Open quantum theory of magnetoresistance in mesoscopic magnetic materials

TL;DR

This work develops a microscopic open-quantum-system theory of magnetoresistance by solving the Liouville–von Neumann equation for a hybrid electron–local-moment system with the time-convolutionless projection-operator method. MR emerges from temperature- and field-dependent spin decoherence, including spin relaxation, dephasing, and a spin-exchange field that shifts Hanle precession; the resistance is governed by the magnetization in ferromagnets and the Néel vector in antiferromagnets. The authors derive an anisotropic spin-diffusion framework and present quantitative expressions for ferromagnetic and antiferromagnetic MR, linking MR to microscopic spin-bath parameters and order parameters, thereby providing a comprehensive, testable description of MR in mesoscopic magnetic materials. The results illuminate how spin Hall effects, magnon scattering, and anisotropic relaxation conspire to produce diverse MR behaviors and offer guidance for interpreting experiments and designing spintronic devices.

Abstract

Magnetoresistance (MR) in magnetic materials arises from spin-exchange coupling between local moments and itinerant electrons, representing a challenging many-body open-quantum problem. Here we develop a comprehensive microscopic theory of MR within an open-quantum-system framework by solving the Liouville-von Neumann equation for a hybrid system of free electrons and local moments using the time-convolutionless projection operator method. Our approach reveals both ferromagnetic and antiferromagnetic MR as consequences of temperature- and field-dependent spin decoherence, encompassing spin relaxation and dephasing. In particular, the resistance associated with spin decoherence is governed by the order parameters of magnetic materials, such as the magnetization in ferromagnets and the Néel vector in antiferromagnets. This theory deepens the fundamental understanding of MR and offers guidance for interpreting and designing experiments on magnetic materials.

Figures (3)

• Figure 1: (Color online) The MR effect: An interacting and nonequilibrium problem in an open quantum system.
• Figure 2: (Color online) The MR effect arises from a two-step charge–spin conversion process in a monolayer ferromagnetic material. The left panel plots the spin Hall effect, where electric field ($\boldsymbol{E}$), the spin polarization ($\sigma_y$) and flowing direction ($\hat{z}$) of spin Hall current ($\boldsymbol{J}_{\text{SH}}$) are perpendicular to each other.
• Figure 3: (Color online) Diverse MR behaviors. (a,b) Resistivity as a function of $\hat{x}$-axis magnetic field, $B_{x}$, for different values of (a) temperature $T$ and (b) spin-exchange coupling $\mathcal{J}_{sd}$. (c,d) $\rho_{\text{L}}$ vs (c) $B_{x}$ and (d) $T$, for various $\mathcal{J}_{sd}$. The $B$- and $T$-dependent $\mathcal{B}_{sd}$ causes a minimum in resistivity with $B$ (a-c) and $T$ (d) at $B_x=\mathcal{B}_{sd}$. Other parameters: $\theta _{\mathrm{SH}}=0.1$, $S=2$, $\ell _{0}=3.0$ nm, $d_{N}=5$ nm, $E_F=1.0$ eV, $m_{F}=1.0$$m^0_e$, $\rho_{L0}=2.0\times 10^{6}$$\Omega\cdot m$, and $\mathcal{D}=1.0*10^{-6}$ m$^2$/s.