Anisotropic spin filtering by an altermagnetic barrier in magnetic tunnel junctions

The spin filtering effect, distinct decaying lengths experienced by oppositely spin-polarized electrons in a magnetic barrier, generally occurs in ferromagnetic (FM) insulators or semiconductors. With the rise of altermagnetic (ALM) materials which exhibit similar capability of spin-polarizing electrons with ferromagnets, it is a nature question whether the ALM insulators or semiconductors can also act as unique barriers for the spin splitting effect. Here, through first-principles calculations, we investigated the complex band structure of the ALM insulator FeF$_2$ and found that it possesses an anisotropic spin filtering effect: along the [001] direction of FeF$_2$, a current remains spin-neutral but has locally nonvanishing spin polarizations in the momentum space; moreover, along the [110] direction of FeF$_2$, a current will be globally spin-polarized by different attenuation lengths of oppositely spin-polarized electrons. Leveraging this anisotropic spin filtering effect, we designed two types of MTJs with the ALM barrier: ALM electrode/ALM insulator barrier/non-magnetic (NM) electrode and FM electrode/ALM insulator barrier/NM electrode, using RuO$_2$(001)/FeF$_2$/IrO$_2$ and CrO$_2$(110)/FeF$_2$/IrO$_2$ as the corresponding prototypes, respectively. We found that these two proposed MTJs exhibited the tunneling magnetoresistance (TMR) ratios of 216\% and 3956\%, by matching the conduction channels of the electrodes and the spin-resolved lowest decay rate of the barrier in the momentum space. Our work deepens and generalizes understanding toward the spin filtering effect for the rising ALM insulators and semiconductors, and broadens applications of the AFM spintronics.