Antiferromagnetic Spin Waves Research Articles

Excitation spectrum of the homogeneous spin liquid

We discuss the excitation spectrum of a disordered, isotropic and translationally invariant spin state in the 2D Heisenberg antiferromagnet. The starting point is the nearest-neighbor RVB state which plays the role of the vacuum of the theory, in a similar sense as the Neel state is the vacuum for antiferromagnetic spin wave theory. We discuss the elementary excitations of this state and show that these are not Fermionic spin-1/2 `spinons' but spin-1 excited dimers which must be modeled by bond Bosons. We derive an effective Hamiltonian describing the excited dimers which is formally analogous to spin wave theory. Condensation of the bond-Bosons at zero temperature into the state with momentum (pi,pi) is shown to be equivalent to antiferromagnetic ordering. The latter is a key ingredient for a microscopic interpretation of Zhang's SO(5) theory of cuprate superconductivity

EFFECTIVE FIELD THEORY APPROACH TO FERROMAGNETS AND ANTIFERROMAGNETS IN CRYSTALLINE SOLIDS

We present a systematic construction of effective Lagrangians for the low energy and momentum region of ferromagnetic and antiferromagnetic spin waves in crystalline solids. We fully exploit the spontaneous symmetry breaking pattern SU(2)→U(1), the fact that spin waves are its associated Goldstone modes, the crystallographic space group and time reversal symmetries. We show how to include explicit SU(2) breaking terms due to spin-orbit and magnetic dipole interactions. The coupling to electromagnetic fields is also discussed in detail. For definiteness we work with the space group [Formula: see text] and present our results to next to leading order.

SKYRMIONS IN QUANTUM HALL FERROMAGNETS

Properties of skyrmions in quantum Hall systems are reviewed. It is shown that, using a Hartree-Fock technique, the size of skyrmions near filling factor ν=1 may be computed, yielding a result in close agreement with experiment. Finite densities of skyrmions are shown to lead to a crystal state with square symmetry due to the spin-dependent nature of their mutual interactions. The square lattice state has an unusual spin ordering which leads to a new gapless mode, analogous to spin waves in a two-dimensional XY antiferromagnet. The stability of the ordered spin state is assessed using a time-dependent Hartree-Fock approach, and a phase diagram is derived which shows the parameter range for which long-range spin ordering is destroyed by quantum fluctuations.

Specific heat ofPr0.6(Ca1−xSrx)0.4MnO3(0<~x<~1)

We present the results of a specific heat study of the ${\mathrm{Pr}}_{0.6}({\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{)}_{0.4}{\mathrm{MnO}}_{3}(0<~x<~1)$ manganite system as a function of doping concentration x and temperature. The low-temperature specific heat data indicate that these materials have Debye temperatures of 333--344 K and reveal the presence of a ${1/T}^{2}$ hyperfine term. For $x>~0.25$ the samples are metallic ferromagnets at low temperature with $\ensuremath{\gamma}$ values of 4.5--5.7 mJ/mol ${\mathrm{K}}^{2}.$ However, no ${T}^{3/2}$ term associated with the presence of ferromagnetic spin waves can be resolved in the data. As x decreases below $x=0.25,$ the materials become increasingly insulating in character and antiferromagnetic order is preferred. The $x=0.0$ sample is an antiferromagnetic charge ordered insulator. In this doping regime, the low-temperature specific heat contains an additional contribution which is attributed to the presence of antiferromagnetic spin waves. The high-temperature specific heat data clearly show the onset of the charge and magnetic ordering. The entropy loss accompanying the magnetic transition in each of these materials is much smaller than expected. This discrepancy is attributed to a combination of factors, including the localization of charge carriers around the metal-insulator transition which occurs at the Curie temperature ${T}_{C}$ in the $x>~0.25$ ferromagnetic materials and the presence of short range magnetic correlations, well above the magnetic ordering temperature.

Shadow bands of the spin polaron

We discuss the difference between a local spin polaron (in a spin liquid state with only short-range antiferromagnetic (AFM) order) and a spin polaron of infinite radius (if the spin system possesses AFM long-range order) within the scope of the t– J model. The local spin polaron wavefunction is found by a variational ansatz. The shadow bands occur due to the coupling of the local spin polaron to antiferromagnetic spin wave excitations with a wavevector Q=( π, π) . This leads to a dispersion which is symmetric with respect to the antiferromagnetic Brillouin zone (BZ) but has strongly asymmetric spectral weight. The evolution of the spectrum with temperature is discussed.

Studies of the modulational instability of antiferromagnetic spin waves in 1D

For antiferromagnetism spin chains the modulational instability of extended nonlinear spin waves has been investigated both analytically within the framework of linear stability analysis and also numerically by means of molecular dynamics simulations. For the particular case of on-site easy-axis anisotropy treated here linear stability analysis predicts the instability region and the growth rates of modulation satellites. Our numerical simulations demonstrate that the analytical predictions correctly describe the onset of instability. For long time scales when the instability is fully developed the linear stability analysis fails and the time evolution of the modulated spin waves can show both regular and chaotic behavior.

Spin-wave theory of exchange-induced anisotropy

It is shown that exchange interactions of spins across the boundary between ferromagnetic and antiferromagnetic layers can cause a shift in the observed hysteresis loop of the ferromagnetic layer. The effect may be interpreted as a self-energy shift of each ferromagnetic spin due to emission and reabsorption of virtual antiferromagnetic spin waves. Emission of these waves by one ferromagnetic spin and reabsorption by another also results in an extra exchange coupling among the ferromagnetic spins, but this is not calculated here in detail. A crucial test of the effectiveness of this mechanism as compared with others that have been proposed would be the observation of a reversal of the loop shift upon reversal of the magnetization of the ferromagnetic layer. However, the reversal time could be very long, and is estimated here. {copyright} {ital 1998} {ital The American Physical Society}

Magnetism in disordered spin-Peierls systems

The magnetic excitations in disordered spin-Peierls systems are investigated theoretically. Reflecting the characteristic properties of the ground state, where the true long-range orders of antiferromagnetism and spin-Peierls lattice dimerization coexist with spatially varying order parameters, two kinds of excitations with intrinsic mode broadenings are found. They are acoustic antiferromagnetic (AF) spin wave mode and gapped spin-Peierls (SP) lattice distortion mode. The effects of magnetic field is also discussed. These results are compared with experimental results.

Magnetic Excitations in the Si Doped Spin-Peierls CompoundCuGe1-xSixO3

The magnetic excitations of CuGe 1- x Si x O 3 single crystals ( x =0.011 and 0.03) have been studied by inelastic neutron-scattering techniques. We confirm the coexistence of the antiferromagnetic and spin-Peierls excitations as well as a splitting of the antiferromagnetic excitation peak at the magnetic zone center ( q =0) due to orthorhombic anisotropy. The q dependence of the antiferromagnetic spin-wave width Γ scales well with q 2 for small q ( q <0.1 A -1 ). We also find that the spin-wave velocity increases as the size of induced magnetic moment becomes larger. These experimental results strongly support recent theoretical predictions by Saito and Fukuyama.

Exact nonlinear spin waves in some models of interacting classical spins on a one-dimensional lattice

We present exact finite-amplitude spin wave solutions for the nonlinear differential-difference equations describing the dynamics of spin vectors in a ferromagnetic (FM) and an antiferromagnetic (AFM) classical Heisenberg model of interacting spins on a one-dimensional lattice. We find that the dispersion relation between the frequency and wave vector of the FM nonlinear spin wave has the same form as that of the well-known low-amplitude spin wave, but with a prefactor which is explicitly dependent on its amplitude. This is in contrast with the AFM nonlinear spin wave, where we obtain the following intriguing results: Both the frequency and the wave vector acquire complicated dependences on the sublattice spin wave amplitudes. However, the dispersion relation between them is identical to that of the usual low-amplitude AFM spin wave, with no explicit dependence on the amplitudes. We outline how such solutions can also be supported in certain variants of the above models.

Magnetic Excitations in Disordered Spin-Peierls Systems

The magnetic excitations in disordered spin-Peierls systems are investigated theoretically. Reflecting the characteristic properties of the ground state, where the true long range orders of antiferromagnetism and spin-Peierls lattice dimerization coexist with spatially varying order parameters, two kinds of excitations with intrinsic mode broadenings are found. They are acoustic antiferromagnetic (AF) spin wave mode and gapped spin-Peierls (SP) lattice distortion mode. These results are qualitatively consistent with inelastic neutron scattering experiments by Martin et al. on Cu 1- y Zn y GeO 3 with y =0.032.

Redistribution of the hole spectral weight due to longrange spin correlations in the three-band Hubbard model

In the framework of the three-band model for CuO_2 plane in high-temperature superconductors the spectrum of the spin-polaron hole exitation is investigated. The problem is treated taking into account the coupling of a local polaron with the antiferromagnetic spin wave with Q=(pi,pi). This leads to the essential changes of the lowest polaron band E(k) and the strong redistribution of the bare electron filling.

One spin-polaron problem in the two-dimensional Kondo lattice

Using the spin-polaron concept and the spherically symmetric state for the antiferromagnetic spin background, one-particle motion is studied for the two-dimensional Kondo lattice. The elementary excitations are represented by a Bloch superposition of four one-site electron states: two local states - a bare electron state and a local spin-polaron of small radius -and two states of delocalized polarons which correspond to the coupling of local states to the antiferromagnetic spin wave with momentum Q = ( π, π), so-called Q-polarons. We show that the lowest band of elementary excitations is essentially determined by Q-polaron states in the strongly coupled regime. Taking into account Q-polarons shifts the band bottom from (π,π) to (0,0). The spectral weight of a bare particle in the lowest band states can greatly differ from 1. This may lead to a large Fermi surface for a relatively small particle concentration.

Magnon-vortex interaction in a two-dimensional XY antiferromagnet

In this paper we semiclassically calculate the quantum corrections to the classical energy of a vortex configuration in a two-dimensional XY antiferromagnet arising from long-wavelength antiferromagnetic spin waves. This is done by calculating the zero-point energy due to the antiferromagnetic spin waves in the presence of the vortex background.

Polarized and unpolarized neutron-scattering study of the dynamical spin susceptibility of YBa2Cu3O7.

We report an extensive study of magnetic excitations in fully oxygenated Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, using neutron scattering with and without spin polarization analysis. By calibrating the measured magnetic intensity against calculated structure factors of optical phonons and against antiferromagnetic spin waves measured in the same crystal after deoxygenation to Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.2}$, we establish an absolute intensity scale for the dynamical spin susceptibility, ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\mathrm{q}, \ensuremath{\omega})$. The integrated spectral weight of the sharp magnetic resonance at $\ensuremath{\hbar}\ensuremath{\omega}=40$ meV and ${\mathrm{q}}_{\ensuremath{\parallel}}=(\frac{\ensuremath{\pi}}{a}, \frac{\ensuremath{\pi}}{a})$ in the superconducting state is $\ensuremath{\int}d(\ensuremath{\hbar}\ensuremath{\omega}){\ensuremath{\chi}}_{\mathrm{res}}^{\ensuremath{'}\ensuremath{'}}(\mathrm{q}, \ensuremath{\omega})=(0.52\ifmmode\pm\else\textpm\fi{}0.1)$ at low temperatures. The energy and spectral weight of the resonance are measured up to $T=0.8{T}_{c}$. The resonance disappears in the normal state, and a conservative upper limit of 30 states/eV is established for the normal state dynamical susceptibility at ${\mathrm{q}}_{\ensuremath{\parallel}}=(\frac{\ensuremath{\pi}}{a}, \frac{\ensuremath{\pi}}{a})$ and $10 \mathrm{meV}&lt;~\ensuremath{\hbar}\ensuremath{\omega}&lt;~40 \mathrm{meV}$. Our results are compared to previous neutron-scattering data on Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, theoretical interpretations of NMR data and current models of the 40 meV resonance.

Calculations of spin waves in an infinite cubic frustrated antiferromagnet

A theoretical formalism for calculating the spin-wave spectrum, as well as the spin-wave density of states, is developed in the case of an infinite frustrated Heisenberg antiferromagnet. These systems are described as two ferromagnetic cubic lattices, antiferromagnetically coupled, and the magnetic frustration results from the competition of antiferromagnetic interactions between first ( J 1) and second ( J 2) nearest neighbours. The mathematical description of the Hamiltonian proposed in the present paper includes exchange interactions extended to second-nearest neighbours, external magnetic field, anisotropic field, and antisymmetric exchange (Dzyalozhinsky-Moriya coupling). The spin-wave spectrum and the density of states are analyzed as functions of the magnetic frustration through the ratio J 1/ J 2. The soft magnetic spin-wave mode which is evidenced for J 1/ J 2 ≈ 4 is consistent with the presence of a magnetic phase transition previously predicted by computer simulations.

Spin stiffness in the Hubbard model

The spin stiffness $\rho_{\rm s}$ of the repulsive Hubbard model that occurs in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the same as the thermodynamically defined stiffness involved in twisting the order parameter. New expressions for $\rho_{\rm s}$ are derived, which enable easier interpretation, and connections with superconducting weight and gauge invariance are discussed.

Impurity scattering of spin waves in a doped Mott-Hubbard antiferromagnet.

Impurity scattering of low-energy, long-wavelength spin waves in a Mott-Hubbard antiferromagnet doped with static, nonmagnetic impurities is studied using a perturbative approach within the random phase approximation for the transverse spin-fluctuation propagator. Corrections to spin-wave energy are obtained to first order in impurity concentration, and in two dimensions a logarithmically divergent reduction in spin-wave velocity is obtained. The analysis is extended to a layered Mott-Hubbard antiferromagnet and the logarithmic divergence is shown to be cutoff by the interlayer hopping term. Magnetic dynamics in the layered antiferromagnet is studied, and a quantitative estimate is obtained for the reduction in N\'eel temperature with impurity concentration which is in agreement with neutron-scattering results for zinc-doped ${\mathrm{La}}_{2}$ ${\mathrm{CuO}}_{4}$. \textcopyright{} 1996 The American Physical Society.

Magnetic behavior of the cuprate superconductors

I review recent work on magnetic dynamics of the high temperature superconductors using a model that combines two weakly interacting species of low-energy excitations: the antiferromagnetic spin waves which carry spin-1 and no charge, and Fermi-liquid-like quasiparticles which carry spin- 1 2 and charge e. The model allows conversion of spin waves into electron-hole pairs; however, the low-energy spin waves are not collective modes of the quasiparticles near the Fermi surface, but rather are a separate branch of the low-energy spectrum. With certain experimentally justified assumptions, this theory is remarkably universal: the dependence on the detailed microscopic Hamiltonian and on doping can be absorbed into several experimentally measurable parameters. The z = 1 theory of the insulators and z = 2 theory of the overdoped materials, are both reproduced as limiting cases of the theory described here, which predicts that the underdoped materials remain in z = 1 universality class at sufficiently high temperature. This theory provides a framework for understanding both the experimental results and microscopic calculations, and in particular yields a possible explanation of the spin gap phenomenon. I also discuss some of the important unresolved issues.

Spinons and spin waves in one-dimensional Heisenberg antiferromagnets

The spin excitations of the s = 12 nearly one-dimensional Heisenberg antiferromagnet, KCuF3, have been determined using neutron scattering techniques. The results at high energies show that the excitations are described by pairs of unbound spinons but, at low temperatures and energies, the scattering is described by spin wave theory.