General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Multiferroics

Background:

• The quantum anomalous Hall effect (QAHE) demonstrates quantized Hall conductivity in magnetic insulators.
• Insulators with zero Chern number exhibit zero Hall conductance in linear response.
• Understanding Hall conductivity in magnetic insulators beyond linear response is crucial.

Purpose of the Study:

• To investigate the existence and origin of nonlinear Hall conductivity in general magnetic insulators.
• To identify the relationship between nonlinear Hall conductivity and multiferroic coupling.
• To differentiate this nonlinear Hall conductivity from established quantum Hall effects.

Main Methods:

• Theoretical analysis of magnetic insulators breaking inversion symmetry.
• Calculation of nonlinear Hall conductivity quadratic to the electric field.
• Investigation of induced orbital magnetization via virtual interband transitions.
• Analysis of wavepacket motion contributions (velocity shift, positional shift, Berry curvature renormalization).

Main Results:

• A general magnetic insulator with broken inversion symmetry exhibits nonlinear Hall conductivity.
• This conductivity is quadratic to the applied electric field and linked to induced orbital magnetization.
• Three distinct contributions to wavepacket motion were identified.
• Nonlinear Hall conductivity vanishes for Landau levels in a 2D electron gas.

Conclusions:

• Nonlinear Hall conductivity represents a new type of multiferroic coupling in magnetic insulators.
• The mechanism differs from the QAHE and integer quantum Hall effect, particularly in 2D electron gas systems.
• This finding expands the understanding of transport phenomena in magnetic materials.