Light-induced Magnetization by Quantum Geometry

TL;DR

This work identifies a quantum-geometric origin for light-induced magnetization by linking nonlinear magneto-optical responses to the quantum metric quadrupole and the weighted quantum metric within a semiclassical Boltzmann framework. By treating spatially nonuniform light, it derives a second-order magnetization response proportional to $\tilde{E} \partial_r \tilde{E}^*$, decomposed into inverse Cotton-Mouton (LPL) and inverse Faraday (CPL) contributions through symmetry-aware tensors $\sigma^{\mathrm{LPL}}$ and $\sigma^{\mathrm{CPL}}$, with both terms governed by quantum-geometric quantities. The theory is demonstrated in two-band continuum and hexagonal lattice models, showing that breaking mirror or rotational symmetries enables nonzero responses for both light polarizations, and providing quantitative estimates suggesting detectability in realistic materials. The results offer a direct route to probe quantum geometry via nonlinear optics and to design optically controlled magnetization through geometric quantities.

Abstract

We propose a mechanism for the inverse Faraday and the inverse Cotton--Mouton effects arising from quantum geometry, characterized by the quantum metric quadrupole and the weighted quantum metric. Within a semiclassical framework based on the Boltzmann transport theory, we establish a general formalism describing light-induced magnetization in electronic systems as a second-order response to the electric field of light. Using continuum and tight-binding models, we discuss the symmetry constraints on these effects and estimate the magnitudes of the resulting magnetizations. Our results highlight a direct manifestation of quantum-geometric quantities in nonlinear magneto-optical responses and suggest a viable pathway for experimental detection.

Figures (8)

• Figure 1: Schematic illustration of light-induced magnetization by quantum geometry. In response to the linearly polarized light (LPL) and circularly polarized light (CPL), the magnetization $\bm{M}$ is induced by the quantum metric quadrupole density $\partial\partial g$ and the weighted quantum metric term $\partial\left(Gv\right)$.
• Figure 2: The quantum metric quadrupole density term $(q_0^4\sum_{i,j}\varepsilon_{zij}\partial_a\partial_ig_{jb})$ in the momentum space. The labels above each panel indicate the corresponding $(a,b)$ pairs. Parameters are $\alpha q_0=0.5,\,\beta q_0=0.8$ and $M/(\hbar v q_0)=0.3$, where $q_0$ determines the length scale of this system.
• Figure 3: The weighted quantum metric density term $(q_0^4\sum_{i,j}\varepsilon_{zij}\partial_a\left(G_{jb}v_i\right))$ in the momentum space. The labels above each panel indicate the corresponding $(a,b)$ pairs. Parameters are $\alpha q_0=0.5,\,\beta q_0=0.8$ and $M/(\hbar v q_0)=0.3$, where $q_0$ determines the length scale of this system.
• Figure 4: Calculated $\sigma^{\mathrm{LPL}}_{zab}$ and $\sigma^{\mathrm{CPL}}_{zxy}$ as a function of the chemical potential $\mu$ divided by the energy scale $\hbar vq_0$. The results are normalized by $\sigma^{\mathrm{LPL}}_0=-\tau Q^3/64q_0^2\hbar^2(1+\tau^2\omega^2)$ and $\sigma^{\mathrm{CPL}}_0=-\tau^2\omega Q^3/64q_0^2\hbar^2(1+\tau^2\omega^2)$. The parameters are chosen as $\alpha q_0=0.5,\,\beta q_0=0.8$ and $M/(\hbar v q_0)=0.3$, where $q_0$ determines the length scale of this system.
• Figure 5: Schematic illustration of the tight-binding model on hexagonal lattice. Two kinds of nearest neighbor hoppings $t_1$ and $t_2$ and staggered on-site potential $M$ are introduced. Lattice constant is $a$ and primitive lattice vectors are $\bm{a}_1=\left(3a/2,-\sqrt{3}a/2\right)$ and $\bm{a}_2=\left(3a/2,\sqrt{3}a/2\right)$. Reciprocal lattice vectors are $\bm{b}_1=\left(2\pi/(3a),-2\pi/(\sqrt{3}a)\right)$ and $\bm{b}_2=\left(2\pi/(3a),2\pi/(\sqrt{3}a)\right)$.