Spin transport through a nanojunction with a precessing anisotropic molecular spin: Quantum interference and spin-transfer torque

TL;DR

This work analyzes spin transport through a single molecular orbital exchange-coupled to a precessing anisotropic molecular spin in a static magnetic field. Using nonequilibrium Green's functions with a Floquet treatment, it derives spin currents, $z$-polarized noise $S^{zz}_{LL}$, and spin-transfer torque, including Gilbert-damping-like coefficients. Four Floquet quasienergy channels $\epsilon_{1..4}$ emerge, and spin current and noise exhibit resonant features with a Fano-like interference between elastic and inelastic spin-flip pathways; the precession can be completely suppressed when $\omega=\omega_L-2DS_z=0$, driving STT to zero. Notably, $D$ enables substantial control over transport properties even in the absence of a magnetic field, offering a route to electrically tune molecular-spin-based spintronic devices and to extract anisotropy and other parameters from dc-spin signals.

Abstract

The subject of this study is spin transport through a molecular orbital connected to two leads, and coupled via exchange interaction with a precessing anisotropic molecular spin in a constant magnetic field. The inelastic spin-flip processes between molecular quasienergy levels are driven by the molecular spin precession. By setting the Larmor frequency, the tilt angle of molecular magnetization with respect to the magnetic field, and the magnetic anisotropy parameter, one can modulate the spin current and noise, spin-transfer torque, and related torque coefficients. Moreover, the dc-spin current and spin-transfer torque components provide the quasienergy level structure in the orbital. Quantum interference effects between states connected with spin-flip processes manifest themselves as dips (minimums) and peaks (maximums) in spin-current noise, matching Fano-like resonance profiles with equal probabilities of interfering elastic and inelastic spin-flip pathways. By proper adjustment of the anisotropy parameter and magnetic field, the precession is suppressed and the torque vanishes, revealing the anisotropy parameter via a dc-spin current or torque measurement. The results of the study show that spin transport and spin-transfer torque can be manipulated by the anisotropy parameter even in the absence of the magnetic field.

Figures (7)

• Figure 1: Spin tunneling through a single molecular orbital with energy $\epsilon_{0}$, coupled to the molecular spin $\vec{S}(t)$ with anisotropy parameter $D$, via exchange interaction with the coupling constant $J$, in the presence of a magnetic field $\vec{B}$, connected to two leads with chemical potentials $\mu_{L}$ and $\mu_R$, $eV=\mu_{L}-\mu_R$, with tunnel rates $\Gamma_L$ and $\Gamma_R$. The molecular spin $\vec{S}(t)$ precesses around the magnetic field axis with frequency $\omega=\omega_L-2DS_z$. The spin-transfer torque $\vec{T}(t)$ is exerted on the spin $\vec{S}(t)$ by the spin currents from the leads.
• Figure 2: (a) Spin current $I_{Lz}$ and (b) auto-correlation spin-current shot noise $S^{zz}_{LL}$, as functions of the uniaxial magnetic anisotropy parameter $D$ for different tilt angles $\theta$, at zero temperature. The magnetic field $\vec{B}=B\vec{e}_z$ and Larmor frequency $\omega_{L}=0.5\,\epsilon_0$, except for a zero magnetic field where $\omega_{L}=0$ (orange line). The chemical potentials of the leads are equal: $\mu_{L}=\mu_{R}=0.1\,\epsilon_0$. The other parameters are set to $\Gamma=0.05\, \epsilon_{0},\,\Gamma_{L}=\Gamma_{R}=\Gamma/2,\, J=0.01\,\epsilon_{0}$, and $S=100$. Grid lines for $\theta=\pi/3$ and $\omega_{L}=0.5\,\epsilon_0$ (green line) are positioned at $D=-0.00431\,\epsilon_0$ ($\mu_{L}=\mu_{R}=\epsilon_3$), $D=0.00766\,\epsilon_0$ ($\mu_{L}=\mu_{R}=\epsilon_4$), and $D=0.005\,\epsilon_0$ ($\omega=0$).
• Figure 3: Spin-current shot noise $S^{zz}_{LL}$ as a function of the magnetic anisotropy parameter $D$ at zero temperature for $\theta=\pi/3$, $\mu_{L}=0.65\,\epsilon_0$, and $\mu_{R}=0$, with $\vec{B}=B\vec{e}_z$. Around the resonant anisotropy parameter $D_{\rm res}=0.00129\,\epsilon_0$ (grid line) the spin-current noise $S^{zz}_{LL}$ (black line) matches the Fano-like shape of the resonance profile $\sigma^{z}_S$ (red line). The inset shows contributions of $S^{\uparrow\uparrow}_{LLS}-S^{\uparrow\downarrow}_{LLS}$ (pink line) and $S^{\downarrow\downarrow}_{LLS}-S^{\downarrow\uparrow}_{LLS}$ (purple line) to the resulting shape of the resonance profile in $S^{zz}_{LL}$. The other parameters are set to $\Gamma=0.05\, \epsilon_{0},\,\Gamma_{L}=\Gamma_{R},\,\omega_{L}=0.5\,\epsilon_{0},\, J=0.01\,\epsilon_{0}$, and $S=100$.
• Figure 4: (a) Spin current $I_{Lz}$, (b) auto-correlation spin-current shot noise $S^{zz}_{LL}$, as functions of the chemical potential of the leads $\mu=\mu_{L}=\mu_{R}$, and (c) auto-correlation spin-current shot noise $S^{zz}_{LL}$ as a function of the applied bias voltage $eV=\mu_{L}-\mu_{R}$, with $\mu_{L,R}=\pm eV/2$, for different uniaxial magnetic anisotropy parameters $D$, with $\vec{B}=B\vec{e}_{z}$, at zero temperature. The other parameters are set to $\Gamma=0.05\, \epsilon_{0},\,\Gamma_{L}=\Gamma_{R}=\Gamma/2,\,\omega_L=0.5\,\epsilon_{0},\, J=0.01\,\epsilon_{0},\, S=100$, and $\theta=\pi/3$. All energies are given in the units of $\epsilon_{0}$. For $\mu_{L}=\mu_{R}$ and $D=\omega_{L}/2S_z=0.005\,\epsilon_0$, $I_{Lz}=0$ and $S^{zz}_{LL}=0$ (purple dotted lines).
• Figure 5: (a) Gilbert damping coefficient $\alpha$, (b) coefficient $\beta$, (c) magnitude of the in-plane component of the STT, $T_{\bot}$, and (d) spatial component of the torque along the $z$-direction, $T_z$, as functions of the uniaxial magnetic anisotropy parameter $D$ for different tilt angles $\theta$, at zero temperature. The magnetic field $\vec{B}=B\vec{e}_z$ and Larmor frequency $\omega_{L}=0.5\,\epsilon_0$, except for a zero magnetic field where $\omega_{L}=0$ (orange line). The chemical potentials of the leads are equal to $\mu_{L}=2.5\,\epsilon_0$ and $\mu_{R}=0$. The other parameters are set to $\Gamma=0.05\, \epsilon_{0},\,\Gamma_{L}=\Gamma_{R}=\Gamma/2,\,\omega_L=0.5\,\epsilon_{0},\, J=0.01\,\epsilon_{0},\, S=100$. Grid lines for $\theta=\pi/3$ (green line) are positioned at $D=-0.01312\,\epsilon_0$ ($\mu_{L}=\epsilon_2$), $D=-0.00625\,\epsilon_0$ ($\mu_{R}=\epsilon_3$), $D=0.00875\,\epsilon_0$ ($\mu_{R}=\epsilon_4$), and $D=0.01406\,\epsilon_0$ ($\mu_{L}=\epsilon_1$).