The discovery of quasi-two-dimensional van der Waals (vdW) magnets has provided a novel platform for exploring low-dimensional magnetism and its potential applications in two-dimensional (2D) spintronic devices. Recent advancements focus on the family of iron-based vdW magnets, including Fe_nGeTe₂ (n = 3, 4, 5), particularly Fe₄GeTe₂ and Fe_5−xGeTe₂, due to their ferromagnetic transition temperature (T_C) approaching room temperature. In the 2D limit, the Mermin-Wagner theorem suggests no spontaneous magnetic order at finite temperature; however, the uniaxial magneto-crystalline anisotropy in these vdW systems stabilizes long-range order against thermal fluctuations. The magnetism in these materials is rather complex in nature, differing from typical ferromagnets, due to the presence of different inequivalent Fe atoms in the unit cell. More recently, it has been reported that the Fe₄GeTe₂ single crystal is a metallic ferromagnet that exhibits a change in easy axis of magnetization when cooled below ∼ 120 K (T_SR), termed as the ‘spin reorientation transition’ (SRT), along with a T_C ~ 270 K, making it magnetically unique from the other 2D magnets.

In this study, through a combination of detailed electronic, magneto-transport [1], first-principles calculations [1], and electron spin resonance (ESR) spectroscopic measurements [2], we uncover emergent electronic phases in quasi-2D vdW ferromagnet Fe₄GeTe_2.

By conducting transport experiments [1] on exfoliated nanoflakes of Fe₄GeTe₂ and employing first-principle calculations [1], we identify two distinct electronic transitions in the thin limit of Fe₄GeTe₂, measured and compared in two distinct exfoliated devices with thicknesses of ∼ 95 nm (D95) and ∼ 16 nm (D16). The first transition near the T_SR is marked by a sharp resistivity drop and a sign change in the ordinary Hall coefficient, alongside maximum negative magnetoresistance (MR) and maximum anomalous Hall conductivity [1]. A second, previously unknown transition occurs around 40–50 K (T_Q), where the Hall coefficient changes sign again, resistivity shows a quadratic temperature dependence, and MR becomes positive [1]. The analysis [1] exposes competing inelastic scattering processes, while the DFT-based calculations propose two magnetic phases, elucidating observed magnetotransport phenomena.

ESR spectroscopic study [2] on Fe₄GeTe₂ provides quantitative insights into the non-trivial temperature evolution of the magnetic anisotropy - one of the main contributors to the stabilization of the magnetic order in the low-dimensional systems. At high temperatures, the total magnetic anisotropy (MA) is dominated by the demagnetization effect, with a slight contribution from the counteracting intrinsic easy-axis MA, whose growth below a characteristic temperature T_shape ≈ 150 K renders the sample seemingly isotropic at T_SR [2]. Below T_Q, the intrinsic MA becomes more complex. Thus, this spin reorientation results from the competition between the intrinsic easy-axis anisotropy of Fe₄GeTe₂ and the (extrinsic) shape anisotropy of its plate-like shape [2]. Interestingly, observed characteristic temperatures align in ESR and transport measurements [2], highlighting inherent coupling between magnetic and electronic degrees of freedom. Such a plausible mutual dependence of the spin waves and the charge carriers can open a possibility to tune the transport properties of Fe₄GeTe₂ by controlling the magnetic excitations, and vice versa, which could find an application in the next generation of spintronic devices. 

Details of  Fe₄GeTe₂: High-quality Fe₄GeTe₂ single crystals were grown [1] via the chemical vapor transport (CVT) method using I₂ as a transport agent. A single layer of Fe₄GeTe₂ consists of seven atoms: Fe1 and Fe2 arranged on both sides of the Ge atomic plane, directly connected to Te atoms on both sides, as shown in Figure 1a. The stacking of these Fe₄GeTe₂ monolayers forms a rhombohedral structure with space group R-3m. Single crystals of Fe₄GeTe₂ exhibit a ferromagnetic T_C ≈ 270 K, where dM/dT shows a minimum, followed by a spin reorientation transition at T_SR ≈ 120 K, below which the out-of-plane magnetization exceeds the in-plane value (see Figure 1c). 

Experimental Results: 

Resistivity: The in-plane resistivity (ρ_xx) of Fe₄GeTe₂ exhibits a metallic behavior (see Figure 1d) (conductivity at T_C ~ 9.6 × 10⁵ Ω⁻¹m⁻¹), with almost negligible change near the ferromagnetic transition. However, the resistivity falls dramatically below SRT. ρ_xx shows two anomalies, near T_SR (∼120 K) and T_Q (∼ 40 - 50 K), indicated by the clear kinks in the dρ_xx/dT curve. The analysis exposes competing inelastic scattering processes. At low temperature below T_Q, ρ_xx follows a perfectly quadratic behavior (ρ_xx ∝ T²), corresponding to electron-electron (e-e) scattering, confirmed by its magnetic field independent behavior below T_Q­, suggesting the Fermi liquid behaviour [1]. In the intermediate range (60-130 K), both electron-phonon (e-p) (ρ ∝ T) and electron-magnon scattering (ρ ∝ T²) contribute, confirmed by the strong magnetic field dependence [1]. At higher temperatures above 190 K, only the e-p scattering (ρ ∝ T²) mechanism dominates [1] .

Magnetoresistance: The high-field (9 T) MR [1] exhibits several interesting features (Figure 2b). MR is predominantly negative in the range between ∼ 40 K to 300 K and maximum near the SRT (T_SR), due to the suppression of e-m scattering under external magnetic fields, being ∼ 11% for D95 and ∼ 21.2% for D16 (Figure 2b). Comparatively large negative MR for D16 is possibly due to the enhanced FM interaction and reduced orbital scattering in the thinner limit [1]. Below T_Q, MR is small but positive (∼1.8% for D95 and 0.6 % for D16 at 1.6 K), quite unusual for a metallic ferromagnet. By fitting the positive MR at low temperatures (see Figure 2a inset), we observed an almost B² dependency of MR, being closer to the behavior of a typical metal having pure orbital contributions [1]. To test whether the electronic properties are isotropic, angle-dependent transverse magnetoresistance (TMR) measurements at 9 T were performed at various temperatures, as shown in Figure 2c. Below 100 K, the low-temperature data exhibit a cosine-like behavior, while above T_SR, a 90° phase shift occurs, indicating a change of the magnetic easy axis from the c-axis to the ab-plane with increasing temperature.

Hall measurements: Typically, the Hall resistivity (ρ_xy) of a ferromagnetic material can be described by the empirical formula: ρ_xy = ρ_xy^OHE + ρ_xy^AHE = R₀B + μ₀R_SM. Here, the first term is the ordinary Hall resistivity, and the second term represents the anomalous Hall resistivity. From Hall data (see Figure 3a) [1], ordinary Hall coefficient (R₀) shows the sign change in the proximity of T_SR and T_Q (see Figure 3b), indicates the change in the majority carriers from holes (positive) to electrons (negative), possibly due to Fermi surface reconstruction or a Lifshitz-like transition occurring as a result of SRT. Almost identical behavior was observed [1] in both devices, D95 and D16. The anomalous Hall coefficient (R_S) shows non-monotonic behavior, reaching a maximum near 140 K and decreasing sharply below the SRT (see Figure 3c). A material-specific scaling factor, S_H, defined as R_S = S_Hρ_xx², varies weakly above the SRT but changes significantly below it, reflecting a complex interplay between resistivity and magnetism. The DFT-based theoretical calculations [1] suggest the generation of new electron and hole Fermi surface pockets, which well explain this unusual sign change and enhanced metallicity near T_SR [1]. Also, we obtained larger anomalous Hall conductivity, angle, and scaling coefficient near T_SR [1], making it superior to other 2D magnets.

ESR measurements: The ESR spectroscopy is a unique tool [2] for its extreme sensitivity to magnetic anisotropies that enables a straightforward measurement and accurate quantification of the MA parameters of the studied magnetic material. Moreover, the direct measurement of the magnetic excitations of the studied material allowed us to address the dynamic aspects of the magnetism.

For all magnetic field orientations, the ESR spectra of Fe₄GeTe₂ consist of a single resonance line, with shoulders appearing at certain temperatures [2]. Representative spectra are shown in Ref. [2]. The extracted resonance field H_res is plotted as a function of temperature for both H || ab and H || c configurations (see Figure 4a). The maximum deviation of H_res from the expected isotropic paramagnetic resonance field (H_res^para) occurs near 200 K. It crosses H_res^para near T_cross, indicating the change of the type of total anisotropy below and above T_cross. Although H_res decreases above this temperature, a noticeable shift remains at 300 K, about 30 K above the T_C. This indicates that up to 300 K, ~30 K above T_C, the total anisotropy field doesn’t vanish due to the short-range correlations, signature of a 2D spin system [2].

The extracted total MA field H_a from all measurements is plotted as a function of temperature in Figure 4b. The total MA field [2] is given by H_a = H_int + H_D over the entire measurement temperature range. Here, H_int is the intrinsic (magneto-crystalline) anisotropy field, and H_D = 4πNM_S is the shape anisotropy field (coming from demagnetization effect due to its plate-like shape). To investigate the origin of the measured H_a, we calculated the expected H_D [2] at different temperatures using N ≈ 0.71, estimated from the sample dimensions and its saturation magnetization M_S (see Figure 4b). As observed [2], in the temperature range from 300 K to approximately 150 K, the H_a matches the sign, temperature dependence, and magnitude of the calculated H_D. This indicates that for T > T_shape ≈ 150 K, the dominant contribution to the total MA of Fe₄GeTe₂ arises from the shape anisotropy, with a minor contribution from the opposing intrinsic MA of an easy-axis type [2]. However, its growth with decreasing temperatures (below T_shape) counters the H_D, eventually leading the sample to appear isotropic near T_SR (~ at T_cross) (see Figure 4b). Below T_cross, the easy axis intrinsic MA dominates over the demagnetization effect [2]. Furthermore, just below T_Q (∼50 K), the intrinsic MA becomes even more complex, which cannot be explained by conventional spin-wave theory [2].

Thus, we have found that this spin reorientation results from the competition between the intrinsic easy-axis anisotropy of Fe₄GeTe₂ and the (extrinsic) shape anisotropy of the plate-like crystal [2].  Importantly, all the characteristic temperatures identified in the ESR experiment align with those observed in transport measurements (see Figure 4c), suggesting an inherent coupling between magnetic and electronic degrees of freedom in Fe₄GeTe₂ [2].

Read the full papers here:

References:

[1] R. Pal et al., “Spin-reorientation driven emergent phases and unconventional magnetotransport in quasi-2D vdW ferromagnet Fe₄GeTe₂”, npj 2D Materials and Applications, 8, 30, 2024, www.nature.com/articles/s41699-024-00463-y

[2] R. Pal et al., “Disentangling the Unusual Magnetic Anisotropy of the Near-Room-Temperature Ferromagnet Fe₄GeTe₂”, Advanced Functional Materials, 34, 2402551, 2024, https://doi.org/10.1002/adfm.202402551