Spin swapping for an exchange magnon spin current

We propose the spin-swapping effect for an exchange magnon spin current in a perpendicularly magnetized ferromagnetic medium with in-plane anisotropy on the surface. The excitation of a magnon current flowing along an in-plane direction with an out-of-plane spin polarization leads to the generation of an exchange spin current propagating along the out-of-plane direction, characterized by an in-plane spin polarization. The resulting exchange magnon spin current can induce an inverse spin Hall voltage of microvolts. The exchange coupling at the interface between regions with different magnetic anisotropies plays a crucial role in generating the spin-swapping effect. This is in contrast to the recently reported spin swapping for an exchange spin current in a canted antiferromagnet due to the Dzyaloshiskii-Moriya interaction.

Figure 1

Schematic of magnonic spin swapping for an exchange spin current in a perpendicularly magnetized ferromagnetic medium with a surficial in-plane anisotropy.

Figure 2

Temporal magnon spin current density (a) inner the PMA layer ($z=0$ nm) and (b) on the surface ($z=104$ nm). (c) Changing of $m_x$ and $m_z$ in equilibrium and (d) the exchange magnon spin current density $J_{sw}^x$ and $J_{sw}^z$ along the thickness direction.

Figure 3

(a) $m_x$ in equilibrium as a function of the thickness of the IPA surficial layer ($t_{IP}$). (b) Average surficial magnon spin current ($\langle J_{sw}^z\rangle$) as a function of $t_{IP}$ (Inset: the variation of phase for the oscillation of $m_y$ as a function of $t_{IP}$). (c) $\langle J_{sw}^z\rangle$ under the exciting field acting on different ranges along the thickness direction from 0 to $z$. (d) $\langle J_{sw}^z\rangle$ under different exchange constants at the PMA/IPA interface.

Figure 4

(a) Average $\langle J_{sw}^z\rangle$ as a function of the excitation field frequency for a bilayer with $t_{IP}=4$ nm. (b) Dispersion relationship curve for a bilayer with $t_{IP}=4$ nm. [(c), d)] Dispersion relationship for the exchange magnon spin current flowing along the $z$ direction in the PMA layer for a single PMA medium and a bilayer with $t_{IP}=4$ nm, respectively.