Time-dependent spin and transport properties of a single-molecule magnet in a tunnel junction

In single-molecule magnets, the exchange between a localized spin moment and the electronic background provides a suitable laboratory for studies of dynamical aspects of both local spin and transport properties. Here we address the time evolution of a localized spin moment coupled to an electronic level in a molecular quantum dot embedded in a tunnel junction between metallic leads. The interactions between the localized spin moment and the electronic level generate an effective interaction between the spin moment at different instances in time. Therefore, we show that, despite being a single-spin system, there are effective contributions of isotropic Heisenberg and anisotropic Ising and Dzyaloshinski-Moriya character acting on the spin moment. The interactions can be controlled by gate voltage, voltage bias, the spin polarization in the leads, in addition to external magnetic fields. Signatures of the spin dynamics are found in the transport properties of the tunneling system, and we demonstrate that measurements of the spin current may be used for readout of the local spin moment orientation.