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    Boltzmann-constrained extraction of spin splitting and momentum relaxation in d-wave altermagnets

    Y. X. Gao1,2, Z. W. Fan3, Q. S. Yao1,2,*, Y. D. Ji1,2,†, and H. Geng1,2,‡

    • *Contact author: yaoqiushi@nuaa.edu.cn
    • †Contact author: jiyanda@nuaa.edu.cn
    • ‡Contact author: genghao@nuaa.edu.cn

    Phys. Rev. B 114, 214402 – Published 2 October, 2026

    DOI: https://doi.org/10.1103/mnsj-zcyw

    Abstract

    Altermagnets exhibit spin-split electronic structure without requiring spin-orbit coupling, but transport measurements generally mix intrinsic spin splitting with extrinsic scattering. We examine this identifiability problem for a two-dimensional d-wave altermagnet within a unified semiclassical framework spanning ballistic to diffusive transport. The spin-dependent Fermi-surface anisotropy produces a pronounced size effect, where vastly different longitudinal velocities cause the two spin channels to exhibit markedly different effective relaxation lengths within the same device geometry. However, the altermagnetic coupling α and the momentum relaxation time τ0 strongly compensate each other in longitudinal conductance, producing strong parameter correlation. To address this inverse problem, we formulate a physics-informed neural network (PINN) as a differentiable Boltzmann solver with contact-injection and current-continuity losses and a particle-conserving local distribution. Driven by sparse synthetic conductance spectra, this solver uses the Fermi-level dependence of transport to recover the coupled parameters under the tested conditions, including joint inversion at 1% Gaussian noise and single-parameter extraction at noise levels up to 10%. These results demonstrate parameter recovery by combining Fermi-level-dependent transport data with a physically constrained numerical solver within the model and parameter range studied.

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