The quantum spin-1/2 frustrated Heisenberg model on a stacked square lattice: a spin wave theory study

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The ground state phase diagram and staggered magnetization of the quantum spin-1/2 Heisenberg models in the presence of nearest-neighbor (J1) andnext-nearest-neighbor (J2) interactions (J1–J2 model) on a stacked square lattice, where we introduce an interlayer coupling throughnearest-neighbor bonds of strength , are investigated by using linear spin wave theory. We analyze the order parametermA for the ordered phases: antiferromagnetic (AF,J1 > 0), ferromagnetic(F, J1 < 0) and collinear (CAF—collinear antiferromagnetic and CF—collinearferromagnetic) as a function of the frustration parameter (α = J2/|J1|) and for several values of the interlayer parameter (). We obtain the ground state phase diagram in theλ–α plane. We found different ordered states depending on the values ofλ andα and the signof J1: AF (F)and CAF (CF), and a disordered state: the quantum paramagnetic state (QP). For an intermediate regionα1c(λ) < α < α2c(λ) we observe a QP phasefor the case of J1 > 0 (AF)that disappears for λ below some critical value . For α < α1c(λ) and α > α2c(λ), andbelow λ1, we have the AF and CAF semi-classically ordered states, respectively. Atα = α1c(λ) a second-order transition between the AF and QP states occurs and atα = α2c(λ) a first-order transition between the AF and CAF phases takes place. The boundariesbetween these ordered phases merge at the critical end point—, where αc = 1/2. Above this CEP there is again a direct first-order transition betweenthe AF and CAF phases, with a behavior governed by the pointαc independentlyof λ ≥ λ1. ForJ1 < 0 (F)and λ > 0 the QP intermediate region was not observed; only a small region ofthe disordered state (QP) was predicted in the two-dimensional limit (λ = 0).