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Long-range ordering is typically associated with a decrease in entropy. Yet,it can also be driven by increasing entropy in certain special cases. Wedemonstrate that artificial spin ice arrays of single-domain nanomagnets can bedesigned to produce entropy-driven order. We focus on the tetris artificialspin ice structure, a highly frustrated array geometry with a zero-point Paulientropy, which is formed by selectively creating regular vacancies on thecanonical square ice lattice. We probe thermally active tetris artificial spinice both experimentally and through simulations, measuring the magnetic momentsof the individual nanomagnets. We find two-dimensional magnetic ordering in onesubset of these moments, which we demonstrate to be induced by disorder (i.e.,increased entropy) in another subset of the moments. In contrast with otherentropy-driven systems, the discrete degrees of freedom in tetris artificialspin ice are binary and are both designable and directly observable at themicroscale, and the entropy of the system is precisely calculable insimulations. This example, in which the system's interactions and ground stateentropy are well-defined, expands the experimental landscape for the study ofentropy-driven ordering.

Entropy-driven order in an array of nanomagnets