Coexistence of intrinsic piezoelectricity and ferromagnetism induced by small biaxial strain in septuple-atomic-layer VSiP.

The septuple-atomic-layer VSi2P4 with the same structure of experimentally synthesized MoSi2N4 is predicted to be a spin-gapless semiconductor (SGS) with the generalized gradient approximation (GGA). In this work, the biaxial strain is applied to tune the electronic properties of VSi2P4, and it spans a wide range of properties upon increasing the strain from a ferromagnetic metal (FMM) to SGS to a ferromagnetic semiconductor (FMS) to SGS to a ferromagnetic half-metal (FMHM). Due to broken inversion symmetry, the coexistence of ferromagnetism and piezoelectricity can be achieved in FMS VSi2P4 with the strain range of 0% to 4%. The calculated piezoelectric strain coefficients d11 for 1%, 2% and 3% strains are 4.61 pm V-1, 4.94 pm V-1 and 5.27 pm V-1, respectively, which are greater than or close to a typical value of 5 pm V-1 for bulk piezoelectric materials. Finally, similar to VSi2P4, the coexistence of piezoelectricity and ferromagnetism can be realized by strain in the VSi2N4 monolayer. Our works show that VSi2P4 in the FMS phase with intrinsic piezoelectric properties can have potential applications in spin electronic devices.