Conventional Spin-wave Theory Research Articles

Multiple magnon modes in spin- 12 Heisenberg antiferromagnet on simple square lattice in strong magnetic field

We discuss spin-$\frac{1}{2}$ Heisenberg antiferromagnet on simple square lattice in magnetic field $H$ using a recently proposed bond-operator technique. It is well known that magnetically ordered phases of quantum magnets are well described at least qualitatively by the conventional spin-wave theory that only introduces quantum corrections into the classical solution of the problem. We observe that quantum fluctuations change drastically dynamical properties of the considered model at $H$ close to its saturation value: the dynamical structure factor shows anomalies corresponding to Green's function poles which have no counterparts in the spin-wave theory. That is, quantum fluctuations produce multiple short-wavelength magnon modes not changing qualitatively the long-wavelength spin dynamics. Our results are in agreement with previous quantum Monte Carlo simulations and exact diagonalization of finite clusters.

Spin-wave thermodynamics of square-lattice antiferromagnets revisited

Modifying the conventional spin-wave theory in a novel manner based on the Wick decomposition, we present an elaborate thermodynamics of square-lattice quantum antiferromagnets. Our scheme is no longer accompanied by the notorious problem of an artificial transition to the paramagnetic state inherent in modified spin waves in the Hartree-Fock approximation. In the cases of spin $\frac{1}{2}$ and spin $1$, various modified-spin-wave findings for the internal energy, specific heat, static uniform susceptibility, and dynamic structure factor are not only numerically compared with quantum Monte Carlo calculations and Lanczos exact diagonalizations but also analytically expanded into low-temperature series. Modified spin waves interacting via the Wick decomposition provide reliable thermodynamics over the whole temperature range of absolute zero to infinity. Adding higher-order spin couplings such as ring exchange interaction to the naivest Heisenberg Hamiltonian, we precisely reproduce inelastic-neutron-scattering measurements of the high-temperature-superconductor-parent antiferromagnet $\mathrm{La}_2\mathrm{CuO}_4$. Modifying Dyson-Maleev bosons combined with auxiliary pseudofermions also yields thermodynamics of square-lattice antiferromagnets free from thermal breakdown, but it is less precise unless temperature is sufficiently low. Applying all the schemes to layered antiferromagnets as well, we discuss the advantages and disadvantages of modified spin-wave and combined boson-pseudofermion representations.

Microwave nonreciprocity of magnon excitations in the noncentrosymmetric antiferromagnet Ba2MnGe2O7

We have investigated the microwave non-reciprocity for a non-centrosymmetric antiferromagnet Ba$_2$MnGe$_2$O$_7$. The magnon modes expected by the conventional spin wave theory for staggered antiferromagnets are certainly observed. The magnitudes of exchange interaction and magnetic anisotropy are obtained by the comparison with the theory. The microwave non-reciprocity is identified for one of these mode. The relative magnitude of microwave non-reciprocity can be explained with use of spin wave theory and Kubo formula.

Magnetic excitations from the two-dimensional interpenetrating Cu framework in Ba2Cu3O4Cl2

We report detailed neutron scattering studies on Ba$_2$Cu$_3$O$_4$Cl$_2$. The compound consists of two interpenetrating sublattices of Cu, labeled as Cu$_{\rm A}$ and Cu$_{\rm B}$, each of which forms a square-lattice Heisenberg antiferromagnet. The two sublattices order at different temperatures and effective exchange couplings within the sublattices differ by an order of magnitude. This yields an inelastic neutron spectrum of the Cu$_{\rm A}$ sublattice extending up to 300 meV and a much weaker dispersion of Cu$_{\rm B}$ going up to around 20 meV. Using a single-band Hubbard model we derive an effective spin Hamiltonian. From this, we find that linear spin-wave theory gives a good description to the magnetic spectrum. In addition, a magnetic field of 10 T is found to produce effects on the Cu$_{\rm B}$ dispersion that cannot be explained by conventional spin-wave theory.

Influence of next-nearest neighbor interaction on low temperature properties of the spin-1/2 one-dimensional ferromagnetic XY model

In this paper, we apply spin-wave theory to the one-dimensional spin-1/2 ferromagnetic XY model with the next-nearest neighbor interaction. The thermodynamic divergences which the conventional spin-wave theory encounters with, are solved by implementing Takahashi’s idea through introducing a Lagrange multiplier in the Hamiltonian to keep zero magnetization. It is shown that the next-nearest neighbor interaction has an influence on the ground-state and low temperature properties of the system. The exponential laws which are induced by the next-nearest neighbor interaction, are found for heights of maxima of the specific heat and its coefficient, as well as the maximum and minimum of the susceptibility coefficient. The maximum positions of the specific heat and its coefficient fit well to the linear and exponential laws under the next-nearest neighbor interaction, respectively.

MODIFIED SPIN-WAVE THEORY FOR THE FRUSTRATED HEISENBERG ANTIFERROMAGNET ON A SQUARE LATTICE

The effects of quantum fluctuations due to frustration between nearest neighbors and next-nearest neighbors of the quantum spin-half Heisenberg antiferromagnet on a square lattice are investigated by using the modified spin-wave theory (MSW). We have extended Takahashi's MSW theory, and studied the ground-state and finite-temperature properties of this model. The results calculated within this formalism on the thermodynamics agree quite well with the quantum Monte Carlo estimates, and exact diagonalization results. We have also compared the present method with the conventional spin wave theory.

Hubbard-model description of the high-energy spin-weight distribution in La2CuO4

The spectral-weight distribution in recent neutron scattering experiments on the parent compound La$_2$CuO$_4$ (LCO), which are limited in energy range to about 450\,meV, is studied in the framework of the Hubbard model on the square lattice with effective nearest-neighbor transfer integral $t$ and on-site repulsion $U$. Our study combines a number of numerical and theoretical approaches, including, in addition to standard treatments, density matrix renormalization group calculations for Hubbard cylinders and a suitable spinon approach for the spin excitations. Our results confirm that the $U/8t$ magnitude suitable to LCO corresponds to intermediate $U$ values smaller than the bandwidth $8t$, which we estimate to be $8t \approx 2.36$ eV for $U/8t\approx 0.76$. This confirms the unsuitability of the conventional linear spin-wave theory. Our theoretical studies provide evidence for the occurrence of ground-state d-wave spinon pairing in the half-filled Hubbard model on the square lattice. This pairing applies only to the rotated-electron spin degrees of freedom, but it could play a role in a possible electron d-wave pairing formation upon hole doping. We find that the higher-energy spin spectral weight extends to about 566 meV and is located at and near the momentum $[\pi,\pi]$. The continuum weight energy-integrated intensity vanishes or is extremely small at momentum $[\pi,0]$. This behavior of this intensity is consistent with that of the spin waves observed in recent high-energy neutron scattering experiments, which are damped at the momentum $[\pi,0]$. We suggest that future LCO neutron scattering experiments scan the energies between 450 meV and 566 meV and momenta around $[\pi,\pi]$.

Neutron scattering measurements in RbMnF3: A test of spin-wave-region theories at low temperatures and critical behavior near TN

With the discovery of magnetic ordering in RbMnF3, this unique antiferromagnetic system was recognized as a prime case for a test of conventional spin-wave theory (CSWT) because of its negligibly small anisotropy and its simple, cubic structure. CSWT predicts a simple T2 power-law fall-off of the sublattice magnetization. Yet to this day, no stringent tests have been made of this prediction. Seiden [(Phys. Lett. 28 A, 239 (1968)] deduced a T3 low-temperature behavior on the basis of antiferromagnetic resonance measurements, concluding that CSWT was not supported. We have recently carried out neutron scattering measurements of both single-crystal and powdered samples of RbMnF3 in order to test for CSWT, Seiden’s result, and two other more recent semiempirical spin-wave schemes, and we present an analysis of the results. Measurements in the critical regime gave values of the critical exponent β and of TN that are in agreement with previous measurements.

Serious discrepancies between nuclear magnetic resonance and neutron scattering measurements in the critical region of classic two-dimensional magnets and anomalous behaviors at low temperatures

A characterization of 2D critical behavior in the classic 2D antiferromagnets K2NiF4, Rb2MnF4, and K2MnF4 made originally by Birgeneau et al. [Phys. Rev. B 1, 2211 (1970)], using neutron scattering (NS), is used to review NMR data in these compounds and in some classic 2D ferromagnets. On analyzing the NMR data, very serious discrepancies were found between the NMR and NS results for the critical exponent β, with the values of the NMR βs being some 50% higher. Some novel results were also found, including 2D cases where β=0.33 (but characterized by a non-3D parameter, D∼1). The discrepancies surely need to be resolved, and if the present analysis of the NMR data is further validated, these results could present a clear and nontrivial hurdle for current critical-region theories. Additionally, from the NMR data it was found that the low-temperature behaviors of these classical 2D systems are at odds with the predictions of conventional spin-wave theory analyses.

The effect of spin dilution on magnetism of the linear chain system β-Cu2−x Zn x V2O7

We have measured the magnetic susceptibility (χ) and heat capacity (C p) of β-Cu2−x Zn x V2O7 (x = 0, 0.05, 0.1, 0.15, 0.2, 0.3, 2) in the temperature range 2–300 K. A one-dimensional alternating exchange Heisenberg antiferromagnetism (HAF) is observed in all compositions with chains of infinite length. The intra-chain exchange remains uniform and decreases marginally with dilution of the magnetic state. A cooperative ordering is seen in the magnetic chains for all Zn concentrations (x ≤ 0.3). The temperature of occurrence of this transition decreases with increasing Zn concentration. Though the conventional spin-wave theory has been used here to describe the properties of the ordered phase, the presence of some contributions like the lattice heat capacity in C p and the Curie-Weiss term in susceptibility introduces some uncertainties in the estimation of the proportions contributed by the spin system. Therefore, the nature of the ordered phase could not be ascertained unambiguously.

NMR measurements of power-law behavior in the spin-wave and critical regions of ferromagnetic EuO

Precision continuous-wave NMR measurements have been carried out over the entire magnetization curve of EuO and are presented in tabular form. Two very closely spaced resonances are observed and are attributed to domain and domain-wall signals. Both of the signals are useful for analysis in the spin-wave region. Only the domain signal is measurable above ∼50 K. The latter is used for fitting Tc and the critical exponent β. The critical-region fits agree with previous measurements within experimental error. The low-temperature data exhibit a clear-cut T2 behavior, at variance with the expectations of conventional spin-wave theory. This result is discussed in relation to two semiempirical spin-wave schemes, one formulated by Bykovetz, and one by Koebler. The NMR signal at 4.2 K gives no indication of a quadrupole splitting in contradiction to the interpretation of several previous spin-echo NMR spectra observed in EuO. This issue remains unresolved.

Fermionic versus bosonic descriptions of one-dimensional spin-gapped antiferromagnets

In terms of spinless fermions and spin waves, we describe the magnetic properties of a spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On the one hand, we employ the Jordan–Wigner transformation and treat the fermionic Hamiltonian within the Hartree–Fock approximation. On the other hand, we employ the Holstein–Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice relaxation rate with varying bond alternation. These schemes are further applied to a bond-alternating tetramerized chain which behaves as a ferrimagnet. The fermionic language is particularly stressed as a useful tool for investigating one-dimensional spin-gapped antiferromagnets, while the bosonic one works better for ferrimagnets.

Auxiliary-fermion approach to critical fluctuations in the two-dimensional quantum antiferromagnetic Heisenberg model

The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Q=1 on each lattice site, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T. This drawback, which is caused by overdamping, is overcome in a `minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths and in the short-range-order regime. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.

Phase diagram of an anisotropic J1− J2− J3 model of a spin- [formula omitted] square-lattice antiferromagnet

Using conventional spin-wave theory, we present the effect of anisotropic spin coupling on the phase diagram based on an anisotropic J 1− J 2− J 3 model. Parameter space is extended from only frustrated J 1 and J 2 to a more large one including long range spin interactions, both frustrated and unfrustrated. In this extended J 2− J 3 parameter space the Néel ordered phase is located, and it is found that the Néel ordered area can be expanded by enhancing the anisotropy of in-plane spin interaction.

Spinless fermions versus spin waves in describing antiferromagnetic Heisenberg ladders

We investigate magnetic properties of the spin − 1 2 two-leg Heisenberg ladder antiferromagnet developing two formulations, one of which starts from the Jordan–Wigner transformation along an elaborately ordered path, and the other of which modifies the conventional spin-wave theory so as to restore the sublattice symmetry. The static and dynamic quantities are calculated and a novel field dependence of the nuclear spin-lattice relaxation rate, which is peculiar to one-dimensional spin-gapped antiferromagnets, is pointed out in particular.

Studies of transport and magnetic properties of Ce-doped LaMnO 3

The X-ray diffraction, electrical resistivity ( ρ), piezoresistance, thermoelectric power (TEP, S) and magnetisation experiments have been performed on polycrystalline La 1− x Ce x MnO 3 ( x=0–0.6) samples over a temperature range (20–320 K). All the compounds except x=0.1 display a metal–insulator (MI) transition at T MI. From the analysis of the resistivity data we find that the double peaks observed in the ρ( T) data of ceramic samples are originating from the grain boundary effects. Moreover, the charge conduction at higher temperature occurs by means of a thermally activated polaron hopping mechanism. The application of pressure suppresses the resistivity and enhances the resistive transition temperature ( T MI) and hence the Curie temperature ( T C). The thermopower (TEP, S) of all the samples is positive and above T C, both the ρ( T) and S( T) curves show that charge conduction at high temperatures takes place according to Emin and Holstein’s theory of adiabatic polaron hopping. At low temperatures, thermal variation of the magnetization ( M) can be explained considering the conventional spin wave theory containing T 3/2 and T 2 terms. In the paramagnetic region, the M( T) data fits well with the Curie–Weiss law.

Spin–Wave Description of Haldane-Gap Antiferromagnets

Modifying the conventional antiferromagnetic spin-wave theory which is plagued by the difficulty of the zero-field sublattice magnetizations diverging in one dimension, we describe magnetic properties of Haldane-gap antiferromagnets. The modified spin waves, constituting a grand canonical bosonic ensemble so as to recover the sublattice symmetry, not only depict well the ground-state correlations but also give useful information on the finite-temperature properties.

Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

We study the phase diagram at T=0 of the antiferromagnetic Heisenberg model on the triangular lattice with spatially-anisotropic interactions. For values of the anisotropy very close to J_alpha/J_beta=0.50, conventional spin wave theory predicts that quantum fluctuations melt the classical structures, for S=1/2. For the regime J_beta<J_alpha, it is shown that the incommensurate spiral phases survive until J_beta/J_alpha=0.27, leaving a wide region where the ground state is disordered. The existence of such nonmagnetic states suggests the possibility of spin liquid behavior for intermediate values of the anisotropy.

Spiral order in Ba 2CuGe 2O 7

The quasi-dimensional square-lattice antiferromagnet Ba 2CuGe 2O 7 was studied by neutron scattering and bulk magnetic techniques. An incommensurate magnetic spiral structure with the propagation vector (1 + ξ, ξ,0) ( ξ = 0.027) was observed below T N = 3.26 K. The spin dynamics can be adequately described by conventional spin-wave theory with two exchange constants: nearest-neighbor in-plane antiferromagnetic coupling J 1 ≈ 0.48 meV and interplane ferromagnetic interaction J 3 ≈ 0.013 meV. This set of exchange parameters apparently fails to explain the spiral order. The non-centrosymmetric crystal structure suggests that the incommensurate phase may be the result of a Dzyaloshinskii-Moriya instability of the Neel ground state.

Spiral phase and spin waves in the quasi-two-dimensional antiferromagnet Ba2CuGe2O7.

The quasi-two-dimensional square-lattice antiferromagnet ${\mathrm{Ba}}_{2}$ Cu${\mathrm{Ge}}_{2}$ ${\mathrm{O}}_{7}$ was studied by neutron scattering and bulk magnetic techniques. An incommensurate magnetic spiral structure with the propagation vector ($1+\ensuremath{\zeta}, 1+\ensuremath{\zeta}, 0$) ($\ensuremath{\zeta}=0.027$) was observed below ${T}_{N}=3.26$ K. Magnetic ordering occurs with a two-dimensional-like critical exponent $\ensuremath{\beta}\ensuremath{\approx}0.15$. The spin dynamics can be adequately described by conventional spin-wave theory with two exchange constants: nearest-neighbor in-plane antiferromagnetic coupling ${J}_{1}\ensuremath{\approx}0.48$ meV and interplane ferromagnetic interaction ${J}_{\ensuremath{\perp}}\ensuremath{\approx}0.013$ meV. This set of exchange parameters apparently fails to explain the spiral order. The noncentrosymmetric crystal structure suggests that the incom-mensurate phase may be the result of a Dzyaloshinskii-Moriya instability of the N\'eel ground state.