On the detection of nuclear spin waves by inelastic neutron scattering

The possibility of measuring nuclear spin waves (NSW) by inelastic neutron scattering is discussed. The differential cross section and scattered state polarization for the scattering of thermal neutrons from systems described by the Suhl-Nakamura Hamiltonian are developed in the Van Hove correlation function formalism; the relevant correlation functions for the Suhl-Nakamura system are computed. The implications of these calculations for the feasibility of detecting nuclear spin wave modes in neutron scattering experiments are discussed.     

Electromagnetic waves reflected from the plate of a magnetic with a ferromagnetic spiral

The spectrum of coupled spin and electromagnetic waves is obtained for a magnetic with a ferromagnetic spiral structure determined by nonuniform exchange and relativistic interactions. It is shown that resonant interaction between spin and electromagnetic waves is possible. The electromagnetic wave reflectance from the plate of a magnetic with a ferromagnetic spiral is calculated for different spiral angles.     

Cross section of inelastic polarized neutron scattering by superconducting rings

A general expression for the cross section of inelastic magnetic scattering of cold polarized neutrons by superconducting rings has been derived. In this scattering process, the metastable superconducting current changes via quantum jumps corresponding to a decrease in the number of fluxoids in the superconducting ring by one or several units and the change in the energy of the ring is transferred to the kinetic energy of the scattered neutron. For rings from type-II superconductors with a thickness smaller than the field penetration depth but larger than the electron mean free path, the cross sections of inelastic scattering with neutron spin flip have been obtained for the first time. The possibility of increasing the cross section of neutron scattering by a system of rings has been discussed.     

Complementary application of neutron and synchrotron X-ray scattering to the determination of the magnetic microstructure of exchange-coupled layered nanoheterostructures

Complementary neutron and synchrotron X-ray scattering techniques have been considered as applied to the investigation of an inhomogeneous magnetic microstructure typical of exchange-coupled nanoheterostructures consisting of alternating ferromagnetic and antiferromagnetic metal layers. It has been demonstrated that changes in magnetic moments in both the magnitude and the direction within ferromagnetic layers can be determined by combining polarized neutron and resonant X-ray magnetic reflectometry, and those within antiferromagnetic layers, by combining X-ray and neutron diffractometry.     

Theory of resonant inelastic x-ray scattering by collective magnetic excitations

I present a tractable theory for the resonant inelastic x-ray scattering (RIXS) of magnons. The low-energy transition operator is written as a product of local spin operators and fundamental x-ray absorption spectral functions. This leads to simple selection rules. The scattering cross section linear (quadratic) in spin operators is proportional to the fundamental magnetic circular (linear) dichroic spectral function. RIXS is a novel tool to measure magnetic quasiparticles (magnons) and the incoherent spectral weight, as well as multiple magnons up to very high energy losses, in small samples, thin films, and multilayers, complementary to neutron scattering.     

Spin wave dispersion of FeBO3 at small wavevectors

Brillouin scattering from thermally excited magnons and ferromagnetic resonance are used to determine the spin wave dispersion of the low-frequency spin wave branch in FeBO₃, a transparent weak ferromagnet. In addition to the dominant exchange and Zeeman contributions, the investigation takes into account magnetic dipole and magnetoelastic interactions. Due to the antisymmetric exchange enhancement the material exhibits a broad spin wave band and a large gap energy at small magnetic fields. Competing directional dependences of the dipole and the exchange energy produce a degeneracy of spin waves with a certain magnitude of the wavevector propagating in different directions. The gap energy is shown to be due to magnetoelastic coupling, whereas the contribution of the anisotropy in the easy plane is negligible atT=300 K.     

Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P2₁3) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k _s polarized by a magnetic field is larger than the critical field H_C2 of the transition to the ferromagnetic phase and has the form E _q = A(q ? k _s ) + gμ_B(H ? H_С2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ _x , θ _y ) is two circles of the radii θ_C with the centers ±θ _S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θ_C are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: \(\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}\), where \({\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}\) and E _n and m _n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ₀ ≤ θ _S and θ _S ≥ θ₀ are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ _S → 0.     

Zur Streuung langwelliger Magnonen an Gitterfehlern

The scattering of ferromagnetic magnons by point defects is calculated within the framework of a phenomenological theory. This theory essentially takes account of the magnetic dipole interaction, and the magnetoelastic interaction, which are usually neglected. The scattering is due to an effective magnetic field, which is produced by the longrange strains of the lattice. For small wavenumbers this effective field is more important than the local disturbance of the exchange coupling in the vicinity of the defect, which hitherto has been considered almost exclusively, within the Heisenberg model. Due to the magnetic dipole interaction, the scattered wave and the differential cross section depend on the angle in a rather complicated manner: For each direction of scattering there are up to three groups of scattered waves, running away from the defect with different velocities. The differences between the classical and the quantum mechanical calculation are worked out.     

Spin excitations and spin wave gap in the ferromagnetic Weyl semimetal Co_3Sn_2S_2

We report a comprehensive neutron scattering study on the spin excitations in the magnetic Weyl semimetal Co3Sn2S2 with a quasi-two-dimensional structure.Both in-plane and out-of-plane dispersions of the spin waves were revealed in the ferromagnetic state.Similarly,dispersive but damped spin excitations were found in the paramagnetic state.The effective exchange interactions were estimated using a semi-classical Heisenberg model to consistently reproduce the experimental TCand spin stiffness.However,a full spin wave gap below Eg=2.3 meV was observed at T=4 K.This value was considerably larger than the estimated magnetic anisotropy energy(~0.6 meV),and its temperature dependence indicated a significant contribution from the Weyl fermions.These results suggest that Co3Sn2S2 is a three-dimensional correlated system with a large spin stiffness,and the low-energy spin dynamics can interplay with the topological electron states.     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

Spin waves in static non-periodic magnetic structures

We have studied the propagation of spin waves in a number of static non-periodic magnetic structures. We have established that (1) a ferromagnetic spin wave can ride over a domain wall with little reflection if its wavelength is less than twice the thickness of the wall; (2) in a ferromagnet with a set of parallel but irregularly spaced domain walls the spin wave linewidth is determined by the product of the scattering strength of the walls and the degree of randomness of the wall spacings; and (3) spin waves of rather narrow linewidths can exist in continuously varying irregular spin structures.     

Dipole-exchange spin wave spectrum in an anisotropic ferromagnetic waveguide with a rectangular cross section

A theory has been constructed that strictly describes the spectrum of dipole-exchange spin waves in an arbitrarily magnetized anisotropic ferrite waveguide with a rectangular cross section. The theory takes into account the spatial inhomogeneity of the internal magnetic field in the waveguide cross section. The influence of parameters of the ferrite waveguide on the distribution of the internal magnetic field in the waveguide cross section is analyzed. The dispersion characteristics of two waveguide types most widely used in practice are investigated. The dipole-exchange spin wave spectra calculated for a transversely magnetized waveguide are presented and the distributions of the dynamic magnetization in the waveguide cross section for several types of volume and localized spin-wave modes are constructed.     

Spin pumping with coherent elastic waves

We show that the resonant coupling of phonons and magnons can be exploited to generate spin currents at room temperature. Surface acoustic wave pulses with a frequency of 1.55 GHz and duration of 300 ns provide coherent elastic waves in a ferromagnetic thin-film-normal-metal (Co/Pt) bilayer. We use the inverse spin Hall voltage in the Pt as a measure for the spin current and record its evolution as a function of time and external magnetic field magnitude and orientation. Our experiments show that a spin current is generated in the exclusive presence of a resonant elastic excitation. This establishes acoustic spin pumping as a resonant analogue to the spin Seebeck effect.     

Specific Features in the Spectrum of Nonlinear Magnetoelastic Waves Propagating in a (111) Plate with Combined Anisotropy

Nonlinear magnetoelastic waves with stationary profiles propagating in a cubic ferromagnetic with [111] uniaxial induced anisotropy are investigated theoretically. It is demonstrated that a new type of nonlinear waves engendered by the resonant motion of the 60-degree domain wall propagates along the [111] axis without magnetization escape from the plane of spin rotation. Some other cases of nonlinear magnetoelastic wave propagation in the examined magnetic are also studied.     

The chromium spin density wave: magnetic X-ray scattering studies with polarisation analysis

We report on X-ray magnetic diffraction studies of the spin density wave antiferromagnetism formed in the conduction electron band of chromium. Non-resonant X-ray magnetic scattering was used to directly determine that chromium has zero orbital magnetisation. Furthermore, the azimuthal dependence of this scattering provides unique evidence that chromium forms a linearly polarised wave. In the vicinity of the K absorption edge, resonant X-ray magnetic scattering was observed. A consistent model of the magnetic scattering has been derived from the resonant and non-resonant magnetic amplitudes. The enhancement of the magnetic intensity arises primarily from dipole transitions from the core 1s level to 4p states. Quadrupole transitions to the magnetic 3d states are essentially non-existent due to their sensitivity to (and the absence of) orbital moment. This effect is predicted from atomic considerations of the 3d⁵ ( = 0) transition metal ions. Received 22 September 2000     

Investigating neutron polarizabilities through Compton scattering on 3He

We examine manifestations of neutron electromagnetic polarizabilities in coherent Compton scattering from the helium-3 nucleus. We calculate gamma3He elastic scattering observables using chiral perturbation theory to next-to-leading order [O(e2Q)]. We find that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.     

On the Measurement of the Stiffness of Spin Waves in the Fe<Subscript>0.75</Subscript>Co<Subscript>0.25</Subscript>Si Helimagnet by the Small-Angle Neutron Scattering Method

The stiffness of spin waves in the Fe_0.75Co_0.25Si helimagnet with the Dzyaloshinskii–Moriya interaction in a state fully magnetized by an external field has been measured by the small-angle neutron scattering method. It has been shown that the dispersion of magnons in this state is anisotropic because the neutron scattering pattern consists of two circles for neutrons with obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field H and equal to the wave vector of the spiral ±k_s measured in inverse nanometers. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnitude of the magnetic field. It has been shown that the stiffness of spin waves A for the helimagnet is equal to 46.0 meV Ų at T = 0 K and decreases weakly (by 20%) with increasing temperature up to the critical value T_c = 38 K.     

The total photon deuteron hadronic cross section in the energy range 0.265–4.215 GeV

The total cross section for photoproduction of hadrons on the deutron, σ_T^d, has been measured for photon energies in the range 0.265–40215 GeV. From this, using results for the photon total cross section, obtained previously with the same apparatus, the neutron total cross section has been determined in the resonance region. The resonant structure is found to be quite different from that for the proton. Thereafter the neutron cross section falls off steadily with energy, and the values obtained are consistently lower than those for the proton. Forward scattering amplitudes have been evaluated for the deuteron.     

Antiferromagnetic ordering in superconducting YBa2Cu3O6.5

Commensurate antiferromagnetic ordering has been observed in the superconducting high- Tc cuprate YBa2Cu3O6.5 ( Tc = 55 K) by polarized and unpolarized elastic neutron scattering. The magnetic peak intensity exhibits a marked enhancement at Tc. Zero-field muon-spin-resonance experiments demonstrate that the staggered magnetization is not truly static but fluctuates on a nanosecond time scale. These results point towards an unusual spin density wave state coexisting with superconductivity.     

Resonances and off-specular scattering in neutron waveguides

Off-specular neutron scattering from layered resonant systems has been studied. As an example, tri-layer neutron waveguides have been investigated experimentally by neutron reflectometry. In such systems, the neutron wave function is strongly localized in the guiding layer. The resonant states in the total reflection region lead to enhanced off-specular scattering from the interface roughness. The relation between the resonant states and off-specular scattering is discussed.