Magnetization Dynamics of weakly Interacting sub-100 nm Square Artificial Spin Ices

Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements [1], provides a fascinating opportunity to observe the physics of out of equilibrium systems. Initial studies concentrated on the static, frozen state, whilst more recent studies have accessed the out-of-equilibrium dynamic, fluctuating state [2–4]. This opens up exciting possibilities such as the observation of systems exploring their energy landscape through monopole quasiparticle creation, potentially leading to ASI magnetricity, and to directly observe unconventional phase transitions. In this work [5] we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. We fabricated and measured square Artificial Spin Ice samples formed by nanoimagnets made of Permalloy (Ni 80 Fe 20 with lateral dimensions of 68nm x 22nm, with two different thicknesses: 5nm and 6nm, and three different lattice spacings: 138nm, 175nm and 208nm, forming a total of six samples. We have investigated the effect of the interaction strength on the magnetization dynamics at different temperatures in the range where the nanomagnets are thermally active and have observed that they follow an Arrhenius-type Neel-Brown behaviour. An unexpected negative correlation of the average blocking temperature with the interaction strength is also observed, which is supported by Monte Carlo simulations. The magnetization relaxation measurements show faster relaxation for more strongly coupled nanoelements with similar dimensions. The analysis of the stretching exponents obtained from the measurements suggest 1-D chain-like magnetization dynamics. This indicates that the nature of the interactions between nanoelements lowers the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to quantify the effective interaction energy of a square ASI system, and compare it to the interaction energy calculated from a simple dipole model and also to the magnetostatic energy computed with micromagnetic simulations.