Spin multiplole moments as collective quantum phenomena

In this paper we investigate the occurrence of multipole moments of a collection of spins in a quantum magnetic system. To get insights into the behaviour of such systems we start by considering small spin clusters composed of dimers, trimers, as well as mixed spin systems with four spins. We focus our attention on the quantum multipole states, that gave rise to the widely discussed spin nematic and spin liquid phases. The magnetic properties of these systems are computed and the main differences between bosonic and fermionic multipolar states are discussed.