Stress Effectively Enhances the Ferromagnetic Stability of Monolayer NiZr

Stress is extensively utilized to regulate the electronic structure and associated physical properties of two-dimensional materials. As a high-temperature alloy, Monolayer nickel-zirconium (NiZr) exhibits unstable ferromagnetism in the absence of external stress. Nevertheless, the stability of its ferromagnetic state is significantly enhanced under applied stress, where tensile stress induces an increase in magnetic moment. The effect of stress on the magnetic moment can be attributed to variations in the band structure. Specifically, the band structure of monolayer NiZr, which is characterized by stable ferromagnetism under stress, and exhibits both semiconductor and semi-metallic characteristics. This variation in band structure originates from spin fluctuations among d and p electrons, which are influenced by the surrounding potential field. In detail, d and p orbitals form nonorthogonal linear combinations such as p_z-d_xx-yy, p_x-d_zx, and p_y-d_yz. The stress-induced modulation of magnetic properties is primarily manifested through the response of the d_zx and d_zy spin orbitals. With an increase in tensile stress, the occupancy of the d_zy orbital increases correspondingly, while the spin orientation of other orbitals is reversed, simultaneously. Notably, under tensile strain, the occupancy of the d_zx spin orbital increases, whereas that of the d_zy spin orbital decreases. In contrast, the changes in other orbitals remain relatively negligible under compressive stress. Consequently, this phenomenon leads to variations in orbital coupling, as well as in distributions within both orbital space and spin charge space. Under stress, the coupling between d and p orbitals results in the formation of σ bonds and π bonds. The interaction between p orbitals and σ bonds is significantly stronger than that between p orbitals and π bonds, and this discrepancy constitutes one of the primary factors driving the stress-induced changes in the magnetic properties of monolayer NiZr.