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

Abstract

Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements, 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-ofequilibrium dynamic, fluctuating state. 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 we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. 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. We have observed that they follow an Arrhenius-type Néel-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 computed with micromagnetic simulations. Artificial Spin Ice (ASI) systems are patterns of interacting ferromagnetic nanoelements whose particular geometry forces the ground state of the system to be magnetically frustrated, as not all the pairwise magnetic dipolar interactions between elements can be satisfied simultaneously 1-3. These lithographically defined nanostructures mimic the behaviour of the spin-ice pyrochlores, where the arrangement of the rare earth magnetic moments leads them to lie in a frustrated state 4-6. In turn, the pyrochlore crystals take the spin-ice name from water ice, due to the fact that the magnetic moments in the spin-ices map to the proton ordering in the molecules of water ice 7. The basic ingredient of the ASIs is that the dimensions of the nanomagnets that form the array force them to have an Ising-like single-domain bistable behaviour of the magnetization, so that they can be treated as macrospins. These two-dimensional analogues of naturally-occurring spin-ice materials are being extensively studied, as their properties can be tuned at will by changing the nanomagnets' dimensions, materials and/or geometries 8 , providing a huge landscape of possibilities to explore.