Second-order quantum corrections for the frustrated spatially anisotropic spin-12Heisenberg antiferromagnet on a square lattice

Abstract

The effects of quantum fluctuations due to directional anisotropy and frustration between nearest neighbors and next-nearest neighbors of the quantum spin-1 2 Heisenberg antiferromagnet on a square lattice are investigated using spin-wave expansion. We have calculated the spin-wave-energy dispersion in the entire Brillouin zone, renormalized spin-wave velocities, and the magnetization up to second order in 1 / S expansion for the antiferromagnetic Neél and collinear antiferromagnetic stripe phases. It is shown that the second-order corrections become significant with increase in frustration. With these corrections magnetizations and spin-wave velocities for both the phases become zero at the quantum critical points as expected from other numerical and analytical methods. We have shown that the transition between the two ordered phases are always separated by the disordered paramagnetic phase. the intermediate paramagnetic state at 1c is of second order and from the paramagnetic state to the collinear state at 2c is of first order. 52,53 A generalization of the frustrated J 1 -J 2 model is the J 1 -J 1 Ј-J 2 model where = J 1 Ј/ J 1 is the directional anisotropy parameter. 28,31 It is known that the spatial anisotropy reduces the width of the disordered phase. Extensive band structure calculations 46 for the vanadium phosphate compounds Pb 2 VO͑PO 4 ͒ 2 , SrZnVO͑PO 4 ͒ 2 , BaZnVO͑PO 4 ͒ 2 , and BaCdVO͑PO 4 ͒ 2 have shown four different exchange couplings: J 1 and J 1 Ј between the NN and J 2 and J 2 Ј between NNN. For example Ϸ 0.7 and J 2 Ј/ J 2 Ϸ 0.4 were obtained for SrZnVO͑PO 4 ͒ 2 . A possible realization of the J 1 -J 1 Ј-J 2 model may be the compound ͑NO͒Cu͑NO 3 ͒ 3 ͑Ref. 54͒ though recent band-structure calculations show a uniform spin chain model with different types of anisotropy and weak interchain couplings. 55 Within the spin-wave expansion the effect of directional anisotropy on the spin-wave-energy dispersion and the transverse dynamical structure factor has been studied before. 15 However, the effect of NNN frustration has not been incorporated in that study.For the J 1 -J 1 Ј-J 2 model using a higher order coupled cluster method Bishop et al. 45 reported existence of a quantum triple point ͑QTP͒ at Ϸ 0.60, Ϸ 0.33. Below this point they predicted a second-order phase transition between the quantum Neél and stripe phases whereas above it these two

Magnon-phonon coupling effects on the indirect K -edge resonant inelastic x-ray scattering spectrum of a two-dimensional Heisenberg antiferromagnet

“…The choice of (ζ, η) parameters are dictated by the magnetization phase diagram of the J x − J y − J 2 model [52]. (c) q=(π/2,π/2) 28 In the absence of a magnetic field magnons in a 2D square lattice are not damped [71,72].…”

Spectrum splitting of bimagnon excitations in a spatially frustrated Heisenberg antiferromagnet revealed by resonant inelastic x-ray scattering

“…where S is the value of spin. The 1/S order term coming from the one-loop correction of the quartic interactions 43,44 reads as…”

“…The choice of (ζ, η) parameters are guided by the magnetic phase diagram of the J x − J y − J 2 model to ensure that quantum fluctuations have not completely destroyed the two sub-lattice magnetic order. 43 The classical phase diagram is given by the relation ζ > 2η (AF) and ζ < 2η (CAF). 1 2…”

The quasi-one-dimensional character of spin waves in K2Fe7Se8

“…The linear spin wave theory is good enough to capture the main properties of the spin wave [25,26]. But if one wants to obtain more details about the spin wave, the second order perturbation theory [27][28][29][30], self-consistent spin wave theory [31][32][33][34] or coupledcluster calculations [35][36][37] can be employed. As we discussed above, due to the 14 sites in the magnetic unit cell, it is very hard to obtain the explicitly analytical expressions for the spin wave dispersion relations.…”