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arXiv · 2602.03597

Quantum Christoffel Nonlinear Magnetization

Xiao-Bin Qiang·Xiaoxiong Liu·Hai-Zhou Lu·X. C. Xie
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Abstract

The Christoffel symbol is an essential quantity in Einstein's general theory of relativity. We discover that an electric field can induce a nonlinear magnetization in quantum materials, described by a Christoffel symbol defined in the Hilbert space of quantum states (quantum Christoffel symbol). Quite different from the previous scenarios, this orbital magnetization does not need spin-orbit coupling and inversion symmetry breaking. Through symmetry analysis and first-principles calculations, we identify a number of point groups and 2D material candidates (e.g., BiF$_3$, ZnI$_2$, and Ru$_4$Se$_5$) that host this quantum Christoffel nonlinear magnetization. More importantly, this nonlinear magnetization allows the quantum Christoffel symbol to be probed by optical techniques such as magneto-optical Kerr spectroscopy or transport measurements such as tunneling magneto-resistance. This quantum Christoffel nonlinear magnetization gives a paradigm of how geometry dictates physics.

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Xiao-Bin Qiang, Xiaoxiong Liu, Hai-Zhou Lu, X. C. Xie. 2026-02-03. Quantum Christoffel Nonlinear Magnetization. https://doi.org/10.1103/4kmy-59l9

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