Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides

Abstract

Recent neutron scattering studies revealed the three dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J1-J2-Jc Heisenberg model with S = 1 using selfconsistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson representation. Remarkably their respective mean-field theories do not lead to the same results, even at zero temperature. They are gauged in the Néel phase in comparison to exact diagonalization and series expansion. The J1-J2-Jc model is analyzed under the influence of the biquadratic exchange J bq and a detailed description of the staggered magnetization and of the magnetic excitations is given. The biquadratic exchange increases the renormalization of the in-plane exchange constants which enhances the anisotropy between the exchange parallel and perpendicular to the spin stripes. Applying the model to iron pnictides, it is possible to reproduce the spin-wave dispersion for CaFe2As2 in the direction perpendicular to the spin stripes and perpendicular to the planes. Discrepancies remain in the direction parallel to the spin stripes which can be resolved by passing from S = 1 to S = 2. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided.

Ising-nematic order in the bilinear-biquadratic model for the iron pnictides

“…Instead, the inclusion of a biquadratic term in Eq. (1) dynamically generates the anisotropy in the effective NN Heisenberg couplings, in agreement with the experimental results [48][49][50] . In this work, we show that the spin wave dispersion and dynamical spin structure factor from INS measurements 16,52 can be modeled semi-quantitatively using the effective spin model Eq.…”

“…The latter are important to correctly capture the dispersion of the spin excitations near the Brillouin zone boundary [48][49][50] observed via the INS 51,52 . Indeed, without the biquadratic K-term, one is forced to adopt an anisotropic nearest neighbor (NN) coupling constant 51,53,54 J 1x = J 1y even when modeling the neutron spectra above the structural transition 52 , which is unphysical.…”

Possible nematic spin liquid in spin-1 antiferromagnetic system on the square lattice: Implications for the nematic paramagnetic state of FeSe

“…Semiclassical calculations for this model find various magnetic ordered phases to interpret the observed magnetic orders in iron pnictides and FeTe 36,42,[47][48][49][50][51][52] . Recent mean-field studies propose an antiferroquadrupolar (AFQ) state for FeSe 39,40 , which exhibits a nematic order accompanied by the quadrupolar fluctuations at wave vector q = (0, π)/(π, 0).…”

Competing superconducting channels in iron pnictides from the strong coupling theory with biquadratic spin interactions

“…pair of spins. [15][16][17][18][19][20][21] From the theoretical perspective, the emergence of the biquadratic interaction is natural when the system contains multiple orbitals and when the correlations are strong in the metallic ground state: the low-energy effective Hamiltonian in the spin sector should consist of not only two-spin Heisenberg interactions, such as J 1 and J 2 Heisenberg exchange between n.n. and next-nearest-neighbor (n.n.n.)…”