Quasispins of vacancy defects and their interactions in disordered antiferromagnets

Vacancy defects in disordered magnetic materials are established to act as effective spins, “quasispins,” when subjected to an external magnetic field. The contribution of these “quasispins” to the magnetic susceptibility is proportional to N_vac/T in the limit of low temperatures T and dilute vacancies N_vac in the system, similar to that of free spins. As the density of vacancies increases, their interactions may become essential in understanding the magnetic behaviour of the system. Motivated by frustrated and quasi-one-dimensional magnetic materials, we study analytically quasispins and their interactions in a generic system that has short-range antiferromagnetic order and lacks long-range order. We argue that a vacancy defect that does not disrupt the short-range antiferromagnetic order around it corresponds to a quasispin value that matches the value of spins of the magnetic atoms in the material, and the correlators of the quasispins of different vacancies match the spin-spin correlators in the vacancy-free material. We confirm our conclusions by exact calculations for Ising chains with nearest-neighbour and next-to-nearest-neighbour interactions. We compute the magnetic susceptibility up to the first virial correction that arises from the interactions of the vacancy quasispins.