[Paper Review] Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets

Da Ma, Arpit Arora+2 more|PubMed|Oct 26, 2022

Topological Materials and Phenomena6 citations

TL;DR

This paper proposes a novel anomalous skew-scattering nonlinear Hall effect (ASN) in PT-symmetric antiferromagnets, where spin-dependent skew-scattering and Berry curvature cooperate to generate a second-order nonlinear Hall current despite the vanishing of intrinsic and conventional extrinsic Hall effects under PT symmetry. The key result is that ASN produces helicity-dependent chiral photocurrents in the THz range, enabling a new probe of antiferromagnetic order.

ABSTRACT

Berry curvature and skew scattering play central roles in determining both the linear and nonlinear anomalous Hall effects. Yet in PT-symmetric antiferromagnetic metals, Hall effects from either intrinsic Berry curvature mediated anomalous velocity or the conventional skew-scattering process individually vanish. Here we reveal an unexpected nonlinear Hall effect that relies on both Berry curvature and skew-scattering working in cooperation. This anomalous skew-scattering nonlinear Hall effect (ASN) is PT even and dominates the low-frequency nonlinear Hall effect for PT-symmetric antiferromagnetic metals. Surprisingly, we find that in addition to its Hall response, ASN produces helicity dependent photocurrents, in contrast to other known PT-even nonlinearities in metals that are helicity blind. This characteristic enables us to isolate ASN and establishes new photocurrent tools to interrogate the antiferromagnetic order of PT-symmetric metals.

Motivation & Objective

• To resolve the paradox of whether Berry curvature and skew-scattering can produce nonlinear Hall effects in PT-symmetric antiferromagnets, where both intrinsic and conventional extrinsic Hall effects vanish.
• To identify a new mechanism—ASN—that arises from the cooperative action of spin-dependent anomalous velocity and skew-scattering distribution, surviving under PT symmetry.
• To demonstrate that ASN generates helicity-dependent chiral photocurrents in the metallic limit, contrasting with other PT-even nonlinearities that are helicity-blind.
• To establish ASN as a dominant, extrinsic nonlinear Hall response in clean PT-symmetric antiferromagnets, outperforming intrinsic nonlinear Hall effects at low frequencies.
• To provide a new experimental tool for probing antiferromagnetic order via frequency- and helicity-resolved photocurrent measurements.

Proposed method

• Theoretical analysis of a minimal two-band Bloch Hamiltonian with spin-orbit coupling and Néel order, respecting PT symmetry, to model PT-symmetric antiferromagnetic metals.
• Derivation of the anomalous skew-scattering nonlinear Hall current using a semiclassical Boltzmann approach, incorporating spin-dependent skew-scattering rates and anomalous velocity from Berry curvature.
• Use of unitary transformations to block-diagonalize the Hamiltonian and identify pseudo-spin eigenstates, enabling a valid semiclassical treatment despite broken spin quantization.
• Calculation of nonlinear Hall susceptibility (χ_xy_x) for both ASN and intrinsic nonlinear Hall (INH) mechanisms, comparing their frequency and chemical potential dependence.
• Analysis of the imaginary part of the susceptibility to distinguish ASN from INH, as only ASN shows frequency-dependent imaginary components.
• Numerical evaluation of nonlinear responses in a 2D CuMnAs model with Néel vector along [110], using realistic parameters (t = 1 eV, λ = 0.8t, Jₙ = 0.6t, t′ = 0.08t).

Experimental results

Research questions

• RQ1 Can a nonlinear Hall effect persist in PT-symmetric antiferromagnets when both intrinsic Berry curvature and conventional skew-scattering contributions vanish?
• RQ2 What is the nature of the nonlinear Hall response arising from the cooperation of skew-scattering and Berry curvature in PT-symmetric systems?
• RQ3 Does the proposed anomalous skew-scattering nonlinear Hall effect (ASN) produce helicity-dependent photocurrents, and if so, how can it be distinguished from other PT-even nonlinearities?
• RQ4 How does the ASN response compare quantitatively to the intrinsic nonlinear Hall effect in terms of magnitude and frequency dependence in the clean limit?
• RQ5 Can the frequency- and helicity-resolved photocurrents mediated by ASN serve as a diagnostic tool for probing antiferromagnetic order?

Key findings

• The anomalous skew-scattering nonlinear Hall effect (ASN) is PT-even and survives in PT-symmetric antiferromagnets, despite the vanishing of both intrinsic and conventional extrinsic Hall effects.
• ASN dominates the low-frequency nonlinear Hall response in clean PT-symmetric antiferromagnets, outperforming the intrinsic nonlinear Hall effect (INH) in magnitude under realistic scattering times (τ ≈ 15–40 fs).
• The imaginary part of the ASN susceptibility is nonzero and frequency-dependent, while the INH susceptibility is real, enabling clear experimental distinction between the two mechanisms.
• ASN generates helicity-dependent chiral photocurrents in the THz range, a unique feature absent in other known PT-even nonlinearities in metals.
• In the 2D CuMnAs model with Néel vector along [110], ASN susceptibility exceeds INH by a factor of 2–3 in the conduction band, with peak values reaching ~10⁻¹³ cm²/eV for V₀ = 2.7×10⁻¹³ cm²/eV.
• The sign of ASN and INH responses are opposite in the conduction band, providing a signature for their separation in transport measurements.