Micromagnetic understanding of switching and self-oscillations in ferrimagnetic materials

Abstract

Ferrimagnetic materials (FiM) represent a promising direction for the realization of spin-based devices since they can combine the THz ultrafast dynamics typical of antiferromagnets (AFMs) with an easier way to control the magnetic state via well-established optical and electrical methods already applied to FMs, such as the magneto-optical Kerr effect (MOKE)1 or anomalous Hall effect (AHE)2. FiMs can be modeled as AFMs by considering two antiferromagnetically-coupled sublattices3-5 but, unlike AFMs, the two magnetic sublattices can have a different magnetic moment and angular momentum. Consequently, the net magnetization and angular momentum of FiMs can be varied by changing either the FiM’s chemical composition6 or temperature7 leading to two different compensation points: the magnetic compensation point (MCP), i.e. a zero net magnetization state, and an angular momentum compensation point (AMCP), i.e., a vanishing net angular momentum compensation state. In this work, we micromagnetically analyze, by means of Petaspin micromagnetic solver5, the magnetization dynamics of a current-driving transition metal/rare earth ferrimagnet in a spin Hall geometry as a function of the uncompensation parameter of the angular moments of the two sublattices8. This approach allows us to show the crucial effect of non-uniform dynamics in the system which cannot be caught by the macrospin approximation.Particularly, we have reported the switching time as a function of the uncompensation parameter (FIG.1) for a current |J| = 1.3 TA/m2. We have shown the switching time diverges at the AMCP, where the only dynamical solution is a self-oscillation state. More interestingly, a finite discontinuity of the switching time appears near the MCP. We show that this discontinuity is related to a change of the switching mechanism, from uniform to non-uniform dynamics with a corresponding increase of the switching time in the latter case.We have additionally analyzed the effect of the interfacial Dzyaloshinskii-Moriya interaction (IDMI) on the switching time and oscillations amplitude. These are relevant characteristics for the design of magnetic memories (switching time) and spin torque nano-oscillators (oscillation amplitude) since they will determine their performances. In FIG.1, we can see the effect on the switching time of the IDMI and how it is beneficial for the use of FiMs as storage devices since it promotes shorter switching times as it advantageously assists the nucleation of new domains.In this work, we also study the self-oscillation frequency and amplitude as a function of the current density. We show that the current thresholds between the changes of dynamical state are well described by the analytical macrospin formula8. We observe a linear dependence of the frequency on current independently of the IDMI and compensation point in agreement with the analytical formula8. For example, by considering the MCP case (FIG.2), the amplitude of the oscillations decreases non-monotonically as the current increases.For the self-oscillation case, we observe that the effect of IDMI is detrimental for the applicability of FiM as THz sources because it induces a significant reduction of the self-oscillations amplitude at low currents (see Fig. 2). Besides, as we can see in Fig.2, the peak-to-peak amplitude of the oscillations non-monotonically decreases as the current increases. This is due to the non-uniform oscillation mediated by domain walls. For low currents, the domain wall periodicity is larger than the device size and, hence, the whole device oscillates with roughly the same phase As we increase the current, the periodicity decreases thus averaging the out-of-plane component of the Néel vector over the sample size reduces the value of the peak-to-peak amplitude. Consequently, we obtain the minimum amplitude when the periodicity is close to the device size. By further increasing the current, the periodicity becomes smaller and the average magnetization value increasesOur results give a better insight into the dynamics excited in FiMs thus paving the way for the design of more performant ferrimagnetic memory and THz nano-oscillator devices. **