Re-entrant spin reorientation transition and Griffiths-like phase in antiferromagnetic TbFe 0.5 Cr 0.5 O 3

The perovskite ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_{3}$ shows two anomalies in its magnetic susceptibility at ${T}_{N}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}257$ K and ${T}_{\mathrm{SR}}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}190$ K which are, respectively, the antiferromagnetic and spin-reorientation transition that occur in the Fe/Cr sublattice. Magnetic susceptibility of this compound reveals canonical signatures of a Griffiths-like phase: a negative deviation from the ideal Curie-Weiss law and in less-than-unity power-law susceptibility exponents. Neutron-diffraction data analysis confirms two spin-reorientation transitions in this compound. The first one from ${\mathrm{\ensuremath{\Gamma}}}_{2}$ (${\mathrm{C}}_{x}, {\mathrm{G}}_{y}, {\mathrm{F}}_{z}$) to ${\mathrm{\ensuremath{\Gamma}}}_{4}$ (${\mathrm{A}}_{x}, {\mathrm{F}}_{y}, {\mathrm{G}}_{z}$) occurs at ${T}_{N}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}257$ K and a second one from ${\mathrm{\ensuremath{\Gamma}}}_{4}$ (${\mathrm{A}}_{x}, {\mathrm{F}}_{y}, {\mathrm{G}}_{z}$) to ${\mathrm{\ensuremath{\Gamma}}}_{2}$ (${\mathrm{C}}_{x}, {\mathrm{G}}_{y}, {\mathrm{F}}_{z}$) at ${T}_{\mathrm{SR}}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}190$ K in the $Pnma$ space-group setting. The ${\mathrm{\ensuremath{\Gamma}}}_{2}$ (${\mathrm{C}}_{x}, {\mathrm{G}}_{y}, {\mathrm{F}}_{z}$) structure is stable down to 7.7 K, leading to an ordered moment of 3.34(1) ${\ensuremath{\mu}}_{\mathrm{B}}/{\mathrm{Fe}}^{3+}({\mathrm{Cr}}^{3+}$). In addition to the long-range magnetic order, experimental indication of diffuse magnetism is observed in neutron-diffraction data at 7.7 K. Tb develops a ferromagnetic component along the $z$ axis at 20 K. Thermal conductivity and spin-phonon coupling of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_{3}$ studied through Raman spectroscopy are also presented in the paper. The magnetic anomalies at ${T}_{N}$ and ${T}_{\mathrm{SR}}$ do not appear in the thermal conductivity of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_{3}$, which appears to be robust up to 9 T. On the other hand, they are revealed in the temperature dependence of full-width-at-half-maximum curves derived from Raman intensities. An antiferromagnetic structure with $\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}$ arrangement of Fe/Cr spins is found as the ground state through first-principles energy calculations, supporting the experimentally determined magnetic structure at 7.7 K. The spin-resolved total and partial density of states show that ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_{3}$ is insulating with a band gap of $\ensuremath{\sim}0.12$ (2.4) eV within GGA ($\mathrm{GGA}+U$) functionals.