First-order transition on the frustrated spin-1/2 Heisenberg ferromagnet on an anisotropic square lattice

•We study the ferromagnetic J1−J1′−J2 model on an anisotropic square lattice by using effective-field theory.•We obtain the ground phase diagram in the λ−α   plane (λ=J1′/J1 and α=J2/J1).•A comparison with the results of the antiferromagnetic J1−J1′−J2 model.•We propose a functional for the free energy.

We have studied the quantum spin-1/2 frustrated Heisenberg model with two ferromagnetic interactions: nearest-neighbor (NN) with different coupling strengths J1 and J1′ along x and y directions, respectively, competing with a next-nearest-neighbor (NNN) with coupling J2. Using the effective-field theory we obtain the ground-state phase diagram in the (λ,α  ) space, where λ=J1′/J1 and α=J2/J1. Depending on the values of λ and α we observe three different states: ferromagnetic (F), collinear ferromagnetic (CF) and quantum paramagnetic (QP). We observe a QP state between the ordered F and CF phases in the region λ1<λ<1 (λ1≃0.62).