First-Order Phase Transition Induced by Quantum Fluctuations in Heisenberg Helimagnets

We calculate the ground-state energy of an isotropic quantum Heisenberg ferromagnet on an hexagonal lattice with ferromagnetic exchange interactions J1 and J’ between nearest neighbors in the same basal plane and adjacent basal planes and, respectively, competing interactions J2 and J3 between second- and third-nearest neighbors in the same basal plane, respectively. When the ground-state energy of a helical state with wave vector Q is expanded for small Q as EG(Q)=E0+E2Q2+E4Q4+...., then the coefficients E2 and E4 can be evaluated exactly at zero temperature, with the result that E2 is given by its classical (S→∞) value, whereas E4 has quantum corrections. At the ferromagnet-helix transition (at which E2=0) E4 is positive for S=∞ indicating that this transition is continuous, whereas as S−1 is nonzero, a region develops wherein the transition becomes discontinuous.