Anomalous planar Hall effect in two-dimensional trigonal crystals

Abstract

It is well known that the planar Hall effect (PHE) is deeply intertwined with the anisotropic magnetoresistance (AMR) characterizing strongly spin-orbit coupled materials. The amplitude of the PHE is indeed precisely set by the AMR magnitude, and vanishes when the driving electric field is aligned with the external magnetic field. Here we demonstrate that two-dimensional trigonal crystals with strong spin-orbit coupling can display a PHE of a completely different nature. This effect has a quantum origin arising from the Berry curvature of the Bloch states, and survives even when the applied current is aligned with the planar magnetic field. Moreover when the electric and magnetic fields are aligned perpendicular to a mirror line of the crystal, the PHE can occur as a second-order response at both zero and twice the frequency of the applied electric field. We demonstrate that this non-linear PHE possesses a quantum part that originates from a Zeemaninduced Berry curvature dipole.

Emergence of Unconventional Interfacial Magnetic Phenomenon in Topological Insulator-Based Magnetic Heterostructures

“…This observed anomalous signal is symmetric about B = 0, as seen in fig. 3 (e), which is different from the proposed anomalous PHR in two dimensional systems [35][36][37]. Outside region III, there is no significant ϕ dependence of R xx and R xy , conventional PHE signal of Bi 2 Te 3 is observed at high fields (B ≥ 1 T -see SI) [28].…”

Unconventional anomalous Hall effect from magnetization parallel to the electric field

“…Like the conventional AHE, PAHE changes sign as reversing the m direction. It is distinct from the planar Hall effect [11][12][13][14], which remains the same when flipping the magnetic field and originates in the anisotropic magnetoresistance.…”

Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations

“…Moreover this symmetry acts locally in momentum space since it brings the two-dimensional momentum k back to itself. These two properties imply that the Berry curvature is forced to vanish for all momenta in the two-dimensional BZ 34 . Consequently, a non-vanishing BCD can only appear in two-dimensional crystals where there is either a threefold rotation symmetry or all rotation symmetries are broken.…”