We consider a two-magnon systems in an ν-dimensional isotropic non-Heisenberg ferromagnet with spin value S = 3/2 and nearest-neighbor interactions. Spectrum and bound states (BS) of the system for all values of full quasi-momentum Λ, and for arbitrary value of lattice dimensionality ν, and for all values of Hamiltonian parameters are investigated. We show that (i) for arbitrary ν ≥ 2 and for full quasi-momentum in the form Λ = (Λ1; Λ2; … ;Λν) = (Λ0;Λ0; …; Λ0) the change of energy spectrum of the system is similar to that observed in the case of ν = 1. In this case the operator [Formula: see text] with J + J1 - 23J2 ≠ 0 has only one additional BS. (ii) The energy z of this additional BS is degenerate ν - 1 times. (iii) If Λ ≠ (Λ0;Λ0;…;Λ0), we show the existence no more 2ν + 1 bound states in the system in ν-dimensional lattice.
The two-magnon problem for the frustrated XXZ spin-
1∕2 Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field
Bs is considered. We show that the problem can be exactly mapped onto an effective tight-binding impurity problem. It allows to obtain explicit exact expressions for the two-magnon Green's functions for arbitrary dimension and number of interactions. We apply this theory to a quasi-one-dimensional helimagnet with ferromagnetic nearest-neighbor
J1<0 and antiferromagnetic next-nearest neighbor
J2>0 interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field
Bs from its classical value
Bscl which coincides with the one-magnon instability. For the refined frustration ratio $\ensuremath{\mid}{J}_{2}∕{J}_{1}\ensuremath{\mid}>0.374\phantom{\rule{0.2em}{0ex}}661$ the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin zone. Based on the two-magnon approach, we propose general analytic expressions for the saturation field
Bs, confirming known previous results for one-dimensional isotropic systems, but explore also the role of interchain and long-ranged intrachain interactions as well as of the exchange anisotropy.
The stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.