Possible existence of a Josephson effect in ferromagnets.

Abstract

When a current density ${j}_{x}$ crosses a 180\ifmmode^\circ\else\textdegree\fi{} domain wall in a metallic ferromagnet, the spin s of each conduction electron exerts an s-d exchange torque on the localized wall spins. Hence, the wall moment of a Bloch wall is canted out of the wall plane by an angle \ensuremath{\psi}, given by ${j}_{x}$=(eC/\ensuremath{\Elzxh})sin(2\ensuremath{\psi}), where C is the maximum restoring torque at \ensuremath{\psi}=45\ifmmode^\circ\else\textdegree\fi{}. This equation is the exact analog of the dc Josephson effect, and 2\ensuremath{\psi} is the analog of the superconducting phase difference \ensuremath{\varphi} across a junction. For \ensuremath{\Vert}${j}_{x}$\ensuremath{\Vert}>eC/\ensuremath{\Elzxh}\ensuremath{\simeq}${10}^{6}$ A/${\mathrm{cm}}^{2}$, the s-d exchange torque overcomes the restoring torque, and the wall moment precesses with a frequency \ensuremath{\omega}=d(2\ensuremath{\psi})/dt. A dc voltage \ensuremath{\delta}V is expected to appear across the wall, satisfying the famous ac Josephson relation 2e\ensuremath{\delta}V=-\ensuremath{\Elzxh}\ensuremath{\omega}. This wall precession can be described as a translation of Bloch lines, and the Bloch lines are the exact analog of superconducting vortices. The electric current exerts a transverse force on Bloch lines.