Dependence of spin wave modes on the geometry of nanomagnets in square artificial spin ice vertices

Abstract

In this work, we report our micromagnetic simulation results on the correlation between spin wave modes and emergent microstates in square artificial spin ice (S-ASI), consisting of elliptical and stadium shape magnetic nanoislands. S-ASI1 is a lithographically patterned engineered dipolar coupled nanostructure array, consisting of orthogonal square sublattices of highly shape anisotropic nanoislands. These islands behave as a macrospin due to high shape anisotropy where each macrospin, according to the dumbbell model, can be considered as a magnetic dipole of charge separated by the length of the nanoisland. Recently, there is a growing interest in the low-energy collective spin excitation of magnetic nanostructures of vastly different shapes resulting in the development of the field of magnonics. These excitations or spin waves are the magnetic analogs of electromagnetic waves, phonons, and plasmons which can be treated as a perturbation in terms of phase-coherent precession of magnetization vector that propagates in coupled magnetic media. The field of magnonics offers new functionalities in modern technological devices e.g., magnonics logic, phase shifters, microwave antenna, directional coupler, SW-based multiplexer, grating, and neuromorphic computing, etc.S-ASI exhibit geometrical frustration and therefore, it shows ground state degeneracy. The microstates in S-ASI enable the possibility of tunability of associated spin-wave modes and alter the spin-wave band gap without structural deformation. This key feature of S-ASI makes it a potential candidate for reconfigurable magnonics2. The interesting dynamic behavior of ASI suggests that it can be perceived as magnonic crystals with potential applications in logic devices3, data storage4, microwave filter5, spin logic gate3, etc. Hence, detailed investigation6, 7 of spin wave dynamics and evolution of modes in ASI systems involving highly shape anisotropic nanoislands of different shapes is very important. The question of the correlation between underlying magnetic states of dipolar coupled nanoislands of shapes such as ellipse and stadium, etc., and the spin wave modes is far from properly understood.In this work, we have performed a detailed study of the dynamical behavior of emergent microstates in S-ASI, using micromagnetic simulations. For these studies, we have considered S-ASI to be consisting of four square ring-type structures with elliptical and stadium shaped nanoislands of permalloy with dimensions 300 nm × 100 nm × 25 nm and lattice constant 150 nm (edge-to-edge distance of nanoislands). The magnetization reversal behavior of stadium-shaped magnetic nanoislands in S-ASI geometry involves the formation of vortices, antivortices, etc. whereas for the case of elliptical nanoislands the reversal involves sharp switching of spins. In order to investigate the dependence of the behavior of spin wave dynamics on local magnetic behavior in the S-ASI of two different shapes, we have investigated the spin wave modes and emergent microstates in both the shapes as a function of a number of square-type rings (i.e., single ring, double ring, triple ring, and quadruple ring e.g., S-ASI) of nanoislands. For S-ASI involving elliptical nanoislands, our studies reveal that emergent microstates at remanence with net local magnetic charges at the junction of the nanoislands for head-to-head or tail-to-tail configuration enhances spin wave generation in the proximity islands up-to ∼95% as compared to islands in the proximity of zero local charges ( in head-to-tail or tail-to-head configuration). Thus, we observe that the power profiles in remanence map the local charges present in the S-ASI or ring-type structures. We observe the presence of ubiquitous switching identifier mode at ~ 18 GHz (saturation) in nanoislands with an easy axis along the external bias field. This mode shows marked power variation in the switched nanoislands with respect to un-switched nanoislands. Our simulation results show that observed spin wave spectra and calculated mode profiles remain consistent as a function of rings. Our studies of S-ASI involving stadium shaped nanoislands further show that the spin wave spectra are significantly different than for the elliptical case (see Fig. 1). In the case of stadium-shaped nanoislands, the demagnetization field is inhomogeneous which creates variation in the local field within the nanoislands whereas, in the case of elliptical nanoisland, demagnetization field variation is observed near the edges. However, for a similar magnetization configuration, we have observed several new spin-wave modes with complex mode profiles in the case of stadium shape nanoislands (Fig. 2). Thus, our study gives new insight in understanding the origin of spin wave mode behavior in terms of the evolved microstates and demonstrate spin wave modes as a tool to investigate magnetization reversal and local magnetic charges in artificial spin ice system. **