Robust magnetotransport in disordered ferromagnetic kagome layers with quantum anomalous Hall effect

The magnetotransport properties of disordered ferromagnetic kagome layers are investigated numerically. We show that a large domain-wall magnetoresistance or negative magnetoresistance can be realized in kagome layered materials (e.g., ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$, ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, and ${\mathrm{Mn}}_3\mathrm{Sn}$), which show the quantum anomalous Hall effect. The kagome layers show a strong magnetic anisotropy and a large magnetoresistance depending on their magnetic texture. These domain-wall magnetoresistances are expected to be robust against disorder and observed irrespective of the domain-wall thickness, in contrast to conventional domain-wall magnetoresistance in ferromagnetic metals.

Figure 1

Schematic figure of two-terminal geometry of the straight-edged kagome ribbon (red sites). One-dimensional ideal leads (gray sites) are attached on both zigzag ends. The cyan and pink bonds represent nearest- and next-nearest-neighbor hopping, respectively.

Figure 2

(a) Band structure of a nonmagnetic kagome ribbon. Green bands correspond to the helical edge states. Conductance maps for clean kagome nanoribbons with (b) out-of-plane and (c) in-plane magnetizations. The vertical axis is the Fermi energy $E$, and the horizontal axis is the strength of the spin-exchange coupling $JM$. The light-green regions correspond to the quantum spin Hall phase (near $JM=0$) or the QAH phase with Chern number 2. The dark-green regions in (b) are the QAH phase with Chern number $\pm 1$.

Figure 3

Conductance maps for disordered (with disorder strength $W/t=2$) kagome nanoribbons with (a) out-of-plane and (b) in-plane magnetizations. The metallic (yellow) regions in Fig. 2 become insulating (purple) in the presence of disorder. We took the disorder realization average over ${10}^3$ samples.

Figure 4

Conductance as a function of the angle $\theta$ (in units of $\pi$) of magnetization $\mathit{M}=M(sin\theta ,0,cos\theta )$ at $W/t=0$ (dotted), 1 (dashed), and 2 (solid). The parameters are set to $JM/t=1$ and $E/t=-0.4$, which is around the center of the QAH region with Chern number 2 in Fig. 2. Averages are taken over up to ${10}^4$ samples, so that the error bars are smaller than $0.005e^2/h$.

Figure 5

(a) Averaged conductance $\langle G\rangle$ for (green) out-of-plane magnetization, (yellow) in-plane magnetization, (red) Néel, and (blue) head-to-head walls with the domain-wall thickness $\xi /a=30$. The parameters are set to $JM/t=1$ and $E/t=-0.4$. (b) Magnetoresistance ratio MR for (red) Néel, (blue) head-to-head, and (yellow) in-plane walls with $\xi /a=0.5$. The black line shows the MR in a conventional half-metal state (at $JM/t=1$ and $E/t=4$) for Néel wall with $\xi /a=0.5$.

Figure 6

(a) Magnetoresistance ratio MR as a function of domain-wall thickness for (red) Néel, (blue) head-to-head, and (yellow) in-plane walls. The black line shows the conventional DWMR effect in a half-metal, which vanishes in a thick wall. The disorder strength $W/t=2$. (b) Spatial configuration of an out-of-plane component of magnetization for a Néel wall with (solid) $\xi /a=30$ and (dotted) $\xi /a=5$. (c) Schematic figure of the chiral edge state coupled at the domain wall.