Tuning domain wall oscillation frequency in bent nanowires through a mechanical analogy.

In this work, we present a theoretical model for domain wall (DW) oscillations in a curved magnetic nanowire with a constant curvature under the action of a uniaxial magnetic field. Our results show that the DW dynamics can be described as that of the mechanical pendulum, and both the NW curvature and the external magnetic field influence its oscillatory frequency. A comparison between our theoretical approach and experimental data in the literature shows an excellent agreement. The results presented here can be used to design devices demanding the proper control of the DW oscillatory motion in NWs.

Curvature-induced stabilization and field-driven dynamics of magnetic hopfions in toroidal nanorings.

Three dimensional magnetic textures are a cornerstone in magnetism research. In this work, we analyze the stabilization and dynamic response of a magnetic hopfion hosted in a toroidal nanoring with intrinsic Dzyaloshinskii-Moriya interaction simulating FeGe. Our results evidence that unlike their planar counterparts, where perpendicular magnetic anisotropies are necessary to stabilize hopfions, the shape anisotropy originated on the torus symmetry naturally yields the nucleation of these topological textures. We also analyze the magnetization dynamical response by applying a magnetic field pulse to differentiate among several magnetic patterns. Finally, to understand the nature of spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases and describe the differences among bulk and surface modes. Importantly, hopfions lying in toroidal nanorings present a non-circularly symmetric poloidal resonant mode, which is not observed in other systems hosting hopfions.

Motion-induced inertial effects and topological phase transitions in skyrmion transport.

When the skyrmion dynamics beyond the particle-like description is considered, this topological structure can deform due to a self-induced field. In this work, we perform Monte Carlo simulations to characterize the skyrmion deformation during its steady movement. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. These transitions are characterized by the proliferation of skyrmions and a different total topological charge, which is obtained as a function of the skyrmion velocity. Our findings provide an alternative way to describe the dynamics of a skyrmion that accounts for the deformations of its structure. Furthermore, such motion-induced topological phase transitions make it possible to control the number of ferromagnetic skyrmions through velocity effects.

Scattering modes of skyrmions in a bilayer system with ferromagnetic coupling.

Magnetic skyrmions are quasiparticle-like textures that are topologically different from a single domain magnetization state. Their topological protection, combined with the low current density needed to move them, make these objects relevant to be used as information storage structures. In such a context, the analysis of the interactions between skyrmions is interesting and relevant for future applications. In this work, through micromagnetic simulations and numerical calculations, we studied the interaction between two skyrmions living on different parallel ferromagnetic racetracks connected by an exchange-like interaction. The upper and lower racetracks are separated by a height offset and the interaction between the upper and the lower skyrmion is analyzed in terms of the magnetic and geometrical parameters. Three states are predicted, as a function of these parameters: scattered or free skyrmions, bound skymions, and annihilated skyrmions. Our results, presented in a phase diagram, demonstrate that even in the case here called free skyrmions, there is a small and brief interaction when both are close enough, but the skyrmion in the top layer does not drag the skyrmion in the bottom layer. For bound skyrmions, both keep linked during larger times. In the latter case, there are strong changes in the velocity of the skyrmions induced by the effect of a higher effective mass when both are coupled.

Dynamic and static properties of stadium-shaped antidot arrays.

In this work we performed a detailed numerical analysis on the static and dynamic properties of magnetic antidot arrays as a function of their geometry. In particular, we explored how by varying the shape of these antidot arrays from circular holes to stadium-shaped holes, we can effectively control the magnetic properties of the array. Using micromagnetic simulations we evidenced that coercivity is very sensitive to the shape of antidots, while the remanence is more robust to these changes. Furthermore, we studied the dynamic susceptibility of these systems, finding that it is possible to control both the position and the number of resonance peaks simply by changing the geometry of the holes. Thus, this work provides useful insights on the behavior of antidot arrays for different geometries, opening routes for the design and improvement of two-dimensional technologies.

Synchronization of two spin-transfer-driven nano-oscillators coupled via magnetostatic fields.

The magnetization dynamics of nano-oscillators may be excited by both magnetic fields and spin-polarized currents. While the dynamics of single oscillators has been well characterized, the synchronization of several ones is not fully understood yet. An analytical and numerical study of the nonlinear dynamics of two magnetostatically coupled spin valves driven by spin-transfer torques is presented under the macrospin approximation. The oscillators interact via magnetostatic fields and exhibit a robust synchronized magnetization motion. We describe the magnetization dynamics of the system using the Landau-Lifshitz-Gilbert-Slonczewski equation. Using a modal decomposition technique, we describe the dynamics, synchronization, and competition of oscillatory modes as a function of the current density, and the geometrical parameters of the setup. Simulations of the Landau-Lifshitz-Gilbert-Slonczewski equation show good agreement with an approximate analytic solution.

Thermal gradients for the stabilization of a single domain wall in magnetic nanowires.

By means of Monte Carlo simulations we studied field driven nucleation and propagation of transverse domain walls (DWs) in magnetic nanowires subjected to temperature gradients. Simulations identified the existence of critical thermal gradients that allow the existence of reversal processes driven by a single DW. Critical thermal gradients depend on external parameters such as temperature, magnetic field and wire length, and can be experimentally obtained through the measurement of the mean velocity of the magnetization reversal as a function of the temperature gradient. Our results show that temperature gradients provide a high degree of control over DW propagation, which is of great importance for technological applications.

Tailoring the nucleation of domain walls along multi-segmented cylindrical nanoelements.

The magnetization reversal of three-segment cylindrical nanoelements comprising alternating nanowire and nanotube sections is investigated by means of Monte Carlo simulations. Such nanoelements may feature a three-state behaviour with an intermediate plateau in the hysteresis curve due to a metastable pinning of the domain walls (DWs) at the wire-tube interfaces. It turns out that vortex as well as transverse DWs contribute to the magnetization reversal. By varying the geometric parameters, the sequence, or the material of the elements the nucleation location of DWs, as well as their nucleation field, can be tailored. Especially interesting is the novel possibility to drive DWs coherently in the same or in opposite directions by changing the geometry of the hybrid nanoelement. This important feature provides additional flexibility to the construction of logical devices based on DW movement. Another prominent outcome is that DWs can be nucleated near the centre of the element and then traverse to the outer tips of the cylindrical structure when the applied field is increased, which also opens the possibility to use these three-segment nanoelements for the field-induced delivery of DWs as substitutes for large nucleation pads.

Asymmetric hysteresis loop in magnetostatic-biased multilayer nanowires.

The hysteresis of multilayer nanowires composed by a soft magnetic cylindrical wire, a non-magnetic spacer layer and an external hard magnetic shell is investigated. The external magnetic shell originates a non-homogeneous magnetic field on the inner wire, which is responsible for a displacement and a change of the width of the hysteresis curve of the wire. Moreover, different reversal modes occur at each branch of the hysteresis loop, which can be understood by analyzing the interaction magnetostatic field along the wire. Our results open the possibility of controlling two parameters of the hysteresis loop, the coercivity and the bias, providing an interesting system to be investigated.

Geometry dependence of coercivity in Ni nanowire arrays.

Magnetic properties of arrays of nanowires produced inside the pores of anodic alumina membranes have been studied by means of vibrating sample magnetometer techniques. In these systems the length of the wires strongly influences the coercivity of the array. A simple model for the coercivity as a function of the geometry is presented which exhibits good agreement with experimental results. Magnetostatic interactions between the wires are responsible for a decrease of the coercive field.

Scaling approach to the magnetic phase diagram of nanosized systems.

Based on the discovery of a simple scaling relation, a new technique for the investigation of the phase diagram of nanosized magnetic systems is proposed. By scaling the exchange interaction between magnetic moments, the magnetic phase diagram of currently lithographically produced particles can be obtained from those corresponding to much smaller systems. Such a technique reduces the computation time by several orders of magnitude, and provides a new approach to the investigation of the relative stability of distinct internal magnetic configurations of nanosized systems. The technique is illustrated by the determination of the phase diagram of cylindrically shaped Co particles.