Twisting Magnetism: How Quantum Geometry Controls Material Response
![The Zeeman metric connection, spin-rotation Berry curvature, and spin-rotation quantum metric exhibit monopolar, dipolar, and quadrupolar characters, respectively, correlating with non-vanishing or vanishing non-equilibrium Green’s function (NGM) conductivity-a behavior consistent with time-reversal symmetry-and demonstrated in a hexagonally warped Dirac system with parameters [latex]vf=1[/latex] eV, [latex]\lambda=255[/latex] eV⋅ų at [latex]T=10[/latex] K and [latex]\chi_{0}=\left(\frac{g\mu_{B}}{2}\right)^{2}\,\mathrm{A\,m^{-1}\,T^{-2}}[/latex].](https://arxiv.org/html/2601.22019v1/x1.png)
New research reveals the fundamental link between a material’s quantum geometry and its nonlinear magnetic behavior, opening doors for designing materials with tailored magnetic properties.








