Dimensionality Reduction in Artificial Spin Ice*

Over the past ten years, square and hexagonal arrays of single-domain nanomagnets, known as artificial spin ice, have been used to study the microscopic properties of geometrical frustration. Here we describe the fabrication of a new type of artificial spin ice, the tetris lattice. The ground state configuration of the nanomagnets' moments was determined with photoemission electron microscopy. This lattice is designed such that its vertices (small clusters of nanomagnets) cannot all simultaneously achieve their ground state. As a consequence, the lattice decomposes into alternating ordered and disordered one-dimensional bands of moments. The disordered bands can be described by a thermal one-dimensional Ising model, underscoring the emergent dimensionality reduction found in this lattice.