Anomalous Nernst effect in amorphous Tb-Fe-Co thin films

We conducted a comprehensive study on the compositional dependence of the anomalous Nernst effect (ANE) in amorphous (amo.) Tb-Fe-Co thin films. The anomalous Nernst coefficient strongly depends not only on the Tb composition but also on the transition metal composition, reaching a maximum of 1.8 uV/K for amo. Tb11.0(Fe50.0Co50.0) 89.0. By evaluating the electrical and thermoelectric properties, it was clarified that this maximum is achieved by the superposition of two large contributions: S_1 arising from direct transverse electron conduction due to a temperature gradient, and S_2 resulting from the combined Seebeck and anomalous Hall effects. We discovered that the anomalous Nernst conductivity, which is attributed to Berry curvature, varied significantly with the transition metal, even in an amorphous material lacking long-range crystalline order. Our research indicates that it is possible to control the electronic states that influence thermoelectric properties, even in the amorphous state.

💡 Research Summary

In this work, the authors present a systematic investigation of the anomalous Nernst effect (ANE) in amorphous Tb‑Fe‑Co thin films, focusing on how the effect depends on the alloy composition. Using RF and DC magnetron sputtering, a series of SiN‑capped amorphous films with the general formula SiN(10 nm)/amorphous Tbₓ(Fe_yCo_{100‑y})_{100‑x}(20 nm)/SiN(3 nm) were fabricated. The Tb concentration was varied from 0 to 30 at % while the Fe/Co ratio was tuned across five compositions: Fe₀Co₁₀₀, Fe₂₅Co₇₅, Fe₅₀Co₅₀, Fe₇₅Co₂₅, and Fe₁₀₀Co₀. Electron probe microanalysis confirmed the intended stoichiometries, and X‑ray diffraction verified the amorphous nature of all samples.

Magnetic measurements using an alternating gradient magnetometer revealed the classic ferrimagnetic compensation behavior of RE‑TM alloys. As Tb content increased, the net saturation magnetization (Mₛ) decreased due to antiferromagnetic coupling between Tb moments and the transition‑metal sublattice, reaching a magnetic compensation point (MCP) near 25 at % Tb. Substituting Co with Fe shifted the MCP toward the RE‑rich side, indicating that the Fe‑rich sublattice carries a larger moment than Co‑rich, and thus requires more Tb to achieve compensation.

Electrical transport was characterized by four‑probe resistivity (ρ) and Hall measurements (ρ_xy). ρ increased monotonically with Tb doping, reflecting enhanced scattering from the large spin‑orbit Tb atoms. The anomalous Hall resistivity displayed a pronounced peak for the Fe₇₅Co₂₅ composition, consistent with the intrinsic regime of the Onoda scaling diagram where Berry‑curvature‑driven AHE dominates. The Hall angle and anomalous Hall conductivity (σ_xy) were extracted, showing that the samples span both the dirty and intrinsic regimes depending on composition.

Thermoelectric measurements were performed by applying an in‑plane temperature gradient (∇T) while a perpendicular magnetic field generated a transverse voltage. The anomalous Nernst coefficient α_N was obtained from the linear relation E = α_N ∇T. Across the composition space, α_N varied from negative values (for most Fe‑Co alloys) to a maximum positive value of 1.8 µV K⁻¹ for the specific composition Tb₁₁.0(Fe₅₀Co₅₀)₈₉.0. This peak is comparable to the 2.0 µV K⁻¹ reported for amorphous Fe‑Sn, highlighting the effectiveness of Tb‑Fe‑Co as an ANE material.

The authors decompose α_N into two additive contributions: S₁, a direct transverse electron response to the temperature gradient, and S₂, a product of the longitudinal Seebeck effect (S) and the anomalous Hall effect (ρ_xy). Using the relation α_N = σ·α_xy + S·ρ_xy·σ, they calculate the anomalous Nernst conductivity σ_xy, which is directly linked to Berry curvature. σ_xy shows a strong dependence on the transition‑metal composition: it is largest for Co‑rich alloys, decreases with Fe substitution, and reaches a minimum for Fe₇₅Co₂₅. This systematic variation demonstrates that even in the absence of long‑range crystalline order, the electronic states near the Fermi level—and consequently the Berry curvature—can be tuned by the d‑electron count of the transition metal.

The paper emphasizes that the observed ANE results from the superposition of S₁ and S₂, and that the maximum α_N occurs when both contributions add constructively. The ability to switch the sign of α_N by adjusting the base pressure during sputtering (which influences Tb oxidation and effective magnetic moment) further illustrates the tunability of the effect.

In conclusion, the study provides compelling evidence that amorphous RE‑TM alloys can host sizable Berry‑curvature‑driven transport phenomena. By carefully selecting Tb content and the Fe/Co ratio, one can engineer both the magnitude and sign of the anomalous Nernst coefficient, achieving values competitive with the best known amorphous thermoelectric materials. These findings open pathways for designing flexible, low‑thermal‑resistance ANE devices such as heat‑flux sensors and spin‑caloritronic components without the need for high‑temperature annealing or crystalline ordering. The work thus bridges the gap between spin‑orbit physics traditionally associated with crystalline systems and the practical advantages of amorphous thin‑film technology.