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

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 alpha-RuCl3. 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 rho<SIC> (lambda<SIC>) to (thermal) conductivity sigma<SIC> (kappa<SIC>) requires protocols beyond the widely-used simplified formula sigma xy = rho yx/(rho x2x + rho 2yx) (kappa xy = lambda yx/(lambda 2 xx+ lambda 2yx)) due to the lack of in-plane-rotational symmetry. In princi-ple, two independent sample devices are necessary to accurately estimate the sigma xy (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 alpha-RuCl3. For an accurate measurement of the thermal Hall effect, it is necessary to avoid crystals with the merohedral twins contributing oppositely to 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.