Signatures of hidden octupolar order from nonlinear Hall effects

Abstract

Detecting symmetry-breaking hidden orders with conventional probes has been a long-standing challenge in the field of magnetism. Higher-rank multipolar ordering $-$ anisotropic charge and magnetization distributions arising from a combination of spin-orbit coupling and crystalline environments $-$ is a quintessential example of such hidden orders, where new protocols of direct detection remain highly desirable. In this work, we propose non-linear Hall effects as a novel probe for multipolar ordering in metallic systems. Taking inspiration from the family of Pr-based heavy-fermion compounds, Pr(Ti,V)${}_2$Al${}_{20}$, we formulate a minimal cubic-lattice model of conduction electrons coupled to a ferro-octupolar order parameter. The time-reversal-breaking order leads to a band structure that supports strong quadrupolar moments of the Berry curvature (BC). Using a semi-classical Boltzmann formalism in conjunction with a symmetry analysis, we demonstrate that the BC quadrupoles produce a third harmonic generation of the Hall voltage $[V_H(3\omega )]$ measurable in an AC Hall experiment. Properties of the Hall response such as its anisotropy, its dissipationlessness, and its dependence on the order parameter are also examined. Our work encourages a new realm of investigation of multipolar ordering from non-linear transport experiments.

5+5 pages, 4+5 figures; the two authors contributed equally to this work; v2: published in Phys. Rev. B

References in corpus (31)

• Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries
• Nonlinear Hall Effects
• Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Heavy Fermion Superconductivity in the Quadrupole Ordered State of PrV2Al20
• Parity-breaking phases of spin-orbit-coupled metals with gyrotropic, ferroelectric and multipolar orders
• Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce${}_2$Zr${}_2$O${}_7$
• Fermi surface instability at the hidden-order transition of URu2Si2
• Quantum geometry induced nonlinear transport in altermagnets
• Novel Magnetism and Local Symmetry Breaking in a Mott Insulator with Strong Spin Orbit Interactions
• Berry connection polarizability tensor and third-order Hall effect
• Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles
• The case for a U(1)${}_{\pi }$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Successive Symmetry Breaking in a Jeff = 3/2 Quartet in the Spin-Orbit Coupled Insulator Ba2MgReO6
• Hidden and antiferromagnetic order as a rank-5 superspin in URu2Si2
• Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: implication to 5$d$ transition metal oxides $A$OsO${}_4$ ($A=$ K, Rb, and Cs)
• Physical properties of a candidate quantum spin-ice system Pr2Hf2O7
• Dissipation and geometry in nonlinear quantum transports of multiband electronic systems
• Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5{\mathbf{d}}^2$ Mott insulators
• Ferro-octupolar order and low-energy excitations in d${}^2$ double perovskites of Osmium
• Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion
• Sleuthing Hidden Order
• Orbital polarization and third-order anomalous Hall effect in WTe2
• Probing octupolar hidden order via Janus impurities
• Evidence for the Confinement of Magnetic Monopoles in Quantum Spin Ice
• Theory of Nonlinear Response for Charge and Spin Currents
• Lone octupole and bulk magnetism in osmate 5d2 double perovskites
• Rise and Fall of Non-Fermi Liquid Fixed Points in Multipolar Kondo Problems
• Diffraction by multipoles in a 5d2 rhenium double perovskite

Cited by in corpus (11)

• Elasto-Hall conductivity and the anomalous Hall effect in altermagnets
• Nonlinear Magnetoelectric Effect under Magnetic Octupole Order: Its Application to a $d$-Wave Altermagnet and a Pyrochlore Lattice with All-In/All-Out Magnetic Order
• Light-induced charge and spin Hall currents in materials with $C_{4}K$ symmetry
• Antichiral surface states and Su-Schrieffer-Heeger physics in rutile altermagnets
• Thermodynamic formulation of the spin magnetic octupole moment in bulk crystals
• Activation of anomalous Hall effect and orbital magnetization by domain walls in altermagnets
• Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems
• Emergence of quadrupolar order under magnetic field in $5d^2$ double perovskites
• Band Geometry Induced Third-Harmonic Generation
• Possibility of ferro-octupolar order in Ba${}_2$CaOsO${}_6$ assessed by X-ray magnetic dichroism measurements
• Electric field controlled second-order anomalous Hall effect in altermagnets