First-principles study on magnetism of Ru monolayer under an external electric field

Electric field control of magnetic properties such as magnetic moment and magnetic anisotropy has been attracted. For the 4$d$ TM films, on the other hand, it was recently reported that the ferromagnetism Pd thin-film is induced by application of an external electric field otherwise Pd thin-film shows paramagnetic [1]. However, little attention has been paid to the magnetism of other 4$d$ TMs. Here, we investigate the magnetism of the free-standing Ru monolayer and that on MgO(001) substrate under an external electric field by using first-principles FLAPW method [2]. We found that the free-standing Ru monolayer is ferromagnet with magnetic moment of 1.50 $¥mu_B$/atom. The MA energy is 3.45 meV/atom, indicating perpendicular MA, at zero electric field ($E$=0) and increases up to 3.84 meV/atom by application of $E$=1 (V/{¥AA}). The Ru monolayer on MgO(001) substrate is also ferromagnet with magnetic moment of 0.89 $¥mu_B$/atom. The MA energy is 1.49 meV/atom, indicating perpendicular MA, at $E$=0 and decreases to 1.33 meV/atom by application of $E$=1 (V/{¥AA}). [1] Y. Sun, J. D. Burton, E. Y. Tsymbal, PRB 81, 064413 (2010). [2] K. Nakamura, T. Ito, A. J. Freeman, L. Zhong, J. Fernandez-de-Castro, PRB, 67, 014420 (2003).