Theory of $I\text{−}V$ characteristics of magnetic Josephson junctions

We analyze the electrical characteristics of a circuit consisting of a free thin-film magnetic layer and source and drain electrodes that have opposite magnetization orientations along the free magnet’s two hard directions. We find that when the circuit’s current exceeds a critical value there is a sudden resistance increase which can be large in relative terms if the currents to source or drain are strongly spin polarized and the free magnet is thin. This behavior can be partly understood in terms of a close analogy between the magnetic circuit and a Josephson junction.

Figure 1

(Color online) A magnetic Josephson junction consists of a free magnetic layer with a well-defined easy-plane and weak in-plane anisotropy separated by nonmagnetic spacers from magnetic source and drain electrodes whose magnetizations are opposite and perpendicular to the easy plane. In this paper we choose the spin $\widehat{z}$ axis along a free magnet hard direction.

Figure 2

(Color online) The ratio of dynamic and static resistance $\zeta \equiv R_D/R_S$ plotted as a function of damping parameter $\alpha$ and polarization $p$. The parameters used here are $g=G=10$ (per ${\text{nm}}^2$), $P=0.5$, $\eta ={\eta }^{\prime }=2$, $M_s={10}^5\text{A}/\text{m}$, and $d=1\text{nm}$. This ratio $\zeta$ diverges as $\alpha \to 0$ and $p\to 1$.

Figure 3

(Color online) The ratio between $\hslash \dot{\varphi }/e$ and the magnetization dynamics induced emf in a MJJ plotted as a function of polarization $p$ for different values of damping parameter $\alpha$. These results were obtained for $P=p$, $g=G=10$ (per ${\text{nm}}^2$), $\eta ={\eta }^{\prime }=2$, $M_s={10}^5\text{A}/\text{m}$, and $d=1\text{nm}$. The straight line $\beta =p$ applies for smooth magnetization textures.