Classical generalized constant-coupling method for geometrically frustrated magnets: Microscopic formulation and effect of perturbations beyond nearest-neighbor interactions

Abstract

The critical behavior of the pyrochlore lattice with nearest-neighbor (NN) interactions, next-nearest-neighbor (NNN) interactions, and site dilution by nonmagnetic impurities is studied within the framework of the microscopic formulation of the generalized constant-coupling method. In the paramagnetic regime, we recover all the results previously obtained in a more phenomenological way, which were shown to be in excellent agreement with Monte Carlo calculations for this lattice. In the absence of applied magnetic field, it is found that, for antiferromagnetic interactions, the equilibrium configuration is a noncollinear configuration in which the total magnetization of the unit is zero and the condition under which such an ordered state occurs is also obtained from the calculation. However, frustration inhibits the formation of such a state, and the system remains paramagnetic down to 0 K, if only nearest-neighbor interactions are taken into account, in agreement with the now generally accepted idea. NNN interactions, however, can stabilize a noncollinear ordered state, or ferromagnetic one, depending on the relation between NN and NNN interactions, in agreement with mean-field calculations, and the phase diagram is calculated. Finally, it is found that site dilution is not enough by itself to form such an ordered state.