Competing antiferromagnetic and spin-glass phases in a hollandite structure

We introduce a simple lattice model with Ising spins as a zeroth-order approximation of the hollandite-type magnetic compounds. We argue that geometrical frustration of the lattice in combination with nearest-neighbor antiferromagnetic (AFM) interactions are responsible for the appearance of a spin-glass phase in presence of disorder. We investigate this system numerically using parallel tempering. The model reproduces magnetic transitions present in some oxides with hollandite structure and displays a rich phenomenology: in the absence of disorder we have identified five different ground states, depending on the relative strength and sign of the interactions: one ferromagnetically ordered, three antiferromagnetically ordered, and one disordered, macroscopically degenerate ground state. Remarkably, for the sets of AFM couplings having an AFM ground state in the clean system, there exists a critical value of the disorder above which the ground state becomes a spin glass while maintaining all the couplings antiferromagnetically. This model presents this kind of transition with nearest-neighbor frustrated AFM interactions. We argue that this model is useful for understanding the relation between AFM coupling, disorder, and appearance of spin-glass phases.