Theoretical study of spin-dependent transport in WSe$_2$-based vertical spin valves

Abstract

We theoretically investigate spin-dependent transport in a TMD-based vertical spin valve, taking WSe$_2$ as a representative example. Using effective Hamiltonians for the heterostructure and the Landauer formula, we derive the transmission and reflection coefficients within a transfer-matrix approach. The calculated magnetoresistance shows an oscillatory dependence on the WSe$_2$ thickness when the Fermi level is tuned near the valence-band maximum. The effects of gate voltage and exchange fields on the magnetoresistance are further analyzed. We also identify a Fabry-Pérot-like interference contribution to the magnetoresistance, which can enhance or even induce negative magnetoresistance in certain thickness regimes. Our results provide a qualitative understanding of the negative magnetoresistance observed in WSe$_2$-based spin valves and may offer useful insights for the design of tunable spintronic devices.

Figures (7)

• Figure 1: Schematic illustrations of the vertical spin valve based on WSe$_2$ spacer for (a) parallel and (b) anti-parallel configurations. The device consists of three regions: bottom electrode (region I, $z<0$), central WSe$_2$ spacer (region II, $0<z<d$), and top electrode (region III, $z>d$). Exchange fields in the electrodes are represented by arrows: in the parallel configuration (P) both electrodes have magnetization along the same direction; in the anti-parallel configuration (AP), the magnetizations are opposite.
• Figure 2: (a) Potential profile along the vertical transport direction, and (b) The in-plane band structures in the three regions. Note that in this figure the three regions are arranged horizontally for clarity, which is rotated $90^\circ$ with respect to Fig. \ref{['fig:verticalspinvalve']}. The horizontal arrangement is adopted to better illustrate the band alignment and Fermi level matching.
• Figure 3: Magnetoresistance (MR) as a function of the WSe$_2$ thickness $d$. The blue, red, and green curves correspond to calculations with $d$ treated as a continuous variable for $m_0 = m_e$, $0.7m_e$, and $1.3m_e$, respectively. The red dots represent the MR values for discrete layer numbers, namely for $d = n d_0$ with integer $n$ and $d_0 = 6.5\,\text{\AA}$.
• Figure 4: Magnetoresistance MR as a function of $V_g$ for monolayer (red), bilayer (black), trilayer (blue) and four-layer (green) WSe$_2$. The vertical dashed line indicates the value of the gate potential $V_g=0.57{\rm eV}$.
• Figure 5: Magnetoresistance MR as a function of exchange field $h_{\rm I}$ for monolayer (red), bilayer (black), trilayer (blue) and four-layer (green)WSe$_2$ . The vertical dashed linea indicate the value $h_{\rm I}=\pm 0.25{\rm eV}$.