Measuring magnetic fields in plasmas by means of light scattering

The theory of light scattering in plasmas containing a magnetic field yields the special case of modulated scattering spectra. The modulation frequency is governed by the field in the plasma and is equal to the electron cyclotron frequency. In this investigation magnetic fields in a plasma were determined by a laser scattering experiment. The experimental data were: electron densityn _e=10¹⁶cm^?3, electron temperatureT _e=3.2 eV, scattering angle θ=90 °, scattering parameter α=0.6, and a maximum field in the plasma of 125 kG. The spectrum measured at the maximum magnetic field was modulated with 3.6 × 10¹¹ Hz. In scattering experiments with a field reduced by about 20% the observed modulation frequency was 2.8 × 10¹¹ Hz. A thermal spectrum with a smooth profile was found when no field was present in the plasma. Applying the theory of cyclotron modulated spectra one obtains from the scattering experiment magnetic fields of 128, 100, and 0 kG. Within the experimental accuracy these values agree well with the fields determined by means of magnetic probes. Other possible interpretations of the measured deviations from thermal spectra (modulation with the plasma frequency or additional cold electron components in the plasma) are discussed, but they afford no explanation. This experiment has domonstrated that magnetic fields in plasmas can be measured locally and almost without disturbance by means of light scattering.     

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     

Partial differential cross section of inelastic magnetic neutron scattering in the paramagnetic phase of LaCoO3

The partial differential cross section of inelastic magnetic neutron scattering from the compound LaCoO₃ in the paramagnetic phase is studied theoretically. The contribution to scattering from the high-spin state of an ion in zero magnetic field and the modification of this contribution upon application of a magnetic field are calculated using the effective Hamiltonian for the ⁵ D term. The amplitude of the peak in the dependence of the scattering cross section on the energy of scattered neutrons, which corresponds to the transition from the low-spin to the intermediate-spin state, is estimated.     

Charge-magnetic interference resonant scattering studies of ferromagnetic crystals and thin films

The element- and site-specificity of X-ray resonant magnetic scattering (XRMS) makes it an ideal tool for furthering our understanding of complex magnetic systems. In the hard X-rays, XRMS is readily applied to most antiferromagnets where the relatively weak resonant magnetic scattering (10⁻²–10⁻⁶ I _c ) is separated in reciprocal space from the stronger, Bragg charge scattered intensity, I _c . In ferro(ferri)magnetic materials, however, such separation does not occur and measurements of resonant magnetic scattering in the presence of strong charge scattering are quite challenging. We discuss the use of charge-magnetic interference resonant scattering for studies of ferromagnetic (FM) crystals and layered films. We review the challenges and opportunities afforded by this approach, particularly when using circularly polarized X-rays. We illustrate current capabilities at the Advanced Photon Source with studies aimed at probing site-specific magnetism in ferromagnetic crystals, and interfacial magnetism in films.     

Resolving 3D magnetism in nanoparticles using polarization analyzed SANS

Utilizing a polarized ³He cell as an analyzer we were able to perform a full polarization analysis on small-angle neutron scattering (SANS) data from an ensemble of 7 nm magnetite nanoparticles. The results led to clear separation of magnetic and nuclear scattering plus a 3D vectorial decomposition of the magnetism observed. At remanence variation in long-range magnetic correlation length was found to be highly dependent on temperature from 50 to 300 K. Additionally, we were able to compare the magnetic scattering from moments along and perpendicular to an applied field at saturation and in remanence.     

Determination by polarization analysis of the scattering amplitudes a+ and a- and of the degree of orientation of nuclei polarized by hyperfine fields in magnetically ordered substances

Improvements of the Ito-Shull techniques are suggested for measuring the scattering amplitudes a₊ and a_- associated with the compound states $\text{I +}\text{1}\text{2}$ and $\text{I -}\text{1}\text{2}$ which are formed by the nucleus of spin I and the incident neutron. In ferro- and ferri-magnets one can increase the sensitivity by suppressing the electronic part of the magnetic scattering when polarizing the neutrons along the scattering vector. In anti-ferromagnets one can separate the nuclear magnetic part by substracting the electronic magnetic scattering with unpolarized neutrons from the total magnetic scattering (electronic + nuclear) obtained by measuring the spin-flip amplitudes U^+- or U^-+.     

Measuring of low atomic vapour pressures by the method of forward scattering in a transverse magnetic field

Level crossing in forward scattering in a transverse magnetic field allows the detection of atomic densities lower than 10⁹ atoms/cm³ and is preferable to other optical methods such as absorption or forward scattering in a longitudinal magnetic field.     

Magneto-Raman scattering inp-type indium antimonide

We report for the first time stimulated magneto-Raman scattering inp-type InSb. Two different Raman scattering processes were observed. The first one has a Raman shift of about 2cm⁻¹/kG and is observed at magnetic fields up to 30kG. The other one is observable only at high magnetic fields above 30kG and shows Raman shifts between 1.2cm⁻¹ and 3.0cm⁻¹ with a tuning rate of about 0.2cm⁻¹/kG. The first process can be interpreted either as spin-flip Raman scattering by photo-excited electrons in the conduction band or as Raman scattering by holes in the valence band involving transitions from heavy to light hole states. The other Raman shift observed seems to occur on account of transitions between the heavy hole ladders.     

Study of the heavy-fermion compound CeRu<Subscript>2</Subscript>Si<Subscript>2</Subscript> by the small-angle neutron scattering method

In order to directly observe neutron scattering by heavy fermion quasiparticles at low temperatures, a CeRu₂Si₂ single crystal has been studied by the small-angle neutron scattering method. In the experiment, neutron scattering is observed at T = 0.85 K for momentum transfers q ≤ 0.04 Å^?1, which is treated as the orbital component of magnetic scattering by heavy fermion quasiparticles. It has been found that the application of a magnetic field H = 1 T leads to both an increase in the observed scattering and its anisotropy with respect to the field direction. Moreover, measurements in the magnetic field reveal additional scattering for q > 0.04 Å^?1, which is well described by a Lorentzian and is interpreted as neutron magnetic scattering by spin-density fluctuations with a correlation radius R_c ≈ 30 Å.     

Configuration mixing and elastic magnetic electron scattering from nuclei

The role of configuration mixing in the analysis of recent elastic magnetic electron scattering experiments on ⁴⁹Ti, ⁵⁹Co, ⁸⁷Sr and ⁹³Nb is examined. In particular the dependence of the rms radius of the valence nucleon extracted from such analyses on the detailed nuclear configurations used is studied. In addition, the effects of meson-exchange currents together with configuration mixing are discussed. It is found that configuration mixing does play a significant role and that high-precision studies of elastic magnetic electron scattering should proceed beyond the framework of the extreme single-particle model.     

Investigation of three-particle spin correlations during critical scattering of polarized neutrons from a nickel single crystal

The critical small-angle scattering of polarized neutrons from spin fluctuations in a nickel single crystal with a special inclined geometry of the magnetic field has been studied. The method of inclined geometry makes it possible to investigate not only two-particle spin correlations but also three-particle spin correlations that determine the polarization-dependent contribution to scattering, which is asymmetric with respect to the momentum transfer q. This contribution depends on the momentum transfer q as 1/(q ² + ξ^?2)^5/2, where f is the neutron scattering correlation length; it linearly increases with an increase in the magnetic field H in the low-field range and then reaches saturation. The results obtained are in good agreement with the similarity theory.     

High pressure experiments with synchrotron radiation

Using a diamond anvil cell (DAC), high pressure ⁵⁷Fe Mössbauer spectroscopy has been performed with the nuclear forward scattering of synchrotron radiation. We used monochromatized synchrotron radiation from an in‐vacuum type undulator as a high‐density strong Mössbauer source with a quite small beam size. Pressure‐induced magnetic hyperfine interactions at ⁵⁷Fe in SrFeO_2.97 has been detected at 74 GPa by a quantum‐beat modulation of the decay rate after collective nuclear excitation with the synchrotron radiation pulse. Evidence for a transition from antiferromagnetism to ferromagnetism of Fe in SrFeO_2.97 at 74 GPa and 300 K has been obtained from the nuclear forward scattering under a transverse magnetic field.     

Possible mesonic effects on inelastic proton scattering to the 10.24 MeV 1+ state in 48Ca

Differential cross sections and analyzing powers were measured for inelastic scattering of 160 MeV protons to the ⁴⁸Ca 10.24 MeV, 1⁺ state. DWIA calculations with shell-model wave functions which fit inelastic electron scattering form factors predict too much cross section at small q and too little at large q for inelastic proton scattering. These results are consistent with the q-dependent modification of magnetic transitions anticipated from mesonic effects such as virtual Δ(1232)-hole excitations.     

The special features of the ground state in CeAl3

The temperature (3–60 K) and transferred momentum (0.3–2.3 Å^?1) dependences of the intensity of quasi-elastic magnetic neutron scattering were studied for the polycrystalline heavy-fermion CeAl₃ compound to elucidate the special features of its ground state. Transferred momentum variations caused oscillations of the intensity of quasi-elastic magnetic neutron scattering, which was evidence of magnetic correlations in the f-electron subsystem occurring in a fairly wide temperature range.     

NMR on superfluid<Superscript>3</Superscript>He in aerogel

The transition to superfluidity of³He in high porosity (98.2%) acrogel has been observed by nuclear magnetic resonance techniques. The onset of the transition at all pressures above 13 bar is marked by a sharp increase in NMR frequency similar to that observed in bulk³He-A. This suggests that the aerogel/superfluid phase is highly homogeneous although both the transition temperature, T_c, and the amplitude of the order parameter are substantially suppressed. The acrogel strands are ≈ 50Å in diameter, much smaller than the superfluid coherence length. Consequently, we have attempted to interpret our observations as an impurity scattering problem. Based on our measurements of the magnetic field dependence of T_c it appears that both magnetic and potential scattering play important roles where the magnetic scattering can be associated with solid³He on the aerogel surface. This is determined by isotopic exchange with⁴He, a process which appears to stabilize a new superfluid state similar to the bulk B-phase.     

On-chip free-flow magnetophoresis: Separation and detection of mixtures of magnetic particles in continuous flow

The complete separation of mixtures of magnetic particles was achieved by on-chip free-flow magnetophoresis. In continuous flow, magnetic particles were deflected from the direction of laminar flow by a perpendicular magnetic field depending on their magnetic susceptibility and size and on the flow rate. 2.8 and 4.5 μm superparamagnetic particles with magnetic susceptibilities of 1.1×10⁻⁴ and 1.6×10⁻⁴ m³ kg⁻¹, respectively, could be completely separated from each other reproducibly. The separated particles were detected by video observation and also by on-chip laser light scattering. Potential applications of this separation method include sorting of magnetic micro- and nanoparticles as well as magnetically labelled cells.     

Raman scattering in magnetic US3

A Raman scattering investigation of magnetic US₃ has been made from 7 to 300 K. Comparison of room temperature spectra with those of the non magnetic isostructural sulfide HfS₃ allowed the assignment of most of the lines to $\textcolor{red}{}\text{=}\text{0}$ optical phonons. Drastic changes take place in the 10?150 cm^?1 range when lowering the temperature down to 7 K : four equally spaced lines appear at 54, 72.5, 91 and 109.5 cm^?1. Three of them broaden significantly with increasing temperature and disappear near 50 K, at which previous measurements indicate a maximum in the magnetic susceptibility and suggest a magnetic phase transition. The stronger fourth line is still observed at 100 K and merges into a phonon line at higher temperature. These four lines are attributed to electronic transitions within the 5f² configuration of U⁴⁺. Their temperature dependences appear to involve a spin-dependent scattering mechanism and are consistent with antiferromagnetic ordering.     

Parametric dependence of ion temperature and electron density in the summa hot-ion plasma using laser light scattering and emission spectroscopy

Hot-ion plasma experiments were conducted in the NASA Lewis SUMMA facility. A steady-state modified Penning discharge was formed by applying a radially inward d.c. electric field of several kilovolts near the magnetic mirror maxima. Results are reported for a hydrogen plasma covering a wide range in midplane magnetic flux densities from 0.5 to 3.37 T. Input power greater than 45 kW was obtained with water-cooled cathodes. Steady-state plasmas with ion kinetic temperatures from 18 to 830 eV were produced and measured spectroscopically. These ion temperatures were correlated with current, voltage, and magnetic flux density as the independent variables. Electron density measurements were made using an unusually sensitive Thomson scattering apparatus. The measured electron densities ranged from 2.1 x 10¹¹ to 6.8 x 10¹²1/cm³.