A first-principles study of magnetic switching and hysteresis effect in the ferromagnetic Fe metal

Abstract

The first-principles calculation method used in this study has an extended Hamiltonian, which contains both spin states, so that the spin magnetic moment per unit cell, m , and magnetization vector, M , can be obtained via the spinors of atomic orbitals. Both spin- and orbital- B -field couplings are considered. The magnetic field, B , induces not only components of m and M along their directions, which vanish when the field is cut off, but also bi-stable spontaneous z components, m z and M z . This study reveals that the spin- B -field coupling is energetically too weak to reverse m z / M z directly. The B field is found to reverse the spin polarization of itinerant s p electrons first when B reaches a threshold, which then triggers the reversal of m z / M z via nonlocal exchange interactions with localized d electrons. The hysteresis effect is found to be due to the existence of bi-stable m z / M z and that without a reversed B the spin-polarization of itinerant s p electrons won’t be reversed to trigger magnetic switching. • The first use of spinors to obtain the 3-D magnetization vector in Fe. • The conventional magnetic field is energetically too weak to cause magnetic switching directly. • The magnetic field reverses spin polarization of sp electrons first, which then triggers reversal of magnetization through nonlocal exchange couplings. • The relationship between the calculated magnetization and the magnetic field is hysteresis-loop-like. • The magnetic switching can be assisted by an accompanying strong transverse magnetic field.