Collapse in the Stoner-Wohlfarth noninteracting-particle model

A theory of Mössbauer spectra of noninteracting Stoner-Wohlfarth (SW) particles interacting with rf magnetic fields is developed. The theory makes it possible to calculate the absorption spectra for arbitrary frequency and amplitude of the rf field. The main features of the Stoner-Wohlfarth model are discussed. The Liouville superoperator formalism is used to generalize the results to the case of arbitrarily time-varying hyperfine fields at a nucleus. To understand the qualitative features of the collapse effect that are observed in the Mössbauer spectra of SW particles the particular case of a circularly polarized hyperfine field is studied, and an analytical expression is obtained describing the Mössbauer spectra for this case. An analysis is also made for weak rf magnetic fields and in this case the resonance behavior of the Mössbauer lines is traced as a function of the frequency of the rf field.     

Magnetic properties of ferrihydrite

The magnetic properties of a sample of synthetic ferrihydrite have been investigated by use of Mössbauer spectroscopy. The area ratios of the Mössbauer lines are not significantly changed by application of magnetic fields at 5 K, indicating an amorphous magnetic structure. An average magnetic moment per particle of 3.1×10^?21 JT^?1 was estimated from the dependence of the hyperfine splitting of the Mössbauer spectra on external magnetic fields at 80 K.     

Nuclear quadrupole resonance in the gamma-resonance spectra of soft matter

It is shown that the harmonic librations (oscillations) of the principal axis of the electric field gradient tensor in “cages” of liquids, glasses, ferroliquids, and other “soft” systems qualitatively change the shape of the Mössbauer spectra of the quadrupole hyperfine structure. In addition to an effective decrease in the quadrupole coupling constant in the fast-libration limit, nuclear quadrupole resonance is predicted, which must be manifested in the Mössbauer spectra at the libration frequency that is approximately equal to the quadrupole splitting of spectral lines. By analogy with nuclear magnetic resonance, simple analytical expressions are derived, which describe resonance Mössbauer spectra in terms of the effective quadrupole coupling constant and the resonance splitting constant for the main lines. The observed features of the formation of quadrupole hyperfine structure spectra can be manifested in the Mössbauer spectra of soft matter and must be taken into account in analysis of experimental data.     

Mössbauer studies of hyperfine fields in disordered Fe2CrAl

Heusler-like alloy Fe₂CrAl was prepared and studied. Structure determination was done by X-ray. The structure was found to conform to the B₂ type. Magnetic hyperfine fields in this sample were studied by the Mössbauer effect. The Mössbauer spectra were recorded over a range of temperature from 40 to 296 K. The Mössbauer spectra showed the co-existence of a paramagnetic part with a magnetic hyperfine portion at all recorded temperatures. Even with the distribution in the magnetic hyperfine field, the average hyperfine field follows the (T/T _c)^3/2 law. The paramagnetic part of the hyperfine field is explained in terms of the clustering of Cr atoms.     

Radiofrequency mössbauer forward scattering spectra in magnetic materials

Radiofrequency (RF) Mössbauer spectra in experiments on forward scattering by thick samples of iron borate (FeBO₃) below the Neel temperature are measured. The spectra have satellites spaced by doubled RF-field frequency. A semiclassical model of Mössbauer transmission through a magnetic absorber exposed to RF reversals of a hyperfine field on nuclei is proposed. The model reproduces all features of the measured spectra. Experiments and modeling calculations indicate additional possibilities for studying soft magnetic materials using this measurement scheme.     

Mössbauer studies of iron-rich metallic glasses

Iron-based metallic glasses have recently become an important class of ferromagnetic materials exhibiting excellent soft magnetic properties coupled with good mechanical properties. These glasses are usually prepared by rapid quenching techniques and are produced in thin long ribbon form with widths ranging from a few mm to 150 mm or more.⁵⁷Fe Mössbauer spectroscopy has been extensively used to study hyperfine interaction parameters in these metallic glasses to understand ferromagnetism in amorphous structure. In particular, Mössbauer spectra have been carefully analyzed to reveal information about the distribution of hyperfine fields resulting from the randomness of the atomic arrangement and to understand the temperature dependence of hyperfine fields, spin-wave excitations, magnetic structure, thermal stability and crystallization, the quenched-in magnetization axis, the Curie temperature and its dependence on compositions, the effect of stress and pressure on the magnetic properties, corrosion behaviour, local order and atomic arrangement, phase transformation, etc. This paper reviews the application of⁵⁷Fe Mössbauer spectroscopy to magnetic studies on metallic glasses mainly based on the iron-boron alloy system, and some of the significant results obtained which are characteristic of the glassy/amorphous state.     

Observation of the double optical-gamma resonance in Mössbauer spectra of 151 Eu in EuP 5 O 14 single crystal

A theoretical analysis has been made and calculation procedures have been developed for describing the hyperfine structure of ¹⁵¹Eu Mössbauer spectra and the effect of double optical-gamma resonance (DOGR) in the presence of hyperfine quadrupole interaction with an arbitrary symmetry of the electric field gradient tensor. An experimental setup was designed for DOGR-effect observation, incorporating the pumping argon laser and the tunable dye laser combined with the Mössbauer spectrometer on a common platform. The Mössbauer absorption spectra of ¹⁵¹Eu^3?+? nuclei in single crystals of europium pentaphosphate, EuP₅O₁₄, have been measured at T = 5 K and 80 K under the absence and presence of optical pumping tuned to the ⁷F $_{0}-^{5}$ D₀ electronic transition at the 578 nm wavelength. A simultaneous analysis of these spectra in terms of the spin Hamiltonian of hyperfine quadrupole interaction has allowed us to evaluate the DOGR-effect magnitude with the population of the excited (⁵D₀) electronic state under optical pumping of about 10 %.     

Mössbauer spectra of a paramagnetic ion in an axial crystal field in the presence of spin-lattice relaxation

The influence of spin-lattice relaxation on the Mössbauer hyperfine spectra of the Fe³⁺ ion is investigated in the case of an axial crystal field. All the various influences of the relaxation process on the spectra can be explicitly described using two relaxation parameters. A detailed analysis of the Mössbauer relaxation spectra for the various temperatures, relations between the relaxation parameters and external magnetic field directions is carried out. When the magnetic field direction is nearly collinear with the symmetry axis and one of the relaxation parameters is small, the dynamics of Mössbauer spectra is shown to have anomalous features. The influence of random magnetic fields is shown to give an unconventional development of patterns as a function of the relaxation parameters.     

Radiofrequency forward Mössbauer scattering method in study of magnetic materials

Mössbauer spectra in forward scattering scheme were measured for iron borate (FeBO ₃) exposed to radiofrequency (rf) field below the Neel temperature. The spectra have satellites spaced by doubled rf field frequency. The semiclassical model of Mössbauer transmission through a thick magnetic sample under rf reversals of a hyperfine field is proposed. This model reproduces all features of the measured spectra. Experiments and model calculations indicate additional possibilities of this measurement scheme for study the soft magnetic materials.     

151Eu and57Fe Mössbauer effect studies of magnetic interactions in europium transition element oxides solution

The solid state solutions of europium transition element oxides Eu (Fe0.8M0.2)O₃ (M=Sc,Cr,Mn,Co) are synthesized. The X-ray diffraction of the compound shows that all the compounds possess the perovskite structures. Both the¹⁵¹Eu Mössbauer spectra and the⁵⁷Fe Mössbauer spectra are measured. The hyperfine magnetic field and non-axisymmetric electric field gradient are observed in the¹⁵¹Eu Mössbauer spectrum. The⁵⁷Fe Mössbauer spectrum shows that there are four components of hyperfine fields corresponding to four kinds of different neighbours of the Fe ion.     

Temperature investigations of the spatial spin-modulated structure of multiferroic BiFeO<Subscript>3</Subscript> by means of Mössbauer spectroscopy

The results from ⁵⁷Fe Mössbauer spectroscopic studies of multiferroic BiFeO₃ in a range of tem-peratures including that of the magnetic phase transition are presented. The Mössbauer spectra are processed and analyzed by reconstructing the hyperfine magnetic field distributions and interpreting the spectra with a cycloid-type spatial spin-modulated structure model. The temperature dependences of the hyperfine spectrum parameters (the Mössbauer line shift, the quadrupole shift, and the isotropic and anisotropic contributions to the hyperfine magnetic field) are obtained, along with the anharmonicity parameter of an incommensurate spin wave.     

Mössbauer effect studies of some trimeric iron compounds

Mössbauer spectra of some basic iron (III) carboxylates are reported. The zero field spectra are quadrupole doublets with a characteristic temperature dependent asymmetry. In applied magnetic fields at 4·2°K large hyperfine magnetic fields are observed. These can only result from a Hamiltonian which is not symmetric in all three sites. This asymmetry may be due to a structural asymmetry or to small intercluster magnetic interactions.     

On the influence of coherent inelastic resonance scattering on the Mössbauer absorption spectra

It is shown that an unusual angular distribution in coherent inelastic Mössbauer scattering (MCIS) manifests itself in Mössbauer absorbtion spectra (MAS). This is due to the fact that MCIS connected with the phonon assisted processes is concentrated in the direction of the incident Mössbauer beam propagation. The manifestation of MCIS in MAS in the case of MAS hyperfine splitting is analyzed. The effect reveals itself in the ratios of hyperfine line intensities in MAS due to the fact that the MCIS cross-section is different for different MAS hyperfine lines. In particular, for the case of thick nuclear resonance absorber the dips in MAS are different for the different hyperfine lines. (Usually it is assumed that for thick absorber the amplitudes of the dips are the same for all lines.) The general expressions for the intensity ratios for different MAS hyperfine lines which take into account MCIS are given in the case of hyperfine magnetic splitting. Estimates show that the corrections to the conventionally assumed ratios of line intensities in MAS are usually not large but quite measurable. However in the favorable cases (isotopes with low values of internal conversion coefficients) they can be as large as ten percent.     

Mössbauer spectra of Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Cr<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>S solid solutions

Compounds in the CrS-FeS system over a wide range of compositions are investigated by Mössbauer spectroscopy. The analysis of the Mössbauer spectra demonstrates that the materials under investigation are substitutional solid solutions with a random distribution of chromium and iron atoms. The assumption is made that the observed broadened Zeeman sextets are superpositions of partial sextets corresponding to iron atoms with different nearest environments. The observed decrease in the hyperfine fields for the broadened sextets with an increase in the chromium content in the samples is in good agreement with a change in the concentration of the corresponding environments.     

Mössbauer effect in natural strunzite, ferristrunzite and ferrostrunzite

The temperature dependence of the ferric and ferrous hyperfine fields in natural samples of strunzite, ferristrunzite and ferrostrunzite is determined by Mössbauer spectroscopy between 4.2 K and their magnetic transition temperatures (T _N), i.e. 50.5±0.5 K, 43.0±0.5 K and 44.0±0.5 K respectively, which are determined by Mössbauer thermoscanning. Two dominating magnetically split ferric subspectra were consistently present in all of the samples and are related to the Fe(1) and Fe(2) sites in the crystallographic structure, but an unambiguously assignment to a specific site is not possible. The difference between the corresponding hyperfine fields is very small. In the strunzite sample these fields are well defined and rather weakly dependent of temperature. In the other samples the corresponding hyperfine fields are more distributed especially at higher temperatures (below T _N). The relative contribution in the spectra of the third magnetic ferric component differs strongly between the samples and is assigned to ferric ions at the Mn site. At the lowest temperatures applied, its hyperfine field exceeds all other field values, but it decreases rather rapidly with increasing temperature, in so far that the corresponding spectral lines make a crossover with the lines of the other ferric subspectra. The magnetically split spectra of ferrostrunzite consist additionally of a ferrous magnetic component, which could be successfully analysed by introducing two magnetically split ferrous subspectra, which strongly overlap with each other but also with the ferric components. At higher temperatures in the magnetic region all subspectra overlap more and in the case of ferri- and ferrostrunzite the ferric hyperfine fields were distributed over a wider range.     

Magnetism of nanocrystalline materials

Nanocrystalline solids are materials consisting of small crystallites (typically 1–10 nanometers). These materials have a high proportion of atoms located in the interfacial regions between the crystallites. Therefore their magnetic properties are strongly determined by the interfaces. In this work we present Mössbauer studies carried out on various nanocrystalline materials. Beneath the normal crystalline component the Mössbauer spectra clearly indicate the existence of an component with modified magnetic properties which corresponds to the interfaces in this type of material. For nanocrystalline α-Fe an enhancement of the hyperfine field was observed in the interfacial component at low temperatures, whereas a decrease was found for nanocrystalline Ni.     

Mössbauer spectroscopy of Fe-based nanomaterials

X-ray diffraction, magnetic measurements and Mössbauer spectroscopy were used to study magnetic properties and hyperfine interaction parameters of nanocrystalline (< 10 nm) and bulk bcc Fe, Fe₉₀Ge₁₀, and Fe₇₇Al₂₃ alloys. It has been established that nanocrystalline state does not influence the formation of specific saturation magnetization, Curie temperature, isomer shift and hyperfine magnetic field. No additional sextets in Mö ssbauer spectra as well as special features in temperature dependences of a.c. magnetic susceptibility have been found. A slight increase (～ 20%) of the width of the nanocrystalline Fe Mössbauer spectral lines has been observed.     

Evidence of magnetic broadening in Mössbauer spectra of superconducting FeTe 0.8 S 0.2

Magnetic properties of the FeTe_0.8S_0.2 superconductor were studied by Mössbauer spectroscopy. Low-velocity Mössbauer spectra that were recorded in the temperature range from 5.7 K up to 300 K show a paramagnetic doublet with a broadening at temperatures below 77 K. The broadening can be explained by the appearance of a distribution of hyperfine magnetic fields due to the magnetic ordering of a part of the sample. The magnetically ordered fraction starts to decrease at temperatures below 20 K indicating a possible competition with the onsetting superconductive state.     

Mixed hyperfine interactions in amorphous materials: A model study

⁵⁷Fe Mössbauer absorption profiles were calculated supposing distributions of all hyperfine parameters: hyperfine magnetic fields, isomer shifts, and electric field gradients. The effect of mixed hyperfine interactions was taken into account in all orders of perturbation theory. The shapes of the spectra were systematically studied for varying average values and widths of the hyperfine magnetic field distribution (HMFD). From the simulated spectra, the shapes of the HMFD were reconstructed using standard techniques of Mössbauer spectra processing which neglect the effects of random isomer shifts and electric field gradients. It has been shown that the reconstructed shapes of the HMFD differ qualitatively from the original single-peaked distributions and exhibit a double-peaked structure similar to the distributions found in many experiments on amorphous alloys with low iron content. A brief review of various mechanisms responsible for either apparent or real double-peaked structure of HMFD has been given.     

The influence of small magnetic fields on the Mössbauer relaxation spectra of Au: Yb alloys

The influence of an external magnetic field on the hyperfine structure of the Γ₇ CEF ground state of dilute Yb impurities in Au is investigated through the Mössbauer effect. Strong changes in the shape of the hyperfine spectra are observed when small magnetic fields (?1 kG) are applied. The dependence of the hyperfine structure on applied magnetic fields is shown through a Breit-Rabi diagram. The electronic relaxation rate for this system is found to be independent of the fields applied. The nature of polarized radiation emitted by such sources is discussed.