Giant magnetoresistance and anomalous transport in phosphorene-based multilayers with noncollinear magnetization

We theoretically investigate the unusual features of the magnetotransport in a monolayer phosphorene ferromagnetic/normal/ferromagnetic (F/N/F) hybrid structure. We find that the charge conductance can feature a minimum at parallel (P) configuration and a maximum near the antiparallel (AP) configuration of magnetization in the F/N/F structure with $n$-doped F and $p$-doped N regions and also a finite conductance in the AP configuration with the N region of $n$-type doping. In particular, the proposed structure exhibits giant magnetoresistance, which can be tuned to unity. This perfect switching is found to show strong robustness with respect to increasing the contact length and tuning the chemical potential of the N region with a gate voltage. We also explore the oscillatory behavior of the charge conductance or magnetoresistance in terms of the size of the N region. We further demonstrate the penetration of the spin-transfer torque into the right F region and show that, unlike graphene structure, the spin-transfer torque is very sensitive to the chemical potential of the N region as well as the exchange field of the F region.

Figure 1

Schematic illustration of the monolayer phosphorene F/N/F junction: The two F regions with the magnetization vectors ${\mathit{m}}_i$ are coupled through the N region located at $0<x<L$.

Figure 2

(a) The dispersion relation in momentum space of the monolayer phosphorene along the Y-$\mathrm{\Gamma }$-X direction in the Brillouin zone. The black lines correspond to the N phosphorene, while the red (blue) line corresponds to the $\sigma$ ($\overline{\sigma }$) band of the F phosphorene with the magnetization $m=0.03$ eV. (b), (c) Isofrequency contour surfaces in the $k$ space of $n$-type and $p$-type doped phosphorene layers, respectively, for $E=0.4557$ eV and $E=-0.4557$ eV, with the step of 0.1 eV. Red (blue) isofrequency contour surface corresponds to the $\sigma$ ($\overline{\sigma }$) band of the F phosphorene at $E={\mu }_F\pm m$, with the chemical potential ${\mu }_F=0.54$ eV. The energies $E_{BE}^{\sigma ,\tau \left(\overline{\tau }\right)}$ and $E_{BE}^{\overline{\sigma },\tau \left(\overline{\tau }\right)}$ define the conduction (valance) band edges for the two spin subbands of F phosphorene ($\sigma =1,\overline{\sigma }=-\sigma$) with $\tau =1$ ($\overline{\tau }=-\tau$). Note that the zero-point energy in the band structure of N phosphorene is shifted to the middle of its energy band gap.

Figure 3

Top (bottom) panel: The transmission probabilities for incoming electrons from $\sigma$ and $\overline{\sigma }$ bands of the left F region in the F/N/F structure with $n$- ($p$-) doped N region versus the angle of incidence ${\theta }_{F_1}$ for the parallel (${\varphi }_1={\varphi }_2=0$) and antiparallel (${\varphi }_1=0,{\varphi }_2=\pi$) configuration of magnetization, when ${\mu }_F=0.54$ eV for both F regions and $m=0.03$ eV. The energy of the propagating electrons is equal to ${\mu }_F$.

Figure 4

Top (bottom) panel: The charge conductance of the F/N/F structure with $n$- ($p$-) doped N region (in units of $g_{0}W/2\pi$) versus the magnetization direction of the left F region ${\varphi }_1$ and the chemical potential of the N region ${\mu }_N$ for two values of the chemical potential of the F regions ${\mu }_F=0.44$ eV (left panel) and ${\mu }_F=0.54$ eV (right panel), when $m=0.03$ eV, ${\varphi }_2=0$, and $L/a_x=20$.

Figure 5

Magnetoresistance of the spin valve structure versus the chemical potential ${\mu }_N$ for $m=0.03$ eV, when $L/a_x=20$ (a) and the length of the N region $L/a_x$, when ${\mu }_N=0.65$ eV (b) for different values of ${\mu }_F$.

Figure 6

The spin-transfer torques (a) ${\tau }_{STT}^y$ and (b) ${\tau }_{STT}^z$ (in units of $W/4\pi$) as a function of the distance from the N/F interface for three different values of ${\varphi }_1$, when ${\mu }_F=0.44$ eV, ${\mu }_N=0.65$ eV, $m=0.03$ eV, ${\varphi }_2=0$, and $L/a_x=20$.

Figure 7

Top panel: The spin-transfer torques (a) ${\tau }_{STT}^y$ and (b) ${\tau }_{STT}^z$ (in units of $W/4\pi$) versus the orientation of the magnetization vector ${\mathit{m}}_1,{\varphi }_1$, and the chemical potential of the N region ${\mu }_N$, when $m=0.03$ eV. Bottom panel: (c) ${\tau }_{STT}^y$ and (d) ${\tau }_{STT}^z$ versus ${\varphi }_1$ and the magnitude of the exchange field $m/{\mu }_F$ (in units of the chemical potential of the F region), when ${\mu }_N=0.65$ eV. The magnetization vector ${\mathit{m}}_2$ is fixed to $x$ axis (${\varphi }_2$=0), ${\mu }_F=0.44$ eV, and $L/a_x=20$.