High-order AMR in two-dimensional magnetic monolayers from spin mixing

Abstract

Anisotropic magnetoresistance (AMR) is a well-known magnetoelectric coupling phenomenon, commonly exhibiting two-fold symmetry relative to the magnetic field. In this study, we reveal the existence of high-order AMRs in two-dimensional (2D) magnetic monolayers. Based on density functional theory (DFT) calculations of Fe3GeTe2 and CrTe2 monolayers, we find that different energy bands contribute uniquely to AMR behavior. The high-order AMR is attributed to strong spin mixing at band crossing points, which induces significant Berry curvature. This curvature also contributes to the AMR for electrons with dominant spin-up or spin-down polarization characteristics. However, for electrons exhibiting strong spin mixing, the Berry curvature effect becomes nontrivial, resulting in high-order AMR. Our findings provide an effective approach to identifying and optimizing materials with high-order AMR, which is critical for designing high-performance spintronic devices.

Figures (6)

• Figure 1: (a)-(b) Top and side views of atomic structures of monolayer Fe$_3$GeTe$_2$, where red and blue balls represent two distinct Fe atoms, silver balls represents Ge atoms, and light green balls represents Te atoms. (c) Schematic diagram defining the angle $\alpha$ in Cartesian coordinates. (d) Electronic conductivity ($\sigma_{xx}$) for different magnetization directions and chemical potentials $\Delta\mu$. (e)–(f) $\sigma_{xx}$ for different magnetization directions at $\Delta\mu$ = 0 eV (e) and $\Delta\mu$ = – 0.2 eV (f), respectively. In (e), expanding the AMR up to $\cos(2\alpha)$ is sufficient to replicate the computed results, while, in (f) a good fitting can be obtained only when the expanding is up to $\cos(6\alpha)$.
• Figure 2: Magnetization direction dependent Fermi surface of monolayer FGT at $\Delta\mu$ = 0 eV (a)-(c) and $\Delta\mu$ = -0.2 eV (d)-(f). (a) and (d) for $\alpha$ = 0$^\circ$, (b) and (e) for $\alpha$ = 60$^\circ$, (c) and (f) for $\alpha$=90$^\circ$.
• Figure 3: Band structure of spin projection for monolayer FGT (a), and spin projections on the First Brillouin Zone isoenergetic plane at $\Delta\mu$= 0 eV (b) and $\Delta\mu$= - 0.2 eV (c), respectively. In (a), seven special bands are marked by index 1-7, two green lines mark the chemical potentials of $\Delta\mu$= 0 eV and $\Delta\mu$= - 0.2 eV, respectively. In (b) and (c), the red and blue lies represent spin-up and spin-down projections, respectively.
• Figure 4: The electrical conductivity at two different chemical potentials $\Delta\mu$ for monolayer FGT. The red solid line represents the total conductivity, and the black lines represent the conductivity from each band with the same index marked in Fig. 3(a). (a) In case of $\Delta\mu$= 0 eV, and (b) In case of $\Delta\mu$= -0.2 eV.
• Figure 5: Calculated Kohn–Sham (KS) orbitals at $\Delta\mu$=0 eV (a - d) and $\Delta\mu$= -0.2 eV (e - h) for energy bands of index 3 (a, c, e, g) and index 4 (b, d, f, h) of monolayer FGT, with an isosurface value of $3\times 10^{-10}$. Red and blue colors indicate spin-up and spin-down projections, respectively. At $\Delta\mu$=0 eV, energy band of index 3 exhibits only spin-down characteristic (a, c), while at $\Delta\mu$= -0.2 eV, it additionally presents some spin-up characteristic (e, g). Similarly, at $\Delta\mu$=0 eV, energy band of index 4 exhibits nearly pure spin-up characteristic (b, d), whereas at $\Delta\mu$= -0.2 eV the spin-down characteristic becomes sizable (f, h).