Re-entrant spin reorientation transition and Griffiths-like phase in antiferromagnetic ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$

The perovskite ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ shows two anomalies in its magnetic susceptibility at $T_N=257$ K and $T_{\mathrm{SR}}=190$ 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 ${\mathrm{\Gamma }}_2$ (${\mathrm{C}}_x, {\mathrm{G}}_y, {\mathrm{F}}_z$) to ${\mathrm{\Gamma }}_4$ (${\mathrm{A}}_x, {\mathrm{F}}_y, {\mathrm{G}}_z$) occurs at $T_N=257$ K and a second one from ${\mathrm{\Gamma }}_4$ (${\mathrm{A}}_x, {\mathrm{F}}_y, {\mathrm{G}}_z$) to ${\mathrm{\Gamma }}_2$ (${\mathrm{C}}_x, {\mathrm{G}}_y, {\mathrm{F}}_z$) at $T_{\mathrm{SR}}=190$ K in the $Pnma$ space-group setting. The ${\mathrm{\Gamma }}_2$ (${\mathrm{C}}_x, {\mathrm{G}}_y, {\mathrm{F}}_z$) structure is stable down to 7.7 K, leading to an ordered moment of 3.34(1) ${\mu }_{\mathrm{B}}/{\mathrm{Fe}}^{3+}({\mathrm{Cr}}^{3+}$). 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 $\uparrow \downarrow \uparrow \downarrow$ 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 $\sim 0.12$ (2.4) eV within GGA ($\mathrm{GGA}+U$) functionals.

Figure 1

$\mathrm{X}–$ray photoelectron spectra of (a) Cr $2p$, (b) Fe $2p$, (c) Tb $3d$, and (d) O $2p$ are shown in open circles. Solid lines are fitted peaks, deconvoluted components and background, respectively, in each graph. Oxidation state of $3+$ is inferred for Fe, Cr, and Tb from this data.

Figure 2

(a) Magnetization $M\left(T\right)$ at 100 Oe shows a bifurcation of ZFC and FC curves and anomalies at $T_N\approx$ 257 K and $T_{\mathrm{SR}}\approx$ 190 K. The inset shows the magnetization at 500 Oe. (b) Inverse susceptibility, ${\chi }^{-1}\left(T\right)$, at 500 Oe along with Curie-Weiss fit (red solid line). The upper inset shows the derivative $dM/dT$ to identify the anomalies at $T_N$ and $T_{\mathrm{SR}}$. The lower inset shows the inverse magnetic susceptibility at 100 Oe, 500 Oe, and 10 kOe, which shows that the negative curvature vanishes at higher fields. (c) The magnetization isotherms, $M\left(H\right)$, at 100 K, 220 K, 250 K, and 300 K. A weak hysteresis that develops below the $T_{\mathrm{SR}}$ is shown in the upper inset for $T$ = 100 K and the lower inset shows a magnified view of an isotherm above the $T_N$, at $T$ = 340 K.

Figure 3

(a) Power-law fit (red solid lines) to ${\chi }^{-1}\left(T\right)$ at 100 Oe is plotted in a log-log scale. $t_m$ = ($T/T_c^R–$ 1) is the reduced$–$temperature. (b) Thermoremanant magnetization, $M_{\text{TRM}}$, measured at 50 Oe, 100 Oe, and 200 Oe cooling fields, shows the onset of spin reorientation transition $T_{\text{SR}}$ and the antiferromagnetic $T_N$. The lower and upper insets show magnified regions near the $T_N$ and $T_{\mathrm{SR}}$, respectively.

Figure 4

(a) The variation of thermal conductivity, ${\kappa }_{\mathrm{t}}\left(T\right)$ of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ as a function of temperature. As seen, there is no appreciable change in ${\kappa }_t\left(T\right)$ with the application of 9 T. The magnetic anomalies at $T_N$ and $T_{\mathrm{SR}}$ seen in the derivative of magnetization are not observed in ${\kappa }_{\mathrm{t}}\left(T\right)$ or in the derivative (not shown). The blue solid line represents the minimum thermal conductivity (see text). (b) Solid and dashed lines represent $T^{1.7}$ and $T^3$ dependencies of ${\kappa }_{\mathrm{t}}\left(T\right)$, respectively.

Figure 5

Top panel: Raman spectrum of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ as a function of temperature. The most intense phonon modes are assigned. Lower panel: (a) Temperature dependence of phonon frequency obtained from the fit of the spectral profile with Lorentzian function is shown. Red solid line is a fit using the anharmonic function, Eq. (1). (b) Temperature dependence of phonon linewidth. Vertical violet dashed lines in (a) and (b) mark the positions of $T_N$and $T_{\mathrm{SR}}$.

Figure 6

(a)–(e) Rietveld refinement of the neutron powder diffraction patterns of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ at 300 K, 215 K, 100 K, 20 K, and 7.7 K. There is a weak magnetic contribution even at 300 K which is above the $T_N$, observed in magnetometry. A magnified view of the low-$Q$ region is provided in the inset of (a), (b), and (e). (f) Diffuse scattering intensity at 7.7 K, after subtracting the contribution from the empty can, along with a curve fit (solid line) using a Lorentzian function.

Figure 7

The magnetic structure of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ at (a) 300 K (${\mathrm{\Gamma }}_2$), (b) 215 K (${\mathrm{\Gamma }}_4$), and (c) 100 K (${\mathrm{\Gamma }}_2$). The ${\mathrm{\Gamma }}_2$ structure remains stable down to 7.7 K, which was the lowest probed temperature by neutrons in this study. (d), (e) The magnetic structure at 20 K and 7.7 K, respectively (magnetic moment of ${\mathrm{Tb}}^{3+}$ is multiplied by three to make it visible).

Figure 8

Total and partial DOS of ${\mathrm{TbFe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ in AFM1 configuration: Total DOS within GGA (top) and GGA$+U$ (bottom) (left) functionals; partial DOS contributions from $\mathrm{Tb}–4f, \mathrm{Fe}–3d, \mathrm{Cr}–3d<$, and $\mathrm{O}–2p$ states, respectively, within GGA (middle) and GGA$+U$ (right) functionals for the spin$–\mathrm{up}$ and spin$–$down channels.