Fully-Compensated Ferrimagnetic Spin Filter Materials within the Cr$textit{M}textit{N}$Al Equiatomic Quaternary Heusler Alloys

XXYZ equiatomic quaternary Heusler alloys (EQHAs) containing Cr, Al, and select Group IVB elements ($textit{M}$ = Ti, Zr, Hf) and Group VB elements ($textit{N}$ = V, Nb, Ta) were studied using state-of-the-art density functional theory to determine their effectiveness in spintronic applications. Each alloy is classified based on their spin-dependent electronic structure as a half-metal, a spin gapless semiconductor, or a spin filter material. We predict several new fully-compensated ferrimagnetic spin filter materials with small electronic gaps and large exchange splitting allowing for robust spin polarization with small resistance. CrVZrAl, CrVHfAl, CrTiNbAl, and CrTiTaAl are identified as particularly robust spin filter candidates with an exchange splitting of $sim 0.20$ eV. In particular, CrTiNbAl and CrTiTaAl have exceptionally small band gaps of $sim 0.10$ eV. Moreover, in these compounds, a spin asymmetric electronic band gap is maintained in 2 of 3 possible atomic arrangements they can take, making the electronic properties less susceptible to random site disorder. In addition, hydrostatic stress is applied to a subset of the studied compounds in order to determine the stability and tunability of the various electronic phases. Specifically, we find the CrAlV$textit{M}$ subfamily of compounds to be exceptionally sensitive to hydrostatic stress, yielding transitions between all spin-dependent electronic phases.