Spin nematic phase in one-dimensional and quasi-one-dimensional frustrated magnets in a strong magnetic field

Abstract

We discuss spin-1 2 one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor J1 and antiferromagnetic next-nearest-neighbor J exchange interactions in a strong magnetic field H. It is well known that due to attraction between magnons quantum phase transitions (QPTs) take place at H = Hs from the fully polarized phase to nematic ones if J > |J1|/4. Such a transition at J > 0.368|J1| is characterized by a softening of the two-magnon bound-state spectrum. Using a bond operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations whose spectrum coincides at H ≥ Hs with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at H = Hs makes the QPT consideration substantially standard. In the 1D case at H < Hs, we find an expression for the magnetization which describes well existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before either in the limiting case of J |J1| or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the H-T plane between the fully polarized and the nematic phases is given by Hs(0) − Hs(T ) ∝ T 3/2 . Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to 1/ ln(1 + |J1|/J). Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel. 1 1 ' , J J J 2 1 ' , J J J

Magnetic phase diagram of the frustrated spin chain compound linarite PbCuSO4(OH)2 as seen by neutron diffraction and HHeinze1, Bastien2, Ryll3 et al. 2019Phys. Rev. B152211View full textAdd to dashboardCite

“…While the transverse dynamical spin correlation S a ⊥ a ⊥ , S cc and S a ⊥ c were predicted to show an exponential spin gap in the bound magnon state 13,16,18,58 the longitudinal dynamical spin correlation S bb was predicted to follow a power law behavior in temperature 25,56,59 . The NMR relaxation rate was also studied theoretically in the lowtemperature limit and a step at the multipolar ordering from the longitudinal spin fluctuations was predicted 22 .…”

Collective excitations in spin- 12 magnets through bond-operator formalism designed both for paramagnetic and ordered phases

“…As in Refs. 20,27 , we use a technique which operates with anomalous Green's functions of the type G cc (ω, k) = −i dte iωt T c k (t)c −k (0) and Green's functions of the "mixed" type G ab (ω, k) = −i dte iωt T a k (t)b −k (0) not involving Bogoliubov transformations. Then, one deals with sets of Dyson equations for the Green's functions within this approach.…”

“…The presence of the bosonic mode in the theory which softens at QCP makes substantially standard the QPT consideration. 27 One of the aims of the present paper is to show that there exist quasiparticles inside ordered phases whose role has not been fully clarified yet. We propose below BOTs for two and for four spins in the unit cell.…”

“…28 We double the unit cell along the chain in Ref. 27 and develop a BOT which takes into account all spin degrees of freedom in each unit cell. Three bosonic quasiparticles arise in that technique two of which carry spin 1 and describe two parts of the conventional magnon mode.…”

“…We argue in Ref. 27 that the third boson carries spin 2 and describes the two-magnon bound states which "condense" at QCP. The problem is exactly solvable within that formalism in the saturated phase.…”