Self-consistent Spin-wave Theory Research Articles

The Ising Nematic in the J1–J2 Heisenberg Model on a Square Lattice in a Self-Consistent Spin-Wave Theory

The Ising Nematic in the J1–J2 Heisenberg Model on a Square Lattice in a Self-Consistent Spin-Wave Theory

Ground-state selection by magnon interactions in a fcc antiferromagnet

We study the nearest-neighbor Heisenberg antiferromagnet on a face-centered cubic lattice with arbitrary spin S. The model exhibits degenerate classical ground states including two collinear structures AF1 and AF3 described by different propagation vectors that are prime candidates for the quantum ground state. We compute the energy for each of the two states as a function of S using the spin-wave theory that includes magnon-magnon interaction in a self-consistent way and the numerical coupled cluster method. Our results unambiguously demonstrate that quantum fluctuations stabilize the AF1 state for realistic values of spin. Transition to the harmonic spin-wave result, which predicts the AF3 state, takes place only for S > 10. We also study quantum renormalization of the magnon spectra for both states as a function of spin.

Interplay between lattice topology, frustration, and spin quantum number in quantum antiferromagnets on Archimedean lattices

The interplay between lattice topology, frustration, and spin quantum number, $s$, is explored for the Heisenberg antiferromagnet (HAFM) on the 11 two-dimensional Archimedean lattices (square, honeycomb, CaVO, SHD, SrCuBO, triangle, bounce, trellis, maple-leaf, star, and kagome). We show that the coupled cluster method (CCM) provides consistently accurate results when compared to the results of other approximate methods. The CCM also provides valuable information relating to the selection of ground states and we find that this depends on spin quantum number for the kagome and star lattices. Specifically, the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ model state provides lower ground-state energies than those of the $q=0$ model state for the kagome and star lattices for most values of $s$. The $q=0$ model state provides lower ground-state energies only for $s=1/2$ for the kagome lattice and $s=1/2$ and $s=1$ for the star lattice. The kagome and star lattices demonstrate the least amount of magnetic ordering and the unfrustrated lattices (square, honeycomb, SHD, and CaVO) demonstrate the most magnetic ordering for all values of $s$. The SrCuBO and triangular lattices also demonstrate high levels of magnetic ordering, while the remaining lattices (bounce, maple-leaf, and trellis) tend to lie between these extremes, again for all values of $s$. These results also clearly reflect the strong increase in magnetic order with increasing spin quantum number $s$ for all lattices. The ground-state energy, ${E}_{g}/(NJ{s}^{2})$, scales with ${s}^{\ensuremath{-}1}$ to first order, as expected from spin-wave theory, although the order parameter, $M/s$, scales with ${s}^{\ensuremath{-}1}$ for most of the lattices only. Self-consistent spin-wave theory calculations indicated previously that $M/s$ scales with ${s}^{\ensuremath{-}2/3}$ for the kagome lattice HAFM, whereas previous CCM results (replicated here also) suggested that $M/s$ scales with ${s}^{\ensuremath{-}1/2}$. It is probable, therefore, that different scaling for $M/s$ than with ${s}^{\ensuremath{-}1}$ does indeed occur for the kagome lattice. By using similar arguments, we find here also that $M/s$ scales with ${s}^{\ensuremath{-}1/3}$ for the star lattice and with ${s}^{\ensuremath{-}2/3}$ for the SrCuBO lattice.

Effects of frustration and cyclic exchange on the spin-1/2 Heisenberg antiferromagnet within the self-consistent spin-wave theory

The relevance of the quasi-two-dimensional spin-1/2 frustrated quantum antiferromagnet (AFM) due to its possibility of modeling the high-temperature superconducting parent compounds has resulted in numerous theoretical and experimental studies. This paper presents a detailed research of the influence of the varying exchange interactions on the model magnetic properties within the framework of self-consistent spin-wave theory based on Dyson–Maleev (DM) representation. Beside the nearest neighbor (NN) interaction within the plane, the planar frustration up to the third NNs, cyclic interaction and the interlayer coupling are taken into account. The detailed description of the elementary spin excitations, staggered magnetization, spin-wave velocity renormalization factor and ground state energy is given. The results are compared to the predictions of the linear spin-wave theory and when possible also to the second-order perturbative spin-wave expansion results. Finally, having at our disposal improved experimental results for the in-plane spin-wave dispersion in high-[Formula: see text] copper oxide La2CuO4, the self-consistent spin-wave theory (SCSWT) is applied to that compound in order to correct earlier obtained set of exchange parameters and high-temperature spin-wave dispersion.

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

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 ${J}_{1}$-${J}_{2}$-${J}_{c}$ Heisenberg model with $S=1$ using self-consistent 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 N\'eel phase in comparison to exact diagonalization and series expansion. The ${J}_{1}$-${J}_{2}$-${J}_{c}$ model is analyzed under the influence of the biquadratic exchange ${J}_{\text{bq}}$ 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 CaFe${}_{2}$As${}_{2}$ 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 $S=3/2\phantom{\rule{0.28em}{0ex}}\mathit{or}\phantom{\rule{0.28em}{0ex}}S=2$. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided.

Three-dimensional generalization of theJ1-J2Heisenberg model on a square lattice and role of the interlayer couplingJc

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg ${J}_{1}$-${J}_{2}$ model has been actively discussed recently. However, recent neutron-scattering data have shown that the pnictides have a relatively large spin-wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model that is the three-dimensional generalization of the ${J}_{1}$-${J}_{2}$ Heisenberg model for $S=1/2$ and $S=1$. Using self-consistent spin-wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling ${J}_{c}$ suppresses the quantum fluctuations and strengthens the long-range ordering. In the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable on increasing ${J}_{1}$. Either the magnetization or one of the spin-wave velocities vanishes. For $S=1/2$ renormalization due to quantum fluctuations is significantly stronger than for $S=1$, in particular close to the quantum phase transition. Our findings for the ${J}_{1}$-${J}_{2}$-${J}_{c}$ model are of general theoretical interest; however, the results show that it is unlikely that the model is relevant to undoped pnictides.

Pnictides as frustrated quantum antiferromagnets close to a quantum phase transition

We present a detailed description of the dynamics of the magnetic modes in the recently discovered superconducting pnictides using reliable self-consistent spin-wave theory and series expansion. Contrary to linear spin-wave theory, no gapless mode occurs at the N\'eel wave vector. We discuss the scenario that the static magnetic moment is strongly reduced by magnetic fluctuations arising from the vicinity to a quantum phase transition. Smoking gun experiments to verify this scenario are proposed and possible results are predicted. Intriguingly in this scenario, the structural transition at finite temperature would be driven by an Ising transition in directional degrees of freedom.

Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation

The magnetic properties of a frustrated Heisenberg antiferromagnet with the fcc lattice and exchange interaction between the nearest (J 1) and next-to-nearest (J 2) neighbors are studied in this work. For the collinear phase with the wave vector Q= (π,π,π), the equations of the self-consistent spin-wave theory are obtained and solved numerically for the sublattice magnetization and the averaged short-range order parameter. The dependence of the Néel temperatureT N on the ratio J 2/J 1 is found. It is shown that, in the case of a sufficiently strong frustration, strong short-range magnetic order persists over a wide temperature range above T N. The possible application of this result to the mechanism of structural phase transition from α-Fe to γ-Fe is considered.

Extracting signatures of quantum criticality in the finite-temperature behavior of many-body systems

We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a $T=0$ quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum $S=1∕2$ Ising chain is exactly solvable and extensively studied, results for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ of such model are lacking, and we supply them here. They are obtained numerically, via the transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to the thermal ones.

Thermodynamics of a two-dimensional Heisenberg ferromagnet with dipolar interaction

Thermodynamics of quantum and classical two-dimensional (2D) Heisenberg models with long-range dipole--dipole interaction has been investigated using various forms of self-consistent spin-wave theory (SSWT). It has been found that SSWT gives a much lower transition temperature ${T}_{c}$ than the free-magnon (spin-wave) theory. For the classical spin, the ${T}_{c}$ from SSWT lies within 9% of the Monte Carlo value, making SSWT the best approximation among those considered. It is proven that the random phase approximation vertex corrections to SSWT are rather small. The results depend strongly on the value of the spin, emphasizing the importance of using the quantum and not the classical 2D Heisenberg model even for large spins such as $S=7∕2$.

Theory for disordered phase in Heisenberg and non-Heisenberg two-dimensional S=1 ferromagnets

We apply a modification of self-consistent spin-wave theory to investigation of two-dimensional S=1 isotropic Heisenberg and non-Heisenberg ferromagnets at nonzero temperatures. We use Hubbard operators method and bosonization technique. We calculated chemical potential and found dependence of correlation length on temperature. Specific heat has Schottky-type peak and decreases at high temperatures. Disordered phase in non-Heisenberg ferromagnet is also studied. The results for such a model differ from those of Heisenberg one.

Self-consistent spin-wave theory of two-dimensional magnets with impurities

The self-consistent spin-wave theory is applied to investigate the magnetization distribution around the impurity in isotropic and easy-axis two-dimensional ferro- and antiferromagents. The temperature dependences of host magnetization disturbance and impurity magnetization are calculated. The short-range order in the isotropic case is investigated. Importance of dynamic and kinematic interactions of spin waves is demonstrated.

Self-consistent spin-wave theory of layered Heisenberg magnets

The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the nonlinear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and the short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.

On the self-consistent spin-wave theory of quasi-2D and anisotropic 2D magnets

We present a new version of the self-consistent spin wave theory (SSWT), based on slave boson and fermion representations and a variational principle, to describe quasi-2D systems which possess finite values of magnetic ordering temperature because of weak interlayer coupling and/or magnetic anisotropy. Applications to a description of pronounced short-range order well above the ordering point are demonstrated.

Kosterlitz-Thouless transition in a two-dimensional isotropic antiferromagnet in a uniform field.

The transition temperature in the classical two-dimensional isotropic antiferromagnet in a uniform magnetic field, applied perpendicular to the xy plane, is calculated using a self-consistent spin-wave theory. The effect of vortex-antivortex bound pairs to the transition temperature is estimated.

J1-J2 quantum Heisenberg antiferromagnet: improved spin-wave theories versus exact-diagonalization data

We reconsider the results concerning the extreme-quantum S=1/2 square-lattice Heisenberg antiferromagnet with frustrating diagonal couplings (the J1-J2 model) drawn from a comparison with exact-diagonalization data. A combined approach, also using some intrinsic features of the self-consistent spin-wave theory, leads to the conclusion that the theory strongly overestimates the stabilizing role of quantum fluctuations with respect to the Neel phase in the extreme-quantum case S=1/2. On the other hand, the analysis implies that the Neel phase remains stable at least up to the limit J2/J1=0.49, which is larger than some previous estimates. In addition, it is argued that the spin-wave ansatz predicts the existence of a finite range (J2/J1<0.323 in linear spin-wave theory) where the Marshan-Peierls sign rule survives the frustrations,.

Phase transition and spin dynamics in the two-dimensional easy-plane ferromagnet.

With the use of self-consistent spin-wave theory, the spin stiffness for the two-dimensional classical easy-plane ferromagnet is calculated. The Kosterlitz-Thouless transition temperature for the classical XY model is obtaind. The contribution of vortex-antivortex bound pairs to the central peak at low temperatures is discussed.

Calculation of the spin stiffness for 2D easy-plane magnets

We calculate the spin stiffness constant for the 2D classical easy-plane Heisenberg model through a self-consistent spin-wave theory. An estimate of the topological transition temperature is obtained for the entire range of the anisotropy parameter λ:0⩽ λ<1. In particular, it is found that T c (λ=0)⋍0.73T c (planar rotator). We also show that the specific heat has a strong maximum at T c as was already suggested by numerical simulations.

On the self-consistent spin-wave theory of frustrated Heisenberg antiferromagnets

The phase diagrams of Heisenberg antiferromagnets with frustrated exchange interactions are obtained by using the self-consistent spin-wave approximation. The square, simple-cubic and quasi-1D antiferromagnets are considered with different values of spin S. An important role of spin-wave renormalizations of exchange parameters is demonstrated. The temperature dependences of the correlation length and spin-wave damping are calculated. It is shown that a wide temperature region above TN with a strong short-range order exists in frustrated 3D systems.

Quantum effects in the critical properties of the X-Y model in a transverse magnetic field: crossover scaling near zero temperature

The susceptibility of a quantum X-Y model in a transverse field Gamma is studied in the vicinity of the multicritical point ( Gamma c,T=0). For dimensions d between two and four we obtain a Hartree type approximation an equation for the corresponding crossover function which is solvable analytically in three dimensions. The critical line Gamma c(T)- Gamma c(0) approximately Tpsi is asymptotically described by the shift exponent psi =d/2 in accord with self-consistent spin wave theory. For the variable of the crossover scaling function T/( Gamma - Gamma c(T))phi one obtains the crossover exponent phi =(4-d)/2 which is characteristic for the Gaussian multicritical point. A dimensional-analysis argument suggests that this is valid beyond the approximation.