Many body theory of magnetic susceptibility of bloch electrons

We present a theory of the total susceptibility (χ) of solids using a finite temperature Green's function formalism. The many body effects on orbital (χ_o), spin (χ_s) and spin-orbit (χ_s-o) contributions to χ are calculated. Our expression for χ_s is equivalent to the earlier results but with the g-factor replaced by the effective g-factor. An important aspect of our work is the analysis of many body effects on χ_s?o.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

The Spin Density Distribution in the Hydrocarbon Radical Anions

In this note we wish to report our calculations of the spin density distribution in the several hydrocarbon radical anions using the “half-electron” SCF MO [variable beta] method of Dewar^1,2. This method calculates the energy of a system in which the unpaired electron is replaced by two “half-electrons” of the opposite spin. In this way one has the pseudo closed-shell system at equilibrium geometry and the resulting energy [E] differs from that [E_o] given by Roothaan's³ procedure only for ¼ J_mm

E_o=E - ¼ J_mm

Term ¼ J_mm represents the correction due to the spurious repulsion of the two “half-electrons”.     

Knight shift in PbTe and Pb1−xSnx Te

The importance of various contributing mechanisms to the Knight shift (K) in PbTe and Pb_1−xSn_xTe is analyzed using a perturbation theory and a general experession for K which includes the spin (K_s), orbital (K_o) and spin-orbit (K_so) contributions to the Knight shift. It is found that K_s is the dominant contribution. However, with increase in the carrier concentration, the strength of K_so increases, and becomes of the same order as K_s at high density of carriers. K_o is found to be small throughout the range of the carrier density considered. Further, it is seen that the electron-electron exchange enhancement parameter increases with increase in the carrier density. We have also considered the effect of temperature. The results and the trends obtained in our calculation are in overall agreement with the experiment for the range of the carrier density considered.     

Peculiarities of the band magnetism in the higher manganese silicide

Magnetism of MnSi_x, x=1.746 (Mn₂₇Si₄₇) was investigated by SANS, neutron diffraction, magnetization and magnetic susceptibility measurements. MnSi_x single crystalline specimens were characterized by X-ray and neutron diffraction. A spiral spin structure with periodicity ?=(163±4) Å along the c axis and a spiral component of the magnetic moment per Mn of p_o=0.056 was determined. From the field dependence of ? it is indicated that the magnetic order below T_N=42 K is an incommensurate state. From the large difference of the magnetic moments in the paramagnetic state and ordered state MnSi_x is classified as an itinerant magnet. Below T_N the difference of the magnetic moments per Mn between p_o=0.056 at H = 0 from SANS and p_s = 0.014 at saturation field from magnetization measurements is explained by longitudinal spin fluctuations.     

Observation of associated Kos-electron production in e+e− annihilation

We have observed K^o_s production in e⁺e^? annihilation between 3.6 and 4.4 GeV CMS energy. In the 4.0–4.1 GeV range K^o_s mesons occur correlated with prompt electrons, indicating the formation and weak decay of charmed particle. Within the sensitivity of the experiment, no K^o_s-electron correlation is seen at 3.6 and around 4.4 GeV.     

Observation of the K1(1780) in the reaction K+p → Ksoπ+p at 10 GeV/c

An analysis of the Kπ-system in the mass region of the K¹(1780), based on a sample of 46000 K_s^oπ⁺ final states, is presented. Evidence for a relatively narrow width, τ ≈ 100 MeV, and for the spin parity assignment J^P = 3^? is found.     

Isotopic shifts and the hyperfine structure of the samarium spectral lines at 672 and 686 nm

Spectra of saturated absorption of Sm atomic vapor from the ground state ⁷ F ₀ and the first even metastable level ⁷ F ₁, ε′=292.58 cm^?1 of the 4f ⁶6s ² configuration to the odd level 4_f ⁶(⁷ F)6s6p(³ P ^o)⁹ F ₁ ^o , ε,=14863.85 cm^?1 were recorded. The lines of the isotopic series were identified, and the hyperfine structure of lines in the spectra of isotopes with a nonzero nuclear spin was determined. The relative isotopic shifts and the hyperfine splitting of the even level 4f ⁶6s ²(⁷ F ₁) were determined.     

Approximately linear relations between two-nucleon and three-nucleon parameters

The correlation between the triton binding energyE _t and then-d scattering length² a and the zero energy singlet and triplet wound integral I_os and I_ot is investigated, with phaseequivalent separableNN interactions obeying all the important off-shell constraints. It is found that the correlation betweenE _t and² a is stronger than betweenE _t (² a) andI _os ,I _ot separately. A strong correlation is also found between the percentageD-state in the deuteronP _d andI _ot . Fixing all the other off-shell parameters but allowing variations ofI _os andI _ot leads to surprisingly accurate linear relations betweenE _t(² a) andI _os ,I _ot (P _d). These relations depend strongly on the other off-shell parameters.     

High pressure X-ray diffraction study on p-FeS2, m-FeS2 and MnS2 to 340 kbar: A possible high spin-low spin transition in MnS2

Pyrite p-FeS₂, marcasite m-FeS₂ and MnS₂2 have been investigated using the high-pressure X-ray diffraction technique to 340 kbar. MnS2 undergoes a pressure-induced phase transition at about 140 kbar from the pyrite to the marcasite type phase with a volume contraction of about 15%. The high-pressure marcasite type m-MnS₂ is found to belong to the B type of marcasite with an axial ratio $\text{c}\text{a}\text{= 0.76}$ and $\text{c}\text{b}\text{= 0.62.}$ p-FeS₂ and m-FeS₂ do not undergo any phase transition in the pressure range investigated. The high spin p-MnS₂ has been found to be much more compressible (B_o = 760 kbar, B′_o = 5.4) than the low spin p-FeS₂ (B_o = 2154 kbar, B′_o = 5.5) and m-FeS₂ (B₀ = 1465 kbar, B′_o = 4.9) while the high-pressure m-MnS₂ has comparable compressibility (B_o = 2138 kbar, B′₀ = 5.0) with those of low spin p-FeS₂ and m-FeS₂. The p-MnS₂-m-MnS₂ phase transition might be accompanied by a high spin-low spin transition of Mn²⁺.     

The anomalous Knight shift in beryllium

We calculate the Knight shift (K) in beryllium and magnesium by using the pseudopotential formalism and degenerate perturbation theory. We have included the effects of electron-electron interaction and spin-orbit interaction. We show that K_s, the spin contribution to K, is not linearly related to the spin susceptibility (χ_s) when spin-orbit effects are included. This non-linearity between K_s and χ_s is the origin of the negative Knight shift in beryllium.     

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.     

Surface demagnetizing field as a source of uniaxial surface anisotropy in GdCoMo thin amorphous films

Surface magnetic anisotropy energy was studied for (Gd_0.26Co_0.74)_0.96Mo_0.04 and (Gd_0.29Co_0.71)_0.96Mo_0.04 thin amorphous films by means of microwave spectroscopy at the X-band within the temperature range 4–295 K. Excitations of surface spin waves were observed in the spin wave resonance spectra. The experiment was performed in a rotating external magnetic field. The angular dependence of the resonance field for the uniform mode (spin wave vector k=0) and the surface mode made it possible to determine the surface uniaxial anisotropy constant K_s and its temperature dependence. An inhomogeneity of the saturation magnetization M_s within a close-to-surface layer of thickness d can generate the surface anisotropy energy with anisotropy constant K_s given by the formula: K_s=4πM^b_s (M^b_s−M^surf_s)d, where the indexes b and surf correspond to the bulk and surface values, respectively. The temperature dependence of K_s calculated by means of the formula agrees qualitatively with temperature dependence of K_s found in the experiment.     

μ+SR in amorphous spin glasses Pd75Fe5Si20 and Pd75Fe5P20

The zero-field muon spin relaxation functionG _zz (t) has been measured as a function of reduced temperaturet=T/T _g in the amorphous metallic spin glasses Pd₇₅Fe₅Si₂₀ and Pd₇₅Fe₅P₂₀. The results are in qualitative agreement with earlier measurements on dilute alloy spin glasses, including an onset of static order belowT _g and a [t/(t-1)]² dependence of the correlation time τ_c aboveT _g. Both samples have the same τ_c (t) aboveT _g and almost identical static width Δ_S→Δ_o?43 μS^?1) asT»0, but thet-dependence of Δ_s nearT _g differs markedly.     

Landau parameters for nuclear matter using the Skyrme interaction

Landau parameters for nuclear matter are calculated for several Skyrme interactions. Resulting values of G_o and G′_o are in disgreement with empirical values and lead to instability against spin collapse in several cases. A suitable generalization of the interaction is suggested to overcome these difficulties.     

Density-functional calculations of the nuclear magnetic shielding and indirect nuclear spin–spin coupling constants of three isomers of C20

The parameters of the nuclear magnetic resonance (NMR) spectrum – shielding constants and indirect spin–spin coupling constants – of three isomers of C₂₀ are studied using density-functional theory. The performance of different exchange–correlation functionals is analysed by optimising the geometry for the ring, bowl and cage isomers, followed by a computation of the NMR constants at the optimised structure. The results are analysed and rationalised by performing comparisons of the three isomers with one another and with related systems such as polyynes (for the ring), o-benzyne (for the bowl) and C₆₀ (for the cage). The shielding and spin–spin parameters calculated using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional are sufficiently reliable to assist in future experimental NMR studies of C₂₀ and, in particular, the identification of its isomers.     

Explicit construction of conserved currents for massless fields of arbitrary spin

We give an explicit construction of conserved currents for massless fields of arbitrary spin. These currents are gauge invariant and conserved on shell. Also they allow for the construction of a large class of trilinear interaction terms for the interaction between a massless spin-s₁ field and two spin-s₂ fields. The class is restricted only to 2s₂⩽s₁. In case s₁ = 4 and s₂ = 2, the current is the linearized Bel-Robinson tensor. To these conserved currents corresponds an infinite dimensional Lie algebra of global infinitesimal invariances of the action of a free massless field of arbitrary spin.     

Spin density functional theory of the temperature-dependent spin susceptibility: Pd and Pt

The finite temperature spin density functional (SDF) formalism is used to derive a variational expression for the temperature-dependent spin susceptibility χ_p(T) of an inhomogeneous electron gas. The use of a simple trial function in the variational expression results in a Stoner form for χ_p(T), i.e., χ_p(T) ≥ χ_s(T)/[1 - I(T) χ_s (T)] where χ_s(T) is the single-particle spin susceptibility including exchange-correlation (XC) effects on the band structure within the framework of the density functional formalism and I(T) is the SDF analog of the Stoner parameter. It should be emphasized that this form for χ_p(T) is derived for a general XC free energy functional F_xc[n, m; T]. χ_s(T) has been calculated self-consistently, including relativi stic effects, using the local approximation for F_xc for Pd and Pt. These results have been used to investigate the temperature dependence of I(T) required to explain their experimental susceptibilities. It is found that when the spin-orbit interaction is included in the calculation of χ_s(T), the temperature variation of I(T) is stronger than that of χ_s(T).     

Nuclear spin induced collapse and revival shape of Rabi oscillations of a single electron spin in diamond

A collapse and revival shape of Rabi oscillations in an electron spin of a single nitrogen-vacancy centre has been observed in diamond at room temperature. Because of hyperfine interaction between the host ¹⁴N nuclear spin and the nitrogen-vacancy centre electron spin, different orientations of the ¹⁴N nuclear spins lead to a triplet splitting of the transition between ground state (m_s =0) and excited state (m_s =1). The manipulation of the single electron spin of nitrogen-vacancy centre is achieved by using a combination of selective microwave excitation and optical pumping at 532 nm. Microwaves can excite three transitions equally to induce three independent nutations and the shape of Rabi oscillations is a combination of the three nutations.     

Soft phonon behavior and magnetism at the low temperature structural phase transition of La1.65Nd0.35CuO4

We report a neutron scattering investigation of a La_1.65Nd_0.35CuO₄ single crystal which undergoes a second order structural transition with decreasing temperature from a high temperature orthorhombic phase (space group Bmab) to a distinct low temperature orthorhombic phase (space group Pccn) atT _s =76 K. The transition is induced by the softening of the phonon mode that involves rotations of the tilt axis of the CuO₆ octahedra. Antiferromagnetic long range order is established belowT _N =316 K, and a hysteretic reorientation to a noncollinear spin structure occurs belowT _s . The low energy spin dynamics of La_1.65Nd_0.35CuO₄ aboveT _s are closely similar to those of stoichiometric La₂CuO₄; at 100 K the gaps for in-plane and out-of-plane polarized spin waves are 2.3 meV and 5 meV, respectively. Out-of-plane polarized magnons are little affected by the structural transition, but the gap for in-plane polarized magnons increases markedly belowT _s .