Magnon Gap Research Articles

Doping dependence of the spin gap in a two-leg ladder

A spin-fermion model relevant for the description of cuprates ladders is studied in a path integral formalism, where, after integrating out the fermions, an effective action for the spins in term of a Fermi-determinant results. The determinant can be evaluated in the long-wavelength, low-frequency limit to all orders in the coupling constant, leading to a non-linear $\ensuremath{\sigma}$ model with doping dependent coupling constants. An explicit evaluation shows that the magnon gap diminishes upon doping, as opposed to previous mean-field treatments.

Order from disorder: Quantum spin gap in magnon spectra ofLaTiO3

A theory of the anisotropic superexchange and low energy spin excitations in a Mott insulator with t_{2g} orbital degeneracy is presented. We observe that the spin-orbit coupling induces frustrating Ising-like anisotropy terms in the spin Hamiltonian, which invalidate noninteracting spin wave theory. The frustration of classical states is resolved by an order from disorder mechanism, which selects a particular direction of the staggered moment and generates a quantum spin gap. The theory explains well the observed magnon gaps in LaTiO_3. As a test case, a specific prediction is made on the splitting of magnon branches at certain momentum directions.

Magnetic properties of undoped YBa 2 Cu 3 O 6 + x system

In the present paper, we study the magnetic properties of bilayer cuprate antiferromagnets. In order to evaluate the expressions for spin-wave dispersion, sublattice magnetization, Neel temperature and the magnetic contribution to the specific heat, the double time Green's function technique has been employed in the random phase approximation (RPA). The spin wave dispersion curve for a bilayer antiferromagnetic system is found to consist of one acoustic and one optic branch. The “optical magnon gap” has been attributed solely to the intra-bilayer exchange coupling (J ⊥ ) as its magnitude does not change significantly with the inter-bilayer exchange coupling (Jz). However Jz is essential to obtain the acoustic mode contribution to the magnetization. The numerical calculations show that the Neel temperature (T N ) of the bilayer antiferromagnetic system increases with the Jz and a small change in Jz gives rise to a large change in the Neel temperature of the system. The magnetic specific heat of the system follows a T2 behaviour but in the presence of Jz it varies faster than T2.

Temperature dependence of magnetization and optical magnon gap in bilayer antiferromagnetic YBa 2Cu 3O 6

We study the magnetization and spin excitations of anisotropic bilayer antiferromagnets. We consider a model Hamiltonian which incorporates the inplane, the intrabilayer and the interlayer exchange couplings for a cuprate which has two CuO 2 layers per unit cell. The expression for the sublattice magnetization is obtained by employing the Green’s function technique and we have used the Callen decoupling approximation. The numeral results, obtained using the parameters appropriate for YBa 2Cu 3O 6, a bilayer antiferromagnet, show that Callen decoupling procedure gives a value of the Neél temperature which is in reasonable agreement with the measured value of 450 K for YBa 2Cu 3O 6. We have discussed the effects of anisotropy in exchange coupling constants on the Neél temperature of the system and results for the 3D case are also presented. Further, we obtain energy values for the spin excitations (magnons) of the bilayer systems. The excitation spectrum consists of two branches namely the acoustic branch and the optic branch. These branches are separated by an energy gap and the value of this gap at zero wave vector is known as optical magnon gap E G. This gap is found to be dependent on temperature as well as on the anisotropy in the values of the exchange coupling parameters of the system. We have numerically evaluated the anisotropy and the temperature dependence of E G for YBa 2Cu 3O 6.

Magnon dispersion and thermodynamics inCsNiF3

We present an accurate transfer matrix renormalization group calculation of the thermodynamics in a quantum spin-1 planar ferromagnetic chain. We also calculate the field dependence of the magnon gap and confirm the accuracy of the magnon dispersion derived earlier through a $1/n$ expansion. We are thus able to examine the validity of a number of previous calculations and further analyze a wide range of experiments on ${\mathrm{CsNiF}}_{3}$ concerning the magnon dispersion, magnetization, susceptibility, and specific heat. Although it is not possible to account for all data with a single set of parameters, the overall qualitative agreement is good and the remaining discrepancies may reflect a departure from ideal quasi-one-dimensional model behavior. Finally, we present some indirect evidence to the effect that the popular interpretation of the excess specific heat in terms of sine-Gordon solitons may not be appropriate.

Spin-wave contributions to nuclear magnetic relaxation in magnetic metals

The longitudinal and transverse nuclear magnetic relaxation rates 1/T 1(T) and 1/T 2(T) are calculated for three- and two-dimensional (3D and 2D) metallic ferro- and antiferromagnets (FM and AFM) with localized magnetic moments in the spin-wave temperature region. The contribution of the one-magnon decay processes is strongly enhanced in comparison with the standard T-linear Korringa term, especially for the FM case. For the 3D AFM case this contribution diverges logarithmically, the divergence being cut at the magnon gap ω due to magnetic anisotropy, and for the 2D AFM case as ω-1. The electron-magnon scattering processes yield T 2ln(T/ω) and T 2/ω1/2-terms in 1/T 1 for the 3D AFM and 2D FM cases, respectively. The two-magnon (“Raman”) contributions are investigated and demonstrated to be large in the 2D FM case. Peculiarities of the isotropic 2D limit (where the correlation length is very large) are analyzed.

Magnon dispersions in quantum Heisenberg ferrimagnetic chains at zero temperature

Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets composed of two different spins $(S_1,S_2)$ in the elementary cell. It is shown that the spin-wave theory can produce precise quantitative results for the low-energy excitations. The spin-stiffness constant $\rho_s$ and the optical magnon gap $\Delta$ of different $(S_1,S_2)$ ferrimagnetic systems are calculated, respectively, to second and third order in the quasiparticle interaction. The spin-wave results are compared with available numerical estimates.

Minute zero–magnon component and predominant multi-magnon one in photoemission spectra of the two-dimensional half-filled Hubbard system

We show how the coherent and the incoherent components contribute to the one-body Green's function for the two-dimensional half-filled Hubbard model. By adding a site-diagonal staggered potential, a magnon gap artificially opens and, as a result, the zero–magnon coherent component is clearly separated from the multi-magnon incoherent one. We show that the incoherent component predominates the spectrum of the usual Hubbard system, while the coherent component makes only a minute contribution.

Spin-wave contributions to nuclear magnetic relaxation in magnetic metals

The longitudinal and transverse nuclear magnetic relaxation rates $1/T_1(T)$ and $1/T_2(T)$ are calculated for three- and two-dimensional (3D and 2D) metallic ferro- and antiferromagnets (FM and AFM) with localized magnetic moments in the spin-wave temperature region. The contribution of the one-magnon decay processes is strongly enhanced in comparison with the standard $T$-linear Korringa term, especially for the FM case. For the 3D AFM case this contribution diverges logarithmically, the divergence being cut at the magnon gap $\omega_0$ due to magnetic anisotropy, and for the 2D AFM case as $\omega_0^{-1}$. The electron-magnon scattering processes yield $T^2\ln (T/\omega_0)$ and $T^2/\omega_0^{1/2}$-terms in $1/T_1$ for the 3D AFM and 2D FM cases, respectively. The two-magnon (``Raman'') contributions are investigated and demonstrated to be large in the 2D FM case. Peculiarities of the isotropic 2D limit (where the correlation length is very large) are analyzed.

Magnetic interactions and magnon gap in the ferromagnetic superconductorRuSr2GdCu2O8

By means of X- and Q-band magnetic-resonance measurements we have investigated the magnetic interactions and derived the magnon gap in the ferromagnetic superconductor ${\mathrm{RuSr}}_{2}{\mathrm{GdCu}}_{2}{\mathrm{O}}_{8}.$ Two microwave absorptions are observed: first, a paramagnetic resonance of the ${\mathrm{Gd}}^{3+}$ ions, and second, appearing below the Curie temperature ${(T}_{\mathrm{Curie}}),$ a ferromagnetic resonance due to the ruthenium lattice. Located between the superconducting ${\mathrm{CuO}}_{2}$ planes, the Gd ions serve as intrinsic probes of the internal magnetic fields near the Cu sites. Below ${T}_{\mathrm{Curie}}$ the ${\mathrm{Gd}}^{3+}$ signal shifts, evidencing the appearance of a homogeneous internal field, ${H}_{\mathrm{Ru}\ensuremath{-}\mathrm{Gd}}\ensuremath{\sim}600\mathrm{Oe}.$ We show that ${H}_{\mathrm{Ru}\ensuremath{-}\mathrm{Gd}}$ is due to a Ru-Gd ferromagnetic exchange interaction. The Ru ferromagnetic resonance indicates the existence of a magnon anisotropy gap $\ensuremath{\omega}/\ensuremath{\gamma}\ensuremath{\gtrsim}4600\mathrm{Oe}.$ We estimate the out-of-plane and in-plane anisotropy fields to be, respectively, ${H}_{z}\ensuremath{\sim}110\mathrm{kOe}$ and ${H}_{x}\ensuremath{\sim}200\mathrm{Oe}.$

S=12alternating chain using multiprecision methods

In this paper we present results for the ground state and low-lying excitations of the $S=1/2$ alternating Heisenberg antiferromagnetic chain. Our more conventional techniques include perturbation theory about the dimer limit and numerical diagonalization of systems of up to 28 spins. An application of multiple precision numerical diagonalization allows us to determine analytical perturbation series to high order; the results found using this approach include ninth-order perturbation series for the ground state energy and one magnon gap. We also determine the fifth-order dispersion relation and third-order exclusive neutron scattering structure factor for one-magnon modes and numerical and analytical binding energies of $S=0$ and $S=1$ two-magnon bound states.

Domain excitations in spin-Peierls systems

We study a model of a Spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an inter-chain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic Spin-Peierls compound CuGeO$_3$

NONLINEAR EXCITATIONS IN ONE DIMENSIONAL HEISENBERG FERROMAGNETIC CHAIN WITH BOND ALTERNATION

About the one-dimensional Heisenberg ferromagnetics chain with bond alternation,research results show,in first-order approximation,that (1) magnon gap solitons (with the vibrating frequency lying in the gap between magnon frequency band) and resonant kinks (with the vibrating frequency lying in the magnon frequency band) are found; (2) an instrinsic localized mode (with the vibrating frequency being above the magnon frequency band) is impossible.

Spin-waves on a planar heisenberg frustrated antiferromagnet with Dzyaloshinsky-Moriya type coupling

A semi-infinite bidimensional Heisenberg frustrated antiferromagnet system is considered, where the magnetic frustration phenomena are due to the competition of the first inter-sublattice ( J 1v AB) and the second intra-sublattice ( J 2v AA(BB)) exchange interactions. The bulk and surface spin-waves are calculated as a function of the frustration parameter J 1 v AB J 2 v AA(BB) , accounting for Dzyaloshinsky-Moriya (DM) type coupling. The principle of the matching method is detailed by coupling the properties of bulk magnons with evanescent spin-waves along the direction perpendicular to the surface. It is shown that the behaviour of the bulk magnon, as well as acoustic and optic surface spin-waves, is very sensitive to surface exchange and anisotropy. The evolutions of acoustic and optic surface modes are interpreted by means of a frustration parameter, and the DM term induces a bulk magnon gap band, consistent with an anisotropic term

Magnetic excitation spectrum of dimerized antiferromagnetic chains.

Motivated by recent measurements on CuGe${\mathrm{O}}_{3}$, the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.

Magnon specific heat of CuGeO 3 in the spin-Peierls state

We have used ac calorimetry to measure the specific heat of CuGeO 3 below its spin-Peierls transition temperature in magnetic fields up to 7T, and have compared it to values calculated from a model triplet magnon dispersion curve. We find that the observed field dependence is much smaller than that calculated with Zeeman splitting of the magnon gap, but is consistent with that calculated assuming m=0 excitation (and mean-field, quadratic magnetic field dependence) only. This result implies weak coupling between thermal phonons and m=±1 magnons, so that population of the latter are frozen for times < 40 ms. A similar assumption accounts for the zero-field specific heat at temperatures above 4.5 K.

Magnetic correlations in random anisotropy magnets: a spin wave approach

A modified version of the spin-wave (s.w.) approximation is devised to calculate the zero-point and finite-temperature contributions to the spin correlation functions (SCF) and small wavevector neutron scattering structure factors (SF), longitudinal and transverse to a magnetic field, H, for random magnetic anisotropy (RMA) magnets, in the quasi-saturated regime. All possible origins for spin deviations are considered, and several contributions to the SF have been identified. For the transverse structure factor (TSF), the zero-point static spin deviations due to the RMA give rise to a squared Lorentzian ( L 2). The s.w. scattering off the RMA disorder leads to a new TSF in form of a power L 1 2 . The s.w. scattering leads to a renormalization of the s.w. spectrum and to a negative shift of the magnon gap. The inclusion of 1 S -order operator expansions for magnon interactions yields L 2 as well, although weaker than the above L 2. In all situations the magnetic correlation length (MCL) has been determined for both H=0 and H≠0, identifying several magnetic regimes. The finite-temperature s.w. excitation leads to: a Lorentzian ( L), and to a new TSF of the form L 3 2 , due to RMA s.w. scattering. All of the above results apply without structural correlations (SCs). The presence of SCs keeps the TSF as L 2, although they substantially enlarge the MCL at both H=0 and H≠0. For the longitudinal spin correlation (LSCF), an important result is that, at 0 K, the RMA does not destroy the long-range ferromagnetic order (LRFO) induced by the magnetic field, although the LSCF is weaker than for a good ferromagnet and the longitudinal SF becomes L 2. The LRFO only appears above a threshold magnetic field. The comparison of these results and small-angle neutron scattering observed in rare earth intermetallics is discussed. We should stress that the main aim of this work is to provide a comprehensive microscopic background to the phenomenological, continuous spin and mean field theories for RMA magnets.

Evidence for the exchange origin of the magnon gap in the garnet Ca 3Fe 2Ge 3O 12

The two acoustic magnon branches exhibit each an energy gap at the Brillouin zone center. The higher one is predicted to arise from a coupling of the antiferromagnetic subsystems due to the zero-point spin fluctuations. The temperature dependence of the gap frequency supports this hypothesis.

Brillouin Scattering in Itinerant Ferromagnet MnP

Thermal magnons within the optical skin layer of ferromagnetic MnP single crystal ( T c ∼290 K) have been studied by Brillouin light scattering in a temperature range between 80 K and 310 K under zero magnetic field. For temperatures below ∼ T c /2, the magnon energy gaps obtained from Brillouin scattering show good agreement with the bulk magnon gaps obtained from neutron scattering and torque method. Well below the Curie temperature, Brillouin scattering has been established as a convenient technique to determine the energy gaps in itinerant ferromagnets. The spins near the surface seem to undergo a surface magnetic phase transition at much lower temperatures than the bulk T c . A complete set of the elastic constants at room temperature has been determined.

Magnons and approach to saturation in random anisotropy magnets

A model of spin waves is developed for random anisotropy (RMA) magnets, where the deviations produced by the RMA are introduced. A negative shift in the magnon gap is found. The laws of approach to saturation of both magnetization and magnetostriction are of the form, a/√ H + b/H, where the a and b constants are functions of the usual D/J ratio.