Transition from antiferromagnetic to quadrupole order in a modified square artificial spin ice

The results of a numerical study of an ordered substitution of a double-segment into the unit cell of square artificial spin ice are presented. Each pattern vertex has three magnetic moment configurations that compete to form a magnetic ground state in zero applied magnetic field, including nearest-neighbor and next-nearest-neighbor interaction contributions to the total magnetostatic energy. The ground state depends on the number of lattice sites considered and the spacing between the two film segments that comprise the double segment. Monte Carlo simulations reveal that the double-segment sublattice undergoes long-range antiferromagnetic order that can be supplanted by magnetic quadrupole order by applying an in-plane magnetic field perpendicular to the double-segment easy axis. The quadrupole-ordered state consists of a sublattice of weakly correlated chains of double-segments with antiparallel polarizations, which admits many different ground states that reflect a very high degree of frustration.