Showing papers on "Spin states published in 1969"

Theory of Magnetic Ordering in the Heavy Rare Earths

Abstract: A detailed account is given of the calculation of the generalized susceptibility functions of Gd, Dy, Er, and Lu using realistic energy bands. These susceptibilities clearly show the influence of the Fermi-surface geometry in determining the helical ordering arrangements of the heavy rare earths, and the ferromagnetic ordering of Gd. A microscopic discussion of the magneto-elastic effect for a general ordered spin state is also presented. The first-order transition from the helical state to the ferromagnetic or conical ferromagnetic state in Tb, Dy, Ho, and Er is explained by this effect. Dy is used as an example of the application of the formalism, and a fundamental understanding is obtained of the transition between the helical and the ferromagnetic state and of the anomalous thermal expansion in both ordered states.

Computing ligand field potentials and relative energies of d orbitals: A simple general approach

Abstract: This approach to ligand field theory permits the derivation of the expressions for ligand field potentials and the quantitative evaluation of the energies of d orbitals in a large variety of geometrical situations.

Electronic, Vibrational, and Zeeman Spectra of Triplet NO2

Abstract: The lowest‐energy singlet–triplet transition of NO2− has been studied in emission and absorption in single crystals of NaNO2 at 4.2°K. The space symmetry of the lowest triplet state at 18 959 cm−1 is shown to be 3B1. This assignment is in agreement with molecular orbital predictions. The spin‐state substructure of the 3B1 level has been studied using the Zeeman effect, and it is shown that the main portion of the transition (f ∼ 8 × 10−8) (3B1←1A1) arises because of the electric‐dipole activity of the |Tz〉 spin state. The observed spectrum is therefore mainly of type B2←A1, which is consistent with the polarization measurements. A small fraction of the intensity is induced by a b2 vibration (ν3′ = 1170 cm−1), and for that portion the |Ty〉 spin states of each vibronic level carry the electric‐dipole intensity, possibly by virtue of a vibronic spin–orbit coupling mechanism. The assignments are confirmed by calculations of the spin–orbit matrix elements which suggest that a low‐energy 1B2(π2→π3*) state is sp...

Chapter 1-1 – theory of nuclear magnetic resonance

Abstract: Publisher Summary Apart from the use of atomic numbers and isotopic weights, the organic chemist has largely developed his subject without any special knowledge of the properties of atomic nuclei. The recent advent of nuclear magnetic resonance spectroscopy and, to a much lesser extent, microwave and pure quadrupole spectroscopy has altered this state of affairs, and organic chemists of the present generation have now to become acquainted with certain subjects hitherto the domain of the nuclear physicist and the spectroscopist. In a uniform magnetic field, the angular momentum of a nucleus is quantized, the nucleus taking up one of (2I + 1) orientations with respect to the direction of the applied field. Each orientation corresponds to a characteristic potential energy of the nucleus equal to μ. Ho.cos θ where Ho is the strength of the applied field and the angle θ is the angle that the spin axis of the nucleus makes with the direction of the applied field. I and μ define the number and energies of the possible spin states that the nuclei of a given isotope can take up in a magnetic field of known strength. A transition of a nucleus from one spin state to an adjacent state may occur by the absorption or emission of an appropriate quantum of energy.

Theory of nuclear magnetic resonance

Abstract: Apart from the use of atomic numbers and isotopic weights, the organic chemist has largely developed his subject without any special knowledge of the properties of atomic nuclei. The recent advent of nuclear magnetic resonance spectroscopy and, to a much lesser extent, microwave and pure quadrupole spectroscopy has altered this state of affairs, and organic chemists of the present generation have now to become acquainted with certain subjects hitherto the domain of the nuclear physicist and the spectroscopist. In a uniform magnetic field, the angular momentum of a nucleus is quantized, the nucleus taking up one of (2 I + 1) orientations with respect to the direction of the applied field. Each orientation corresponds to a characteristic potential energy of the nucleus equal to μ. H o .cos θ where H o is the strength of the applied field and the angle θ is the angle that the spin axis of the nucleus makes with the direction of the applied field. I and μ define the number and energies of the possible spin states that the nuclei of a given isotope can take up in a magnetic field of known strength. A transition of a nucleus from one spin state to an adjacent state may occur by the absorption or emission of an appropriate quantum of energy.

Mössbauer Effect in the System Co1−xFexS2

Abstract: X‐ray diffraction analysis and magnetic‐susceptibility measurements of samples in the system, Co1−xFexS2, where x = 0.01, 0.25, 0.50, and 0.75, indicate formation of a solid‐solution series having the pyrite structure. These compounds are ferromagnetic with Curie temperatures in the range of 0°–125°K. In spite in the appearance of long‐range magnetic order, Mossbauer effect measurements of 57Fe at 300°, 100°, and 5°K do not exhibit magnetic hyperfine splitting. This is interpreted as evidence that the divalent iron ions remain in the low spin state throughout the system and that the magnetic ordering process involves electrons localized on the cobalt ions. Trends in isomer shift and quadrupole splitting are discussed relative to changes in the lattice constant.

Magnetic and Crystallographic Studies of Compounds Mn1-xCrxAs (0.3≧x>0)

Abstract: Magnetic and crystallographic natures of compounds Mn 1- x Cr x As (0.3≧ x >0) were studied in the temperature ranges from 4.2° to 900°K and from 100° to 320°K. The compounds had MnP-type (B31) structure at low temperatures and transformed into NiAs-type (B8 1 ) structure at high temperatures. These compounds were metamagnetic at low temperatures. It was further confirmed that the deformation induced a low spin state of metal ions in the compounds, while with decease in deformation due to the rise of temperature, the metal ions in the compounds transfer to a high spin state, as in the case of MnAs 0.9 P 0.1 .

Theory of ferromagnetic alloys

Abstract: An analysis of the dynamical spin states of alloys typified by palladium-iron is given. It is shown that the spin-wave spectrum of Doniach and Wohlfarth is valid only over a very small momentum range. In general, the dynamical states are spin waves but with finite damping. The enhancement of the electronic specific heat is calculated. The results are in reasonable agreement with experiment, where the comparison is possible.

Localized Magnetic Mode in MnF2:Fe2+ and MnF2:Co2+

Abstract: We have observed a magnetic dipole‐active localized mode in MnF2, doped with 0.04 mol% FeF2 at 94.8 cm−1 at 1.2°K, using an ir lamellar interferometer. To our knowledge, this is the first direct spectroscopic evidence using far ir techniques for a magnetic dipole‐active impurity mode in an otherwise magnetically ordered system. The line has the following features: the half‐width is 0.4 cm−1 and the absorption strength ∫αdv∼1 cm−2. With increasing temperature, the line shifts to lower frequencies and finally disappears at about 25°K. Magnetic fields up to 45 kG have been applied parallel to the c axis of the sample, yielding a linear splitting of the line. A g factor of 2.3 is derived from the data. The experimental results at 1.2°K can be understood satisfactorily both with a simple molecular field picture and, also, with the help of a simple spin‐wave calculation. In the molecular field approximation, the line is correlated to a transition of the ground spin state to the first excited state of the orbital ground state of Fe2+. The observed value for the frequency is fitted by a Fe2+–Mn2+ exchange coupling constant J=1.9 cm−1 in both models. Preliminary results on a localized mode in MnF2:Co2+ are also reported.

Metalloproteins as Studied by Electron Paramagnetic Resonance

Abstract: Low-temperature EPR spectroscopy has been used to study copper- and iron-containing proteins. The information derived from these studies includes the oxido-reduction function of the metal, special features of the ligand field of the metal especially as they pertain to the protein environment, and interactions between paramagnetic centers. Correlations which exist between spectrophotometric and magnetic properties are related to the spin states of paramagnetic species. These are used to describe spin exchange phenomena in such systems as oxyhemoglobin, oxyhemocyanin, cytochrome c oxidase, copper uroporphyrin, and various model metal complexes.

Heilter-London Calculation on Complex FeF63-. I. 6A1 (High Spin) State

Abstract: The wave function of the ground 6 A 1 state of the complex FeF 6 3- has been calculated in the Heitler-London scheme with configuration interactions. Our basic configurations are constructed from the eigenfunctions of free ions (Fe 3+ , Fe 2+ , Fe - ) and of free atom F. The Hamiltonian matrix elements have been calculated according to the method of “Atoms in Molecules”, where the empirical atomic energies are inserted appropriately into the matrix elements. As the large ionization energy of Fe 2+ ion (30.64 eV) decreases the excitation energies of the charge transfer configurations, the polarization energy associated with electron transfer becomes a relatively important factor. We have checked the ground state wave function by comparing the calculated hyperfine spin densities and the crystal field splitting parameter 10 D q with the experimental data. Satisfactory agreements between the calculated and observed quantities have been obtained. Some qualitative discussions on the quartet states are also given.

H - Impurity States and Nuclear Magnetic Relaxation

Abstract: PH YSICAL REVIEW' VOLUM E 182, NUMBER 10 JUN E 1969 H —Impurity States and Nuclear Magnetic Relaxation* GREGoRY BENPQRD Laurence Radiation Laboratory, University of California, Lieermore, California 94550 AND NQRMAN RosTQKERt' Un& ersity of California, San Diego, La Jolla, California 9Z037 (Received 31 January 1969) It is shown that a hydrogenic impurity will bind a second electron in high magnetic fields, because of contraction of the electron wave functions about the lattice sites. The binding energy of the second electron exceeds kT for semiconductors at helium temperatures when p=kco, /2 Ry»1. This H ion may then provide a new density of states g+(E) for electrons with spin up (o. = 1). Nuclei which relax by mutual spin-flip processes with conduction electrons have a relaxation rate 1/T1 proportional to g+(E). In the last Landau state n = 0, 0-= — 1, the conduction electron g+(E) vanishes so the additional g+(E) from the H state can produce a large change in T1. The magnitude of this effect is estimated for InSb and comparison is made with the experiments of Bridges and Clark, with some success. Alternative explanations involving plasma modes are investigated and found wanting. The presence of H impurities in concentrations on the order of one-tenth of the conduction electron concentration may also affect the negative magnetoresistance and the theory of scattering from localized spins. I. INTRODUCTION 'HE contact interaction with conduction electrons mecha- is a well-known nuclear-spin-relaxation nism in metals, semimetals, and semiconductors. At low temperatures in InSb it is dominant until the tempera- ture exceeds =10'K, at which point phonon relaxation coupling through the nuclear quadrupolar moment be- comes more favored. In order for nuclear relaxation to proceed via the contact interaction, there must exist a density of states for the final electron eigenstate. During the relaxation process, the electron and nucleus flip their spin (con- serving the total spin of the system), so the final density of states for electrons must be of opposite spin from the initial state. This paper deals with the possibility that additional densities of states may arise in semicon- ductors, due to the formation of hydrogenic states which bind tzvo electrons in a high magnetic field. We shall limit ourselves to consideration of a strongly degenerate conduction electron gas in a solid having a simple nondegenerate energy band with an isotropic, quadratic dispersion law, within the effective-mass ap- proximation. The conduction electron Quid is in equi- librium. The applied magnetic field is taken to be so strong that quantization of the electron motion (Landau quantization) is important. Generally, the phenomena we treat will only be important when the electrons all occupy the lowest Landau level and the lowest spin state within that level. In Sec. II, we give a short review of electron dynamics in high fields. This work was originally prompted by the experi- * Work performed under the auspices of the U. S. Atomic Energy Commission. A portion of this work is based upon material submitted by Gregory Benford in partial fulfillment of the require- ments for the Ph. D. degree, University of California, San Diego. t Present address: Applied Physics Department, Clark Hall, Cornell University, Ithaca, N. Y. ments of Bridges and Clark' (thereafter referred to as BC), which determined the nuclear relaxatjon times of InSb nuclei in high magnetic fields. Before describing our work, we therefore brieQy summarize the BC results. This is done in Sec. III. Feher' has suggested that the BC experiments in very high fields may be explicable in terms of plasma effects in the conduction electron gas. In Sec. IV, we discuss various plasma modes which have been proposed, and the schemes necessary for them to relax nuclear spins in a semiconductor. We conclude that all the mechanisms thus far advanced fail to agree qualitatively with experiment. In Secs. V and VI, the possibility of additional densities of states in semiconductors is examined, and the binding energy of the high 6eld H ion is calculated. The formation of this ion makes a new density of states available for conduction electrons with spin index g = i. It is then possible for this new state to participate in relaxation of neighboring nuclear spins by making energetically possible a spin-Qip process between con- duction electrons and nuclei. The relaxation rate due to this impurity is estimated in Sec. VII. A He-like ion could also contribute a 0 = 1 density of states. We consider the binding energy of this impurity in Sec. VIII. We compare our model with the BC ex- penments in Sec. IX. Although the BC work is the only data currently available for comparison, it should be noted that our theory applies to any semiconductor in which the H— binding energy may exceed kT. (This will usually mean the dielectric constant X&)1. ) The important point of this work is that formation of the H state for high fields (y) 1) does occur, and it may have important consequences in many areas of current interest, such as the theory of scattering from 'F. Bridges and W. G. Clark, Phys. ' G. Feher (private communication). Rev. 182, 463 (1969).

Resonant spin states and the anomalous rotation of Mercury.

Abstract: Resonant spin and anomalous rotation of Mercury, analyzing influence of tidal degradation and permanent deformation of planet