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

Abstract

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 cl s which coincides with the one-magnon instability. For the refined frustration ratio |J 2 /J 1 | > 0.374661 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.

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

“…However, as shown by earlier studies, 4,6,10,11,12 this is not the true instability for the quantum case in the whole parameter region −4J 2 < J 1 < 0.…”

“…At the boundary J 1 = −4J 2 the zero-field ground state is highly degenerate such that states from vanishing magnetization to full polarization share the same energy. 9 For the parameter range −4J 2 < J 1 < 0 of our main interest, Chubukov 6 suggested that the ground state just below the saturation field should be a nematic state made up of bound magnon pairs with a commensurate total momentum k = π if −2.67J 2 < J 1 < 0 (2.67 ≈ 1/0.38) and with an incommensurate momentum k < π otherwise, which was partly verified by mean-field theory, 10 numerical study, 11 Green's function analysis which fixed the commensurate-incommensurate transition point to J 1 /J 2 = −2.66908 (= −1/0.374661), 12 and weak-coupling bosonization analysis. 4,11,13 While earlier calculations of the ground-state magnetization process suggested metamagnetic transitions, 10,14 recent densitymatrix renormalization group (DMRG) study 11 finds that the total magnetization of finite-size chains changes by ∆S z = 2 at J 1 = −J 2 , ∆S z = 3 at J 1 = −3J 2 , and ∆S z = 4 at J 1 = −3.75J 2 below saturation, implying that the magnetization curve is continuous in the thermodynamic limit.…”

“…For general k this involves finding roots of a transcendental equation. 12 The eigenvalue problem (6) is greatly simplified at k = π, where the excitation energy of the two-magnon bound state is 6,12…”

Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

“…. .. 5 Beyond the commensurate-incommensurate transition point, the total momentum k changes continuously as Fig. 7.…”

Phase diagram of an anisotropic frustrated ferromagnetic spin-12chain in a magnetic field: A density matrix renormalization group study

“…According to Ref. 44, the field h s,2m at which the two-magnon bound-state gap closes is given by h s,2m / J 2 = ͓1+͑⌬ +1͒ 2 − ⌬ 2 ͑1−␤͒ 2 ͔ / ͓2͑1−␤⌬͔͒ while the respective value for one-magnon states is given by h s,1m / J 2 = ͑⌬ −1͒͑1+␤͒ + ͑4+␤͒ 2 / 8. Comparing those two fields, one finds, for example, that for ␤ = −0.3 the instability of the fully polarized state at the saturation field is by condensation of the two-magnon bound states at ⌬Ͼ⌬ s Ӎ 0.54, and by one-magnon states below that value.…”