Tunneling magnetoresistance in a junction made of $X$-wave magnets with $X=p,d,f,g,i$

Abstract

We investigate the tunneling magnetoresistance (TMR) of a bilayer system made of $X$-wave magnets with $X=p,d,f,g,i$, where $X=d,g,i$ corresponds to altermagnets. A universal analytic formula is derived for the TMR ratio. It is proportional to $\left\vert J\right\vert /\left( N_{X}\Gamma \right) $ for small $\Gamma $, where $N_{X}$ is the number of the nodes of the $X$% -wave magnet, $J$ is the strength of the $X$-wave magnet, and $\Gamma $ is the self-energy. It is contrasted with the TMR ratio made of ferromagnets, where it is proportional to $J^{2}/\Gamma ^{2}$ for small $\Gamma $. Therefore, the TMR ratio is larger in ferromagnets for $\left\vert J\right\vert >\Gamma $. However, the $X$-wave magnets are expected to achieve high-speed and ultra-dense memory owing to the zero net magnetization.