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Theoretical and Mathematical Physics

Investigation of the energy operator spectrum for a two-magnon system in a one-dimensional anisotropic heisenberg ferromagnet with second neighbor interactions

Sadulla Mamarazhabovich Tashpulatov

Published Apr 1, 1996• 8 citations
Publisher
DOI
10.1007/bf02071461

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SPECTRA AND BOUND STATES OF THE ENERGY OPERATOR OF TWO-MAGNON SYSTEM IN A NON-HEISENBERG FERROMAGNET WITH SPIN S = 3/2 AND NEAREST-NEIGHBOR INTERACTIONS

Sadulla Mamarazhabovich Tashpulatov

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.

Infinite Dimensional Analysis Quantum Probability and Related Topics•Mar 1, 2009•0 citations

Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field

Roman O. Kuzian, S.‐L. Drechsler

The two-magnon problem for the frustrated XXZ spin-$1∕2$ Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field ${B}_{s}$ 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 ${J}_{1}<0$ and antiferromagnetic next-nearest neighbor ${J}_{2}>0$ interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field ${B}_{s}$ from its classical value ${B}_{s}^{\mathrm{cl}}$ 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 ${B}_{s}$, 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.

arXiv:cond-mat/0610801•Physical Review B•Jan 2, 2007•45 citations
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∕21∕21∕2 Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field Bs{B}_{s}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{J}_{1}<0J1​<0 and antiferromagnetic next-nearest neighbor J2>0{J}_{2}>0J2​>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{B}_{s}Bs​ from its classical value Bscl{B}_{s}^{\mathrm{cl}}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{B}_{s}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.