Quasiantiferromagnetic 120° Neacuteel state in two-dimensional clusters of dipole-quadrupole-interacting particles on a hexagonal lattice

The magnetostatic interactions of colloidal particles, capped with radially magnetized Co/Pt multilayers, are modeled. Motivated by experiment the particles are arranged in microscopic two-dimensional clusters on a hexagonal lattice and are free to rotate. The thermodynamically stable states of clusters containing up to 108 particles are calculated theoretically by means of Monte Carlo simulations in the framework of multipole expansion. It is shown analytically that radially magnetized hemispheres have higher-order multipole moments beyond the dipole. Depending on geometrical details also even order moments appear. The even order moments break the inversion symmetry of the magnetic potential of a single particle. For a specific mixing ratio of dipole and quadrupole moments, the experimentally observed antiferromagnetic 120 degrees Neacuteel state in the clusters is found.