweep rate of 25 Oe s–1.

The importance of the strong axial crystal field in the Dy-5* cation combined with the absence of an equatorial field is illustrated further by comparing the Ueff and TB values for 3 with those of the precursors 1 and 2. In the case of 1, the CpiPr5 ligand provides a strong axial field, but the pseudo-octahedral coordination geometry introduces a non-negligible equatorial field and, although slow magnetic relaxation in zero field is observed with this system, the positions of the maxima in χ′′(ν) are temperature-independent up to 10 K and only observed up to 30 K (figs. S13 to S16). The resulting energy barrier of 241(7) cm–1 is comparatively small, and the rate of QTM is, at 5.0(1) × 10−3 s (fig. S17), some seven orders of magnitude faster than found with 3. The competing equatorial field in 2 is more prominent, because the maxima in χ′′(ν) are very weakly temperature-dependent from 3 to 20 K, with the resulting energy barrier a negligible 7(1) cm–1 (figs. S19 to S22). In both 1 and 2, the M(H) hysteresis loops collected at 2 K and 200 Oe s–1 are waist-restricted, with no coercivity and only small openings as the field magnitude increases (figs. S18 and S23).

Ab initio calculations have enabled quantitative analysis of the properties of SMMs on a microscopic scale (20), particularly systems with ηn-bonded organometallic ligands (2130). Calculations on the Dy-5* cation were performed at the XMS-CASPT2//SA-CASSCF/RASSI level (31, 32): The resulting energies, principal components of the g-tensors, and the principal magnetic axes of the eight lowest Kramers’ doublets in Dy-5* corresponding to the crystal-field (CF) states of the 6H15/2 ground multiplet are listed in table S11. The principal magnetic axis in the ground doublet of Dy-5* (Fig. 4) is projected toward the centroids of the two cyclopentadienyl ligands, with the principal axes of the next six doublets almost collinear and the largest deviation angle 5.3° with the fifth doublet. The highest doublet is perpendicular to the ground doublet.

Fig. 4 Magnetic relaxation in the Dy-5* cation.

(A) The principal magnetic axis of the ground Kramers’ doublet. (B) Relaxation mechanism for Dy-5*. Blue arrows show the most probable relaxation route, and red arrows show transitions between states with less probable, but non-negligible, matrix elements; darker shading indicates a higher probability.

The g-tensor of the ground doublet is calculated to be perfectly axial, that is, gx = gy = 0.000 and gz = 20.000 (table S11), which is consistent with the experimental hysteresis measurements in which QTM is completely blocked at zero field. In the six lowest doublets, the CF is highly axial, and each state can be assigned to a definite projection (greater than 96% character) of the total angular momentum, MJ (table S12). The transverse components of the g-tensors increase roughly by an order of magnitude in each doublet upon moving to higher energy. In the fifth doublet, the transverse components are non-negligible, and in the sixth doublet, the transverse components are large enough to allow considerable tunneling. In the two highest states, the axiality is weaker and considerable mixing occurs under the CF, which most likely results from the asymmetry of the coordination environment.

The ab initio CF parameters were calculated for the Dy-5* cation following a previously established methodology (33, 34) and are listed in table S13. The off-diagonal elements of the CF operator clearly have non-negligible elements owing to the low C1 point symmetry of Dy-5*; however, the axial second-rank parameter Embedded Image is at least two orders of magnitude larger than any other parameter. This creates a highly axial CF environment despite the absence of point symmetry (or pseudosymmetry) that would be needed for a strictly axial CF. The off-diagonal elements of the CF play some role, and, in the higher-lying doublets of the ground multiplet, the axial nature of the CF is lost (vide infra). This demonstrates that strict point symmetry is not required to achieve a highly axial CF, provided that the axial parameters are sufficiently strong in comparison to the other CF parameters arising from the low-symmetry components of the CF.

The magnetic relaxation in the Dy-5* cation was studied further by constructing a qualitative relaxation barrier from the ab initio results, which follows a methodology in which the transition magnetic moment between the different states was calculated and the relaxation pathway follows the largest matrix elements (Fig. 4B and table S14) (35). The results predict that the barrier is crossed at the fourth excited doublet, corresponding to a Ueff value of 1524 cm–1 for the Orbach process, which is consistent with the calculated g-tensors for this doublet and is in excellent agreement with the experimentally determined barrier height of 1541(11) cm–1. To gain deeper insight into the nature of the spin-phonon relaxation, the first-order spin-phonon couplings with the optical phonons (approximated as the molecular vibrations) were evaluated from first-principles calculations (tables S15 to S18). In earlier work on [(Cpttt)2Dy]+ (14), vibrations of the C–H oscillators in the Cp rings were recognized as the most important contribution to the Orbach relaxation, because they initiated the transition from the ground doublet to the first excited doublet. In the case of Dy-5*, these oscillators are absent, and the analogous transition from the ground to the first excited doublet is most likely initiated by out-of-plane vibrations of the Cp* ligand when comparing the frequency of these modes (632.9 and 640.5 cm–1) to the calculated gap between the ground and first excited doublets (672 cm–1) (see movies S1 to S7). Because the out-of-plane vibrations couple strongly to vibrations of the Cp* methyl groups, it is conceivable that their energies can be tuned by choosing ligand substituents that would bring the vibrational modes out of resonance with the excitation gap. Such an approach should lead to further improvements in SMM performance beyond those of the Dy-5* cation and therefore enhance their potential for applications in magnetic information storage materials.

Supplementary Materials

Materials and Methods

Figs. S1 to S51

Tables S1 to S18

References (3777)

Movies S1 to S7

Data S1 to S3


Note added in proof: A study describing the properties of related cationic dysprosium metallocenes was recently published by Long, Harvey, and others (36).

References and Notes

Acknowledgments: The authors thank the CSC-IT Center for Science in Finland, the Finnish Grid and Cloud Infrastructure (persistent identifier urn:nbn:fi:research-infras-2016072533), and H. M. Tuononen (University of Jyväskylä) for providing computational resources. Funding: The authors thank the European Research Council (CoG grant 646740), the EPSRC (EP/M022064/1), the NSF China (projects 21620102002 and 91422302), the National Key Research and Development Program of China (2018YFA0306001), and the Academy of Finland (projects 282499 and 289172). Author contributions: R.A.L. conceived the original idea and formulated the research aims. Synthetic and crystallographic work was carried out by F.-S.G. and B.M.D. Magnetic measurements were conducted by Y.-C.C. and M.-L.T. The theoretical analysis was carried out by A.M. All authors analyzed the data. R.A.L. wrote the manuscript, with contributions from all authors. Competing interests: The authors declare no competing interests. Data and materials availability: Metrical data for the solid-state structures of 1 to 3 are available free of charge from the Cambridge Crystallographic Data Centre under reference numbers CCDC 1854466 to 1854468. All other data are in the main text or supplementary materials.

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