Effect of Dzyaloshinskii-Moriya Interaction at Ferrimagnet and Heavy Metal Interface

Ferrimagnets (FiMs) are divided into small domains comprising of oppositely polarized magnetic moments and weak anisotropy. FiM possesses a small net magnetization with strong exchange coupling energy. When FiM comes in contact with a material having strong spin-orbit coupling, such as heavy spin Hall metal, the nonlinear magnetic exchange interaction known as Dzyaloshinskii-Moriya interaction (DMI) becomes significant, especially at the FiM/heavy metal (HM) interface. In this paper, we derive the contribution of DMI in FiM magnetization and show that DMI plays a crucial role in FiM magnetization dynamics. We show that torque is being exerted on the interfacial magnetic moments due to DMI, trying to reorient the interfacial magnetization landscape in FiM. On the other hand, exchange coupling tries to resist the external perturbation due to DMI and keep the interfacial magnetic moments at their respective equilibrium positions. Our analysis shows that simultaneous action of DMI and exchange coupling result in small tilting of the interfacial magnetic moments. Moreover, spin-polarized current, injected into the FiM, introduces oscillation due to two different types of spin-transfer torques-namely, field-like torque and dampinglike torque. We also show that the oscillation frequency of magnetic moments near the FiM/HM interface is a function of only internal FiM exchange coupling and interfacial DMI when the injected spin current density is low.