Description
Anisotropic magnetoresistance (AMR) is a fundamental spin-dependent transport phenomenon arising from spin-orbit coupling [1,2]. In polycrystalline ferromagnets, the angular dependence of longitudinal resistivity is typically described by a two-fold term, while cubic single crystals exhibit an additional four-fold contribution due to crystal symmetry. Higher-order angular harmonics are often neglected in cubic systems.
Here, we investigate the angular dependence of AMR in high-quality epitaxial Fe(001) thin films grown on MgAl2O4(001) substrates [3]. At low temperatures, ρxx exhibits pronounced six-fold angular dependence in addition to the conventional two- and four-fold components, despite the nominal four-fold symmetry of the Fe(001) plane. Fourier-transform analysis of consecutive rotation cycles resolves higher-order harmonics up to the 18th order, which are consistent with phenomenological models based on crystal symmetry. Planar Hall effect (PHE) measurements show reciprocal angular behavior with AMR, further supporting the intrinsic, symmetry-allowed nature of high-order AMR. Thickness-dependent measurements reveal that both the 2nd- and 6th-order AMR components change sign with increasing film thickness, while temperature-dependent measurements show that the amplitude of high-order harmonics decreases with increasing temperature.
To probe the microscopic band origin of high-order AMR, we utilize quantum well state (QWS) oscillations as a band-selective tool [4,5]. Wedge-shaped Fe(001) films with thicknesses from 1-6 nm are studied, and all measured AMR harmonics (2nd, 4th, 6th, and 8th order) exhibit pronounced thickness-dependent oscillations at low temperatures with a common period of ~1.0 nm. This period matches the thickness-dependent oscillation of the projected density of states (PDOS) of the majority-spin Δ2′ band from first-principles calculations, indicating that confinement-modulated Fermi-level DOS directly regulates the amplitude of high-order AMR.
These findings demonstrate that high-order AMR is not merely a symmetry-allowed curiosity, but an intrinsic and robust feature of cubic Fe(001) films. Importantly, our results reveal that its microscopic origin is tied to the majority-spin Δ2′ band. This work highlights the fundamental role of specific electronic bands in controlling angle-dependent magnetotransport and provides a pathway to engineer high-order AMR in ferromagnetic thin films.
References
[1] T. McGuire and R. Potter, IEEE Trans. Magn. 11, 1018 (1975).
[2] P. Ritzinger and K. Výborný, R. Soc. Open Sci. 10, 230564 (2023).
[3] H. Chen, Y. Chen, Y. Feng, R. Guo, Y. Fan, H. Xu, T. Wu, Z. Guo, D. Yue, X. Jin, Y. Liu, Z. Yuan, and Y. Wu, Phys. Rev. Lett. 136, 086704 (2026).
[4] J. Li, M. Przybylski, F. Yildiz, X. D. Ma, and Y. Z. Wu, Phys. Rev. Lett. 102, 207206 (2009).
[5] Y. Chen, H. Chen, X. Shen, W. Chen, Y. Liu, Y. Wu, and Z. Yuan, Phys. Rev. Lett. 134, 136701 (2025).
