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

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 $\mid J\mid \mathrm{/}\left(N_X\mathrm{\Gamma }\right)$ for small $\mathrm{\Gamma }$, where $N_X$ is the number of the nodes of the $X$% -wave magnet, $J$ is the strength of the $X$-wave magnet, and $\mathrm{\Gamma }$ is the self-energy. It is contrasted with the TMR ratio made of ferromagnets, where it is proportional to $J^2\mathrm{/}{\mathrm{\Gamma }}^2$ for small $\mathrm{\Gamma }$. Therefore, the TMR ratio is larger in ferromagnets for $\mid J\mid >\mathrm{\Gamma }$. However, the $X$-wave magnets are expected to achieve high-speed and ultra-dense memory owing to the zero net magnetization.