Research ArticlePHYSICS

Spin chirality induced skew scattering and anomalous Hall effect in chiral magnets

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Science Advances  09 Feb 2018:
Vol. 4, no. 2, eaap9962
DOI: 10.1126/sciadv.aap9962


  • Fig. 1 Configuration of spins and skew scattering.

    (A) Schematic picture of the scattering process in the second Born approximation in Eq. 5, which contributes to the skew scattering. The blue arrows are the localized spins, and the dotted lines Embedded Image and Embedded Image, indicate scattering processes from the first- and second-order terms in the Born approximation, respectively. The skew scattering arises from the interference between the two processes. (B) A schematic figure of the triangular configuration of spins considered in the main text. (C) The square lattice model considered in MC simulation. The arrows show δi vectors in Eq. 20, where a is the lattice constant (distance between the localized moments).

  • Fig. 2 Classical Monte Carlo simulation of two-dimensional chiral magnet.

    (A) The phase diagram of the 2D chiral magnet in Eq. 18; the transverse axis is the temperature T and the longitudinal axis is the magnetic field h perpendicular to the plane. The squares (circles) are the phase boundary estimated from spin structure factor S(q) using the gradient of S(q) along the T/JHh/JH) axis. Open (solid) symbols indicate the phase boundary for the helical (skyrmion crystal) order. The lines are merely a guide for the eyes. The contour plot in the paramagnetic (PM)/ferromagnetic (FM) phase shows the thermal average of the scalar spin chirality χ. The low-temperature region shaded in gray is the region where the MC simulation freezes because of low temperature. See the text for details. (B) Temperature dependence of spin structure factor S(q) and chirality χ for h/JH = 2.0; the two curves are for N = 302 and 602.

  • Fig. 3 Field dependence of χ, bz, and Embedded Image (a quantity that is proportional to the anomalous Hall conductivity) calculated by MC simulation.

    The numbers in square brackets are the magnetic field in Tesla, assuming the upper critical field to be 12 T, which is the case for MnGe. The temperatures are at (A) T/JH = 0.1 (~20 K) and (B) T/JH = 0.5 (~100 K) with γ = 2. The definition and description of Embedded Image are given in Eq. 26 and the paragraphs above it. In the figure, the blue and yellow shading indicates helical and skyrmion crystal phases, respectively. See the main text for details. (C) Experimental measurement of Hall conductivity in MnGe at 50 and 100 K. Reproduced from data from the work of Kanazawa et al. (29).