Magnon equilibrium spin current in collinear antiferromagnets

Abstract

We theoretically predict that Dzyaloshinskii-Moriya interaction can induce magnon equilibrium spin current in collinear antiferromagnets. Such a current, being a response to the effective magnon vector potential, can be considered as magnon analog of the superconducting supercurrent or the persistent current. Large amplitude of the predicted effect may compensate for the smallness of the Dzyaloshinskii-Moriya interaction, making the equilibrium spin currents to be experimentally observed. We suggest that external electric field can play the role of effective flux magnons interact with and propose an experiment based on the interference of magnons in the ring geometry as a verification of the concept.

Figures (4)

• Figure 1: Two collinear antiferromagnets on the honeycomb-like lattice. On the left is the genuine mirror-symmetric antiferromagnet while on the right is a ferrimagnet. Red and blue sites correspond to the Néel order with $\pm {\bf S}$ spins. The green atom is non-magnetic and its role is to create a Dzyaloshinskii-Moriya interaction on the links depicted here by the arrows. The $\pm$ signs correspond to the $\nu_{ij}=\pm$ in Eq. (\ref{['exchange']}). If the charges on the red/blue and green sites are of opposite signs, the external electric field ${\bf E}$ can tune the position of the green atom in the unit cell.
• Figure 2: Left: Spectrum of magnons for $\theta = 0.2$ of the genuine mirror-symmetric antiferromagnet. The plot emphasizes the spin-momentum splitting of magnons at the ${\bm \Gamma}$ point. Similar spin-momentum splitting of the magnon modes occurs for any position of the green atom in the unit cell. Right: Magnon equilibrium spin current in the genuine mirror-symmetric antiferromagnet plotted as a function of temperature for blue $\theta = -0.2$ and yellow $\theta = -0.4$. Parameter $SJ$ can be of the order of $1 \mathrm{eV}$ in antiferromagnets.
• Figure 3: Magnon equilibrium spin currents, $j_{x}^{\mathrm{s}}$ and $j_{y}^{\mathrm{s}}$ plotted as a function of temperature in the ferrimagnet phase for blue $\theta = -0.2$ and yellow $\theta =- 0.4$.
• Figure 4: Ring geometry. Static electric field (between + and -) creates a flux the magnons interact with. Left: there is a magnon equilibrium spin current as a result of the flux in the ring. Opposite spins denoted by red and blue propagate in opposite directions. Right: interference experiment. Blue rectangles are sources and sinks of the magnon spin polarized currents. Variation of the electric field would produce oscillations $\propto \cos(2\pi \theta R/a )$ in the interference of equal spin magnons propagated in the different sides of the ring. Here $R$ is the radius of the ring and $a$ is the distance between neighbor lattice sites. Recall that DMI parameter $\theta$ is dimenisonless and is linear in the electric field.