Electrically Tuning Quantum-Geometric Hall States

Schematic of electric-current manipulation of the QgNLH state with different patterns of quantum geometry and magnetic orders in Mn3Sn.
Image Credit: ©Tomohiro Uchimura, Jiahao Han, and Shunsuke Fukami

Scientific Frontline: Extended "At a Glance" Summary: Electrical Control of the Quantum-Geometric Nonlinear Hall State

The Core Concept: The quantum-geometric nonlinear Hall (QgNLH) state is an unconventional quantum transport phenomenon where the transverse Hall voltage response scales with the cube of the applied electric current rather than proportionally. Researchers have successfully achieved electrical control of this state for the first time by exploiting the coupling between spin structures and quantum geometry in an electrically switchable chiral antiferromagnet.

Key Distinction/Mechanism: Unlike conventional electrical conduction, which obeys Ohm's law and standard linear Hall effects, the QgNLH state violates these linear relationships due to the geometric structure of its electronic quantum states. Instead of treating quantum geometry as a fixed, built-in material property, this mechanism uses a spintronic approach—specifically spin-orbit torque from an adjacent heavy metal layer—to actively switch the magnetic order of the chiral antiferromagnet, thus manipulating the nonlinear Hall response.

Major Frameworks/Components:

• Quantum Geometry: The underlying geometric structure of electronic quantum states that drives unconventional nonlinear voltage-current responses.
• Chiral Antiferromagnetism: The specific magnetic order observed in epitaxial thin films of \(\text{Mn}_3\text{Sn}\), whose spin structure is intrinsically linked to its electronic states.
• Third-Order Nonlinear Hall Effect: A transport phenomenon where the generated Hall voltage is proportional to the cube of the driving electric current.
• Spin-Orbit Torque: A spintronic mechanism where an electric current in an adjacent heavy metal layer exerts torque on the antiferromagnet, enabling the deterministic switching of its magnetic spin structure.

Branches of Science: Condensed Matter Physics, Quantum Mechanics, Spintronics, Materials Science, and Electromagnetism.

Future Application: This breakthrough provides a foundational approach for developing electric-current-tunable nonlinear electronics, such as advanced frequency multiplexers and rectifiers. These components could integrate seamlessly with magnetoresistive random access memory (MRAM) architectures, leveraging spintronic techniques for enhanced operational speed and energy efficiency.

Why It Matters: By demonstrating that quantum geometry can be actively and electrically controlled rather than remaining a static material property, this research bridges quantum mechanics, nonlinear electronics, and spintronics. It paves the way for on-demand manipulation of quantum states, significantly advancing the development of highly efficient, tunable, and next-generation quantum-electronic signal processing devices.

Researchers at Tohoku University and the Japan Atomic Energy Agency (JAEA) have successfully controlled a unique quantum phenomenon—the quantum-geometric nonlinear Hall (QgNLH) state—using electric current for the first time. This breakthrough was achieved by revealing and exploiting the coupling between the spin structure and the QgNLH state in an electrically switchable chiral antiferromagnet. This mechanism provides a foundational framework for developing electrically tunable devices that use quantum-geometric effects to perform nonlinear signal processing functions.

Detection of the QgNLH state in a Hall bar device of Mn3Sn. The nonlinear Hall voltage is proportional to the cube of the current.
Image Credit: ©Tomohiro Uchimura, Jiahao Han, and Shunsuke Fukami

Going Beyond Ohm's Law

Electrical conduction underpins modern electronics. In an ordinary conductor, the longitudinal voltage and current are proportional, as described by Ohm's law, while transverse voltage responses are governed by the linear Hall effect. In some materials, however, these linear laws can be violated. A typical example is the nonlinear Hall effect, in which the Hall voltage appearing in the transverse direction of the current no longer follows the usual linear relationship.

Quantum geometry—the geometric structure of electronic quantum states—plays a crucial role in producing such an unconventional nonlinear voltage-current response. The corresponding quantum-geometric nonlinear Hall (QgNLH) state is therefore of interest both as a way to explore the quantum properties of solids and as a new basis for nonlinear signal processing. For practical electronic devices, however, it requires not only observing this response but also controlling it by electric current. This has remained challenging because quantum geometry has historically been interpreted as a built-in property of the material.

Switching of the QgNLH state by alternating positive and negative current pulses.
Image Credit: ©Tomohiro Uchimura, Jiahao Han, and Shunsuke Fukami

Electrically Controlling the Response Through Magnetic Order

The research team investigated epitaxial thin films of the chiral antiferromagnet \(\text{Mn}_3\text{Sn}\). Its spin structure is closely connected to its electronic states, making \(\text{Mn}_3\text{Sn}\) a promising material to explore how the control of magnetic properties can be used to manipulate the unconventional responses from quantum geometry. They first observed a third-order nonlinear Hall effect at room temperature, a state wherein the nonlinear voltage is proportional to the cube of the current. Combining experiments with theoretical calculations, they verified that the observed effect has a quantum-geometric origin and is reversible by switching the spin structure of \(\text{Mn}_3\text{Sn}\), thereby revealing the interplay between the QgNLH state and the spin structure.

The team subsequently used spintronic approaches to electrically control the magnetic order and the associated QgNLH state. When an electric current flows in a heavy metal layer adjacent to \(\text{Mn}_3\text{Sn}\), the resulting spin-orbit torque acts on the spin structure of \(\text{Mn}_3\text{Sn}\) and is capable of switching it. In their experiment, the researchers switched the sign of the third-order nonlinear Hall response by applying current pulses with opposite polarities, thus demonstrating the electrical control of the QgNLH state through current-induced magnetic dynamics.

"We are able to realize on-demand electrical manipulation of the QgNLH state under different external conditions," noted Tomohiro Uchimura, lead author of the paper. "Deterministic switching and fluctuation of the QgNLH state can be achieved under finite and zero bias magnetic fields, respectively."

Toward Electrically Tunable Nonlinear Electronics

The corresponding authors of the paper, Jiahao Han and Shunsuke Fukami, further discussed the significance of connecting quantum geometry, nonlinear electronics, and spintronics in this study. "Instead of treating quantum geometry as a fixed property of the material, we showed how the nonlinear electronic responses from quantum geometry can be actively manipulated by electrically controlling the material's magnetic order. The approach may help to develop electric-current-tunable nonlinear devices such as frequency multiplexers and rectifiers. They have the potential to benefit from the inherent advantages of magnetoresistive random access memory (MRAM) in energy efficiency and speed, owing to the introduction of spintronic methods that made the manipulation possible."

Published in journal: Newton

Title: Electric-current manipulation of quantum-geometric nonlinear Hall state in a chiral antiferromagnet

Authors: Tomohiro Uchimura, Jiahao Han, Yasufumi Araki, Yuta Yamane, Shun Kanai, Jun’ichi Ieda, Hideo Ohno, and Shunsuke Fukami

Source/Credit: Tohoku University

Edited by: Scientific Frontline

Reference Number: phy110526_01

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