Quantum Spin Transfer of Spin-Correlated Electron Pairs

Abstract

We theoretically investigate quantum spin transfer from spin-correlated conduction-electron pairs to localized spins in a ferromagnet, given that electrons are correlated intrinsically. We show that even spin-singlet pairs and triplet pairs with $m=0$, both carrying no net spin, can transfer finite angular momentum through the quantum fluctuation term inherent to the $sd$ exchange interaction. The amount of transferred spin differs between the singlet and triplet $m=0$ states due to quantum interference. The difference is such that the independent-electron approximation remains valid for spin transfer when injected spin currents are completely incoherent. However, in partially coherent systems, like superconductor/ferromagnet junctions, coherent spin-singlet currents can directly convert into equal-spin triplet currents in generic ferromagnets, without requiring magnetic inhomogeniety or spin-orbit coupling.

Figures (4)

• Figure 1: Schematic illustration of the model. A conduction-electron pair is initially placed on the left side of the spin chain. Each electron is described by a Gaussian wave packet, $\varphi_1(x)$ and $\varphi_2(x)$, sharing the same wavevector $k_e$ and width $\sigma_d$. Their centers are separated by a distance $d$. As time evolves, the pair traverses the spin chain. The hopping constant is $t_h$. Localized spins occupy sites $n_1$ to $n_L$ and interact with the conduction spins through the $sd$ exchange interaction with coupling strength $J_{sd}$. This model generalizes the single-electron injection considered in Ref. [mitrofanov2021] to the injection of a spin-correlated electron pair.
• Figure 2: (a) Time evolution of the spin transfer. The red solid line corresponds to the singlet state, blue dotted line to the triplet $m=0$ state, orange solid line to the triplet $m=-1$ state, and black dotted line to a single spin-$\downarrow$ state. The wave-packet distance is set to 30$a$, where $a$ denotes the atomic spacing. The shaded regions represent the time intervals during which $\varphi_1$ and $\varphi_2$ stay within the spin chain, respectively. (b) Spin transfer as a function of the wave-packet distance for the singlet, triplet $m=0$, and triplet $m=-1$ states. Parameters: $t_h=0.5, J_{ex}=0.2, J_{sd}=0.3$ (in units of eV), $N=200, L=4, k_e=1/a$ and $\sigma_d=5a$.
• Figure 3: Time evolution of the spin-state probabilities as the conduction electron pair traverses the spin chain, with the initial spin state chosen as the singlet state (left column) or the triplet m=0 state (right column). The shaded regions represent the time intervals during which $\varphi_1$ and $\varphi_2$ stay within the spin chain, respectively. Panels (a)-(b) include only the $\hat{\sigma}_z\hat{S}_z$ term, panels (c)-(d) include only the $(\hat{\sigma}_{+}\hat{S}_-+\hat{\sigma}_-\hat{S}_+)$ term, and panels (e)-(f) show the results for the full Hamiltonian in Eq.(\ref{['eq7']}).
• Figure 4: (a) Spin transfer as a function of the relative phase $\theta$. The incoming state is given in Eq.(\ref{['eq9']}), and $\theta$ is varied from 0 to $2\pi$. (b) Time evolution of the spin transfer for an incoherent spin state, obtained by averaging $(\Delta\sigma_z)_\theta$ over $\theta$. The spin transfer of a single spin-$\downarrow$ is shown as a black dotted line for comparison.