Magnetization dynamics in a Majorana-wire–quantum-dot setup

We theoretically study the quench dynamics of the local magnetization in a hybrid Majorana-wire--quantum-dot system coupled to external leads. In order to thoroughly understand the origin of the dot magnetization dynamics, we consider either normal metal or ferromagnetic electrodes. In the first case, the magnetization arises exclusively from the proximity to the topological superconductor hosting Majorana zero-energy modes and the associated development of an induced exchange field. We predict a nonmonotonic dependence of the dot's magnetization in the odd-occupation regime and show that the dynamics is governed by the magnitude of the coupling to Majorana wire. However, when the system is coupled to ferromagnetic leads, the ferromagnet and Majorana contributions to the effective exchange field are competing with each other and reveal a nontrivial dynamical behavior. As a result, the time-dependent magnetization can undergo multiple sign changes preceding the relaxation to a new thermal value. We also identify the transport regime, where fine tuning of the coupling to Majorana wire within a narrow range allows one to manipulate the magnetic state of the system. The effect of spin polarization of the leads and influence of the finite overlap between the Majorana edge modes are also examined. Moreover, we analyze the quench in the energy of the quantum dot orbital level and demonstrate that the rather straightforward charge dynamics can disguise nontrivial time evolution of the magnetization. Finally, we compare predicted dynamics with results obtained for quantum dot coupled to spin-polarized fermionic bound state instead of Majorana zero-energy mode.