Electric field controlled second-order anomalous Hall effect in altermagnets

Abstract

Altermagnets are a recently discovered class of compensated magnets with momentum-dependent spin splittings and unusual transport properties, even without a net magnetization. In the presence of combined four-fold rotation and time-reversal ($C_4\mathcal{T}$) symmetry, linear and also second-order, driven by a Berry curvature dipole, anomalous Hall responses are forbidden in any pure $d$-wave altermagnet. Nevertheless, here we find that the nontrivial quantum metric of the occupied Bloch states allows for an electric field induced Berry curvature dipole, which generates a strong and tunable second-order Hall current, enabling it to be switched on or off by simply adjusting the relative orientation between the symmetry-reducing dc field and the ac probe field. Specifically, we investigate the electric field induced second-order anomalous Hall response in a two-dimensional Rashba-coupled hybrid altermagnet that interpolates between $d_{x^2-y^2}$ ($B_{1g}$) and $d_{xy}$ ($B_{2g}$) altermagnet symmetry, motivated by recent proposals for mixed-symmetry states. Crucially, the nonlinear signal is highly sensitive to the underlying symmetry of the altermagnetic order at specific doping levels, offering a purely electrical method to distinguish distinct altermagnetic orders. Our results position hybrid altermagnets as a promising platform for controllable nonlinear transport and spintronic applications.

12 pages, 13 figures

References in corpus (38)

• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Quantum metric-induced nonlinear transport in a topological antiferromagnet
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
• Essay: Where Can Quantum Geometry Lead Us?
• Landau Theory of Altermagnetism
• Altermagnetic Routes to Majorana Modes in Zero Net Magnetization
• X-ray Magnetic Circular Dichroism in Altermagnetic $\alpha$-MnTe
• Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Topological transition from nodal to nodeless Zeeman splitting in altermagnets
• Quantum geometry induced nonlinear transport in altermagnets
• Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
• Mirror Chern Bands and Weyl Nodal Loops in Altermagnets
• Berry connection polarizability tensor and third-order Hall effect
• Control over Berry Curvature Dipole with Electric Field in WTe2
• $\phi$ Josephson junction induced by altermagnetism
• Structure, control, and dynamics of altermagnetic textures
• Tunable band topology and optical conductivity in altermagnets
• Altermagnetism and superconductivity in a multiorbital t-J model
• Experimental evidence for Berry curvature multipoles in antiferromagnets
• Third-order intrinsic anomalous Hall effect with generalized semiclassical theory
• The quantum metric of electrons with spin-momentum locking
• Elasto-Hall conductivity and the anomalous Hall effect in altermagnets
• RKKY interaction in Rashba altermagnets
• Tuning of altermagnetism by strain
• Hybrid d/p-wave altermagnetism in Ca${}_3$Ru${}_2$O${}_7$ and strain-controlled spin splitting
• Intrinsic nonlinear conductivity induced by quantum geometry in altermagnets and measurement of the in-plane Néel vector
• Strain controlled g- to d-wave transition in altermagnetic CrSb
• Light-induced charge and spin Hall currents in materials with $C_{4}K$ symmetry
• Signatures of hidden octupolar order from nonlinear Hall effects
• Altermagnetism from coincident Van Hove singularities: application to $\kappa$-Cl
• Polarization and third-order Hall effect in III-V semiconductor heterojunctions
• Electric field induced second-order anomalous Hall transport in unconventional Rashba systems