Thermally induced magnetic relaxation in square artificial spin ice

Abstract

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice – we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.

Collective magnetic dynamics in artificial spin ice probed by ac susceptibility

“…28 Micromagnetic calculations using MuMax 329 revealed non-collinearities of the moment within the islands. A reduced effective moment of approximately m 0,eff = 0.65 × m 0 = 4.2 × 10 6 µ B at T = 0 K, is used to compensate for the dynamic non-collinear internal magnetic structure of the elements (see Andersson et al 16 , Bessarab et al 30 , Bessarab et al 31 and Gliga et al 32 ).…”

“…Furthermore, the intrinsic effective moment m eff (T ) of the mesospins is temperature dependent 6,8,16 :…”

“…In the framework of a weak-coupling regime in spin glasses, Shtrikman and Wohlfarth 36 offered a recipe for extracting the typical interaction energy between the magnetic components by using the mean-field based formula: Fig. 3, assuming a fixed τ0 = 1 · 10 −11 s, as done in Andersson et al 16 for the same samples. Right column: Characteristic magnetostatic interaction energies obtained from the VFT fits in the weak coupling formalism using Eq.…”

“…We study arrays that are composed of close to identical mesospins, with different gaps between the elements, in order to explore the influence of coupling strength on the collective dynamics. Exploring the frequency dependence of the AC susceptibility signal we employ the VFT law, that can be used for describing the low-field magnetic relaxation of weakly interacting nanoparticle systems 24,25 but has recently been applied also to ASI systems 16,17 , attempting to extract parameters that can be directly related to the magnetostatic energies of the ASI arrays.…”

Disordered kagomé spin ice

“…10 The combination of experimental and computational work on artificial spin ice has led to a better understanding of the phases, dynamics, and interactions that take place in physical systems. [11][12][13] Square lattices of artificial spin ice have been created and shown to preserve the 2-in/2-out, low temperature configuration, at each vertex. 14 By increasing the temperature, or reducing the magnetic coupling by increasing the spacing between islands, magnetic charge excitations (monopoles) can be created which then propagate through the lattice; a subject of intense investigation.…”