Spin transport analysis for a spin pseudovalve-type L_l/SC/L_r trilayer for L = {FeCr, Fe, Co, NiFe, Ni} and SC = {GaSb, InSb, InAs, GaAs, ZnSe}

Abstract

In this work, we present a theoretical study of spin transport in a trilayer pseudospin-valve (PSV) heterostructure composed of electrode (L_l)/insulator/electrode (L_r). The insulating layer corrresponds to a semiconductor (SC) with a zinc-blende crystal structure from the III-V (GaSb, InSb, InAs, and GaAs) or the II-VI (ZnSe), while the electrodes are ferromagnetic materials L_j = {FeCr, Fe, Co, NiFe, Ni}. This combination yields 125 possible PSV configurations. The theoretical model implemented is based on the approach proposed by J. C. Slonczewski. In our approach, the exchange splitting in the ferromagnetic materials and the spin-orbit coupling (SOC) of the Dresselhaus and Rashba types in the semiconductors are included, allowing control of the wave vector associated with the spin states. The tunnel magnetoresistance (TMR) is calculated at low temperature as a function of the semiconductor thickness, parameterized with respect to the crystallographic axis that favors the magnetization direction in the ferromagnetic electrodes, within the Landauer--Büttiker formalism in the single-channel regime. The results show that the TMR reaches its maximum value independently of the relative orientation between the magnetization vector and the crystallographic direction. The most efficient configuration corresponds to Fe_{90}Cr_{10}/GaSb/Fe_{90}Cr_{10}, with a TMR value of 83.60%. Furthermore, the Dresselhaus SOC contributes more significantly to the TMR than the Rashba SOC. Finally, the TMR varies when the electrodes L_j are permuted, due to differences in their Fermi energies. The obtained results are compared with previous studies reported in the literature based on alternative theoretical frameworks or assumptions, showing good agreement.

Figures (7)

• Figure 1: Schematic representation of a rectangular potential barrier (antiparallel magnetic configuration), defined by the energy eigenvalues of the FM ($E_{\sigma}^j$) and of the SC with SOC ($E_{\sigma}^{\varepsilon}$), along the growth direction of the heterostructure $[0\,0\,1]$, where $V_{eff}$ and $a$ denote the effective barrier height and thickness, respectively. Here, $\Delta^j_{xs}$ represents the exchange splitting, and the magnetization vector $\mathbf{n}_r$ rotates parallel to the barrier plane.
• Figure 2: Spin orientation corresponding to the spinors $|\chi_\sigma^j\rangle$ and $|\chi_\sigma^\varepsilon\rangle$ in the $k_{xl} \text{-} k_{yl}$ and $k_{x\sigma} \text{-} k_{y\sigma}$ planes for FM and SC, respectively, in the case where both are parallel to the barrier plane. The orientation of the wave vector $k_{\|l}$ is related to $k_{\|\sigma}^{+}$ (spin-up state) and $k_{\|\sigma}^{-}$ (spin-down state) by $\varphi_{\sigma}^{\varepsilon} = \theta_l + \varepsilon\sigma\frac{\pi}{2}$. Moreover, $\mathbf{s}_{\sigma}$ and $\mathbf{s}_{\sigma}^{\varepsilon}$ represent spins that are elements of $\mathbf{S}_{\sigma}$ and $\mathbf{S}_{\sigma}^{\varepsilon}$, respectively.
• Figure 3: Schematic representation of the k-space in 2D for the energy eigenvalues $E_{\sigma}^j$ corresponding to FM materials and $E_{\sigma}^{\varepsilon}$ related to SCs with Dresselhaus and Rashba SOC. For this analysis $E = E_F$, $\theta_m = \pi/4$, $\mathbf{n}_l \parallel [1\,1\,0]$ and $k_{z\sigma} = 0.44\,\text{\AA}^{-1}$ was considered.
• Figure 4: Calculated TMR for the Ll/SC/Lr PSV structures as a function of the SC layer thickness for $E = E_F$, $\theta_m = \pi/4$, $\mathbf{n}_l \| [1\,1\,0]$ and $k_{z\sigma} = 0.44\,\text{\AA}^{-1}$. Results are shown for InSb (black solid line), GaSb (red dashed line), InAs (blue dash-dotted line), GaAs (green custom dashed pattern), and ZnSe (magenta custom compound dashed pattern).
• Figure 5: TMR for the PSV $\mathrm{L}_k$/SC (equivalent to $\mathrm{L}_k$/SC/$\mathrm{L}_k$), as a function of the SC thickness and the wave vector $k_{z\sigma}$ for $E = E_F$, $\theta_m = \pi/4$ and $\mathbf{n}_l \| [1\,1\,0]$. The thick black curve correspond to the $k_{z\sigma}$ value defined in this work , the blue curve indicates the ridge of the surface. *Ref. Autes10 (TMR = 30%).