Spin-ice behavior of three-dimensional inverse opal-like magnetic structures: Micromagnetic simulations

We perform micromagnetic simulations of the magnetization distribution in inverse opal-like structures (IOLS) made from ferromagnetic materials (nickel and cobalt). It is shown that the unit cell of these complex structures, whose characteristic length is approximately 700 nm, can be divided into a set of structural elements some of which behave like Ising-like objects. A spin-ice behavior of IOLS is observed in a broad range of external magnetic fields. Numerical results describe successfully the experimental hysteresis curves of the magnetization in Ni- and Co-based IOLS. We conclude that ferromagnetic IOLS can be considered as the first realization of three-dimensional artificial spin ice. The problem is discussed of optimal geometrical properties and material characteristics of IOLS for the spin-ice rule fulfillment.