Spin-orbit-derived giant magnetoresistance in a layered magnetic semiconductor ${\mathrm{AgCrSe}}_2$

Two-dimensional magnetic materials have recently attracted great interest due to their unique functions as the electric field control of a magnetic phase and the anomalous spin Hall effect. For such remarkable functions, a spin-orbit coupling (SOC) serves as an essential ingredient. Here we report a giant positive magnetoresistance in a layered magnetic semiconductor ${\mathrm{AgCrSe}}_2$, which is a manifestation of the subtle combination of the SOC and Zeeman-type spin splitting. When the carrier concentration, $n$, approaches the critical value of $2.5\times {10}^{18}\mathrm{c}{\mathrm{m}}^{\text{–}3}$, a sizable positive magnetoresistance of $\sim 400\%$ emerges upon the application of magnetic fields normal to the conducting layers. Based on the magneto-Seebeck effect and the first-principles calculations, the unconventional magnetoresistance is ascribable to the enhancement of effective carrier mass in the SOC-induced $J=3/2$ state, which is tuned to the Fermi level through the Zeeman splitting enhanced by the $p\text{−}d$ coupling. This study demonstrates an aspect of the SOC-derived magnetotransport in two-dimensional magnetic semiconductors, paving the way to spintronic functions.

Figure 1

(a) Crystal structure and Brillouin zone. Crystal structure is shown by the hexagonal cell (conventional cell). Brillouin zone is based on the rhombohedral cell (primitive cell). (b) Temperature dependence of magnetic susceptibility for No. 2 under out-of-plane magnetic field $\left(H=1\mathrm{T}\right)$. The overall behavior is almost the same among the three samples (No. 1, No. 2, and No. 3). (c) Electronic structure for the induced ferromagnetic state with spin-orbit coupling. Magnetic moments are parallel to $c$ axis. (d) Temperature dependence of electrical resistivity for three types of ${\mathrm{AgCrSe}}_2$ crystals, denoted by No. 1, No. 2, and No. 3. Inset shows a typical single crystal.

Figure 2

Magnetoresistance in three types of ${\mathrm{AgCrSe}}_2$ crystals: No. 1 (a), No. 2 (b), and No. 3 (c). (d) Carrier-concentration dependence of magnetoresistance at selected temperatures in various crystals.

Figure 3

Magnetic field $H$ dependence of (a), (c) magnetization and (b), (d) magnetoresistance under (a), (b) out-of-plane magnetic field and (c), (d) in-plane magnetic field for sample No. 2.

Figure 4

Temperature dependence of magneto-Seebeck effect $\left(H//c\right)$ in two types of ${\mathrm{AgCrSe}}_2$ crystals: (a) No. 2, (b) No. 3. Magnetic field dependence of Seebeck effect for (c) No. 2 and (d) No. 3. Magnetic field dependence of $S/\rho T$ ($S$: Seebeck coefficient, ρ: electrical resistivity, $T$: temperature) for (e) No. 2 and (f) No. 3.

Figure 5

Calculated band structures for (a) the paramagnetic phase and (b) the ferromagnetic phase, respectively ($E_{\mathrm{ed}}$ is the energy of the band edge at Γ point). The magnetic moments of Cr in the FM phase are aligned along the $c$ axis. Spin-orbit coupling is considered in the calculations. Schematic illustrations of the band structures corresponding to (c) the PM and (d) the FM phases, respectively.