  Two-dimensional ferromagnetic (FM) half-metals are promising candidates for
advanced spintronic devices with small-size and high-capacity. Motivated by
recent report on controlling synthesis of FM Cr$_3$Te$_4$ nanosheet, herein, to
explore the potential application in spintronics, we designed spintronic
devices based on Cr$_3$X$_4$ (X=Se, Te) monolayers and investigated their spin
transport properties. We found that Cr$_3$Te$_4$ monolayer based device shows
spin filtering and dual spin diode effect when applying bias voltage, while
Cr$_3$S$_4$ monolayer is an excellent platform to realize a spin valve. The
different transport properties are primarily ascribed to the semiconducting
spin channel, which is close to and away from the Fermi level in Cr$_3$Te$_4$
and Cr$_3$Se$_4$ monolayers, respectively. Interestingly, the current in
monolayer Cr$_3$Se$_4$ based device also displays a negative differential
resistance effect (NDRE) and a high magnetoresistance ratio (up to 2*10$^3$).
Moreover, we found thermally induced spin filtering effect and NDRE in
Cr$_3$Se$_4$ junction when applying temperature gradient instead of bias
voltage. These theoretical findings highlight the potential of Cr$_3$X$_4$
(X=Se, Te) monolayers in spintronic applications and put forward realistic
materials to realize nanosale spintronic device.
