Yuan-Yuan Jiao(焦媛媛), Jian-Ping Sun(孫建平), and Qi Cui(崔琦),4

1The State Key Laboratory of Refractories and Metallury,Wuhan University of Science and Technology,Wuhan 430081,China

2Faculty of Science,Wuhan University of Science and Technology,Wuhan 430062,China

3Beijing National Laboratory for Condensed Matter Physics and Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China

4University of Chinese Academy of Sciences,Beijing 100049,China

Keywords: high-temperature and high-pressure synthesis,ferromagnet,Ca2CrSbO6

1. Introduction

Due to their physical properties and technological applications, double perovskite oxides have been widely studied in recent decades.[1-4]Studies of the double perovskite Sr2FeMoO6have been reported for its room temperature magnetoresistance (MR) and half-metallic conduction properties.[5,6]The general formula of a perovskite-derived double perovskite structure is A2BB′4O6(A = divalent cation or rare-earth metal,and B=transition metal). The ideal double perovskites can be viewed as a regular arrangement of corner-sharing BO6and B′O6octahedra occupied by the large cations(A).The crystal structure of perovskites can be divided into cubic(Fm3m),tetragonal(I4/m)and monoclinic(p2/n)based on the size of A.[7]

Among the various double perovskite oxides, A2CrSbO6(A=Ca,Sr)has received attention most due to their different magnetic structures. Retuerto et al. first synthesized the double perovskite Ca2CrSbO6and reported its structure and magnetic properties.[8]The Ca2CrSbO6shows a monoclinic structure [a=5.4932(3) ?A, b=5.4081(3) ?A, c=7.6901(5) ?A,β =90.0022(1) ?A,at 300 K],and belongs to the space group P21/n. The Cr and Sb cations are almost completely ordered in the B-sublattice of the perovskite structure. They reported that the Ca2CrSbO6behaves as a Curie-Weiss paramagnet at high temperatures withμeff=3.53(1)μBand θP=8 K.It exhibits a robust ferromagnetic component below the ordering temperature of Tc=13 K,with a saturation magnetization of 2.36μB/f.u. at 5 K.The electronic band structure and the ferromagnetic properties of the double perovskite Ca2CrSbO6,calculated by the first-principles method, were reported by Yi et al.[9]The Ca2CrSbO6was found to have a stable ferromagnetic ground state, and the spin magnetic moment per molecule was calculated to be 2.99 μB. The contribution of chromium to the total magnetic moment was found to be the maximum. These results indicate that Ca2CrSbO6is halfmetallic,and it is the first example of a ferromagnetic double perovskite containing a non-magnetic B′cation. Thus, these materials can potentially serve as alternatives to other magneto resistive compounds. Hence,we are motivated to explore the critical behavior of Ca2CrSbO6around Tcby analyzing the isotherms of magnetization M(H) with an iteration process and the Kouvel-Fisher method.

A neutron diffraction investigation of Ca2CrSbO6and Sr2CrSbO6was reported by Alonso et al.[10]According to the neutron powder diffraction (NPD) data, each of the perovskites A2CrSbO6(A = Ca, Sr) has a monoclinic crystal structure (space group P21/n). The Sr2CrSbO6exhibits antiferromagnetic(AFM)long-range ordering below TN=12 K,whereas Ca2CrSbO6has a ferromagnetic(FM)ordering below Tc=16 K.Baidya and Saha-Dasgupta studied Sr2CrSbO6and Ca2CrSbO6by using the first-principles method to get an indepth understanding of the switching from AFM to FM longrange order in Sr2CrSbO6, through replacing Sr by Ca.[11]They revealed that the first-neighbor magnetic interaction mediated by the super-exchange involving Sr/Ca dominates the second-neighbor magnetic interaction. It is the first nearestneighbor interaction that governs its physical behavior. The differences in the hybridization effect between Sr and Cr from those between Ca and Cr,and the differences in the distortion of the crystal structure caused by the difference in size between Sr2+and Ca2+ions,bring about this interesting switching of magnetic properties at the Cr sublattice.

Previous studies have focused on the different magnetic properties of Ca2CrSbO6and Sr2CrSbO6. There are a few experimental studies on the evolution of ferromagnetism of Ca2CrSbO6into antiferromagnetism of Sr2CrSbO6. We successfully obtain the nearly single-phase Ca2CrSbO6polycrystalline material by a solid-state reaction. The critical property associated with the ferromagnetic transition is characterized,and a comprehensive study on the responses of its magnetic behavior to the isovalent chemical substitution of Sr2+for Ca2+on the polycrystalline samples synthesized under highpressure is performed.

2. Experimental details

Polycrystalline Ca2CrSbO6samples were synthesized by solid-state reaction with appropriate stoichiometric amounts of CaCO3(99.99%),Cr2O3(99.97%),and Sb2O5(99.995%),which were heated in air at 800?C for 12 h,and 1100?C for 12 hours and subsequently at 1150?C for 8 h. While the other components of(Ca2?xSrx)CrSbO6(x=0.2,0.4,1.0,1.6,1.8,2.0)were obtained under high pressure and high temperature(HPHT) environment at 4 GPa and 1200?C for 30 min. All HPHT syntheses in the present study were performed with a Kawai-type multianvil module.

Phase purities in the obtained (Ca2?xSrx)CrSbO6(x =0.0, 0.2, 0.4, 1.0, 1.6, 1.8, 2.0) polycrystalline samples were first examined by powder x-ray diffraction (XRD) at room temperature with Cu Kα radiation. The XRD data were analyzed with the Rietveld method by using the FULLPROF program. The direct current(DC)magnetic susceptibility was measured with a commercial magnetic property measurement system(MPMS-III,Quantum Design)in a temperature range of 2 K-300 K under an external magnetic field ofμ0H=0.1 T.Isothermal magnetization M(H) curves were recorded in a field range of ?7 T to 7 T. The isothermal M(H) curves of Ca2CrSbO6were measured in a temperature range of 10 K-17 K,which covers the ferromagnetic transition.

3. Results and discussion

3.1. Critical behavior of Ca2CrSbO6

The temperature dependence of DC magnetic susceptibility χ(T) and its inverse χ?1(T) measured under μ0H =0.1 T in both zero-field-cooled (ZFC) and field-cooled (FC)mode are shown in Fig.1(a). The ZFC curve and FC χ(T)curve overlap with each other, and the ferromagnetic transition around Tc≈13 K is visible from the sharp rise of χ(T)(Fig.1(a)). The Curie-Weiss (CW) fitting to χ?1(T) in a temperature range of 50 K-300 K is used in the paramagnetic region above Tc. The effective moment(μeff=3.55μB)and the Weiss temperature(θCW=18.7 K)are extracted from the plots. The obtained μeffis close to the expected value of 3.87 μBfor S=3/2 of the spin-only paramagnetic Cr3+ions. The positive θCWindicates the dominant ferromagnetic exchange interaction in the system. The M(H) curve at 2 K exhibits a typical ferromagnetic behavior and reaches an expected saturation moment of 2.35μB(Fig.1(b)).These results are consistent with the previously reported data and confirm the high quality of the studied crystals.[10]

Fig.1. (a) Temperature dependence of DC magnetic susceptibility χ(T)and its inverse χ?1(T)measured in both zero-field-cooled(ZFC)mode and field-cooled(FC)mode underμ0H =0.1 T for Ca2CrSbO6,with solid line denoting Curie-Weiss (CW) fitting curve. (b) Isothermal magnetization M(H)curve at 2 K for Ca2CrSbO6. The unit 1 Oe=79.5775 A·m?1.

Fig.2. (a)Isothermal magnetization curves between 10 K and 17 K,and the modified Arrott plots of these curves with critical exponents of(b)mean-field model β =0.5,γ =1,(c)3D Heisenberg model β =0.365,γ =1.386,and(d)3D Ising model β =0.325,γ =1.241.

Usually,a series of critical exponents,β,γ,and δ,which reflects the effective magnetic interactions. is used to characterize the critical behavior of compounds around the ferromagnetic phase transition.[12]Different critical exponents are derived theoretically for different models, e.g., β =0.5 and γ =1 for the mean-field model,β =0.365 and γ =1.386 for the three-dimensional(3D)Heisenberg model,β =0.345 and γ =1.316 for the 3D XY model,and β =0.325 and γ =1.24 for the 3D Ising model.[13]These exponents are obtained by analyzing the isothermal magnetizations M(H)near Tc,viz.,

Figure 2(a) shows the isothermal magnetization curves,M versus H of Ca2CrSbO6in a temperature range of 10 K-17 K, where the demagnetization effect is revised. These M(H) data are replotted in the Arrott plot of M2versus H/M(Fig.2(b))and the modified Arrott plots of M1/βversus(H/M)1/γwith the critical exponents of the 3D Heisenberg model and the 3D Ising model (Figs. 2(c) and 2(d)). The Arrott plot (Fig.2(b)) shows the possibility of a mean-field model, but the positive slope of the M2versus H/M confirms that the paramagnet-ferromagnet transition is continuous. The modified Arrott plots (Figs. 2(c) and 2(d)) show roughly parallel straight lines, which are difficult to distinguish intuitively alternative models to describe the ferromagnetism of Ca2CrSbO6accurately.

Fig.3. Critical exponent β and γ, and critical temperatures and determined from (a) iteration process started from mean-feild Arrott plot,and(b)Kouvel-Fisher plots. (c)Critical isotherm at T =12.75 K in double logarithmic plot and linear ftiting to extract critical exponent δ, satisfying Widom scaling relation,δ =1+γ/β.

To test the reliability of our analysis for the critical behavior in Ca2CrSbO6,isotherm is plotted based on the scaling hypothesis[13]

where f+for T ＞Tcand f?for T ＜Tcare regular analytical functions and ε =T/Tc?1 is the reduced temperature.The M/|ε|βas a function of H/|ε|β+γproduces two universal curves: one is for T ＜Tcand the other is for T ＞Tc(Eq.(5)).The scaled data are obtained by using the values of β and γ obtained by the KF method and Tc=12.6 K (Fig.4); all the points indeed fall on the two curves. These well-scaled curves further confirm the reliability of the obtained critical exponents(Fig.4).

In conclusion, the critical exponents associated with the transition for Ca2CrSbO6are determined as follows: β =0.322, γ =1.241, and δ =4.84. The obtained β and γ values are consistent with the predicted values from the 3D Ising model. As is well known,the 3D Ising ferromagnet is rare in existing magnets since the spin degree of freedom is reduced.Moreover, a thorough study of specific heat is important for the critical behavior research. Therefore, a detailed specific heat study of Ca2CrSbO6may be needed to further confirm the critical behavior of Ca2CrSbO6.

Fig.4. Scaling plots for Ca2CrSbO6 below and above Tc based on critical temperature Tc=12.6 K and β =0.322,γ =1.241.

Table 1. Critical exponents of Ca2CrSbO6 and theoretical values from three models.

3.2. Effect of Sr substitution in(Ca2?xSrx)CrSbO6

Previous studies have mainly focused on the synthesis of a pure phase and the theoretical study of electronic structures. Therefore, the present results may provide a new direction for the further study of Ca2CrSbO6. According to the neutron study of Ca2CrSbO6and Sr2CrSbO6by Retuerto et al.,[10]the crystal structures of Ca2CrSbO6and Sr2CrSbO6at room-temperature are all monoclinic(space group P21/n).These double perovskites exhibit different magnetic properties. The Ca2CrSbO6exhibits long-range ferromagnetic order below Tc=16 K and a saturation magnetization of 2.36 μBat 5 K, while Sr2CrSbO6is an antiferromagnet material with a Ne′el temperature of 12 K and an ordered magnetic moment of 1.64(4) μB/Cr3+. These magnetic effects motivate us to check the mechanism of evolution of the long-range ferromagnetic order of Ca2CrSbO6into the antiferromagnetic property of Sr2CrSbO6via the substitution of Sr2+for Ca2+. The polycrystalline Ca2CrSbO6and Sr2CrSbO6are synthesized by a solid-state reaction. The XRD patterns at room temperature(Fig.5) are refined into a monoclinic structure (P21/n space group). The crystal structure of Ca2CrSbO6and Sr2CrSbO6are displayed in Fig.6. It should be noted that polycrystalline Ca2CrSbO6and Sr2CrSbO6belong to the same crystal structure. The crystal structures of Ca2CrSbO6and Sr2CrSbO6projected onto the a-b plane are illustrated in Figs. 6(c) and 6(d), respectively. The Ca/Sr atoms sit in the hollow structure formed by the corner shared CrO6and SbO6octahedra.The Ca2CrSbO6structure is found to be more distorted than the Sr2CrSbO6which is driven by the smaller ionic radius of Ca2+than that of Sr2+. These results are consistent with the theoretical calculations by Baidya and Saha-Dasgupta.[11]In their reports,the average Cr-O-Sb angle of 180?is larger for Ca compound than for Sr compound. The average Cr-O bond length shows a small expansion for Ca compound compared with that for Sr compound.

Fig.5. The rietveld refinement on the XRD pattern of polycrystalline (a)Ca2CrSbO6 and(b)Sr2CrSbO6.

The average tilting angles of Ca2CrSbO6and Sr2CrSbO6are different. The average tilting angles are estimated at ? =(180 ?θ)/2 where θ =〈Sb?O?Cr〉;[10]for A = Ca,?=13.5?,whereas the tilting is much lower for A=Sr,where ? =5?accompanied with the larger tolerance factor. This result is consistent with the previously reported values.[8]We attempt to synthsize the(Ca2?xSrx)CrSbO6solid solutions with varying Sr content by a solid-state reaction.However,the solid solutions cannot be obtained,for the melting point of mixture of Ca2CrSbO6and Sr2CrSbO6changes due to their mixing.After multiple attempts,(Ca2?xSrx)CrSbO6(x=0.2,0.4,1.0,1.6,1.8)solid solutions are obtained under high pressure and high temperature(HPHT)(4 GPa and 1200?C for 30 min).

The powder x-ray diffraction patterns of a series of(Ca2?xSrx)CrSbO6(x=0.0,0.2,0.4,1.0,1.6,1.8,2.0),forming monoclinic structure are displayed (Fig.7(a)). As expected,the lattice constant increases gradually with x increasing(Fig.7(b)), due to the larger size of Sr2+. It should be noted that the obtained V(x) does not strictly follow a linear behavior or the Vegard’s law. We believe that the deviation from Vegard’s law in the series of (Ca2?xSrx)CrSbO6is due to the different synthetic conditions between x=0.0,2.0,and x=0.2-1.8.

Fig.6. Crystal structure of (a) Ca2CrSbO6 and (b) Sr2CrSbO6. Crystal structure of (c) Ca2CrSbO6 and (d) Sr2CrSbO6 projected onto a-b plane,respectively. The CrO6 and SbO6 octahedra are colored pink and green,respectively.The Ca/Sr atoms sit in hollow formed by corner shared CrO6 and SbO6 octahedra.

Fig.7. (a) XRD pattern of polycrystalline Ca2?xSrxCrSbO6 (x=0.0, 0.2,0.4,1.0,1.6,1.8,2.0)and(b)unit-cell volume V versus Sr content x.

Figure 8 shows the magnetic susceptibility χ(T) for the series of (Ca2?xSrx)CrSbO6under μ0H =0.1 T in both the ZFC mode and FC mode. When x ＜1.0,with the increase in Sr content,the ferromagnetic transition temperature gradually moves toward lower temperature (Fig.8(a)). When x=1.0,the ferromagnetic transition becomes inconspicuous. When x ＞1.0, the ferromagnetic transition disappears and gradually changes into the antiferromagnetic transition. This is evident in χ?1(T)curves(Fig.8(b)). The inflection point TNfor x=0.18 in the plot of χ?1versus T is quite weak and is hard to define accurately. The broad peak in its derivative, dχ?1/dT,corresponds to the point where the curvature changes from convex to slight concave, and matches well to the TN≈8 K in magnetic susceptibility. With the chemical substitution of Sr2+for Ca2, the structural distortions of Ca2CrSbO6gradually diminish, and the magnetic transition gradually changes into antiferromagnetic transition as observed for Sr2CrSbO6.

Fig.8. Temperature dependence of(a)magnetic susceptibility χ(T)and(b)its inverse χ?1(T)for the series of Ca2?xSrxCrSbO6 (x=0.0,0.2,0.4,1.0,1.6,1.8,2.0)measured underμ0H =0.1 T in both zero-field-cooled(ZFC)and field-cooled(FC)modes.

Figure 9 shows the M(H) curves for the series of(Ca2?xSrx)CrSbO6under T =2 K.A steep increase in M(H)takes place between 0 and 1 T. The saturation magnetic moment approaches to ～2.35 μBin Ca2CrSbO6. With the increase in the Sr content,the saturation magnetic moment gradually decreases. When x ＞1.0, the ferromagnetic transition disappears, and the magnetic reaction gradually changes into an antiferromagnetic transition, consistent with the results of the χ(T) curves. The Tcand TNare obtained by fitting the χ(T)curves(Fig.10). The ferromagnetic transition temperature Tcdecreases with Sr varying in an x range of 0-1.0, and gradually converts into the antiferromagnetic transition. The antiferromagnetic transition temperature TNincreases with Sr content changing in an x range of 1.6-2.0. The results suggest that the continuous transition from ferromagnetism of Ca2CrSbO6to antiferromagnetism of Sr2CrSbO6is realized by doping different content of Sr in Ca2CrSbO6.

Fig.9. Isothermal magnetization curves M(H)for series Ca2?xSrxCrSbO6(x=0.0,0.2,0.4,1.0,1.6,1.8,2.0)between+7 T and ?7 T at T =2 K.

Fig.10. Tc and TN versus x for the series of Ca2?xSrxCrSbO6 (x=0.0,0.2,0.4,1.0,1.6,1.8,2.0)obtained by fitting χ(T)curves.

According to the analysis by Alonso et al.,[10]changing the A cation in A2CrSbO6(A = Sr, Ca) from Ca to Sr,causes structural distortions that can be responsible for the evolution from ferromagnetic to antiferromagnetic behavior.According to the Goodenough-Kanamori rules,[19]the direct super-exchange interaction via the half-occupied Cr:t2gorbitals would be antiferromagnetic for an ideal Cr-O-Cr angle of 180?.Retuerto et al.speculated that the antiferromagnetism in Sr2CrSbO6is because of the relatively weak,long-distance super-exchange interactions via the Cr-O-Sb-O-Cr path,thus the Ne′el temperature is relatively low.[10]The Cr-O-Sb-OCr pathways are antiferromagnetic provided that the Cr:t2gorbitals are approximately co-planar (as in Sr2CrSbO6). If the CrO6octahedra are sufficiently twisted with respect to each other,then the ferromagnetic interactions arise as observed in Ca2CrSbO6.

Combined with our magnetic susceptibility results from(Ca2?xSrx)CrSbO6,the CrO6octahedra in Ca2CrSbO6are sufficiently twisted with respect to each other and exhibit ferromagnetic interactions. We obtain the average tilting angle ? in (Ca2?xSrx)CrSbO6. For Ca2CrSbO6, ? = 13.5?;for CaSrCrSbO6, ? = 11.5?; for Sr2CrSbO6, ? = 5?. The greater degree of octahedron tilting in Ca2CrSbO6(the mean tilting angle ? =13.5?) and Sr2CrSbO6(? =5?) are consistent with the results reported by Retuerto et al.[10]With the chemical substitution of Sr2+for Ca2+,the average tilting angle graduallydecreases, the Cr:t2gorbitals gradually become co-planar, and the super-exchange interactions in the Cr-OSb-O-Cr pathways gradually increase. With the increase in Sr content,the ferromagnetic interactions in Ca2CrSbO6continuously convert into the antiferromagnetic interactions in Sr2CrSbO6. Our results showe a continuous magnetic transition between Ca2CrSbO6and Sr2CrSbO6. Further theoretical investigations are needed to achieve a comprehensive understanding of the magnetic behavior in the (Ca2?xSrx)CrSbO6systems.

4. Conclusions

In this work, we studied the ferromagnetic criticality of the double perovskite Ca2CrSbO6at the ferromagnetic transition Tc≈13 K.A comprehensive study on the response of its magnetic evolution process to the isovalent chemical substitution of Sr2+for Ca2+in polycrystalline sample synthesized under high pressure is performed.Our results demonstrate that the critical exponents associated with the transition are determined as follows: β =0.322, γ =1.241, and δ =4.84. The magnetization data in the vicinity of Tccan be scaled into two universal curves in the plot of M/|ε|βversus H/|ε|β+γ,where ε = T/Tc?1. The obtained β and γ values are consistent with the predicted values of the 3D Ising model. With the increase in the content of Sr,the(Ca2?xSrx)CrSbO6polycrystal continuously switches from ferromagnetism to antiferromagnetism.These results offer important experimental data for the ferromagnetic physical connotation study of Ca2CrSbO6. The present study will open a door for future investigating other perovskites.

Acknowledgment

We are grateful to Dr. Cheng J G for his help with the material preparation.