Dome-shaped phase diagram in the spin-1 XY ferromagnet with biquadratic exchange and longitudinal easy-axis crystal field

We investigate the phase diagram of a spin-1 ferromagnetic XY model in the presence of a longitudinal easy-axis crystal field assuming bilinear (J) and biquadratic (I) exchange interactions between nearest neighbors spins and using the two-time Green Functions framework at the level of the Devlin strategy. Employing both analytical estimates and numerical calculations, we find that the structure of the crystal-field-induced phase boundary changes sensibly as the ratio $$\alpha = I/J$$ α = I / J increases. In particular, when $$\alpha $$ α overcomes a characteristic value $$\alpha ^*$$ α ∗ , two quantum critical points appear which are connected by a dome-shaped critical line. Due to the paradigmatic nature of the anisotropic spin model here considered, we believe that our findings may provide useful insights into the physical origin of recent experimental results found for some innovative materials which exhibit two quantum critical points and dome-shaped phase diagrams induced by non-thermal control parameters driving a non-conventional quantum criticality. Graphic abstract