Intrinsic Nonlinear Gyrotropic Magnetic Effect Governed by Spin-Rotation Quantum Geometry

TL;DR

The work establishes a microscopic quantum-kinetic framework for nonlinear gyrotropic magnetic transport in two-dimensional materials, revealing that spin-resolved quantum geometry, encapsulated by the SRQGT and ZQGT, governs second-order responses that are silent in linear regimes. It demonstrates a clear separation: diagonal NGM conductivities are set by SRQM (displacement by SBC/SRBC) while off-diagonal contributions come from Zeeman connections (displacement) and Zeeman metric connections (conduction). Applying the theory to massless Dirac fermions, TI surface states with hexagonal warping, tilted massive Dirac cones, and PT-symmetric CuMnAs shows how specific symmetries selectively activate conduction and/or displacement channels and how Dirac-point physics enhances the response. The results provide symmetry-based design principles for engineering tailored nonlinear magnetic responses in spintronic and optoelectronic devices, making the spin-rotation geometry a practical probe of hidden spin-resolved quantum geometry in multiband systems.

Abstract

Nonlinear magnetic response driven by time-periodic magnetic fields offers a distinct route to probe spin-resolved quantum geometry beyond conventional electric-field-driven nonlinear effects. While linear magnetic responses depend on the Zeeman quantum geometric tensor, the influence of generalized spin-rotation quantum geometries on nonlinear responses has not been established. Here, we develop a microscopic quantum-kinetic framework to elucidate how the Zeeman and spin-rotation quantum geometric tensors govern nonlinear gyrotropic magnetic transport in two-dimensional systems. We derive second-order gyrotropic magnetic currents and reveal a distinct geometric separation: the off-diagonal sector is controlled by the Zeeman symplectic and metric connections, whereas the diagonal sector is dictated by the spin-rotation quantum metric and Berry curvature. This identifies the spin-rotation quantum geometric tensor as a fundamental geometric quantity unique to the nonlinear regime. Applying our theory to massless Dirac fermions, hexagonally warped topological insulator surface states, tilted massive Dirac fermions, and parity-time symmetric CuMnAs, we demonstrate how specific symmetries selectively activate conduction and displacement channels. Our findings link spin-resolved quantum geometry to nonlinear magnetic transport, offering design principles for engineering tailored nonlinear magnetic responses in optoelectronic and spintronic devices.

Figures (3)

• Figure 1: (a) The $xxy$ component of the Zeeman metric connection is plotted, exhibiting a nearly monopolar character that gives rise to a NGM conductivity. (b) The spin-rotation Berry curvature is shown, displaying a dipolar structure that also contributes to a nonvanishing NGM conductivity. (c) The spin-rotation quantum metric is plotted, revealing a quadrupolar character that results in a vanishing NGM conductivity. This behavior is consistent with time-reversal symmetry (TRS), under which the conduction NGM conductivity must vanish. (d) The chemical potential ($\mu$) dependence of the nonvanishing independent components of the displacement NGM conductivity in a hexagonally warped Dirac system is shown. The parameters used are $v_f = 1,\text{eV}$, $\lambda = 255,\text{eV}\cdot\text{\AA}^3$, $T = 10 \text{K}$ and $\chi_0 = \left(\frac{g\mu_B}{2}\right)^2 \,\mathrm{A\,m^{-1}\,T^{-2}}$.
• Figure 2: (a) The $yxy$ component of the Zeeman metric connection is plotted, exhibiting a dipolar behaviour. (b) The spin-rotation Berry curvature displays a nearly monopolar structure and (c) the off-diagonal component of spin-rotation quantum metric shows a quadrupolar character. (d) The chemical potential ($\mu$) dependence of the nonvanishing components of the conduction and displacement NGM conductivity is presented for a tilted massive Dirac system. The parameters used are $v_f = 1~\text{eV}$, $\Delta = 0.6~\text{eV}$, $t = 0.3~\text{eV}$, and $\chi_0 = \left(\frac{g\mu_B}{2}\right)^2 \,\mathrm{A\,m^{-1}\,T^{-2}}$.
• Figure 3: (a) The off-diagonal component of spin-rotation quantum metric shows a quadrupolar character. (b)The chemical potential ($\mu$) dependence of the some of the nonvanishing components of the conduction NGM conductivity is presented for a CuMnAs system. The parameters used are $t_0 = 1~\text{eV}$, $\tilde{t} = 0.08~\text{eV}$, $h_A = [0.85, 0 ,0]~\text{eV}$, $t = 0.3~\text{eV}$, $\alpha_R = 0.08~\text{eV}$, $\alpha_D = 0.0~\text{eV}$, and $\chi_0 = \left(\frac{g\mu_B}{2}\right)^2 \,\mathrm{A\,m^{-1}\,T^{-2}}$.