Ferrimagnetism as a consequence of cation ordering in the perovskite LaSr 2 Cr 2 SbO 9

A polycrystalline sample of LaSr 2 Cr 2 SbO 9 has been synthesised using a standard ceramic method and characterized by x-ray and neutron di ﬀ raction, magnetometry and electron microscopy. The perovskite-related compound crystallises in the triclinic space group I 1 with unit cell parameters of a =5.5344(6) Å, b =5.5562(5) Å, c =7.8292(7) Å, α =89.986(12)°, β =90.350(5)° and γ =89.926(9)° at room temperature. The two crystallogra-phically-distinct, six-coordinate cation sites are occupied by Cr 3+ and Sb 5+ in ratios of 0.868(2):0.132(2) and 0.462(2):0.538(2). Ac and dc magnetometry revealed that LaSr 2 Cr 2 SbO 9 is ferrimagnetic below 150 K with a magnetisation of ~1.25 µ B per formula unit in 50 kOe at 5 K. Neutron di ﬀ raction showed that the cations on the two sites order in a G-type arrangement with a mean Cr 3+ moment of 2.17(1) µ B at 5 K, consistent with a magnetisation of 1.32 µ B per formula unit.


Introduction
Perovskite compounds have the general formula ABO 3 where A is usually a relatively-large divalent or trivalent cation and B is a smaller transition-metal or p-block cation. Due to the chemical flexibility of the perovskite structure, the complexity of these compounds can be increased by the partial substitution of either or both of the cations A and B. This has led to the formation of "double", "triple" and even "quadruple" perovskitesan example of the latter being CaCu 3 Fe 4 O 12 [1]. The large range of accessible compositions has given rise to a plethora of electronic and magnetic properties among perovskite compounds; materials are known that show long-range magnetic order, magnetoresistance [2], giant magnetocaloric effects [3], multiferroic behaviour [4], quantum spin liquid behaviour [5] and relaxor ferroelectricity [6]. One relatively new phenomenon is relaxor ferromagnetism, with La 3 Ni 2 SbO 9 being the prime example, although Cr-Doped Nd 0.5 Ca 0.5 MnO 3 has also been described as relaxor ferromagnet [7,8]. La 3 Ni 2 SbO 9 , or La 2 Ni(Ni 0.333 Sb 0.667 )O 6 , is a double perovskite that crystallises in the space group P2 1 /n and has two crystallographicallydistinct, six-coordinate sites, B and B′, that alternate in a 3D checkerboard pattern. One site is fully occupied by Ni 2+ and the other is occupied by 33% Ni 2+ and 67% Sb 5+ . This creates an ordereddisordered structure as there is complete cation ordering across the B sites but the nickel and antimony cations are randomly distributed over the B′ site. We originally prepared La 3 Ni 2 SbO 9 in the hope that the imbalance of magnetic cations on the two sites would lead to ferrimagnetism, even if the superexchange interactions between pairs of Ni 2+ cations were antiferromagnetic. Magnetometry measurements indicated that La 3 Ni 2 SbO 9 does show a spontaneous magnetisation below 105 K but in early neutron diffraction measurements no magnetic Bragg scattering associated with long-range magnetic order was observed. However, in a later study the intensity of the 011 reflection was seen to increase as a function of applied magnetic field [9]. HAADF-STEM and EDX measurements provided evidence of a varying Sb/Ni stoichiometry across the sample and the presence of Sbrich regions. Thus it was postulated that there were magnetically isolated ferrimagnetic regions in La 3 Ni 2 SbO 9 whose moments only became co-aligned on the application of a magnetic field. In this way La 3 Ni 2 SbO 9 can be compared to relaxor ferroelectrics such as Pb 3 MgNb 2 O 9 where a net polarisation is only observed on the application of an electric field [10]. It is likely that the occurrence of relaxor ferromagnetic behaviour is dependent on many factors such as the extent of the cation ordering across the B sites, the degree of tilting and rotation of the BO 6 octahedra, which will affect the relative strengths of competing superexchange interactions, and the electronic structure of the magnetic cation. To investigate the relative importance of these factors we have previously synthesised La 2 SrNi 2 TeO 9 [11] and Sr 3 Fe 2 TeO 9 [12]. We found that both compounds are markedly different to La 3 Ni 2 SbO 9 with Sr 3 Fe 2 TeO 9 exhibiting a mixture of nano-twinned 1:1 and 2:1 cation-ordered regions while La 2 SrNi 2 TeO 9 predominantly behaves as spin glass but also contains regions of both C-and G-type magnetic order. In a continuation of this work we have now investigated the effect of replacing the σmediated superexchange interactions of La 3 Ni 2 SbO 9 with the solely πmediated superexchange interactions present in the novel compound LaSr 2 Cr 2 SbO 9 . In this paper we report on the structural and magnetic properties of LaSr 2 Cr 2 SbO 9 which have been determined using a combination x-ray and neutron diffraction, magnetometry and electron microscopy.

Experimental
A dark-brown, polycrystalline sample of LaSr 2 Cr 2 SbO 9 was synthesised using the traditional ceramic method. Stoichiometric quantities of SrCO 3 , Cr 2 O 3, Sb 2 O 3 and pre-dried La 2 O 3 were mixed and ground together for 30 min in an agate pestle and mortar and were then fired at 1100°C for 16 h as a loose powder. The reaction mixture was then pelletised and heated at 1150°C for 6 h, reground, and fired at 1150°C for a further 24 h. It was then fired at 1250°C, 1300°C and 1350°C for 48 h at a time. After each firing the sample was quench-cooled to room temperature and re-ground and re-pelleted. The progress of the reaction was monitored by powder x-ray diffraction and the reaction was deemed complete when there was no further change to the x-ray powder diffraction pattern.
X-ray powder diffraction data were collected in our laboratory on a PAN'alytical Empyrean diffractometer operating with Cu K α1 radiation over an angular range of 5≤2θ/°≤125 at room temperature. Further powder diffraction data were collected on instrument I11 at the RAL Diamond Light Source. In the latter case, the sample was loaded into a 0.3 mm diameter borosilicate glass capillary and data were collected at room temperature by conducting a 30 min constant-velocity scan over an angular range of 0≤2θ/°≤150 using the Multi-Analyser-Crystal (MAC) detector. By also measuring a silicon standard, the wavelength was found to be 0.8259 Å. The data were analysed using the Rietveld method [13], as implemented in the GSAS program suite [14], in order to determine the unit cell parameters. A cylindrical absorption correction of 2.74852, estimated using the Argonne X-ray Absorption calculator [15], was applied. Neutron powder diffraction data were collected on the GEM time-of-flight diffractometer at the ISIS spallation source at 5 K and 300 K. The data collected on banks 3-6, which were at angles of 34.96°, 63.62°, 91.30°and 154.40°to the incident beam, were refined simultaneously using the Rietveld method. A pseudo-Voigt function [16] was employed to model the peak shapes and the background was modelled using a 12-term shifted Chebyshev function for all banks. The sample was contained in an 8 mm diameter vanadium canister and a cylindrical absorption correction of 0.0124 was applied following use of the NIST neutron scattering and absorption calculator [17].
Specimens for electron microscopy were prepared by dispersing crushed LaSr 2 Cr 2 SbO 9 powder in ethanol and depositing a few drops of this solution on a copper grid covered with a holey carbon film. Selected-area electron diffraction (SAED) patterns were recorded with a Philips CM20 transmission electron microscope. High-resolution HAADF-STEM images and atomic resolution STEM-EDX maps were collected with a FEI Titan 80-300 "cubed" transmission electron microscope equipped with a Super-X detector and operated at 300 kV.
The dc and ac magnetometry data were collected on a Quantum Design SQUID magnetometer. The dc measurements were taken on warming the sample through the temperature range 5≤T/K≤300 after cooling from room temperature to 5 K firstly in zero field (ZFC) and then in an applied field of 100 Oe (FC). The magnetisation per formula unit (f. u.) of the sample was also measured as a function of applied field at 5 K and 250 K over a field range of −50≤H/kOe ≤50. The ac susceptibility was measured over the temperature range 5≤T/K≤300 in a field of amplitude 3.5 Oe oscillating at frequencies of 1, 10, 100 and 1000 Hz.

Results
The X-ray diffraction pattern collected on the Empyrean diffractometer was initially analysed in the space group I2/m, as reported for Sr 2 CrSbO 6 [18]. This resulted in a good fit with χ 2 =2.331 and R wp =6.5%. The perovskite phase was found to be contaminated with 1.20(2) wt% Sr 2 Sb 2 O 7 . There was no evidence of strontium and lanthanum ordering over the A sites. Higher-resolution x-ray diffraction data were collected on instrument I11 at Diamond light source. A small shoulder was visible on the 200 reflection, which was identified as LaCrO 3. Due the difficulty of separating the contributions of the two phases to the peak, a multi-phase refinement was carried out with the lattice parameters of LaCrO 3 being fixed at the values reported by Qasim et al. [19]. This showed the sample to be contaminated by 1.36 (3)  The molar magnetic susceptibility of LaSr 2 Cr 2 SbO 9 is shown as a function of temperature in Fig. 1. There is a divergence of the ZFC and FC curves below 150 K, with the FC molar susceptibility increasing faster than the ZFC molar susceptibility on cooling. Both susceptibility curves reach a maximum before decreasing slightly on further cooling; the FC susceptibility reaches a maximum of 4.54 cm 3 mol −1 at 14 K and the ZFC reaches 2.24 cm 3 mol −1 at 40 K. χ −1 (T) cannot be considered to be linear below 250 K. Only the data in the temperature range 250≤T/K≤300 were therefore fitted to the Curie-Weiss law, resulting in values of 2.5(2) µ B and +62(10) K for the effective magnetic moment per Cr 3+ cation and the Weiss constant, respectively. The high standard deviations are a consequence of the need to use only a limited temperature range in the data analysis. The field dependence of the magnetisation per formula unit is shown in Fig. 2. M(H) is linear at 250 K, well above the magnetic transition temperature of 150 K, but non-linear at 5 K where a weak hysteresis is observed. The remanent magnetisation is~0.10 µ B per formula unit, the coercive field is 0.2 kOe and the saturation magnetisation is tending towards~1.25 µ B per formula unit. Below 150 K the ac susceptibility, see Fig. 3, is a function of frequency and complex. At each frequency, both the real and imaginary components show maxima at temperatures between 60 and 80 K; the frequency dependence is most obvious close to the temperature of the susceptibility maximum. The parameter ΔT f / T f Δ(log ω) takes a value of 0.032, which is within the range expected for a canonical spin glass [20].  Neutron data collected on GEM were analysed using the Rietveld method. Although the data were initially refined in the space group I2/m, it was found that the I1 space group gave a significantly better fit with χ 2 reduced from 6.515 to 3.698 for the 300 K data set and from 4.687 to 3.736 in the case of the 5 K data set. The space group I1 is an alternative setting of P1 in which the unit cell has twice the volume of the primitive cell. Use of the non-standard setting facilitates comparison with other monoclinic and orthorhombic perovskites. The refined lattice parameters at room temperature are a=5.5344(6) Å, b=5.5562(5) Å, c=7.8292(7) Å, α=89.986(12)°, β=90.350(5)°, γ=89.926(9)°and at 5 K are a=5.5239(5) Å, b=5.5546(5) Å, c=7.8081(7) Å, α=89.8703(18)°, β=90.2482(18)°, γ=90.103(5)°. Statistically significant distortions away from a monoclinic lattice are thus present at both temperatures. The x-ray diffraction data collected on I11 were re-analysed using the space group and oxygen coordinates derived from the neutron refinement and the final fit is shown in Fig. 4. The extent of the B site cation order remained effectively unchanged in this new model with the Cr 3+ :Sb 5+ ratio on the 2 g site being 0.868(2):0.132(2) and 0.462(2):0.538(2) on the 2f site. The level of contaminants also remained similar with 1.47(2) wt% Sr 2 Sb 2 O 7 and 1.36(3) wt% LaCrO 3 detected. From the neutron data, 1.80(4) wt% Sr 2 Sb 2 O 7 and 1.80(6) wt% LaCrO 3 were detected at 300 K.
The I11 data gave a much smaller error on the occupancies of the B sites than the GEM data and so the occupancies were fixed to those derived from the I11 data during the final analysis of both the 300 K and 5 K neutron datasets. The neutron diffraction patterns collected at 5 K and 300 K from the 34.96°and 91.30°banks are shown in Figs. 5 and 6. The neutron patterns collected on the 63.62°and 154.40°banks are included in Figs. S1 and S2 in the Supporting information. These four banks were refined simultaneously to determine the structural parameters, which are listed in Tables 1, 2, and selected bond lengths  and angles are given in Tables 3, 4. The crystal structure of LaSr 2 Cr 2 SbO 9 at room temperature is shown in Fig. 7. Comparison of the neutron diffraction patterns collected at 5 K and 300 K shows that there is additional intensity in the 011 and 121 reflections at 5 K. Since this additional intensity is only apparent at high d-spacings it was assumed to be magnetic in origin and it could accounted for by the addition of a G-type magnetically-ordered phase, see Fig. 8. Assuming that the whole sample orders antiferromagnetically, see below, the best fit was obtained when nearest-neighbour spins were set to be aligned antiparallel along [001] giving a refined Cr(III) moment of 2.17(1) µ B. This gives an overall net magnetisation of 1.32 µ B per formula unit, which is in excellent agreement with the saturation magnetisation obtained from M(H) at 5 K.
Selected-area electron diffraction (SAED) patterns were taken of the different zones, usually connected in tilt series, from many crystallites. Note that because the cell parameters and angles only deviate slightly from those of the cubic parent perovskite, it is impossible with transmission electron microscopy to differentiate geometrically between [100], [1][2][3][4][5][6][7][8][9][10][11]    served showed the same body-centered patterns, we can conclude that the reflection conditions are hkl: h+k+l=2n, 0kl: k+l=2n, h0l: h+l=2n, hk0: h+k=2n, h: h=2n, 0k0: k=2n, 00l: l=2n, consistent with the space group and unit cell derived from the neutron diffraction data. Representative patterns along the < 110 > p and < 100 > p zones are shown in Fig. 9. The underlined indices on these patterns represent one of the possible indexations using the supercell obtained from XRD. The atomic-resolution HAADF-EDX map shown in Fig. 10 confirms that there is no ordering of Sr and La on the A site. On the B position there is an alternation in signal intensity for both Cr and Sb, but in a complementary way, as is also very clear from the combined map shown at the bottom right of the figure, i.e. both elements are present on both positions but Cr dominates one position and Sb the other. This is in agreement with the site occupancies determined from the x-ray diffraction data.

Discussion
LaSr 2 Cr 2 SbO 9 was synthesised in order to provide a perovskite analogue of La 3 Ni 2 SbO 9 that could be used in a comparison of the magnetic behaviour of a d 8 cation, where σ superexchange interactions are dominant, with that of a d 3 cation where π superexchange interactions are dominant. However, we have found that the structures are not directly comparable as La 3 Ni 2 SbO 9 crystallises in the monoclinic space group P2 1 /n whereas LaSr 2 Cr 2 SbO 9 , or La 0.667 Sr 1.333 Cr 1.333 Sb 0.667 O 6, crystallises in the triclinic space group I1. This group is uncommon amongst double perovskites but other examples include Ba 2 LaRuO 6 [21] and Sr 2 FeIrO 6 [22]. These space groups are similar in that they both introduce two crystallographi-cally-distinct six-coordinate cation sites and three independent oxygen positions, thus allowing the BO 6 octahedra to tilt about each of the three unit cell axes. However, the key difference is that the rotations of successive octahedra are out of phase along all three axes in I1 whereas in P2 1 /n two of the rotations are out of phase and one is in-phase [23]. These tilts and rotations are smaller in LaSr 2 Cr 2 SbO 9 , as is reflected by the B-O-B′ bond angles given in Table 4. All three bond angles in LaSr 2 Cr 2 SbO 9 are larger than those in La 3 Ni 2 SbO 9 , the average B-O-B′ bond angles being 167.1°and 154.1°respectively at 300 K. The fact that the B-O-B′ bond angles are much closer to 180°i n LaSr 2 Cr 2 SbO 9 means that the antiferromagnetic superexchange interactions are likely to be much stronger than in La 3 Ni 2 SbO 9 .
Another important difference between the two compounds is that there is full B-site ordering in La 3 Ni 2 SbO 9 whereas in LaSr 2 Cr 2 SbO 9 there is a partial mixing of the cations such that the 2g site is only 86.8% occupied by Cr 3+ . This is not surprising given that there are smaller differences in charge and size between Cr 3+ and Sb 5+ than between Ni 2+ and Sb 5+ . This increased site disorder makes it more probable that a Cr 3+ cation will be surrounded by 6 nearest-neighbour (NN) Cr 3+ cations and also introduces the possibility of an antimony cation being surrounded by one of more NN antimony cations.
In a perovskite compound there are three types of superexchange interaction between six-coordinate cations. These are nearest-neighbour (J1), next-nearest neighbour (J2) and third nearest-neighbour (J3) superexchange interactions as illustrated in Fig. 11. To eliminate the effect of the J1 interaction one can look at the cation-ordered perovskites Sr 2 CrSbO 6 and Ca 2 CrSbO 6 , where in both cases there is nearly complete 1:1 ordering of the B-site cations [24]. The mean B-O-B′ bond angle of Sr 2 CrSbO 6 is comparable to LaSr 2 Cr 2 SbO 9 at 169.2°, while the mean B-O-B′ bond angle of Ca 2 CrSbO 6 is closer to that of La 3 Ni 2 SbO 9 at 152.47°. Sr 2 CrSbO 6 is an A-Type antiferromagnet with T N =12 K and Ca 2 CrSbO 6 is a ferromagnet with T C =16 K. LaSr 2 Cr 2 SbO 9 has a ferrimagnetic transition temperature of 150 K, which is too high a temperature to be attributable to the J3 interaction as demonstrated by CaCu 3 Ti 4 O 12 , where the antiferromagnetic order below 25 K has been shown by x-ray absorption spectroscopy to originate from the Cu-O-Ti-O-Cu superexchange path [25]. The transition is also much higher in temperature than the J2-driven antiferromagnetic transition of Sr 2 CrSbO 6, thus suggesting that the J1 interaction is dominant in this system. The strength of the J1 interaction is indicated by the transition temperature of LaCrO 3 , 290 K [19]. The ferrimagnetic transition of LaSr 2 Cr 2 SbO 9 is lower due to the magnetic dilution of the B sites with~33% diamagnetic Sb. It should be noted that the maximum in the FC curve of LaSr 2 Cr 2 SbO 9 at 14 K is close to the antiferromagnetic transition temperature of Sr 2 CrSbO 6 so it is possible that this feature is caused by the increase in significance of J2 and J3 superexchange interactions. La 2 SrNi 2 TeO 9 also has partial cation ordering with the 2c site having a Ni 2+ :Te 6+ ratio of 0.83(3):0.17(3) and the 2d site a ratio of 0.50(3):0.50(3), which is very similar to the extent of the B-site cation order in LaSr 2 Cr 2 SbO 9 [11]. However, La 2 SrNi 2 TeO 9 is a spin glass with regions of C-and G-type cation order that are estimated to comprise of 19(2) wt% and 17(2) wt% of the sample, respectively. No Bragg reflections corresponding to C-type magnetic order were observed for LaSr 2 Cr 2 SbO 9 . The mean B-O-B′ bond angle in La 2 SrNi 2 TeO 9 at 300 K is 159.3°, which is between those of LaSr 2 Cr 2 SbO 9 and La 3 Ni 2 SbO 9 . The smaller bond angle will weaken the J1 superexchange interaction in La 2 SrNi 2 TeO 9 and the fact that the superexchange interactions are σ rather than π mediated may be responsible for the different magnetic properties. The high degree of nanoscale [100][010] twinning that was found to occur in La 2 SrNi 2 TeO 9 might also be a factor.
However, LaSr 2 Cr 2 SbO 9 is not a simple ferrimagnet as the ac susceptibility clearly shows a frequency dependence of the transition temperature akin to that of a spin glass. Furthermore, the refined Cr(III) moment at 5 K of 2.17(1) µ B and the effective moment of 2.54(18) µ B extracted from the Curie-Weiss fit are both lower than the expected values of~2.5 µ B and 3.7-3.9 µ B [26]. Similar behaviour was seen in our study of La 3 Ni 2 SbO 9 [7,9]. In that case, a moment of 2.2(1) µ B per Ni 2+ cation was extracted from the Curie-Weiss fit, rather than the expected 2.83 µ B , and no magnetic scattering was present in the neutron diffraction pattern [7]. In the present case we cannot place too much emphasis on the value of the effective moment because our data do not extend very far above the temperature of the ferrimagnetic transition. The moment refined from the neutron diffraction data is always expected to be reduced from the theoretical value of 3 µ B by covalency in the Cr-O bonds, but the observed value is lower than in those reported in simple, comparable compounds, for example 2.63(3)   Table 3 Selected bond lengths (Å) in LaSr 2 Cr 2 SbO 9 at room temperature and 5 K.
Room temperature 5 K µ B in LaCrO 3 [27]. (However, we must point out that an even lower Cr(III) moment of 1.64(4) µ B was reported for Sr 2 CrSbO 6 [24].) One possible explanation for the frequency dependence of the transition temperature and the reduced value of the ordered moment is that the entire sample is not involved in long-range magnetic order due to the disruption caused by the presence of Sb-O-Sb NNs and variations in the relative strengths of competing superexchange interactions in the affected regions. We have previously argued that in La 3 Ni 2 SbO 9 there are magnetically isolated domains that only co-align to give long-range magnetic order on the application of an applied magnetic field. While the majority of LaSr 2 Cr 2 SbO 9 clearly exhibits long-range magnetic order that is detectable by neutron diffraction there may still be some magnetically isolated regions that do not contribute to the magnetic Bragg peaks. If we assume that there are regions of the sample that are not fully ordered and assign each ordered Cr(III) a moment of 2.6 µ B then only 83.5(4) % of our sample is involved in the long-range G-type magnetic order. We propose that the remaining atomic moments behave in a glassy fashion and are thus responsible for the frequency dependence of the ac susceptibility.

Conclusion
Our attempts to make a ferrimagnet based on the unequal occupation by magnetic cations of two distinct but similar sites failed in the case of La 3 Ni 2 SbO 9 but they have succeeded in the case of LaSr 2 Cr 2 SbO 9 , which orders ferrimagnetically below 150 K. However, not all of the Cr 3+ ions are involved in the long-range magnetic order; the decoupled spins behave in a glass-like manner. It has been argued that, as a consequence of small differences in the crystal structures, stronger superexchange interactions are present in LaSr 2 Cr 2 SbO 9 than in La 3 Ni 2 SbO 9 and La 2 SrNi 2 TeO 9 and that the increase in strength facilitates the establishment of magnetic coherence in the former, despite the presence of cation disorder, rather than the formation of a dominant spin-glass phase, as occurs in La 2 SrNi 2 TeO 9 , or the forma- Table 4 Selected bond angles (°) in LaSr 2 Cr 2 SbO 9 , La 3 Ni 2 SbO 9 [7] and La 2 SrNi 2 TeO 9 [11] at room temperature and 5 K.  . 7. The crystal structure of LaSr 2 Cr 2 SbO 9 generated from the structural parameters refined from the GEM data collected at 300 K. Green and yellow octahedra represent BO 6 and B′O 6 octahedra, respectively. The A cations are represented by blue circles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) tion of ferrimagnetic microdomains, as occurs in La 3 Ni 2 SbO 9 . Thus it is appropriate to call LaSr 2 Cr 2 SbO 9 a frustrated ferrimagnet rather than a relaxor ferromagnet.