Spin Wave Spectral Probing of Possible Micro-states in building block of Macroscopically Degenerate Artificial Spin Ice

Abstract

Square Artificial Spin Ices (S-ASI)1-3 are the 2-dimensional realization of the standard 3-dimensional spin ice material of the type Dy2Ti2O7 (pyrochlore compound), with the alluring possibility of studying geometric frustration in a controlled way. In addition to the frustration, these kinds of structures enable the investigation of a variety of fascinating phenomena such as frustration, emergent magnetic monopoles, collective magnetization dynamics of interacting spins, and phase transition, etc. Recently, there is a focus on the understanding of dynamical behavior of spins or spin wave (sw) modes in such dipolar coupled systems. Detailed understanding of such behavior may be of importance to the applications in magnonics4,5. Here, we have investigated the sw modes of strongly dipolar coupled, highly anisotropic nanoislands forming S-ASI system using micro-magnetic simulation in MUMAX3 in combination with MATLAB coding. For the same, we have systematically scrutinized the sw spectra of the building block of S-ASI which is a square ring-like structure of highly shape anisotropic nanoislands of permalloy6,7. The evolution of the spectra as a function of no. of rings of up to four rings forming a S-ASI with closed edges exhibit a direct relation between the sw modes and the micro-states of the system. The study reveals that a single ring-type structure can alone be adequately used to understand the sw modes of S-ASI as well as it’s behavior in the presence of an external bias field. All the ring-type structures studied show ubiquitous switching identifier mode at approximately 14 GHz. Detailed analysis of the spin wave propagation modes in the building block as well as individual vertices of S-ASI structure will be discussed in this work.