Fig. 3: Magnetoresistance and Hall effect (\({{{{{{{\bf{H}}}}}}}}\parallel \hat{{{{{{{{\bf{z}}}}}}}}}\)).
From: Anisotropic resistance with a 90° twist in a ferromagnetic Weyl semimetal, Co2MnGa
a The field dependences of the four resistances shown in Fig. 1b at T = 200 K. b The magnetoresistance (MR) of each in-plane resistance for Sample N2 (T = 20 K). The zero-field values have been removed in order to resolve the weak MR of each channel. These are: R14,23 = 0.31 Ω, R12,43 = 1.71 Ω, \({R}_{{1}^{{\prime} }{4}^{{\prime} },{2}^{{\prime} }{3}^{{\prime} }}\) = 1.89 Ω, and \({R}_{{1}^{{\prime} }{2}^{{\prime} },{4}^{{\prime} }{3}^{{\prime} }}\) = 0.48 Ω. Each MR is featureless above H = 1.3 T. Below 1.3 T, the MR ∥\(\hat{{{{{{{{\bf{y}}}}}}}}}\) (∥\(\hat{{{{{{{{\bf{x}}}}}}}}}\)) exhibit local maxima (minima) at ∣H∣ = 0.75 T. Additionally, the MR ∥\(\hat{{{{{{{{\bf{y}}}}}}}}}\) are dominated by an H-antisymmetric component. c Exchanging the current and voltage contacts to opposite edges of the sample, Rij,kl ↔ Rkl,ij, inverts the sign of these antisymmetric MR. d This panel depicts the transverse (Hall) configurations, Rij,kl with \(\overrightarrow{ij}\perp \overrightarrow{kl}\), measured on the upper (cyan) and lower (gray) faces. The curves have the same H dependence but background offsets of differing signs. The opposite planar anisotropies in each face of the crystal can be mapped onto isotropic rectangles that are stretched along opposite x–y axes. The insert diagrams show simulated equipotential contours on these equivalent isotropic rectangles for R13,42 (left) and \({R}_{{1}^{{\prime} }{3}^{{\prime} },{4}^{{\prime} }{2}^{{\prime} }}\) (right). Due to the opposite stretching, with I13, V42 > 0 and with \({I}_{{1}^{{\prime} }{3}^{{\prime} }}\), \({V}_{{4}^{{\prime} }{2}^{{\prime} }} < 0\). This is the origin of the positive (negative) backgrounds in R13,42 (\({R}_{{1}^{{\prime} }{3}^{{\prime} },{4}^{{\prime} }{2}^{{\prime} }}\)). R42,31 and \({R}_{{4}^{{\prime} }{2}^{{\prime} },{3}^{{\prime} }{1}^{{\prime} }}\) develop opposite signs in their background terms by the same mechanism. e High-resolution field sweeps of the transverse resistances (Sample N2, T = 2 K) show sharp hysteretic peaks at the coercive field (30 Oe), indicative of the weak pinning of magnetic domains. f The intrinsic Hall response, derived by adding together the transverse Rij,kl measured in each face. The Hall response measured using the set of contacts on the upper face (cyan) is identical to that of the lower face (gray).
