Electric-field-induced modification in magnetocrystalline anisotropy, exchange interaction, and Curie temperature of transition-metal thin films

Magnetism induced by an external electric field ($E$-field) has received much attention as a potential approach for controlling magnetism at the nano-scale with the promise of ultra-low energy power consumption. For magnetocrystalline anisotropy (MCA) in transition-metal thin films, it is agreed that a change in the screening charge density due to an $E$-field, which causes a small change in band structures around Fermi energy, gives rise to a modification of the MCA energy.\footnote{Nakamura et.al, PRL{\bf 102}, 187201(2009); PRB{\bf 81}, 220409(2010)} Here, we extend our first-principles investigation to Curie temperature of an Fe monolayer in an $E$-field. Calculations were carried out using film-FLAPW method that treats spin-spiral structures in an $E$-field. Results predict that when the $E$-field is introduced, calculated magnon (spin-spiral formation) energy is modified, by a few tens of meV, compared to that in zero field. The exchange parameters within the classical Heisenberg model, by making the back Fourier transformation of the magnon energy, suggest the $E$-field-induced modification of Curie temperature. Taking a large MCA energy of the monolayer into account, the modification of Curie temperature by the $E$-field was demonstrated by Monte Carlo simulations.