First-Order Spin-Reorientation Transition and Incomplete Softening of the Antiferromagnetic Resonance Mode in Multiferroic GdFe$_3$(BO$_3$)$_4$

The multiferroic ferroborate GdFe$_3$(BO$_3$)$_4$ with huntite-type structure exhibits magnetic ordering below T$N$ = 38 K and contains two magnetic subsystems associated with Gd and Fe ions. Competing anisotropies of these subsystems drive a spin reorientation transition at T${SR}$ = 10.7 K, switching the ground state from easy-axis to easy-plane. Using antiferromagnetic resonance, we investigate the spin dynamics across this transition. The observed incomplete softening of a magnon mode during both field- and temperature-induced spin-reorientation transitions indicates the first-order nature of the phase transition, which is accompanied by a discontinuous jump in the effective anisotropy field. We reproduce this behavior using a simple model that attributes the jump in the anisotropy field to the presence of an effective fourth-order anisotropy constant, responsible for the discontinuous character of the transition. Remarkably, for in-plane magnetic fields, we identify a new AFMR mode that persists from 12 K up to T$_N$. This mode likely corresponds to the dynamics of a long period incommensurate state, previously detected by resonant elastic X-ray scattering.

💡 Research Summary

This paper presents a comprehensive investigation of the spin-reorientation transition (SRT) and spin dynamics in the multiferroic compound GdFe3(BO3)4 using antiferromagnetic resonance (AFMR) spectroscopy. The crystal contains two magnetic subsystems (Fe3+ and Gd3+), whose competing anisotropies drive a temperature-induced SRT at T_SR ≈ 10.7 K, switching the ground state from an easy-axis (EA) to an easy-plane (EP) configuration. This transition can also be induced by an external magnetic field.

The core experimental finding is the incomplete softening of a magnon mode observed upon approaching the SRT from both the EA and EP sides, during both temperature- and field-induced transitions. Instead of the frequency dropping to zero as expected for a continuous (second-order) transition, it reaches a finite minimum and then jumps discontinuously to a different value. This behavior is a hallmark of a first-order phase transition, accompanied by a discontinuous jump in the effective anisotropy field, H_A.

To explain this, the authors propose a simple phenomenological model based on the free energy of the system. They show that while a pure second-order anisotropy term would lead to a continuous transition, the inclusion of an effective fourth-order anisotropy constant can create an energy barrier between the EA and EP states. This barrier causes the system to switch discontinuously from one minimum to the other at the transition point, resulting in the observed jump in H_A and the incomplete softening of the resonance mode. This higher-order anisotropy is argued to originate from the complex interplay between the Fe and Gd subsystems.

A second significant result is the discovery of a new AFMR mode (labeled mode N) for magnetic fields applied within the crystal’s basal plane (H ⟂ c). This mode persists from about 12 K all the way up to the Néel temperature (T_N = 38 K), a range where the EP state is stable. The authors suggest that this mode likely corresponds to the dynamics of a long-period incommensurate (ICM) magnetic state, which was previously detected in this temperature range by resonant elastic X-ray scattering but whose dynamical properties were unknown. This finding provides a crucial link between static magnetic ordering and the spin-wave spectrum in complex multiferroics.

The experimental work was performed on high-quality single crystals using a broadband pulsed-field AFMR spectrometer, allowing for detailed mapping of frequency-field diagrams and the observation of hysteresis effects. The data for both principal field orientations (H || c and H ⟂ c) are consistent with established magnetic phase diagrams and are analyzed using standard AFMR theory for EA and EP antiferromagnets.

In summary, this study successfully characterizes the first-order nature of the spin-reorientation transition in GdFe3(BO3)4, attributing it to the presence of effective higher-order magnetic anisotropy. Furthermore, it identifies a novel dynamical mode associated with an incommensurate magnetic phase, offering new insights into the rich spin dynamics of this multiferroic material and highlighting the power of AFMR in probing complex magnetic phase transitions and ground states.