Disentangling the unusual magnetic anisotropy of the near-room-temperature ferromagnet Fe$_{4}$GeTe$_{2}$

TL;DR

This work uses high-field electron spin resonance to dissect the unusual magnetic anisotropy in Fe$_{4}$GeTe$_{2}$, a near-room-temperature ferromagnet with layered, quasi-2D character. By analyzing frequency- and temperature-dependent resonance fields, the authors separate shape (demagnetization) and intrinsic magnetocrystalline contributions to the total anisotropy, revealing a dominant shape component above $T_ ext{shape}\approx 150$ K and an intrinsic easy-axis anisotropy that grows at lower temperatures, with a crossover near $T_ ext{cross}\approx 110$ K and further complexity below $T_ ext{d}\approx 50$ K. X-ray diffraction shows no lattice transition but uncovers a robust in-plane superlattice, indicating the spin reorientation is mainly magnetoelastic and electronic in origin rather than structural. The characteristic temperatures extracted from ESR align with transport measurements, suggesting a strong magnetoelectronic coupling and indicating that the observed low-dimensional magnetism persists toward monolayer behavior, which is promising for spintronic applications. The findings provide a quantitative framework for tuning magnetic and electronic properties via anisotropy management in this material system.

Abstract

In the quest for two-dimensional conducting materials with high ferromagnetic ordering temperature the new family of the layered Fe$_{n}$GeTe$_{2}$ compounds, especially the near-room-temperature ferromagnet Fe$_{4}$GeTe$_{2}$, receives a significant attention. Fe$_{4}$GeTe$_{2}$ features a peculiar spin reorientation transition at $T_\mathrm{SR} \sim 110$ K suggesting a non-trivial temperature evolution of the magnetic anisotropy (MA) - one of the main contributors to the stabilization of the magnetic order in the low-D systems. An electron spin resonance (ESR) spectroscopic study reported here provides quantitative insights into the unusual magnetic anisotropy of Fe$_{4}$GeTe$_{2}$. At high temperatures the total MA is mostly given by the demagnetization effect with a small contribution of the counteracting intrinsic magnetic anisotropy of an easy-axis type, whose growth below a characteristic temperature $T_{\rm shape} \sim 150$ K renders the sample seemingly isotropic at $T_\mathrm{SR}$. Below one further temperature $T_{\rm d} \sim 50$ K the intrinsic MA becomes even more complex. Importantly, all the characteristic temperatures found in the ESR experiment match those observed in transport measurements, suggesting an inherent coupling between magnetic and electronic degrees of freedom in Fe$_{4}$GeTe$_{2}$. This finding together with the observed signatures of the intrinsic two-dimensionality should facilitate optimization routes for the use of Fe$_{4}$GeTe$_{2}$ in the magneto-electronic devices, potentially even in the monolayer limit.

Figures (11)

• Figure 1: a) Crystal structure of Fe$_{4}$GeTe$_{2}$ featuring van der Waals layers along $c$ direction. b) Top view at the crystal structure of Fe$_{4}$GeTe$_{2}$. Te atoms are hidden. c) Local crystal structure of four Fe sites. The isosurface represents the crystal field potential, with the size proportional to the overall potential strength.
• Figure 2: Temperature dependence of the HF-ESR spectra in the $\textbf{H} \parallel c$ configuration (a, b) and $\textbf{H} \parallel ab$ configuration (c, d) at fixed excitation frequencies $\nu \sim 89$ GHz (a, c) and $\nu \sim 199$ GHz (b, d). The spectra are normalized to unity and shifted vertically for clarity. Vertical solid lines represent the expected resonance position of the paramagnetic response according to Eq. (\ref{['eq:Hnu']}).
• Figure 3: Frequency dependence of the resonance fields $H_\mathrm{res}$ at $T =$ 3 K (a), 110 K (b), 200 K (c), and 300 K (d), measured in $\textbf{H} \parallel c$ (squares) and in $\textbf{H} \parallel ab$ (circles) configurations, respectively. Dashed lines represent the paramagnetic response according to Eq. (\ref{['eq:Hnu']}) with the g-factors given in the corresponding legends. Solid lines depict the results of the best fit using Eqs. \ref{['Eq:EA']} and \ref{['Eq:EP']}. Exemplary, normalized spectra are presented for all temperatures with colors corresponding to the respective magnetic field geometries. Insets: same $\nu-H_\mathrm{res}$ plots zoomed to the low-frequency and low-field regions.
• Figure 4: Total anisotropy field $H_\mathrm{a}$ as a function of temperature. Squares represent $H_\mathrm{a}$ for the $\textbf{H} \parallel c$ configuration, and circles depict $H_\mathrm{a}$ for the $\textbf{H} \parallel ab$ configuration obtained from the frequency (closed symbols) and temperature (open symbols) dependences of the resonance position, respectively. Solid line is the calculated anisotropy field $H_{\rm D}$ given by the shape anisotropy. Stars depict the extracted intrinsic anisotropy field $H_{\rm int}$ for the $\textbf{H} \parallel c$ configuration. Vertical dashed lines and the shaded area around them indicate characteristic temperatures $T_{\rm shape}$, $T_{\rm cross}$, and $T_{\rm d}$ revealed in the analysis of the ESR data, as well as the estimation of the uncertainty region, respectively.
• Figure 5: a) Temperature evolution of the intrinsic MA constant $K_{\rm int} = H_{\rm int} / (2 M_{\rm S})$ estimated from the measurements in the $\textbf{H} \parallel c$ (diamonds) and $\textbf{H} \parallel ab$ (triangles) configurations, respectively. b) Resistivity and resistivity derivative as a function of temperature. c) Magnetoresistance and ordinary Hall coefficient as a function of temperature. Data in b) and c) is taken from Pal_arxiv2023. Vertical dashed lines and the shaded area around them in a), b) and c) indicate characteristic temperatures $T_{\rm shape}$, $T_{\rm cross}$, and $T_{\rm d}$ revealed in the analysis of the ESR data, as well as the estimation of the uncertainty region, respectively.