Microscopic theory of an atomic spin diode

TL;DR

This work develops a microscopic theory for an atomic spin diode consisting of two magnetic adatoms on a Rashba 2DEG. It uses a Keldysh path-integral framework to integrate out the electronic bath and derives a generalized LLG equation with nonlocal exchange ${m{K}}_{ij}$, antisymmetric DMI, and Gilbert damping ${m{ m oldsymbol{ abla}}}_{ij}$. By analyzing the magnon susceptibility and linearising the dynamics, the authors derive conditions on the inter-spin spacing $R$ and external field $B_0$ that realize unidirectional magnon transmission, and demonstrate a concrete parameter regime where transmission is allowed in one direction but suppressed in the opposite direction. The work provides explicit microscopic expressions for the coupling and damping tensors and discusses experimental feasibility and extensions toward realizing atomic-scale spin diodes.

Abstract

We present a microscopic theory of an atomic spin diode. Our proposed system consists of two magnetic adatoms deposited on the surface of a two-dimensional electron gas with Rashba spin-orbit coupling. A local s-d type coupling between the local spins and the spins of the electrons induces a non-local Ruderman-Kittel-Kazuya-Yoshida type interaction and a Dzyalonshinskii-Moriya interaction, in addition to dissipative interactions, between the spins. We derive the effective action for the spins using the Keldysh formalism. From the effective action, we also derive equations of motion for the spins which are shown to be of Landau-Lifshitz-Gilbert (LLG) type, and give expressions for the effective field and Gilbert damping which appear in this equation. From our microscopic theory, we find that for an in-plane magnetic field perpendicular to the vector connecting the two atoms, the magnitude of the field and the distance between the atoms can always be tuned to engender perfectly diodic coupling. Our findings may pave the way to experimental realisation of atomic spin diodes.

Figures (5)

• Figure 1: Two atomic spins are deposited on the surface of a two-dimensional electron gas (2DEG). Localised s-d type coupling to an electron bath induces coherent and dissipative interactions between the two spins
• Figure 2: Schematic representation of the time evolution along the Keldysh contour $\mathcal{C}$.
• Figure 3: Exchange and damping parameters in Eqs. (\ref{['eq:exchnspec']}--\ref{['eq:dampspec']}), normalised by the respective prefactors in Eqs. (\ref{['eq:alphatensor']}) and (\ref{['eq:Ktensor']}).
• Figure 4: Condition in Eq. (\ref{['eq:finetuning']}) as a function of $k_FR$, with non-trivial roots plotted as blue crosses. The inset plot depicts the variation of this quantity across the same range of $k_FR$ as depicted in Fig. \ref{['fig:exanddamp']}.
• Figure 5: Normalised magnon susceptibilities $\chi_{12}$ and $\chi_{21}$ with the condition (\ref{['eq:x12cancels']}).