Magnetic and electronic properties of bulk and (111), (001), and (110) surfaces of the Heusler Zr2RhIn alloy

The electronic and magnetism properties of the bulk as well as (111), (110), and (001) surfaces of Heusler alloy Zr₂RhIn have been studied by using first-principles calculations with (GGA-PBE) method. According to calculations, the compound Zr₂RhIn exhibits full spin polarization and half-metallic ferromagnetic behavior at an equilibrium lattice constant of 6.8 ± 0.01 Å. The energy gap and spin flip gap in the minority channel are 0.47 and 0.11 eV, respectively. The total magnetic moment is 2 ± 0.05 µ_B which agrees with the Slater-Pauling rule. The electronic, magnetism properties and atomic relaxation were examined for the (1 1 1), (0 0 1), and (1 1 0) surfaces of the Zr₂RhIn alloy. The results confirm that the half-metallic property was preserved at Zr1-, Zr2-, and In-terminations (1 1 1) surfaces, but disappeared at Rh-terminated (1 1 1) surface due to the surface states, likewise disappeared at (0 0 1) and (1 1 0) surfaces. These findings highlight the sensitivity of half-metallicity to surface orientation and termination, making Zr₂RhIn a promising candidate for spintronic devices.