Spectral Analysis of Topological Defects in an Artificial Spin-Ice Lattice

Abstract

Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasistatic and equilibrium behavior of the spin-ice lattice. Here, we study the eigenmode dynamics of such defects in a square lattice consisting of stadiumlike thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings that can be measured experimentally.

Reconfigurable wave band structure of an artificial square ice

“…The resonant mode spectrum of square ices has been studied numerically by means of micromagnetic simulations, demonstrating the observable effects of magnetic defects [24]. More recently, a detailed numerical study has shown that edge modes arising from the internal degrees of freedom of the magnetization equally have observable consequences in the resonant spectrum in sufficiently thick nanoislands [25].…”

“…1(a), and obeys the "ice rules" in which * ezio.iacocca@colorado.edu low-energy states are characterized by the magnetization in two nanoislands pointing into a vertex and out of the vertex in the two other nanoislands. Dynamically, correlated excitations are supported in spin ices because of the magnetostatic interactions between nanoislands [24]. Because of their intrinsic periodicity and wealth of static states, artificial spin ices offer interesting opportunities as programmable magnonic crystals to control the magnon dispersion and band gap [20].…”

Magnetization dynamics of coupled ferromagnetic disks

“…One example are artifical spin ices 1 , in which geometry is utilized to arrange for competing interactions between individual magnetic nanostructures. Artificial spin ices have been shown to support topological defects [1][2][3] , socalled Dirac monopoles and Dirac strings 4 , that play important roles in the static and quasi-static behavior of the systems [5][6][7][8][9][10][11] , and also give rise to specific signatures in the resonant spectrum 12 . Another deceptively simple system are two stacked ferromagnatic disks of a diameter of the order of one micrometer and a few tens of nanometers thick made from a soft magnetic material, such as Permalloy (Py).…”

Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state

“…Moreover, there is a temperature at which the bent edges 'melt', restoring the time-averaged magnetic symmetry. These results open new possibilities for tailoring collective behavior in artificial spin ice, for example for possible magnonic applications 15,16 , and also sets limits on the applicability of models that do not take into account the internal degrees of freedom present in such systems.…”

“…We have investigated the dynamic behavior of the ground state of artificial square ice at T = 0 K using fully three-dimensional finite-element micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation 15 considering an array of N = 120 stadiumshaped nanoislands ( Fig. 1a) with dimensions 290 nm × 130 nm and variable thicknesses with a lattice constant of 276 nm.…”