  Three-dimensional magnetic metamaterials feature interesting phenomena that
arise from a delicate interplay of material properties, local anisotropy,
curvature, and connectivity. A particularly interesting magnetic lattice that
combines these aspects is that of nanoscale gyroids, with a
highly-interconnected chiral network with local three-connectivity reminiscent
of three-dimensional artificial spin ices. Here, we use finite-element
micromagnetic simulations to elucidate the anisotropic behaviour of nanoscale
nickel gyroid networks at applied fields and at remanence. We simplify the
description of the micromagnetic spin states with a macrospin model to explain
the anistropic global response, to quantify the extent of ice-like
correlations, and to discuss qualitative features of the anisotropic
magnetoresistance in the three-dimensional network. Our results demonstrate the
large variability of the magnetic order in extended gyroid networks, which
might enable future spintronic functionalities, including neuromorphic
computing and non-reciprocal transport.
