Paul J.
Saines
*^{a},
Joseph A. M.
Paddison
^{ab},
Peter M. M.
Thygesen
^{a} and
Matthew G.
Tucker
^{b}
^{a}Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, UK. E-mail: paul.saines@chem.ox.ac.uk
^{b}ISIS Facility, Rutherford Appleton Laboratory, Harwell Oxford, Didcot, OX1 3QR, UK
First published on 21st July 2015
This study probes the magnetic properties and interactions of the Ln(HCO_{2})_{3} (Ln = Tb^{3+}–Er^{3+}) frameworks. We show that the magnetocaloric effect of Tb(HCO_{2})_{3} is significantly higher above 4 K in moderate magnetic fields compared to the promising Gd(HCO_{2})_{3}. While the peak performance of Tb(HCO_{2})_{3} is lower than Gd(HCO_{2})_{3}, we also find that the Gd-rich members of the solid solution Gd_{1−x}Tb_{x}(HCO_{2})_{3} blend the advantages of both end-members. Using neutron diffraction experiments, Tb(HCO_{2})_{3} is found to be antiferromagnetic below 1.7 K with ferromagnetic face-sharing chains and antiferromagnetic coupling between them. Analysis of magnetic diffuse scattering of the paramagnetic phase indicates that ferromagnetic coupling is retained, and it is likely that this plays a role in improving its magnetocaloric performance in low fields.
Conceptual insightsAlternate coolants are needed to replace the use of increasingly scarce liquid helium to reach ultra-low temperatures, required, for example, to cool superconductors used in medical resonance imaging to below 10 K. Paramagnetic magnetocalorics, which posses entropically driven cooling when in a cycled magnetic field, are one such replacement. Recently gadolinium-based coordination frameworks that have amongst the largest magnetocaloric effects have been developed; the cooling power of these materials, however, peaks below 2 K, below the temperatures required for many applications of liquid helium. This work shows that the incorporation of heavier lanthanides, in particular terbium, into a magnetocaloric framework can lead to a significant increase in their performance at higher temperatures—particularly in applied fields reachable using permanent magnets, the most practical for functional cooling devices. The detailed magnetic interactions in terbium formate have also been examined, the first study of the magnetic correlations in a paramagnetic coordination framework, which reveals that Ising-like one-dimensional ferromagnetic coupling is present in the paramagnetic phase. These interactions are likely to play a role in its excellent magnetocaloric performance by increasing its ease of magnetisation. |
Very little is known regarding how the paramagnetic interactions in magnetocalorics relate to their fascinating properties. Neutron scattering is the method of choice for probing magnetic interactions and has recently begun to be applied to study magnetically-ordered frameworks;^{4,11} its application, however, to magnetocalorics and other low dimensional and frustrated frameworks is very limited.^{12} This is because sufficiently large single crystals of coordination frameworks are seldom available, and it has long been considered that little information about the paramagnetic state can be extracted using neutron powder diffraction. While the very large neutron-absorption cross section of Gd also typically restricts studying many magnetocalorics, recent studies have shown that this problem is surmountable.^{13} Our research on frustrated and disordered magnets has shown that significantly more information can be obtained from powder magnetic diffuse scattering than has traditionally been anticipated.^{14,15} Applying such techniques to frameworks would enable a much deeper understanding of their low dimensional or frustrated behaviour.
Here we present a survey of the magnetic properties of the Ln(HCO_{2})_{3} (Ln = Tb^{3+}, Dy^{3+}, Ho^{3+} and Er^{3+}) frameworks. Unexpectedly, we reveal that Tb(HCO_{2})_{3} has a larger MCE than Gd(HCO_{2})_{3} for temperatures between 4 and 10 K and applied fields below 2 T. Doping across the Gd_{1−x}Tb_{x}(HCO_{2})_{3} solid solution series is found to further optimize the MCE properties of this family. Encouraged by the properties of Tb(HCO_{2})_{3}, we also investigated its magnetic interactions using neutron diffraction, characterising both its long-range magnetic order present below 1.7 K and the short-range order in its paramagnetic phase—the first time that such a study has been completed on a coordination framework. We show that ferromagnetic coupling within the TbO_{9} chains in Tb(HCO_{2})_{3} is the dominant interaction in the paramagnetic phase, which may play a role in its interesting magnetocaloric properties.
Time-of-flight neutron powder diffraction patterns were recorded using the GEM diffractometer at the ISIS neutron facility, Rutherford Appleton Laboratories, UK.^{16} Data covered a reciprocal-space range 0.25 < Q < 25 Å^{−1} and were measured at temperatures between 1.4 K and 300 K for 30 μAh (900 μAh at 3 K). The sample was cooled in an 8 mm V can in an Oxford Instruments Variox Cryostat. Data were fitted using the GSAS Rietveld refinement package using the EXPGUI interface.^{17} Refinements were carried out with a profile function featuring a convolution of back-to-back exponentials with a pseudo-Voigt model, with backgrounds fitted using shifted Chebyschev polynomials. Refinement of the D fractional occupancy showed that the sample is perdeuterated.
Likely magnetic structures for the ordered phase were determined using the ISODISTORT software suite^{18} by exploring the magnetic distortion modes and symmetries consistent with the observed magnetic propagation vector, k, and the parent crystal structure. In order to characterise short-range spin correlations in the paramagnetic state, magnetic diffuse scattering data were obtained from the lowest-Q detector bank (bank 1) on GEM. Bragg scattering, as determined from Rietveld refinements, and experimentally measured background contributions, including from the sample environment, were subtracted. The resulting magnetic diffuse-scattering data were fitted using the Spinvert Reverse Monte Carlo (RMC) refinement package.^{15} In RMC refinement, spin orientations in a periodic supercell are fitted to diffuse-scattering data using a Metropolis Monte Carlo algorithm. We used a 5 × 3 × 13 size metrically-orthorhombic supercell related to the trigonal cell by a basis vector of [(1, 0, 0),(1/3, 2/3, 0),(0, 0, 1)]. The magnetic form factor of Tb^{3+} was obtained from tabulated coefficients.^{19} The phase scale and a flat background term were also refined.
Fig. 1 The structure of the Ln(HCO_{2})_{3} frameworks. The Ln^{3+}, oxygen, carbon and hydrogen atoms are represented in purple, red, black and grey, respectively. |
Field cooled (FC) and zero-field cooled (ZFC) magnetic susceptibility data of the Ln(HCO_{2})_{3} frameworks (Ln = Gd^{3+}, Tb^{3+}, Dy^{3+}, Ho^{3+} and Er^{3+}) were measured in a 100 Oe field from 2 K to 300 K and did not show any indication of long range magnetic order. These data were well fitted using the Curie–Weiss law (see Fig. S6–S10, ESI†) with Curie–Weiss temperatures of −0.6 K, −0.9 K, −6.1 K, −10.3 K and −16.0 K, for Gd^{3+}–Er^{3+}. Gd(HCO_{2})_{3}, therefore, has antiferromagnetic interactions but the significant orbital moment of the other lanthanides means their Curie–Weiss temperatures are a sum of any magnetic interactions and the effect of depopulation of the Stark levels so a similar analysis cannot be made. Effective magnetic moments were found to be broadly consistent with the values expected for these trivalent lanthanides according to the Russell–Saunders coupling scheme, with values of 7.86, 9.62, 10.00, 10.48 and 9.68 μ_{B} obtained. Magnetisation measurements exhibit paramagnetic behaviour and appear close to saturation under an applied field of 5 T (see Fig. S11–S16, ESI†). Interestingly, Tb(HCO_{2})_{3} appears close to saturation at 1 T, a much lower field than its Gd^{3+} analogue despite its higher magnetic anisotropy (discussed below); this greater ease of magnetisation increases further with increasing temperature.
Magnetic entropy change, ΔS_{m}, was calculated from the Maxwell relation from 2 K to 12 K for ΔB = 5–0 T. This gave −ΔS^{max}_{m} of 15.7, 20.8, 14.7 and 19.2 J kg^{−1} K^{−1} for Tb^{3+}, Dy^{3+}, Ho^{3+} and Er^{3+}, with T_{max} of 7, 6, 4 and 2 K, corresponding to volumetric values of −ΔS^{max}_{m} of 61.3, 82.9, 60.1 and 79.1 mJ cm^{−3} K^{−1} (see Fig. S17, ESI†). These −ΔS_{m} values are all significantly lower than the 190.4 mJ cm^{−3} K^{−1} we obtain for Gd(HCO_{2})_{3} with T_{max} = 2 K for ΔB = 5–0 T, which is close to the value found in a previous study.^{5} The higher T_{max} temperatures of the other lanthanides, particularly Tb^{3+}, attracted our attention. Indeed, for ΔB = 1–0 T the −ΔS_{m} of Tb(HCO_{2})_{3} is significantly higher than that of Gd(HCO_{2})_{3} above 4 K. The same is true for Ho(HCO_{2})_{3}, albeit to a very small extent (see Fig. 2a). A greater −ΔS_{m} is also observed for Tb(HCO_{2})_{3} for ΔB = 2–0 T above 6 K, although the differences in the values achieved compared to the Gd^{3+} compound are smaller (see Fig. 2b). This result highlights that the incorporation of Tb^{3+} cations into coordination frameworks allows their MCE properties to be optimised at higher temperatures and in lower applied fields, compared to the corresponding Gd^{3+} compound. Previous studies of Gd_{1−x}Tb_{x}Ga_{5}O_{12} showed the same effect, but by a much smaller margin.^{20} This is significant as many of the applications of liquid helium do not require cooling below 4 K, which most paramagnetic MCE materials are optimised for. It should be noted here that the magnetocaloric effect can be probed directly from heat capacity measurements, which is desirable particularly when determining the specific heat transfer, ΔQ.^{21} Recent work on Gd(HCO_{2})_{3} and GdOH(CO_{3}), however, have shown that for similar frameworks excellent agreement is usually obtained between the direct determination of −ΔS_{m} and the indirect method presented in this work.
Fig. 2 Magnetic entropy change for the Ln(HCO_{2})_{3} frameworks for (a) ΔB = 1–0 T and (b) ΔB = 2–0 T. The filled and hollow symbols mark mass and volumetric units, respectively. |
Since the incorporation of Tb^{3+} yielded improved MCE properties at higher temperatures compared to Gd(HCO_{2})_{3} but lower −ΔS^{max}_{m}, the magnetic properties of the Gd_{1−x}Tb_{x}(HCO_{2})_{3} (x = 0.2, 0.4, 0.6 and 0.8) solid solution were investigated. High-resolution X-ray diffraction indicate these compounds are pure single phases, although there was some evidence of peak broadening, suggesting that they exhibit a degree of strain or cation inhomogeneity (see Fig. S18, ESI†). Magnetic susceptibilities were well fitted by Curie–Weiss law, yielding effective magnetic moments consistent with stoichiometries of x = 0.19, 0.40, 0.57 and 0.76 across the series, close to the expected nominal stoichiometries. The Curie–Weiss temperatures were −0.9 K for the whole series except for Gd_{0.4}Tb_{0.6}(HCO_{2})_{3}, which had a value of −1.3 K. Only Gd_{0.4}Tb_{0.6}(HCO_{2})_{3} varied from mean-field behaviour, with an antiferromagnetic cusp present in ZFC measurements at 3 K that is not observed in FC data (see Fig. S19, ESI†); magnetization measurements at 2 K are consistent with paramagnetic behaviour suggesting Gd_{0.4}Tb_{0.6}(HCO_{2})_{3} is not a simple antiferromagnet.
For the x = 0.2 and 0.4 members of the Gd_{1−x}Tb_{x}(HCO_{2})_{3} series the −ΔS_{m} for ΔB = 1–0 T are significantly higher than would be expected for a physical mix of the two end-member phases. This is particularly significant for Gd_{0.8}Tb_{0.2}(HCO_{2})_{3} as at 2 K, the lowest temperature probed its −ΔS_{m} for a ΔB = 1–0 T is equal to that of Gd(HCO_{2})_{3}. It decreases more slowly than for the pure Gd phase, such that for temperatures above 5 K its −ΔS_{m} is between 10–15% higher (see Fig. 3 and Fig. S20–S23 for magnetisation data, ESI†). Similarly, while the −ΔS^{max}_{m} for Gd_{0.6}Tb_{0.4}(HCO_{2})_{3} is about 10% lower than Gd(HCO_{2})_{3} for a ΔB = 1–0 T above 5 K, its −ΔS_{m} is between 14 to 24% higher. The performance of both doped compounds also exceeds that of Gd(HCO_{2})_{3} at higher temperatures for a ΔB = 2–0 T, although this is only above 6 and 7 K for x = 0.2 and x = 0.4, respectively, and the difference remains less than 10%. To the best of our knowledge this is the first study of the magnetocaloric properties of a framework solid solution and has shown the potential advantages of such an approach to optimise the physical properties of such materials – namely, retaining most of the performance of Gd(HCO_{2})_{3} in low fields, while improving on its MCE at moderately higher temperatures.
Fig. 3 Magnetic entropy change for the Gd_{1−x}Tb_{x}(HCO_{2})_{3} series for ΔB = 1–0 T. The filled and hollow symbols mark mass and volumetric units, respectively. |
A neutron diffraction pattern obtained from Tb(DCO_{2})_{3} at 1.4 K revealed the presence of additional reflections, especially at high d-spacing (see Fig. 4), consistent with the emergence of magnetic order. These were found to index on the parent cell but violated the rhombohedral centering conditions. This is consistent with the magnetic structure of Tb(DCO_{2})_{3} belonging to the k-vector Λ, (0, 0, g), which is allowed to be incommensurate but here appears to have locked into a commensurate value of g = 1. Of the possible magnetic structures suggested by ISODISTORT only those belonging to the magnetic space group P3m′1 fitted the data. There were two possible magnetic structures of this type, each of which have ferromagnetic face-sharing chains, with spins found to align along the c-axis. One possible structure has three ferromagnetic chains with one chain having twice the magnetic moment of the others and coupled antiferromagnetically to them (see Fig. 5a). This model is consistent with that proposed in a previous study of Kurbakov et al.,^{24} who briefly analysed the magnetic structure of Tb(DCO_{2})_{3} using a basis vector approach. The other structure has the spins in two ferromagnetic chains coupled antiferromagnetically to each other with the remaining chain being disordered (see Fig. 5b), a so-called spin-idle structure. The fits of these two structures to the 1.4 K data are equivalent (R_{p} = 1.94% for both models and R_{wp} = 2.09% and 2.10% for the spin-idle and unequal spin structure, respectively). The largest magnetic moment is 5.91 μ_{B} and 6.80 μ_{B} for the spin-idle and unequal-spin structure, respectively. These values are well below the expected magnetic moment of 9.72 μ_{B} for isotropic Tb^{3+} moments, consistent with the observation of magnetic diffuse scattering, which persists more weakly up to 10 K. Magnetic reflections appear between 1.65 and 1.72 K, indicating the onset of magnetic order (see Fig. S25 for the evolution of the magnetic moments, ESI†). The square of the observed magnetic moment is proportional to the Landau order parameter, Q; a good linear fit to the square of the ordered magnetic moment is obtained, confirming that the magnetic-ordering transition is second order and occurs at 1.72(12) K.
Fig. 5 The two possible magnetic structures of Tb(DCO_{2})_{3}. The distinct Tb^{3+} cations are shown in different colours with the ordered spin direction indicated by the arrows pointing through them. All other colours are the same as in Fig. 1. |
Both possible magnetic structures of Tb(DCO_{2})_{3} indicate that the dominant intra-chain coupling is ferromagnetic, consistent with the small Tb–O2–Tb bond angle of 105.79(4)°. As the intra-chain super-exchange distances are much smaller than those between chains (cf. 4.98 Å to 7.42 Å), it would be expected that this compound will resemble a one-dimensional system above its long-range ordering temperature. Fits to the diffuse magnetic scattering observed at 3 K using RMC refinement confirm that this is the case (see Fig. 6 for the quality of fit). Initially, unconstrained refinements were performed in which the spins were allowed to point in any direction, in a Heisenberg-like fashion. A plot of 〈S_{0}·S_{r}〉 averaged over ten such refinements show that the dominant spin correlations in this material are ferromagnetic within the chains (see Fig. 7a), with a correlation length of 9.2(1.3) Å. The inter-chain correlations are much weaker and antiferromagnetic, with 〈S_{0}·S_{r}〉 correlations of −0.082(2) and −0.044(3) observed for Tb^{3+} cations separated by the shorter, 6.16 Å and longer, 6.57 Å distances found in the triangles, respectively.
Fig. 6 Comparison of the Heisenberg-like and Ising-like RMC fits to the neutron diffuse scattering of Tb(DCO_{2})_{3} at 3 K. The results are averaged over ten refinements. |
Stereographic projections of the refined spin orientations indicate that even well above the magnetic ordering temperatures the spins are preferentially aligned along the c-axis (see Fig. 7b), indicating an Ising-like magnetic anisotropy. Attempts were therefore made to fit the diffuse scattering data with Ising spins constrained to point along the c-axis. The Ising refinements also yielded a reasonable fit, though of somewhat lower quality than the unconstrained refinement (cf. χ^{2} of 290 and 414 for ten averaged Heisenberg and Ising fits, respectively), which would be expected as the Ising refinement is more highly constrained. This result suggests that the spins have a strong, although probably not purely, Ising character. To the best of our knowledge this is the first RMC study of the magnetic interactions in the paramagnetic phase of a coordination framework.
The significant ferromagnetic intra-chain interactions in the paramagnetic phase of Tb(HCO_{2})_{3} explain the relative ease of its magnetization compared to Gd(HCO_{2})_{3}, whose negative Curie–Weiss temperature indicates predominantly antiferromagnetic interactions. It can be envisaged that the strong ferromagnetic intra-chain interactions, present on a local scale of about 10 Å, will lead to the Tb^{3+} spins aligning readily with an applied magnetic field, easily overcoming the much weaker inter-chain antiferromagnetic coupling. Bulk measurements show that this greater ease of magnetization is retained to higher temperature, leading to a higher peak temperature for −ΔS^{max}_{m} than found in Gd(HCO_{2})_{3}, which may make Tb(HCO_{2})_{3} suitable for cooling applications at moderately higher temperatures. The trade-off for this is a lower −ΔS^{max}_{m} compared to Gd(HCO_{2})_{3}, due to a combination of its lower magnetic moment and a more gradual change of magnetisation with temperature. In the Gd_{1−x}Tb_{x}(HCO_{2})_{3} solid solution a mixture of these two cations leads to a retention of most of the peak performance of the Gd(HCO_{2})_{3} but a slower reduction in −ΔS_{m} with temperature in low applied fields. While to date the development of magnetocaloric frameworks has focused on Gd^{3+} containing-compounds, this study highlights the benefits of incorporating heavier lanthanides into framework structures known to have excellent magnetocaloric properties. By combining a deeper understanding of their magnetic interactions with judicious choices of doping in solid solutions, it should be possible to expand the palate of available magnetocaloric frameworks and optimize their application.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5mh00113g |
This journal is © The Royal Society of Chemistry 2015 |