Tunable Magnetic Relaxation Mechanism in Magnetic Nanoparticles

We investigate theoretically the magnetization dynamics of a conducting magnetic nanoparticle weakly coupled to source and drain electrodes, under the assumption that all relaxation comes from exchange of electrons with the electrodes. In the regime of sequential tunneling, the magnetization dynamics is characterized by a relaxation time $t_1$, which strongly depends on temperature, bias voltage, and gate voltage. While a direct measure of a nanoparticle magnetization might be difficult, we find that $t_1$ can be determined through a time resolved transport measurement. For a suitable choice of gate voltage and bias voltage, the magnetization performs a bias-driven Brownian motion regardless of the presence of anisotropy.

Figure 1

(a) Schematic of the system under consideration: a ferromagnetic nanoparticle (F) is connected via tunneling junctions to two electrodes, which can be normal (N) or ferromagnetic (F) metals. A bias voltage $V_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}$ is applied across the nanoparticle, while a gate voltage $V_{\mathrm{g}}$ can be applied on a gate capacitively coupled to the particle. (b) Structure of the electronic ground state of the nanoparticle. The ground state has $N_{\mathrm{s}}$ singly occupied levels and Fermi levels $E_{\mathrm{M}}$ and $E_{\mathrm{m}}$ for majority and minority electrons, respectively.

Figure 2

Current $I$ (upper) and reduced magnetization $⟨S_z⟩/S$ (lower) as a function of the bias voltage $V_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}$ for a system with $J=1$, $K=0.1$, and $k_{B}T=0.01$. The down (up) arrows correspond to minority (majority) states that become involved in the tunneling processes.