Magnon Frequency Research Articles

Direct observation of Bose–Einstein condensation in a parametrically driven gas of magnons

A gas of thermalized quasi-equilibrium magnons with a non-zero chemical potential created in a magnetic film using parametric pumping is studied. The value of the chemical potential of the gas is determined directly from the measured distribution of magnons over the spectrum. With increasing pumping power the value of the chemical potential increases. At high enough pumping powers it reaches the energy corresponding to the lowest magnon frequency. Under these conditions a very narrow peak of magnon population at the lowest magnon frequency appears. The measured width of the peak is five orders of magnitude smaller than that expected for the thermal distribution. We associate this effect with Bose–Einstein condensation of magnons.

Ferromagnetic relaxation by magnon-induced currents

A theory for calculating spin wave relaxation times based on the magnon-electron interaction is developed. The theory incorporates a thin film geometry and is valid for a large range of magnon frequencies and wave vectors. For high conductivity metals such as permalloy, the wave vector dependent damping constant approaches values as high as 0.2, showing the large magnitude of the effect, and can dominate experimentally observed relaxation.

Anisotropy effects on the magnetic excitations of epitaxial ultrathin films below and above the Curie temperature

Brillouin light scattering is exploited to study magnetic excitations in magnetic films consisting of a few atomic layers, characterized by a strong in-plane uniaxial anisotropy, namely NiFe/Cu(1 1 0) and Fe/Cu(1 1 0). Well below the Curie temperature, a nonmonotonic field dependence of the magnon frequency is measured for magnetic field H applied along the hard in plane direction, while for field along the easy direction the frequency is found to increase almost linearly with increasing H. When temperature is increased, the measured magnon gap at zero field decreases until, for all the investigated systems, it vanishes at room temperature. The anisotropy of the magnetic excitations is found to persist even in the paramagnetic phase: in fact, the magnon frequency is found to increase almost linearly with increasing H, but with different slopes depending on the field direction. The smaller slope is found for the field along the hard axis. A finite-temperature Green’s function theory, recently developed for the study of the field-driven reorientation transition of an anisotropic monolayer, is able to account for the experimental data of the investigated ultrathin films in the whole temperature range.

Ballistic Magnon Transport and Phonon Scattering in the AntiferromagnetNd2CuO4

The thermal conductivity of the antiferromagnet Nd2CuO4 was measured down to 50 mK. Using the spin-flop transition to switch on and off the acoustic Nd magnons, we can reliably separate the magnon and phonon contributions to heat transport. We find that magnons travel ballistically below 0.5 K, with a thermal conductivity growing as T3, from which we extract their velocity. We show that the rate of scattering of acoustic magnons by phonons grows as T3, and the scattering of phonons by magnons peaks at twice the average Nd magnon frequency.

SPIN FLUCTUATIONS AND ANHARMONICITY IN ITINERANT ELECTRON MAGNETISM

The paper overviews recent investigations of thermodynamics and magnetic dynamics of itinerant electron magnets with strongly coupled (anharmonic) spin fluctuations (SF). A novel classification scheme for SF, dependent on their spatial dispersion and quantum effects is presented, including the generalized Fermi liquid (FL), soft-mode (SM), and localized moments (LM) regimes. It is shown that the conventional SCR theory of Moriya holds only in the weak coupling limit of the SM regime and cannot be applied to real magnets where spin anharmonicity induced by zero-point SF is expected to be strong. To account for the effects of strong spin anharmonicity, a variational SM theory of SF is presented. These effects essentially influence thermodynamics of itinerant magnets and affect the criterion for magnetic instabilities, equations of state, low temperature specific heat, non-FL and quantum critical behavior, etc. Nonlinear magnetic dynamics of itinerant magnets is analyzed based on the phenomenological spin-invariant dynamical equations both in the spin wave and relaxational regimes. Macroscopic magnetic dynamics and different mechanisms of magnon damping in the spin wave regime are shown to be essentially different from the results arising for the Heisenberg magnets. The relaxational regime may be strongly influenced by nonlinear effects of mode-mode couplings. The spectrum of overdamped longitudinal SF is shown to be radically changed due to their scattering by magnons, which may result in a quasielasic peak in the SF spectrum and inelastic SF near the magnon frequencies, depending on nonlinear coupling. The quasielastic SF are suppressed at low temperatures and develop at elevated temperatures, dominating near the Curie point. The results are applied to the magnetoresistive manganites.

NEW PATH-INTEGRAL QUANTIZATION APPROACH FOR A LAGRANGIAN MODEL IN TERMS OF HUBBARD OPERATORS

In the present work the renormalized field theory for the Lagrangian formalism in terms of Hubbard operators is given. It is shown that starting from our path-integral representation found recently, it is possible to contruct the perturbative formalism and the standard Feynman diagram approach for operators verifying the Hubbard algebra. We show that by means of the introduction of proper ghost variables, propagators and vertices can be renormalized to each order. Our Lagrangian approach is checked using the Heisenberg ferromagnet and the antiferromagnet simpler models. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details, and it is shown how the softening of the magnon frequency is predicted by the model.

Low-frequency incommensurate magnetic response in strongly correlated systems

It is shown that in the $t\ensuremath{-}J$ model of Cu-O planes at low frequencies the dynamic spin structure factor is peaked at incommensurate wave vectors $(\frac{1}{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta},\frac{1}{2}),$ $(\frac{1}{2},\frac{1}{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}).$ The incommensurability is connected with the momentum dependencies of the magnon frequency and damping near the antiferromagnetic wave vector. The behavior of the incommensurate peaks is similar to that observed in ${\mathrm{La}}_{2\ensuremath{-}x}(\mathrm{B}\mathrm{a},\mathrm{S}\mathrm{r}{)}_{x}{\mathrm{CuO}}_{4+y}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}:$ for hole concentrations $0.02<x\ensuremath{\lesssim}0.12$ we find that $\ensuremath{\delta}$ is nearly proportional to x, while for $x>0.12$ it tends to saturation. The incommensurability disappears with increasing temperature. Generally the incommensurate magnetic response is not accompanied by an inhomogeneity of the carrier density.

Study of magnon mode characteristics in solid oxygen by high resolution spectroscopy

The higher energetic magnon at27 cm−1 was systematically investigated by far-IR-absorption and Raman scattering inα-O2 (T = 11–24 K).The softening of the magnon frequency—described in mean field theory—can beexplained by a weakening of the exchange interaction due to thermal expansionand by a loss of magnetic order due to thermal fluctuations. Bandwidth as afunction of temperature can be fitted by a power law, with a zero bandwidth atT = 0 K(Γ = aT4.4).Dephasing processes via magnon–magnon scattering are the only meaningfulrelaxation mechanisms of this magnon mode. The integrated band intensity,normalized to our low temperature value, directly follows the spin–spincorrelation function and describes the long range magnetic order parameter inα-O2.The spectral characteristics, band frequency and band intensity(ω andI) prove thatthe α–β phasetransition (at Tαβ = 23.8 K)is not purely magnetic.

Nonlinear spin fluctuations in the Fermi liquid of itinerant electron ferromagnets

A microscopic derivation of nonlinear equations of magnetic dynamics for itinerant ferromagnets is presented within the electron Fermi liquid model accounting for both long-range Coulomb and short-range interactions of quasiparticles, which founds the basis for the phenomenological description of nonlinear spin fluctuations (SF) using the Ginsburg–Landau formalism. Crystal lattice is shown to play a significant role screening the long-range Coulomb interaction and affecting magnetic dynamics. The spectrum of longitudinal SF with account of nonlinear mode–mode coupling is shown to result from an interplay of quasielastic SF and inelastic excitations near the magnon frequencies, both having mainly the nonlinear nature and arising due to their emission (absorption) by magnons.

Magnon modes for thin circular vortex-state magnetic dots

The magnetization in a magnetic microdot made from soft magnetic materials can have a vortex-like ground-state structure resulting from competition between the exchange and dipolar interactions. Normal mode magnon frequencies for such dots are calculated taking into account both exchange and magnetostatic effects. The presence of a low-lying mode as well as doublet structure with small splitting is demonstrated. Estimates of the mode frequencies for permalloy dots are obtained, and the possibility of experimental detection of such modes is discussed.

Lagrangian for the t–J Model Constructed from the Generators of the Supersymmetric Hubbard Algebra

In order to describe the dynamics of the t–J model, two different families of first-order Lagrangians in terms of the generators of the Hubbard algebra are found. Such families correspond to different dynamical second-class constrained systems. The quantization is carried out by using the path-integral formalism. In this context the introduction of proper ghost fields is needed to render the model renormalizable. In each case the standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. In the first case a nonperturbative large-N expansion is considered with the purpose of studying the generalized Hubbard model describing N-fold-degenerate correlated bands. In this case the 1/N correction to the renormalized boson propagator is computed. In the second case the perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details. As an example the thermal softening of the magnon frequency is computed. The antiferromagnetic case is also analyzed, and the results are confronted with previous one obtained by means of the spin-polaron theories.

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains**The project supported by the Trans-Century Training Programme Foundation for the Talents by the Education Ministry of China and National Natural Science Foundation of China under Grant No. 19975019

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e. Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.

Fourier transform infrared spectroscopy of electronic excitations to probe magnetic order and phase transitions in solid oxygen

Systematic Fourier transform infrared (FTIR) spectroscopic investigations of interaction-induced electronic transitions ${}^{3}{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}{\ensuremath{-}}^{1}{\ensuremath{\Delta}}_{g}$ $(v=0,\dots{},3)$ of solid and liquid oxygen were carried out in the temperature range 10--90 K at ambient pressure. We interpret these absorption bands as phonon sidebands to an electronic (or an electronic-vibrational) excitations plus (in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2})$ exciton (-vibron)-magnon bound states. A consistent description of electronic spectra in all phases of oxygen (\ensuremath{\alpha}, \ensuremath{\beta}, \ensuremath{\gamma}, liquid) was achieved. It was shown that the combined excitations are assisted by a spin-spin exchange interaction in condensed phases of oxygen. A special procedure to analyze the band shape of these spectra was worked out to determine the unknown frequencies of electronic and electronic-vibrational excitations. The magnon frequencies at boundaries of the Brillouin zone were deduced from electronic-vibrational spectra and their temperature behaviors were explored in magnetically ordered $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}.$ We present several unambiguous direct experimental proofs that the \ensuremath{\alpha}-\ensuremath{\beta} phase transition is of first order and we show that there are no experimental evidences for magnetic disordering as well as for temperature-caused changes in crystal structure in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{O}}_{2}$ as a precursor to the \ensuremath{\alpha}-\ensuremath{\beta} phase transition. We investigated the kinetics of the \ensuremath{\alpha}-\ensuremath{\beta} phase transition and we found out an extreme sensitivity of this transition to impurities (as small as 1 ppm). We discovered that the frequencies of electronic and electronic-vibrational excitations depend strongly on magnetic order in the \ensuremath{\alpha} phase and that they are hardly ruled by changes in molar volume in all phases. Thus, spectroscopy of electronic excitations can be used to probe indirectly the magnetic order and to classify the order of phase transitions in high-pressure phases of solid oxygen, where this information is not available up to now.

Generation and detection of phase-coherent current-driven magnons in magnetic multilayers

The magnetic state of a ferromagnet can affect the electrical transport properties of the material; for example, the relative orientation of the magnetic moments in magnetic multilayers underlies the phenomenon of giant magnetoresistance. The inverse effect--in which a large electrical current density can perturb the magnetic state of a multilayer--has been predicted and observed experimentally with point contacts and lithographically patterned samples. Some of these observations were taken as indirect evidence for current-induced excitation of spin waves, or 'magnons'. Here we probe directly the high-frequency behaviour and partial phase coherence of such current-induced excitations, by externally irradiating a point contact with microwaves. We determine the magnon spectrum and investigate how the magnon frequency and amplitude vary with the exciting current. Our observations support the feasibility of a spin-wave maser' or 'SWASER' (spin-wave amplification by stimulated emission of radiation).

Magnetic anisotropies in dot arrays: Shape anisotropy versus coupling

The magnetization and resonance frequencies of submicron Fe magnetic dot arrays are investigated using Brillouin light scattering (BLS) and magneto-optic Kerr Effect (MOKE). Large in-plane anisotropies, evident in both the BLS and MOKE results, are traced to shape anisotropies of the individual dots. The measured magnon frequencies are in good agreement with values calculated on the basis of isolated ellipsoids without interdot coupling.

Magnon spectrum at the non-RKKY indirect exchange in conducting ferromagnets

The magnon spectrum of conducting ferromagnets is investigated when conditions for the applicability of the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory are not met (double-exchange systems and degenerate magnetic semiconductors). The long-wave magnon frequencies are nonanalytical in the $s\ensuremath{-}f(d)$ exchange integral. The Kohn singularity specific for the RKKY theory is either absent, or the number of the singularities is not less than 2. In the almost-RKKY case there are two different magnon effective masses.

Temperature Dependence of Raman Scattering by Magnons in Bulk-Like MBE-Gwn MnTe Films

Temperature dependence of the magnon frequency was studied for cubic MnTe epilayers by the Raman scattering measurements. Experimental data are compared to the results of theoretical calculations performed within the framework of the Heisenberg model using Green's function formalism.

Exchange and anisotropy effects on spin waves in epitaxial Co films

Using Brillouin scattering we have investigated the effect of large in-plane anisotropy on magnetic excitations in $b$ axis-oriented epitaxial 50-nm Co films. For in-plane fields along the easy axis the magnon frequencies increase monotonically with increasing field. For in-plane fields along the hard axis, nonmonotonic behavior is observed in which the surface to bulk spin-wave character of one magnon mode changes as a function of applied field. Although fits to the data based on a full theoretical treatment are consistent with parameters in the literature and with parameters extracted from the magnetization data, we show that uncertainties in crystal orientation (as small as 1\ifmmode^\circ\else\textdegree\fi{}) can produce dramatic effects in the quantitative data interpretation.

Gap solitons and resonant kinks in Heisenberg ferromagnetic chains with bond alternation

A ferromagnetic Heisenberg spin chain Hamiltonian with bond alternation is used to investigate localized excitations in magnetic systems genuine of the discreteness and nonlinearity. Gap solitons (with the vibrating frequency lying in the gap of magnon frequency bands) and resonant kinks (with the vibrating frequency lying in the frequency bands) are found. It is also shown that an optical upper cutoff soliton (with the vibrating frequency being above the magnon frequency bands) is impossible in such a system.

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.