Realistic modelling of transport properties at finite temperature in magnetic materials by local quantization of a Heisenberg model

TL;DR

This paper tackles the challenge of quantitatively predicting the spin-disorder contribution to electrical resistivity in magnetic materials by marrying ab-initio transport with atomistic spin-disorder modeling. It introduces a semiclassical local quantization of the Heisenberg model to include quantum spin fluctuations and magnetic short-range order, demonstrated for α-Fe, and computes resistivity using a direct NEGF-KKR approach in large disordered supercells. Key findings show that quantum-informed SR-order effects improve ferromagnetic-state descriptions and that SR-order persists above the Curie temperature, contributing to an increasing SDR in the paramagnetic regime; under Matthiessen's rule, the total resistivity aligns well with experiment in α-Fe, though caveats remain regarding lattice disorder, s-d physics, and potential error cancellations. The work outlines a viable path toward ab-initio, finite-temperature transport in magnetic materials and highlights avenues for refinement, such as multi-spin quantization and first-principles determination of the spin quantum number.

Abstract

The quantitative description of the electrical resistivity of a magnetic material remains challenging to this day. Qualitatively, it is well understood that the temperature-induced lattice and spin disorder determines the temperature dependence of the resistivity. While prior publications reached good agreement with experiment in the so-called supercell or direct approach for non-magnetic materials where the spin-disorder contribution to the resistivity is negligible, an accurate, purely theoretical description of magnetic materials remains elusive. This shortcoming can be attributed to the missing accuracy in the description of the temperature-dependent spin-disorder itself. In this work, we employ a joint approach from \textit{ab-initio} transport calculations and atomistic modeling of the temperature-dependent spin-disorder. Using the example of $α$-Fe, we demonstrate that the inclusion of quantum mechanical effects using a semiclassical local quantization of the Heisenberg model significantly improves the description of the spin-disorder component to the electrical resistivity. Compared to previous approaches, this model includes the description of magnetic short-range order effects, enabling us to study temperature effects around and above the Curie temperature, where prior mean-field theory-based approaches inevitably predicted a constant contribution.

Figures (8)

• Figure 1: Visualization of trial-moves in Monte Carlo simulations in the classical case (CMC) and semiclassically quantized case corresponding to a spin quantum number of $s=2$ (SMC) for a given local magnetic field (red dashed axis) and initial spin (blue dot). Classical simulations are performed employing the Hinzke-Nowak strategy for optimized sampling. Visualized trial moves correspond to a temperature of 100 K.
• Figure 2: Schematic representation of the transport geometry employed in the calculations. Lead atoms (blue) are infinitely repeated in positive and negative transport directions. The length of the scattering region, i.e., the thermally disordered material (orange), is modulated to extract the specific resistivity without any effects from the leads. The used $4\times 4$ in-plane supercells are periodically continued (gray).
• Figure 3: Temperature-dependent reduced magnetization for SMC and CMC simulations compared to experimental values taken from ref. crangle_magnetization_1971. MC simulations were performed for $22\times 22\times 22$bcc unit cells. 50,000 equilibration passes are performed before averaging the magnetization over 1,000 spin-cell passes.
• Figure 4: Temperature dependence of the normalized spin correlation functions for nearest and next nearest neighbors in CMC and SMC simulations. Correlators result from averaging scalar products over all spins in a $22\times 22\times 22$bcc cells supercell, equilibrated over 50,000 passes.
• Figure 5: Distribution of nearest neighbor correlators below ($700$ K) and above ($1100$ K) the Curie temperature, for CMC and SMC simulations.