Magnetic Properties of Quasi-One-Dimensional Lanthanide Calcium Oxyborates Ca4LnO(BO3)3

This study examines the lanthanide calcium oxyborates Ca4LnO(BO3)3 (Ln = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er, Yb). The reported monoclinic structure (space group Cm) was confirmed using powder X-ray diffraction. The magnetic Ln3+ ions are situated in well-separated chains parallel to the c axis in a quasi-one-dimensional array. Here we report the first bulk magnetic characterization of Ca4LnO(BO3)3 using magnetic susceptibility χ(T) and isothermal magnetization M(H) measurements at T ≥ 2 K. With the sole exception of Ca4TbO(BO3)3, which displays a transition at T = 3.6 K, no magnetic transitions occur above 2 K, and Curie–Weiss analysis indicates antiferromagnetic nearest-neighbor interactions for all samples. Calculation of the magnetic entropy change ΔSm indicates that Ca4GdO(BO3)3 and Ca4HoO(BO3)3 are viable magnetocaloric materials at liquid helium temperatures in the high-field and low-field regimes, respectively.


■ INTRODUCTION
An ideal one-dimensional (1D) system−a single chain of magnetic ions−would never display long-range order. 1,2 Such systems have been predicted to host exotic magnetic behavior such as spinons 3 but are impossible to realize in the solid state. Certain crystal structures may, however, be quasi-1D if the spin chains are kept well separated by nonmagnetic atoms, but in most cases there is weak coupling between the chains, leading to 3D ordering at low temperatures. Extensive work has been carried out on quasi-1D S = 1/2 systems containing first-row transition metals, but much less is known about lanthanide systems. 4−8 These have very different magnetic properties from the 3d transition metals as a result of strong spin−orbit coupling, and the interplay between superexchange (J), dipolar (D), and crystal electric field (CEF) effects means that they are likely to require different models for the magnetism. Examples of quasi-1D lanthanide systems include the hydroxycarbonates LnOHCO 3 and formates Ln(HCOO) 3 . Both series of compounds have been shown to display unusual magnetic properties and to be viable magnetocaloric materials at temperatures below 10 K, although in some cases interchain coupling produces three-dimensional ordering at temperatures below 2 K. 9−11 Low-dimensional magnetic systems are of interest for solidstate magnetic refrigeration as a more sustainable alternative to liquid helium for cooling to low temperatures. This technology relies on the magnetocaloric effect (MCE) arising from adiabatic demagnetization of the sample: this causes the temperature to drop as magnetic domains dealign from the field direction, enabling large amounts of magnetic entropy to be extracted. The lower limit for magnetic cooling is set by the long-range magnetic ordering temperature of the sample; thus, low-dimensional materials are useful as they usually display suppression of this ordering temperature. Lanthanide compounds have been widely studied for this purpose, particularly those containing Gd 3+ , which has a large spin compared to the transition metals, and usually 12 no crystal field interactions compared with the other lanthanides, since L = 0. 9,10,13,14 For Gd 3+ (e.g., Gd 3 Ga 5 O 12 , "GGG") the MCE is maximized in high fields (μ 0 H > 5 T), where Heisenberg systems have been shown to be optimized, but obtaining such fields still requires liquid helium to cool the superconducting magnets. At low fields μ 0 H ≤ 2 T a permanent magnet can be used to provide the external field; systems with significant single-ion anisotropy (e.g., Dy 3 Ga 5 O 12 ) tend to perform better in this regime. 14,15 The lanthanide calcium oxyborates with general formula Ca 4 LnO(BO 3 ) 3 (Ln = Y, La−Lu) have previously been investigated as nonlinear optic materials. 16,17 The synthesis of these compounds in powder form may be carried out through straightforward solid-state or sol−gel procedures. 18,19 The lanthanide ions in the unit cell are arranged in chains parallel to the c-axis (Figure 1) with ions separated by c ≈ 3.6 Å along the chains. These chains are well separated in the ab plane by 8−9 Å, leading to a quasi-1D Ln 3+ array.
In this Article we report the solid-state synthesis of 12 compounds with the formula Ca 4 LnO(BO 3 ) 3 from across the lanthanide series, followed by structural characterization using powder X-ray diffraction (PXRD). Furthermore, we report the bulk magnetic characterization of these compounds using magnetic susceptibility and isothermal magnetization measurements at T ≥ 2 K. Their potential application in magnetic refrigeration applications is discussed with the aid of magnetic entropy calculations. Room temperature PXRD patterns were collected on a Bruker D8 diffractometer (Cu Kα, λ = 1.541 Å) in the range 10 ≤ 2θ(°) ≤ 90 with a step size of 0.01°and measurement time 1 s per step. Rietveld refinement 21 was carried out using the program Topas. 22 Magnetic susceptibility and isothermal magnetization were measured on a Quantum Design 9 T Physical Properties Measurement System using the ACMS-II option in the temperature and field ranges 2 ≤ T(K) ≤ 300 and 0 ≤ μ 0 H(T) ≤ 9, respectively. In a low field of 500 Oe, the M(H) curve is linear for all T, and the susceptibility can therefore be approximated by χ(T) = M/H.

■ RESULTS
Crystal Structure. From PXRD and Rietveld refinement all samples were found to adopt the previously reported monoclinic Cm structure ( Figure 1); a representative X-ray refinement is given in Figure 2. 18,20,23 The unit cell contains two independent Ca 2+ sites, both six-coordinate but distorted from perfectly octahedral geometry. Additionally the crystal structure contains distorted LnO 6 octahedra, which share edges along the "chains", and trigonal planar BO 3 3− groups, which are tilted at different angles from the c-axis. A previous study found that the tilting of each of these borate groups changed in a regular way as the size of the lanthanide ions was varied, 20 but such analysis is beyond the scope of this work, which is limited by the powder samples and solely X-ray diffraction measurements.
In some cases small amounts, ≤5 wt %, of nonmagnetic impurities (Ca 3 (BO 3 ) 2 , H 3 BO 3 ) remained after multiple heating steps: for details, see Table 1. For Ca 4 YbO(BO 3 ) 3 , 50% excess H 3 BO 3 was required to ensure complete reaction of Yb 2 O 3 , leading to a higher proportion of Ca 3 (BO 3 ) 2 in the final sample. There is also a larger proportion of Ca 3 (BO 3 ) 2 in Ca 4 LaO(BO 3 ) 3 than in the other samples; this is attributed to either incomplete drying or reabsorption of water into La 2 O 3 before weighing out. The series Ca 4 LnO(BO 3 ) 3 obeys Vegard's Law for variation of lattice parameters ( Figure 3).
The insensitivity of X-ray diffraction to oxygen and boron in the presence of heavy elements (Ca, Ln) required the atomic positions of O and B to be fixed at previously reported values, 24 while the atomic coordinates of Ca were refined (Table 1). Considering ionic radii, the trivalent lanthanide ions range in size from 103.2 pm (La) down to 86.8 pm (Yb), while six-coordinate Ca 2+ is 100 pm; 25 the extent of cation mixing might then be expected to increase with increasing Ln 3+ radius. The presence, if any, of Ca 2+ /Ln 3+ site disorder was tested by setting a suitable mixed Ca 2+ and Ln 3+ occupancy in each of  Inorganic Chemistry pubs.acs.org/IC Article the three metal sites and refining with the overall ratio fixed at 4:1. No significant site disorder was observed for any compound, however, in agreement with a previous singlecrystal study of Ca 4 LaO(BO 3 ) 3 . 16 The fractional occupancies were therefore fixed at 1 for each site. Bulk Magnetic Properties. The zero-field-cooled magnetic susceptibility curves, collected on warming at H = 500 Oe, are shown in Figure 4 for Ln = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, and Yb. The samples containing Sm and Eu do not obey the Curie−Weiss law ( χ = θ − C T CW ) but display van Vleck paramagnetism due to the mixing of ground states with lowlying excited states. 26 The broad feature at T > 6 K for Ca 4 PrO(BO 3 ) 3 is attributed to a singlet ground state with van Vleck paramagnetism, in accordance with previous reports of Pr compounds. 27−29 A broad magnetic transition characteristic of low-dimensional ordering is visible at T = 3.6 K for Ln = Tb, while for all other Ca 4 LnO(BO 3 ) 3 no transition occurs at T ≥ 2 K. Linear Curie−Weiss fitting was carried out in both hightemperature (50−150 K) and low-temperature regimes. The susceptibility of lanthanide compounds is strongly dependent on crystal electric field effects, and the low-temperature fitting ranges were therefore varied depending on the lanthanide ion in question. 30,31 The resultant magnetic parameters are given     Figure 5. We conclude that Ca 4 PrO(BO 3 ) 3 has a singlet ground state, as observed in other Pr compounds. [27][28][29]32 The magnetization saturates at 2 K and 9 T in all other compounds. For an isotropic (Heisenberg) spin system the magnetization is expected to saturate at a value of g J J, whereas easy-axis (Ising) systems tend to saturate at half this value, although other contributions may increase M sat above g J J/2. 10,33 In particular, the exact saturation value for a particular lanthanide ion varies depending on the local point group symmetry (i.e., CEF) of the atomic site; further experiments such as inelastic neutron scattering are required in order to confirm the anisotropy. The data for Ca 4 LnO(BO 3 ) 3 indicate that Ca 4 GdO(BO 3 ) 3 is likely a Heisenberg spin system, with the remaining compounds showing substantial local single-ion anisotropy. These results are consistent with other lanthanide compounds such as the Ln 3 Sb 3 Zn 2 O 14 kagome lattices, 32 titanate pyrochlores, 33,34 gallium and aluminum garnets, 35,36 hydroxycarbonates, 10 and metaborates. 29

■ DISCUSSION
The trivalent Ln 3+ ions have highly localized 4f orbitals, meaning that the superexchange between ions−which depends on the orbital overlap−is smaller than for the first-row transition metals. We therefore expect superexchange (J nn , along the 1D spin chains) to be of a similar magnitude to or much larger than the dipolar interactions (D) depending on the electronic configuration of the lanthanide ion in question and hence its magnetic moment. The superexchange can be estimated in the mean-field, isotropic approximation using where S in the denominator is the total spin quantum number, and n is the number of nearest-neighbor spins (here n = 2). 37 For systems containing lanthanide ions, the spin−orbit coupling cannot be neglected, and the quantum number J = |L ± S| is usually substituted for S in eq 1, depending on whether the shell is more or less than half-filled. The mean-   Inorganic Chemistry pubs.acs.org/IC Article field approximation is, in general, a poor model for lanthanide systems due to the strong single-ion anisotropy which is often observed. However, in the absence of inelastic neutron spectroscopy (INS) data the mean-field approximation does allow us to infer some information regarding the magnetic interactions.
In the case of a two-level spin system, it is more appropriate to take S ef f = 1/2. This is true for Nd 3+ , Dy 3+ , Er 3+ , and Yb 3+ , which are Kramers ions with an odd number of f-electrons and therefore symmetry-constrained to have an S ef f = 1/2 doublet ground state at low temperatures. Examples may be found in refs 30 and 38−40. For non-Kramers ions (Tb 3+ , Ho 3+ ) this constraint does not apply if the local point group symmetry of the ion is lower than cubic, 41 as is the case here (Ln 3+ ions in orthorhombic sites). Tb 3+ and Ho 3+ have been reported to have S eff = 1/2 ground states due to mixing of two low-lying singlet states in some compounds, 42,43 but this is not the case for Ho 3 Mg 2 Sb 3 O 14 and Ho 3 Ga 5 O 12 . 28,44 In the absence of INS data we cannot confirm the spin anisotropy for the Ca 4 LnO(BO 3 ) 3 compounds with Ln = Nd, Tb, Dy, Ho, Er, and Yb and will therefore calculate the superexchange using both J = L ± S and S ef f = 1/2.
The dipolar interaction D may be estimated using where r is the distance between adjacent Ln 3+ ions in the same or neighboring chains. 45 This is a general expression for D which does not take into account any single-ion anisotropy. Furthermore, a true calculation for D would be long-range and cover many spins. As with eq 1, however, we here use the general expression to provide a ballpark estimate for D under the stated approximations, since INS data are not yet available.
The sizes of the dipolar and nearest-neighbor exchange interactions were estimated using the magnetic susceptibility data (low-temperature fitting), and the resulting parameters are given in Table 3. It has been proposed that the quasi-onedimensional nature of the magnetism in these compounds is related to the relative sizes of the exchange and dipolar interactions. 29 Regardless of the size of J, we expect to see quasi-1D magnetic behavior with signatures of low-dimensional ordering at low temperatures (as may be the case for Ca 4 TbO(BO 3 ) 3 ) because D intrachain is an order of magnitude larger than D interchain . At this stage we refrain from drawing solid conclusions about the true one-dimensional nature of these compounds, due to the absence of measurements at T < 2 K and the potential inadequacy of the mean-field approximations used to derive the interaction energies.
The potential for these compounds to act as magnetocaloric materials was quantified by calculating the change in magnetic entropy per mole, ΔS m , according to the Maxwell thermodynamic relation: 46 Magnetocaloric data for selected Ca 4 LnO(BO 3 ) 3 samples as a function of applied field are shown in Figure 6. Ca 4 GdO-(BO 3 ) 3 provides the optimal MCE in fields 5 < μ 0 H(T) < 9, while Ca 4 HoO(BO 3 ) 3 is the best magnetocaloric material in this family at fields below 5 T. Selected data for the Ca 4 LnO(BO 3 ) 3 compounds are compared with the standard magnetocaloric materials Gd 3 Ga 5 O 12 (GGG) and Dy 3 Ga 5 O 12 (DGG) at low and high fields in Table 4. 14, 36 Here we define a low field as μ 0 H ≤ 2 T, which is the largest field attainable with a permanent magnet as opposed to a superconducting one. We find that at μ 0 H = 9 T, Ca 4 GdO(BO 3 ) 3 is competitive with GGG in terms of MCE per Gd 3+ ion, but in terms of MCE per kilogram, it performs poorly due to the four heavy Ca 2+ ions   3 , combined with very low (T < 4 K) magnetic ordering temperatures, makes these materials attractive candidates for magnetic refrigeration applications. Tuning of the MCE at different temperatures or fields may be possible through partial chemical substitution of the lanthanide ions. 15 We note particularly that this structure type is highly flexible in allowing substitution of a range of lanthanide ions of different sizes, without any cation mixing that would destroy the quasi-1D magnetic structure. Partial substitution of Sr 2+ for Ca 2+ has also been reported, further increasing the family of related compounds. 20

■ CONCLUSIONS
Twelve compounds in the series Ca 4 LnO(BO 3 ) 3 (Ln = Y, La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb) have been synthesized using a straightforward and repeatable solid-state procedure. The reported structure has been confirmed using Xray diffraction. Bulk magnetic characterization indicates that the quasi-one-dimensional nature of these materials leads to suppression of the magnetic ordering temperatures, which additionally makes these materials good candidates for magnetic refrigeration applications at liquid helium temperatures. These results contribute to the rapidly growing set of lanthanide−alkaline earth borates with low-dimensional structures and novel magnetic properties, such as the Sr 6 LnFe(BO 3 ) 6 , Ba 3 Ln(BO 3 ) 3 , and ABaLn(BO 3 ) 2 (A = Na + , K + , Rb + ) structural families. 31