Two-component anomalous Hall and Nernst effects in anisotropic Fe$_{4-x}$Ge$_x$N thin films

A series of thin films Fe$_{4-x}$Ge$_x$N (x=0-1) was fabricated onto MgO substrates by magnetron sputtering with the aim of studying the possible enhancement of the anomalous Nernst effect (ANE), envisaged based on Density Functional Theory (DFT) calculations. The Nernst and Hall effects of the series were systematically analyzed, complemented with resistivity, magnetic, electron microscopy and Mössbauer experiments, and DFT calculations including elastic properties. The Fe$_4$N phase crystallizes in the cubic symmetry with Pm3m space group, whereas a small tetragonal distortion is realized in for x>0.35. From the comparison of the experimental isomer shift with DFT calculations, we conclude that Ge occupies the 4b site in the tetragonal I4/mcm tructure. Ferromagnetic T$_C$ decreases rapidly from 750 K for x=0 to 100 K for x=1. The tetragonal samples with x=0.8 and 1 display two-component behavior in the Hall and Nernst effects hysteresis loops, which can be analyzed as a sum of positive and negative loops with different saturation fields. This unusual behavior is a product of a combination of several factors. (1) Co-existence of two different crystallographic orientations in the tetragonal thin film, namely with the majority of c-axis and minority of a-axis normal to the film surface. (2) Opposite sign of the anomalous Hall and Nernst effects for the direction of magnetization along the a and c-axis revealed by DFT calculation. (3) The magnetocrystalline anisotropy characterized by an easy ab-plane, which is responsible for the different saturation fields for a and c-axis. The maximum ANE was determined to be 0.9 $μ$V/K for x=0 at room temperature, and -0.85 $μ$V/K for x=1 at T=50 K. The rapid increase of ANE of Fe$_3$GeN from low temperatures indicates that, were it not for its low T$_C$, it could surpass ANE of Fe$_4$N.

💡 Research Summary

In this work the authors systematically investigate the structural, compositional, magnetic, electrical and thermoelectric properties of Fe₄₋ₓGeₓN (x = 0–1) thin films grown by co‑sputtering on MgO(001) substrates at 400 °C. X‑ray diffraction shows that the Fe₄N end‑member (x = 0) crystallises in the cubic Pm3̅m perovskite‑type structure, whereas for x > 0.35 a tetragonal distortion appears and the material adopts the I4/mcm space group. The lattice parameters evolve smoothly with Ge content, giving a c/a ratio that increases from 1.008 to 1.034. Mössbauer spectroscopy combined with density‑functional theory (DFT) calculations reveals that Ge preferentially occupies the large 4b (Fe₂) site, acquiring a negative oxidation state and strengthening the Ge–Fe bond, which contracts the unit cell.

Energy‑dispersive X‑ray analysis confirms that the Fe and Ge stoichiometries are close to the target values, while the nitrogen content is slightly deficient and decreases with increasing x. Transmission electron microscopy of cross‑sectional lamellae shows a well‑defined film stack (≈487 nm Fe₄₋ₓGeₓN, ≈13 nm Al capping) and, for the tetragonal compositions (x = 0.5, 1), the coexistence of two crystallographic orientations: a majority of grains with the c‑axis normal to the film surface and a minority with the a‑axis normal. The relative fractions (≈40 % c : 60 % a for x = 0.5 and ≈80 % c : 20 % a for x = 1) are deduced from the simultaneous presence of 00ℓ and h00 reflections.

Magnetometry (SQUID and VSM) demonstrates a rapid suppression of the Curie temperature from ~750 K for Fe₄N to ~100 K for Fe₃GeN. The magnetic anisotropy is characterised by an easy ab‑plane, i.e. the c‑axis is a hard direction. This anisotropy, together with the two‑orientation microstructure, underlies the unusual transport behaviour observed.

Hall measurements separate the ordinary Hall contribution (calculated with BoltzTraP2) from the anomalous Hall conductivity (AHC) obtained via Berry‑curvature calculations. For x = 0.8 and 1.0 the Hall and Nernst hysteresis loops are not single‑valued; instead they consist of a superposition of two loops of opposite sign and different saturation fields. First‑principles calculations predict that the sign of both the anomalous Hall and anomalous Nernst conductivities reverses when the magnetisation switches from the c‑axis to the a‑axis. Because the film contains both c‑oriented and a‑oriented grains, the measured signal is the sum of a low‑field positive component (c‑oriented grains, saturating around 0.2 T) and a high‑field negative component (a‑oriented grains, saturating near 1 T). This explains the two‑component behaviour and the distinct saturation fields observed experimentally.

The anomalous Nernst effect (ANE) reaches a maximum of 0.9 µV K⁻¹ at room temperature for the undoped Fe₄N film, while Fe₃GeN exhibits –0.85 µV K⁻¹ at 50 K. Notably, the ANE of Fe₃GeN increases sharply at low temperature, suggesting that if its Curie temperature could be raised (e.g., by strain engineering or alternative dopants), it would surpass the ANE of Fe₄N.

In summary, the paper demonstrates that (i) Ge substitution drives a cubic‑to‑tetragonal transition and forces Ge onto the 4b site, (ii) the coexistence of two crystallographic orientations in the tetragonal films generates a two‑component anomalous Hall and Nernst response, and (iii) the combination of magnetocrystalline anisotropy and Berry‑curvature sign reversal with magnetisation direction accounts for the observed transport anomalies. These insights provide a clear pathway for designing Fe‑based nitride spin‑thermoelectric materials with enhanced ANE, which are promising for low‑power thermal sensors and energy‑harvesting devices. Future work should focus on increasing the Curie temperature while preserving the favorable Berry‑curvature topology, possibly through strain, alternative alloying, or multilayer architectures.