Flexocurrent-induced magnetization: Strain gradient-induced magnetization in time-reversal symmetric systems

TL;DR

This work addresses magnetization induced by strain gradients in time-reversal symmetric, nonmagnetic materials by introducing flexocurrent-induced magnetization (FCIM). It develops a general FCIM framework based on a free-fermion model where strain couples to electric quadrupoles and drives electrons via the gradient, with magnetization arising from a dissipative Kubo response characterized by \bar{M}_{\alpha} = f^{\lambda}_{\alpha\beta} \nabla_{\beta} \epsilon_{\lambda}. The authors show that FCIM is symmetry-allowed in all 21 noncentrosymmetric groups and compute finite responses in a decorated square lattice, monolayer MoS$_2$, and monolayer MoSSe, with notable enhancement near band edges in MoS$_2$-type systems. They discuss experimental detectability via NMR or magneto-optical Kerr effect, potential nonlocal strain contributions, and the extension to insulating systems where bosonic quasiparticles may mediate FCIM. The results provide a pathway to control magnetization in nonmagnetic materials through strain engineering and broaden the landscape of cross-correlation responses in quantum materials.

Abstract

Symmetry constraints determine which physical responses are allowed in a given system. Magnetization induced by strain fields, such as in piezomagnetic and flexomagnetic effects, has typically been considered in materials that break time-reversal symmetry. Here, we propose that nonuniform strain can induce magnetization even in nonmagnetic metals and semiconductors that preserve time-reversal symmetry. This mechanism differs from the conventional flexomagnetic effect: the strain gradient acts as a driving force on the electrons, generating magnetization in a manner closely analogous to current-induced magnetization. Treating the strain field as an external field, we derive a general expression for the magnetization induced by a strain gradient and demonstrate that this response is symmetry-allowed even in time-reversal symmetric systems. We apply our formulation to nonmagnetic systems that lack spatial inversion symmetry while preserving time-reversal symmetry, using a decorated square lattice, monolayer MoS$_2$, and monolayer Janus MoSSe as representative examples. We find a finite magnetization response to strain gradients, which is consistent with symmetry arguments, supporting the validity of our theoretical framework. These results offer a pathway for controlling magnetization in nonmagnetic materials using strain fields.

Figures (7)

• Figure 1: Schematic illustration of the flexocurrent-induced magnetization under $\nabla_{x}\epsilon_{xx}$. (a) A system exhibiting Rashba spin–momentum locking in the absence of external strain. (b) In the presence of a strain field with a finite strain gradient $\nabla_x \epsilon_{xx}$, the strain gradient acts as a driving force. With momentum relaxation due to scattering mechanisms such as impurity scattering, a nonequilibrium steady state with an asymmetric distribution is sustained, resulting in a finite magnetization. The shaded regions indicate asymmetric distribution of electrons in momentum space due to the strain gradient.
• Figure 2: (a) Schematic picture of the decorated square lattice. Black and red circles represent sites hosting $p$- and $s$-orbital degrees of freedom, respectively. The red sites are slightly elevated along the $z$ direction. The blue dashed square indicates the unit cell. The numbers represent the sublattice indices. (b) Two-dimensional first Brillouin zone of the decorated square lattice. (c) Nearest-neighbor hoppings for $p$-$p$ and $p$-$s$ orbitals allowed in the present C$_{4v}$ system.
• Figure 3: [(a)--(f)] Band dispersions and color maps of (a) $(\hat{L}_{x,\bm{k}})_n$, (b) $(\hat{L}_{y,\bm{k}})_n$, (c) $(\hat{L}_{z,\bm{k}})_n$, (d) $(\hat{S}_{x,\bm{k}})_n$, (e) $(\hat{S}_{y,\bm{k}})_n$, and (f) $(\hat{S}_{z,\bm{k}})_n$ at $\varepsilon_s = -2$, $\varepsilon_{p_x} = \varepsilon_{p_y} = 0$, $\varepsilon_{p_z} = 0.6$, $t = 0.5$, $t'=0.2$, $t_z = 0.1$, $\tilde{t}_z = 0.1$, $\tilde{t}=0.2$, and $\lambda_{{\rm SO}}=0.4$. [(g)--(l)] Chemical potential dependence of $f_{\alpha x}^{\lambda:{\rm dis}}/ g_{\lambda}$ for (g) $\bar{L}_x$, (h) $\bar{L}_y$, (i) $\bar{L}_z$, (j) $\bar{S}_x$, (k) $\bar{S}_y$, and (l) $\bar{S}_z$, with $k_{{\rm B}} T =0.05$ and $\eta = 0.05$.
• Figure 4: (a) Top and side views of monolayer ${\rm MoS_2}$. The blue dashed rhombus denotes the unit cell. The numbers in the side view represent the sublattice indices. (b) First Brillouin zone of monolayer ${\rm MoS_2}$. (c) Band structure of monolayer ${\rm MoS_2}$ calculated using the tight-binding model in Ref. fang2015.
• Figure 5: [(a)--(f)] Band dispersions and color maps of (a) $(\hat{L}_{x,\bm{k}})_n$, (b) $(\hat{L}_{y,\bm{k}})_n$, (c) $(\hat{L}_{z,\bm{k}})_n$, (d) $(\hat{S}_{x,\bm{k}})_n$, (e) $(\hat{S}_{y,\bm{k}})_n$, and (f) $(\hat{S}_{z,\bm{k}})_n$ for monolayer ${\rm MoS_2}$. [(g)--(l)] Chemical potential dependence of $f_{\alpha x}^{\lambda:{\rm dis}}/ g_{\lambda}$ for (g) $\bar{L}_x$, (h) $\bar{L}_y$, (i) $\bar{L}_z$, (j) $\bar{S}_x$, (k) $\bar{S}_y$, and (l) $\bar{S}_z$, with $k_{{\rm B}} T =0.05$ and $\eta = 0.05$. The length of primitive translation vectors is set to $3.18~\AA$ in (g)--(l) fang2015.