Showing papers on "Spin wave published in 1968"
TL;DR: In this paper, the spin wave contribution to low temperature magnetization is considered in the limits of strong and very weak ferromagnetism, and a simple equation for the magnetic isotherms is obtained in this limit and shown to be valid over a wide temperature range.
Abstract: Calculations are given for the dependence on temperature and magnetic field strength H of the magnetization M of ferromagnetic metals treated on the basis of the itinerant electron model. The spin wave contribution to the low temperature magnetization is considered in the limits of strong and very weak ferromagnetism. For the first limit, problems related to the well-known divergence of the zero field differential susceptibility are briefly discussed. The main part of the paper is concerned with the single particle contributions to the magnetization and associated differential susceptibility for very weak ferromagnetism. A simple equation for the magnetic isotherms is obtained in this limit and shown to be valid over a wide temperature range including 0 °K and the Curie temperature. This equation implies that plots of M 2 against H / M at various temperatures in this range give a series of parallel straight lines. Recently measured isotherms for the material ZrZn 2 are analysed on the basis of the theory, and several characteristic properties of this material are obtained from the analysis.
188 citations
TL;DR: In this paper, the authors considered the itinerant electron model in the limit of very low exchange splitting energies and derived the magnetic isotherms giving M(H, T) to cover a wide range of fields and temperatures.
Abstract: The itinerant electron model is considered in the limit of very low exchange splitting energies. Magnetic isotherms giving M(H, T) are derived to cover a wide range of fields and temperatures. The isotherms are transformed so as to show that plots of M 2 vs H/M at different temperatures give parallel straight lines. The differential susceptibility below and above the Curie temperature is derived as a function of T. The free energy corresponding to this model is calculated and several results concerning the specific heat of very weak itinerant ferromagnets are deduced. Some properties related to spin wave excitations are also considered. New experimental data on the material ZrZn2 are considered on the basis of the theory and shown to be in reasonable agreement with it. Several characteristic parameters of this material are deduced, for example a value of the exchange splitting energy 0.040 eV, and of the effective interation between the itinerant electrons 0.35 eV. The occurrence of very weak itinerant ferromagnetism in other substances is also discussed.
176 citations
TL;DR: In this article, a review is given of recent measurements of spinwave dispersion relations of the 3D metals by the Brookhaven neutron diffraction group using the diffraction technique and triple-axis spectrometry.
Abstract: A review is given of recent measurements of spin‐wave dispersion relations of the 3d metals by the Brookhaven neutron diffraction group using the diffraction technique and triple‐axis spectrometry. The parameters D and β in the relation ħω = Dq2(1 − βq2) have been determined at 295°K for Fe, Co, Ni, and some of their alloys. These values are compared with those obtained by thin‐film resonance and small‐angle scattering.The most extensive measurements were carried out on Fe using a triple‐axis spectrometer. The dispersion relation was measured along the three principal symmetry directions for wavevectors up to q/qmax = 0.4. The stiffness constant D as well as the linewidth of selected spin waves were studied for the temperature range between 77°K and the Curie temperature, 1042°K. Well‐defined magnons were observed up to a reduced temperature T/TC = 0.995, but not above TC.
145 citations
TL;DR: In this paper, the time-scales characterizing spin relaxations near the magnetic transitions in isotropic Heisenberg spin systems are discussed, and the effect of spin relaxation on the magnetic transition is investigated.
Abstract: The time-scales characterizing spin relaxations near the magnetic transitions in isotropic Heisenberg spin systems are discussed.
139 citations
TL;DR: In this paper, the second-order two-and three-magnon processes were studied in magnetic insulators, where a virtual magnon, emitted in the direct process, is scattered by thermal magnons via the exchange interaction or the magnetic dipole-dipole interaction.
Abstract: First-order nuclear spin-lattice relaxation arises in magnetic insulators when a nuclear spin directly interacts with one or more spin waves via the hyperfine interaction. The direct process, in which a single magnon is emitted, is not ordinarily allowed on the basis of energy conservation, since the energy of a nuclear spin flip is considerably lower than the minimum energy of a spin wave. When the hyperfine interaction is isotropic and the axes of quantization of the nuclear and electronic spins are collinear, the conservation of the $z$ component of spin angular momentum forbids the Raman process, in which a thermal magnon is scattered to a state of different wave vector, accompanied by a nuclear spin flip. The three-magnon process is usually allowed. We consider here some second-order two- and three-magnon processes which arise when a virtual magnon, emitted in the direct process, is scattered by thermal magnons via the exchange interaction or the magnetic dipole-dipole interaction. This is possible, since (1) the magnon spectrum is lifetime broadened to overlap the nuclear spin resonance frequency, and (2) the dipole interaction does not conserve spin angular momentum. The second-order three-magnon process, arising from the four-magnon exchange interaction, enhances the three-magnon process relaxation rate by a factor of 8 in ferromagnets, and results in a temperature-dependent enhancement of about one order of magnitude in antiferromagnets. Three-magnon terms in the dipole-dipole interaction may induce a two-magnon process in both ferromagnets and antiferromagnets, which is of significance when the first-order Raman process is forbidden. We also calculate the relaxation rate due to second-order exchange-scattering-induced two-magnon process which is often more important than the first-order process in canted antiferromagnets of both the "easy-axis" and the "hard-axis" anisotropy type.
136 citations
TL;DR: In this paper, the theory of helical and modified-helical spin ordering, confining to molecular field treatments and spin-wave calculations, is discussed, and the role of conduction electrons in the exchange interaction is discussed.
Abstract: Publisher Summary This chapter discusses the theory of helical and modified-helical spin ordering, confining to molecular field treatments and spin-wave calculations Modifications of a helical spin order arise from anisotropy energies and an external magnetic field Also, a description of the theory of complex helical spin configurations in complex crystalline lattices is given A basic assumption made is that there exist isotropic exchange interactions between atomic spin moments of further neighbors as well as between neighboring moments The coefficients of these exchange interactions are assumed as given constants In this sense, the spin system dealt with may be called the Heisenberg magnet Experimental observations relevant to the theory are referred to and are useful to elucidate the theory This chapter deals with the role of conduction electrons in the exchange interaction; it reviews and discusses the observed magnetic and other properties of heavy and light rare-earth metals, and finally discusses the spin density wave in chromium
102 citations
TL;DR: In this paper, the theory of spin fluctuations in nearly ferromagnetic metals is presented and their effect on the properties of such systems is discussed, and the importance of momentum-dependent exchange and band structure effects is stressed.
Abstract: The theory of spin fluctuations in nearly ferromagnetic metals is presented and their effect on the properties of such systems is discussed. The importance of momentum‐dependent exchange and band‐structure effects is stressed.
97 citations
TL;DR: In this paper, the theory of the magnetic behavior of the lattice of localized moments corresponding to the unfilled 4f shells, and a description of the relevant experimental information are treated.
Abstract: Publisher Summary This chapter discusses the theory of the magnetic behavior of the lattice of localized moments corresponding to the unfilled 4f shells, and to a description of the relevant experimental information. It begins by describing the equilibrium magnetic arrangements, the basic model for magnetic behavior of the heavy rate earth metals, and the way in which one obtains transitions between various equilibrium magnetic arrangements within this model. The emphasis is on the theory for the excited magnetic states—that is, spin-wave-like states, and the experimental manifestations of these excited magnetic states. These topics are treated in this chapter. It discusses the theory of spin wave behavior when the equilibrium magnetic arrangement is ferromagnetic. That Part includes a discussion of the temperature dependence, as well as discussion of applied field and magnetoelastic effects. The excited magnetic state behavior for periodic moment arrangements is discussed here.
79 citations
TL;DR: In this paper, an equation-of-motion formalism is used to give a nonlinear spin-wave treatment of fcc solid ortho-hydrogen, and the excitation spectrum, long-range order, and ground-state energy are calculated.
Abstract: An equation-of-motion formalism is used to give a nonlinear spin-wave treatment of fcc solid ortho-hydrogen. The elementary excitations in ortho-hydrogen are librational waves and can be treated in a manner similar to spin waves in magnetism. The excitation spectrum, long-range order, and ground-state energy are calculated. It is found that the spin-wave excitations have a nonvanishing effect on both the long-range order and the ground-state energy. But, because of a large energy gap, the spin-wave-theory results deviate only slightly from their molecular-field values.
75 citations
TL;DR: The magneto-optical rotation in magnetic materials has been studied for many years as mentioned in this paper, where the axis of linear polarization undergoes a rotation proportional to the fractional projection of M on the direction of propagation.
Abstract: Light transmitted by a magnetic crystal interacts with the magnetization. In particular, the axis of linear polarization undergoes a rotation proportional to the fractional projection of M on the direction of propagation. This magneto‐optical rotation, the Faraday rotation in magnetic materials, has been studied for many years. The advent of insulating magnetic materials has led to renewed interest of two sorts:(1) The rotational dispersion coupled with that of the absorption coefficient in some cases makes possible the spectroscopic assignment of optical transitions which show magnetic effects. Thus we may use the rotation to extract information on the magnetic behavior of energy levels well above the ground state.(2) Any experimental or technological use of the rotation makes it necessary to take into account the attendant absorption of light. Some insulating magnetic materials have very high values of the rotation per unit attenuation. The magneto‐optical rotation may then be used to ``see'' both dc (domain structure) and rf (magnetostatic spin waves) magnetization distributions within the crystal. Furthermore, the low rotation attenuation is crucial in a number of magneto‐optical devices: rotators, wide‐band modulators, phase shifters, memories, the YIG laser, etc.
74 citations
TL;DR: The spin-wave dispersion relations have been measured in antiferromagnetic uranium dioxide by inelastic neutron-scattering techniques as mentioned in this paper, and various models are used in attempts to deduce the exchange and anisotropy parameters from the experimental results, none of the models are completely satisfactory, because of the difficulties arising from the multidomain character of the specimen, and from the strong interaction between the magnons and the phonons.
Abstract: The spin-wave dispersion relations have been measured in antiferromagnetic uranium dioxide by inelastic neutron-scattering techniques. The triple-axis crystal spectrometer at the C5 facility of NRU was used throughout in its constant-Q mode of operation. The dispersion relations were obtained for spin waves propagating along the main symmetry directions at 9\ifmmode^\circ\else\textdegree\fi{}K, and less complete measurements were made at higher temperatures both above and below the N\'eel temperature. The theory of spin waves in U${\mathrm{O}}_{2}$ is developed and various models are used in attempts to deduce the exchange and anisotropy parameters from the experimental results. None of the models are completely satisfactory, because of the difficulties arising from the multidomain character of the specimen, and from the strong interaction between the magnons and the phonons. A theory of this interaction is also developed which gives quite reasonable agreement with experiment.
TL;DR: In this article, the angular distribution characteristic of the small-angle scattering of neutrons by long-wavelength spin waves has been observed at temperatures up to and above the Curie temperature in iron and nickel.
Abstract: Angular distributions characteristic of the small-angle scattering of neutrons by long-wavelength spin waves have been observed at temperatures up to and above the Curie temperature in iron and nickel. For temperatures below 09Tc the spin-wave stiffness D, the spin-wave scattering cross section and the spin-wave lifetime have been obtained directly from the measured angular distributions, and the results are compared with the predictions of spin-wave interaction theories. For temperatures up to 042Tc in iron a good fit to the variation of D can be obtained using an expression of the form D0-D1T2-D2T 5/2 based on the itinerant electron model, but above 042Tc the fit becomes progressively poorer and D decreases faster than the fitted expression. The cross section for spin-wave scattering shows a temperature dependence additional to that contained in the thermodynamic factor alone; for iron at temperatures up to 07Tc this additional dependence has the form {1-(030±008)T/Tc} and is stronger than the variation with predicted by Marshall and Murray in a calculation of the effects of kinematic interactions between spin waves in the Heisenberg model. The observed spin-wave lifetimes have the same form of temperature dependence as is obtained from a nearest-neighbour Heisenberg model calculation by Cooke and Gersch. At temperatures above 09Tc the observed angular distributions were corrected for critical scattering using calculated cross sections for the latter due to Villain. D is found to fall slowly on passing through the Curie temperature in both iron and nickel, and is still of the order of a quarter of the room temperature value when the spin-wave scattering intensity falls below the threshold of observability.
TL;DR: In this article, a quasi-potential equation for relativistic scattering amplitude and the wave function of two interacting particles with spin 1/2 was constructed with the help of specific covariant extrapolation of the scattering amplitude off the energy-momentum shell.
Abstract: Quasi-potential equations are constructed for the relativistic scattering amplitude and the wave function of two interacting particles with spin 1/2. This is done with the help of specific covariant extrapolation of the scattering amplitude off the energy-momentum shell. Suitable diagram techniques are developed. The quasi-potential is defined as a sum of «irreducible» diagrams. The free part of the wave equation is spin independent and all features connected with spin appear in the interaction (quasi-potential). The spin structure of the quasipotential is investigated.
TL;DR: In this article, a new type excitation of localized magnons in the Ising-like spin system is reported, where the selection rule Δ m = ± 1, where m is the number of spins in the short range order spin cluster directed oppositely to the majority spins, can be used.
Abstract: A new type excitation of localized magnons in the Ising-like spin system is reported. It was found that in a strongly anisotropic ferro- or antiferromagnetic crystal such as CoC122H2O, nonuniform magnetic resonances with the selection rule Δ m = ± 1, where m is the number of spins in the short range order spin cluster directed oppositely to the majority spins, can be excited. Examples of such a localized spin wave excitation observed in FeCl2 and CoCl22H2O is discussed using a model of the Ising spin system.
TL;DR: In this article, a theory for the temperature and magnetic field dependence expected for the energy of long-wavelength spin waves in ferromagnetic heavy rare-earth metals was developed for examining magnetoelastic effects on the spin-wave energies.
Abstract: The theory is developed for the temperature and magnetic field dependence expected for the energy of long-wavelength spin waves in ferromagnetic heavy rare-earth metals. Emphasis is placed on examining magnetoelastic effects on the spin-wave energies. The resulting theory is applied to understanding recent neutron inelastic-scattering and ferromagnetic-resonance experiments in Tb and Dy. For Tb and Dy, comparison of theoretical predictions with the experimental results, especially the magnetic field dependence of the uniform-mode spin-wave energy, precludes the applicability of the frozen-lattice approximation suggested by Turov and Shavrov for magnetoelastic effects on spin-wave energies. The most striking point found in the present work is the contrast between the behavior of Tb and that of Dy. For Tb, the magnitude of the planar anisotropy constant found in static measurements is much smaller than the value necessary for agreement with the spin-wave experiments, i.e., neutron inelastic scattering and ferromagnetic resonance, which are mutually consistent. In contrast to this puzzling discrepancy for Tb, for Dy the static measured planar anisotropy constant gives absolute calculated values for the spin-wave behavior in excellent agreement with the results of ferromagnetic-resonance experiments.
TL;DR: In this article, a qualitative theory is advanced that excitation takes place by electromagnetic energy being coupled to a spin wave through magnetostatic modes, driven at the minimum value of internal dc magnetic field.
Abstract: The excitation mechanism based on the propagation of magnetoelastic waves in axially magnetized single‐crystal samples of yttrium iron garnet (YIG), of nonellipsoidal geometry, is proposed for microwave delay lines. A qualitative theory is advanced that excitation takes place by electromagnetic energy being coupled to a spin wave through magnetostatic modes, driven at the minimum value of internal dc magnetic field. The theoretical model decomposes the guided wave propagation in a ferrimagnetic slab, between metal plates, into pairs of plane waves, which essentially propagate in an inhomogeneous and anisotropic medium. This theory is supported by experiments in which a YIG rod was precisely translated along the dc field axis, with respect to the coupling antenna. These experiments demonstrate that minimum insertion loss requires that a large transverse rf magnetic field exist at the end face of the rod, that loss increases monotonically when the coupler is moved away from the end face, and that no minimum...
TL;DR: In this article, the ferromagnetic spin wave was investigated for the system with the uniaxial anisotropy energy which is not necessarily small compared with the exchange energy.
Abstract: The ferromagnetic spin wave is investigated for the system with the uniaxial anisotropy energy which is not necessarily small compared with the exchange energy. The double time green functions ≪ A : B ≫ are used with the spin and the quadrupole moment operators of single ion for A and B , and the decoupling procedure is made in the RPA both for these operators. Two types of the excitation spectrum are involved in the interested group of the Green functions. The derived expressions for thermodynamic quantities show the behavior characteristic of the magnon mode at low temperatures with some new correction terms, while they always reduce to the results of the Weiss approximation if the despersion in the two spectra is neglected. In some general cases with the anisotropy energy, numerical computations are made for T c , , , χ // , and χ ⊥ , and some significant deviations from the Weiss approximation are found.
TL;DR: In this article, the high temperature series expansions of the zero field susceptibility and specific heat for the Heisenberg ferromagnet for general spin were given. But they were not considered in this paper.
TL;DR: In this paper, the long wavelength non-interacting spin wave energy for metals at low temperatures is expressed as ǫ q = Dq 2 = (D + D 1 T 2) q 2.
Abstract: The long wavelength non-interacting spin wave energy for metals at low temperatures is expressed as ћω q = Dq 2 = ( D + D 1 T 2) q 2. The dependence of the coefficient D 1 on the density of states function, the number of electrons per atom, n, and the effective short range interaction energy, I , is discussed. The variation of D with T 2 comes from the change with temperature of the relative occupation ζ and the chemical potentials of the ± spin sub-bands as well as from the direct asymptotic expansion of the Fermi distribution functions occurring in the expression for D .
TL;DR: In this article, a simple theory based on the assumption of standing spin waves is given and it is shown that this assumption can explain well the experimental observations, and the frequency of these coherent oscillations is found to vary with the applied dc magnetic field.
Abstract: Low‐frequency oscillations which occur above the threshold for spin‐wave instability are examined in detail. The frequency of these coherent oscillations is found to vary with the applied dc magnetic field. A simple theory based on the assumption of standing spin waves is given and it is shown that this assumption can explain well the experimental observations.
TL;DR: In this article, high field susceptibilities for ferromagnetic iron metal and its alloys with cobalt, nickel, chromium and vanadium are estimated at 0°K, by making use of the density of states curve, determined from the experimental data of the low temperature specific heat and saturation magnetization.
Abstract: On the basis of the band model, high field susceptibilities for ferromagnetic iron metal and its alloys with cobalt, nickel, chromium and vanadium are estimated at 0°K, by making use of the density of states curve, determined from the experimental data of the low temperature specific heat and saturation magnetization. A satisfactory agreement between the calculated and observed results on the concentration dependences of the susceptibility is obtained for iron-cobalt and iron-nickel alloys. The dependences on temperature and magnetic field of the susceptibility are calculated by the model of non-interacting free spin waves. The observed temperature dependence of the susceptibility is explained by the calculated result.
TL;DR: In this article, the effect of the change in the exchange integral accompanying the electronic excitation, or the exciton-magnon interaction, was considered and a general formula was derived to calculate the line shape within the spin wave approximation.
Abstract: In order to discuss the line shape of spin wave sidebands, it is necessary to consider the effect of the change in the exchange integral accompanying the electronic excitation, or the exciton-magnon interaction. A general formula is derived to take this effect into account and to calculate the line shape within the spin wave approximation. The result suggests the line shape may be approximately given by the Green's function of the impurity spin problem. Green's function is calculated for MnF 2 and the spin wave sidebands of 6 A 1 → 4 T 1 are discussed within this approximation. The result is in reasonable agreement with the observation. Modification of the results due to the terms linear in the spin wave operators and temperature dependence is also studied.
TL;DR: In this article, the spin-wave dispersion in permalloys of composition Fe0.2Ni0.8 and Fe 0.5Ni1.5 was investigated by neutron-scattering methods and the values of D in the expression for the spinwave energy were found to agree with spinwave resonance measurements.
Abstract: Spin‐wave dispersion in Permalloys of composition Fe0.2Ni0.8 and Fe0.5Ni0.5 was investigated by neutron‐scattering methods. Values of D in the expression for the spin‐wave energy, ħω = Dq2(1−βq2), were found to agree with spin‐wave resonance measurements, but the quartic coefficients β were an order of magnitude smaller.
TL;DR: In this article, the analysis of many spin problems is greatly simplified by the use of coordinate transformations prior to quantization of the spin operators, which is called coordinate transformation prior to spin quantization.
Abstract: The analysis of many spin problems is greatly simplified by the use of coordinate transformations prior to quantization of the spin operators. To illustrate the use of these transformations, the ei...
TL;DR: In this paper, an exact expression for the coefficient C in the energy CK2 of a spin wave of small wavevector K in a ferromagnetic cubic metal, assuming complete spin alinement in the ground state, is given in a form which applies to a one-band model with short-range interparticle interactions and is compared with the well-known r.p.a.
Abstract: An exact expression is given for the coefficient C in the energy CK2 of a spin wave of small wavevector K in a ferromagnetic cubic metal, assuming complete spin alinement in the ground state. This is given in a form which applies to a one‐band model with short‐range interparticle interactions and is compared with the well‐known r.p.a. formula. The main feature of the new result is a modified superexchange term which, in particular, takes account of two‐particle correlations of the Kanamori type and of magnon‐electron scattering. A necessary condition for the ferromagnetic state to be stable is C > 0 and this is investigated for some special cases. Some doubt is thrown on Nagaoka's demonstration of stability in an infinite crystal for the case of a narrow, almost half‐filled, band.
TL;DR: In this paper, the intrinsic spin-wave linewidth was measured up to temperatures within a few degrees of the Curie temperature, where the authors showed that at low temperatures, up to 30°K, the ferromagnetic relaxation appears to result from two-magnon coupling of the k=0 mode to modes of higher k, which relax by the three-magon confluence process.
Abstract: The rather simple magnetic structure of the ferromagnetic insulator CdCr2Se4 makes it an attractive substance for the study of magnetic relaxation mechanisms in general, but in particular those mechanisms of importance in the vicinity of the ordering temperature. The ferromagnetic relaxation has been studied here by means of both FMR and high‐power parallel‐pump techniques. Using the latter technique, the intrinsic spin‐wave linewidth was measured up to temperatures within a few degrees of the Curie temperature. Near the Curie temperature the linewidth diverges as (T0‐T)−1 with T0=133°K. This value of T0 is in close agreement with our measured value of the Curie temperature 130°K. At low temperatures, up to 30°K, the relaxation appears to result from two‐magnon coupling of the k=0 mode to modes of higher k, which relax by the three‐magnon confluence process.