Electric Fields Induce Magnetism in Normally Non-Magnetic Material at 200 Kelvin

Researchers have long recognised the importance of geometric characterisation in understanding fundamental physics, but its connection to magnetism has remained elusive. Now, Xuan Qian, Wenkai Zhu, and Yuqing Huang, from the Institute of Semiconductors, Chinese Academy of Sciences, alongside Xiao-Bin Qiang and Yiyuan Chen of Southern University of Science and Technology, and Hai-Zhou Lu, demonstrate an electric-field-induced nonlinear magnetization in the semimetal WTe using second-harmonic magneto-optical Kerr effect spectroscopy. Their observations reveal a robust nonlinear signal scaling quadratically with current and persisting up to 200 K, which theoretical modelling links directly to the Christoffel symbol, a quantity analogous to that describing spacetime geometry in general relativity. This work establishes a crucial link between quantum geometry and nonlinear magnetization, potentially offering a new geometric perspective for the development of future orbitronic devices.

Electric-field control of nonlinear magnetization via quantum geometry in tungsten ditelluride offers new routes to spintronic devices

Scientists have uncovered an intrinsic link between quantum geometry and nonlinear magnetization within the nonmagnetic semimetal WTe2. This breakthrough reveals electric-field-induced nonlinear magnetization, a phenomenon previously unexplored in this material, and demonstrates its existence through a highly sensitive second-harmonic magneto-optical Kerr effect (SMOKE) spectroscopy.
The research establishes that this magnetization, scaling quadratically with applied current, persists up to 200 K, opening new avenues for understanding magnetic responses in nonmagnetic materials. Theoretical modelling and scaling analyses confirm that orbital contributions dominate this nonlinear magnetization, connecting it directly to the quantum Christoffel symbol.

This work highlights the importance of quantum geometry, traditionally used to characterize the structure of quantum states, in understanding magnetic phenomena. Researchers developed a high-sensitivity SMOKE spectroscopy employing lock-in detection to isolate second-harmonic Kerr signals, extending conventional magneto-optical Kerr effect techniques into the nonlinear regime.

Observations reveal a robust SMOKE signal, confirming the quadratic scaling with electric field and demonstrating its stability at elevated temperatures. Symmetry analysis and calculations further pinpoint the origin of this magnetization to the deformation of Bloch wavepackets induced by the electric field.

Crucially, the observed deformation is fundamentally governed by the quantum Christoffel symbol, a geometric quantity analogous to its counterpart in Einstein’s general relativity. This establishes a direct correspondence between quantum geometry and nonlinear magnetization, suggesting a new framework for designing orbitronic devices.

Experimental data across a broad temperature range align with theoretical predictions, validating the proposed mechanism. The demonstration of mirror symmetry breaking in multilayer WTe2, confirmed through nonlinear Hall effect measurements, provides the necessary conditions for observing this nonlinear magnetization.

Nonlinear Magneto-Optical Spectroscopy and Magnetization Scaling Analysis reveal complex magnetic phenomena

Second-harmonic magneto- Kerr effect (SMOKE) spectroscopy was central to observing electric-field-induced nonlinear magnetization within the nonmagnetic semimetal WTe2. This technique detected a robust nonlinear SMOKE signal, demonstrating a quadratic scaling with applied current and persisting up to 200 K.

The sensitivity of this spectroscopic method enabled the measurement of magnetization values of 5.42 × 10−9 μB/nm2 for spin magnetization and 1.32 × 10−6 μB/nm2 for orbital magnetization, calculated for a Fermi energy of 0.2 eV, a time-to-velocity ratio of 0.3, and a scattering time of 1.1ps. To distinguish the underlying physical mechanisms, a scaling analysis was performed, building upon methods used in studies of anomalous and nonlinear Hall effects.

This analysis considered that temperature-dependent variations in metals primarily originate from the relaxation time τ, allowing response coefficients to be expressed as polynomials of the longitudinal conductivity σaa, which is proportional to τ. Experimental data confirmed that the coefficient αcaa scales linearly with σaa over a broad temperature range, as predicted by the theoretical model linking quantum-geometric nonlinear magnetization to τ.

Deviations observed below 20 K were attributed to the proximity of the Fermi level to the band edge in WTe2, where Fermi-surface broadening becomes significant. Further support for this interpretation came from the linear scaling observed between the SMOKE signal and the nonlinear Hall signal, indicating a shared dependence on relaxation time and band geometry. These consistent results from scaling analyses in figures 4(c) and 4(d) validated both the experimental observations and the theoretical framework.

Orbital dominance and geometric encoding of nonlinear magnetization coefficients reveal complex magnetic anisotropy landscapes

Calculated nonlinear magnetization coefficients reach 1.32 × 10−6 μB/nm2 for a Fermi energy of 0.2 eV, a t/v ratio of 0.3, and a scattering time of 1.1ps. This magnitude of magnetization is sufficient for detection using high-precision second-harmonic magneto-Kerr effect spectroscopy. Theoretical modeling and scaling analysis demonstrate that this nonlinear magnetization is dominated by the orbital contribution, which is approximately two orders of magnitude larger than the spin contribution.

The full geometric information of the system is encoded in the quantity Λijk n, defined by Λijk n = (F S,ij n + F O,ij n )vk n, where FS/O n represents the spin/orbital polarizability tensor for the nth band and vn is the intraband velocity. The research establishes a direct link between geometry and nonlinear magnetization, mirroring the role of the Christoffel symbol in Einstein’s general relativity.

Specifically, the second term of the orbital polarizability tensor, F O,ij n, arises from the quantum Christoffel symbol Γlkj n = 1/2(∂jgkl n + ∂kglj n −∂lgkj n). Experimental data confirms a linear scaling between the observed SMOKE signal and the longitudinal conductivity σaa across a temperature range of 8 K to 200 K.

This scaling behavior supports the prediction that the quantum-geometric nonlinear magnetization is proportional to the relaxation time τ. Further analysis reveals a linear relationship between the SMOKE signal and the nonlinear Hall signal, demonstrating consistency between experimental results and theoretical analysis.

Slight deviations observed below 20 K in the conductivity scaling are attributed to the proximity of the Fermi level to the band edge in WTe2, leading to increased Fermi-surface broadening at these temperatures. The work highlights the importance of geometric considerations in understanding magnetic phenomena and offers a pathway for designing future orbitronic devices.

Quantum Christoffel Symbol Governs Magnetization in WTe2 films

Electric-field-induced nonlinear magnetization has been observed in the nonmagnetic semimetal WTe₂ using second-harmonic magneto-Kerr effect spectroscopy. A robust nonlinear signal, scaling quadratically with current, was detected and persisted up to 200 K. Theoretical modelling and scaling analyses indicate that orbital contributions dominate this nonlinear magnetization, linking it intrinsically to the Christoffel symbol.

This work establishes a direct connection between quantum geometry and nonlinear magnetization, mirroring the role of the Christoffel symbol in describing spacetime geometry within Einstein’s general relativity. The development of high-sensitivity spectroscopy offers a new optical method for detecting weak magnetic signals and provides spatial resolution for refined measurements.

Although similar to the nonlinear Hall effect, the observed magnetization represents a distinct electric-field-induced magnetic response governed by the quantum Christoffel symbol. The authors acknowledge that Fermi-surface broadening near the band edge becomes non-negligible at the temperatures studied, potentially influencing the observed signals. Future research could explore emergent gravity effects in quantum materials and the development of next-generation orbitronic devices, building upon this experimental paradigm and fundamental framework for characterizing nonlinear magnetization.