Symmetry-based requirement for the measurement of electrical and thermal Hall conductivity under an in-plane magnetic field

Abstract

The in-plane (thermal) Hall effect is an unconventional transverse response when the applied magnetic field is in the (heat) current plane. In contrast to the normal Hall effect, the in-plane Hall effect requires the absence of certain crystal symmetries, and possibly manifests a nontrivial topology of quantum materials. An accurate estimation of the intrinsic in-plane (thermal) Hall conductivity is crucial to identify the underlying mechanisms as in the case of the Kitaev spin-liquid candidate $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. Here, we give the symmetry conditions for the in-plane Hall effect and discuss the implications that may impede the experimental evaluation of the in-plane Hall conductivity within the single-device measurement. First, the lack of symmetry in crystals can create merohedral twin domains that cancel the total Hall signal. Second, even in a twin-free crystal, the intrinsic response is potentially contaminated by the out-of-plane conduction in three-dimensional systems, which is systematically unavoidable in the in-plane Hall systems. Third, even in a quasi-two-dimensional system, the conversion of (thermal) resistivity $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\lambda}}$) to (thermal) conductivity $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}$ ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\kappa}}$) requires protocols beyond the widely-used simplified formula ${\ensuremath{\sigma}}_{xy}={\ensuremath{\rho}}_{yx}/({\ensuremath{\rho}}_{xx}^{2}+{\ensuremath{\rho}}_{yx}^{2})$ (${\ensuremath{\kappa}}_{xy}={\ensuremath{\lambda}}_{yx}/({\ensuremath{\lambda}}_{xx}^{2}+{\ensuremath{\lambda}}_{yx}^{2})$) due to the lack of in-plane-rotational symmetry. In principle, two independent sample devices are necessary to accurately estimate the ${\ensuremath{\sigma}}_{xy}$ (${\ensuremath{\kappa}}_{xy}$). As a case study, we discuss the half-integer quantization of the in-plane thermal Hall effect in the spin-disordered state of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. For an accurate measurement of the thermal Hall effect, it is necessary to avoid crystals with the merohedral twins contributing oppositely to ${\ensuremath{\kappa}}_{xy}$, while the out-of-plane transport may have a negligible effect. To deal with the field-induced rotational-symmetry breaking, we propose two symmetry-based protocols, improved single-device and two-device methods. The considerations in the paper are generally applicable to a broad class of materials and provide a useful starting point for understanding the unconventional aspects of the in-plane Hall effect.

Topics & Concepts