Electron-phonon coupling in magnetic materials using the local spin density approximation

TL;DR

This work extends the EPW framework to handle collinear magnetism, enabling spin-resolved electron–phonon coupling calculations via Wannier interpolation on dense grids. By validating against Abinit and applying to ferromagnetic Fe and Ni, the study shows strong spin-channel dependence in the EPC strength and transport properties, with Fe dominated by electron–phonon scattering and Ni more influenced by magnon-related processes; both Fe and Ni exhibit negligible phonon-mediated superconductivity. The results illustrate that magnetism fundamentally alters phonon dispersions, EPC, and resistivity, and that neglecting the spin degree of freedom can lead to incorrect conclusions. Overall, the approach provides a rigorous first-principles route to predict transport in magnetic materials and informs design strategies for low-loss spintronic devices, while outlining future extensions to include spin–orbit coupling and non-collinear magnetism.

Abstract

Magnetic materials are crucial for manipulating electron spin and magnetic fields, enabling applications in data storage, spintronics, charge transport, and energy conversion, while also providing insight into fundamental quantum phenomena. In numerous applications, the interaction between electrons and lattice vibrations, known as electron-phonon coupling, can be of significant importance. In that regard, we extend the EPW package to be able to interpolate the electron-phonon matrix elements combining perturbation theory and maximally localized Wannier functions. This allows to use dense momentum grids at a reasonable computational cost when computing electron-phonon-related quantities and physical properties. We validate our implementation considering ferromagnetic iron and nickel, where we explore the absence of phonon-driven superconductivity, finding that superconductivity is intrinsically suppressed. Furthermore, we evaluate the carrier resistivity at finite temperatures for both systems, considering the role of the magnetic phase in carrier transport. Our findings indicate that in the case of Fe, the primary contributor to resistivity is electron-phonon scattering. In contrast, for Ni, electron-phonon scattering constitutes less than one-third of the resistivity, underscoring a fundamental difference in the transport properties of the two systems.

Figures (8)

• Figure 1: Direct evaluation of ferromagnetic iron deformation potential for (a) spin up and (b) spin down at $\mathbf{k} = \Gamma$ for $m = n = 5$ along a $\mathbf{q}$ momentum line for all phonon modes $\nu$. Red dots are computed with Quantum ESPRESSO (QE) while blue squares are computed with Abinit. The LDA functional is used.
• Figure 2: Electronic band structure for ferromagnetic (a) Fe and (b) Ni. Red/orange (blue/cyan) lines correspond to spin $\uparrow$ ($\downarrow$) or majority (minority) channel. Phonon band structure for (c) Fe and (d) Ni with LDA (green) and PBE (orange) functionals where the black dots are experimental values from Refs. Birgeneau1964Brockhouse1967. Solid (dashed) lines correspond to QE (EPW) calculations.
• Figure 3: Deformation potential for the second to sixth lowest electronic bands in Fig. \ref{['band-interp']}(a) and \ref{['band-interp']}(b) for (a) Fe and (b) Ni at $\mathbf{k}=\boldsymbol{\Gamma}$ for $\uparrow$ (red) and $\downarrow$ (blue). Solid dots are direct evaluation of the deformation potential with Quantum ESPRESSO. The lines are the EPW interpolated deformation potential from $4^3$, $6^3$, $8^3$, $10^3$ and $12^3$$\mathbf{k/q}$ homogeneous coarse grids with a color gradient from lighter to darker representing coarser to denser grids. Both spin channels are close in Ni while a larger difference is observed for Fe.
• Figure 4: Spin resolved density of states for ferromagnetic (a) Fe and (b) Ni. Positive and negative density of states representing up (red) and down (blue) spin channels.
• Figure 5: Eliashberg spectral function for ferromagnetic (a) Fe and (b) Ni. Red lines corresponds to the spin up (majority) and blue line corresponds to spin down (minority).