Single-doublet model of spin reorientation

TL;DR

The paper tackles spin reorientation in rare-earth orthoferrites and orthochromites by proposing a compact 'single-doublet' free-energy framework that couples 3d-sublattice anisotropy with the splitting of the lowest 4f doublet: $\Phi(\theta)=K_1\cos2\theta+K_2\cos4\theta-kT\ln2\,\cosh(\Delta(\theta)/(2kT))$, with $\Delta(\theta)$ given by the field-induced doublet splitting. The authors derive a master equation $\alpha\mu+\beta\mu^3=\tanh(\mu/\tau)$ governing SR, where $\alpha,\beta,\gamma$ encode the anisotropy ratio $K_2/K_1$ and the doublet splittings $\Delta_a,\Delta_c$, and show how FO, SO, and mixed transitions arise in a $\mu$-$\tau$ phase diagram; they also analyze the effects of non-magnetic dilution via $\alpha(x)=\alpha/x$, $\beta(x)=\beta/x$, predicting nonlinear SR temperature shifts and possible incomplete SR at low concentrations. The framework yields explicit expressions for heat-capacity contributions, $C_{Sch}$ and $C_{SR}$, reproducing Schottky-type anomalies and SR-induced jumps, and provides analytic forms for the rare-earth moment components $m_z(\theta)$, $m_x(\theta)$ that depend on the parameter $\gamma=4K_2/K_1$; these results agree with data for YbFeO$_3$ and ErFeO$_3$. Domain-structure analysis reveals distinct SR pathways depending on $K_2$, including domain-number doubling, wall-kink formation, and phase-coexistence scenarios, offering a unified picture of SR evolution. Overall, the work presents a predictive, experimentally consistent framework for SR phenomena in related rare-earth perovskites with implications for magnetoelectric and domain-engineering applications.

Abstract

A simple theoretical model is developed to describe spin reorientation (SR) transitions in rare-earth orthoferrites and orthochromites RFeO3 and RCrO3. Within a ``single-doublet'' approach, the free energy includes anisotropy contributions from the 3d-sublattice and the splitting of the lower doublet of 4f-ions. The model predicts various types of SR transitions - first-order, second-order, and mixed - depending on anisotropy parameters. Effects of non-magnetic dilution, heat capacity anomalies, and behavior of the rare-earth magnetic moment in the SR region are analyzed.

Figures (9)

• Figure 1: $\mu-\tau$ phase diagram.
• Figure 2: $\tau-x$ phase diagram in the "high-temperature" approximation (straight lines) and in the "single-doublet" model (colored bold lines).
• Figure 3: The magnetic heat capacity behavior \ref{['heat']} for the $G_x$ phase (green line), the $G_z$ phase (red line), and the $G_{xz}$ phase (blue line).
• Figure 4: Comparison the magnetic heat capacity per mole (color lines) with the data for YbFeO$_3$moldover1971 (black dots). $R$ is the molar gas constant, $\Delta_{a} = 88 K_1$, $\Delta_{c} = 81.47 K_1$, $K_2 = 0.014 K_1$.
• Figure 5: Comparison $C/T$ (color lines) with the data for ErFeO$_3$chaudhury2009 (black dots). The red lines are $C_\textbf{Latt}/T$ approximation, and the blue line is $C_\textbf{Mag}/T + C_\textbf{Latt}/T$ at the parameters $\Delta_{a} = 200 K_1$, $\Delta_{c} = 166.3 K_1$, $K_2 = 0.012 K_1$.