| Summary: | 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 α-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 ρ[over ̂] (λ[over ̂]) to (thermal) conductivity σ[over ̂] (κ[over ̂]) requires protocols beyond the widely-used simplified formula σ_{xy}=ρ_{yx}/(ρ_{xx}^{2}+ρ_{yx}^{2}) (κ_{xy}=λ_{yx}/(λ_{xx}^{2}+λ_{yx}^{2})) due to the lack of in-plane-rotational symmetry. In principle, two independent sample devices are necessary to accurately estimate the σ_{xy} (κ_{xy}). As a case study, we discuss the half-integer quantization of the in-plane thermal Hall effect in the spin-disordered state of α-RuCl_{3}. For an accurate measurement of the thermal Hall effect, it is necessary to avoid crystals with the merohedral twins contributing oppositely to κ_{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.
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