Magneto-optical resonance in ferromagnetic gadolinium

The optical constants n and k of ferromagnetic and paramagnetic gadolinium have been measured, at various temperatures, from polarimetric measurements, in the low energy range 0.5 to 1.5 eV. For the ferromagnetic state, evidence of extra-optical conductivity is found near 0.69 eV and attributed to magnetic ordering. It confirms Miwa and Mackintosh predictions, assuming that new energy gaps are introduced in the conduction band through the s-f exchange interaction. From the experimental determination of the energy gap resulting from a splitting of the conduction band between spin up and spin down bands, we have deduced the effective s-f exchange energy J(q) = 1.58 × 10^-13 erg.     

Effects of inelastic spin-dependent electron transport through a spin nanostructure in a magnetic field

The transport properties and current-voltage (I–V) characteristics of a system of spin dimers with antiferromagnetic coupling arranged between metallic contacts are investigated in the tight binding approximation using the Landauer-Buttiker formalism. It is shown that the s-d(f) exchange interaction between the spin moments of the electrons being transported and the spins of the nanostructure leads to the formation of a potential profile as well as its variation due to spin-flip processes. As a result, the spin-dependent transport becomes inelastic, and the transmission coefficient and the I–V characteristic are strongly modified. It is found that the application of a magnetic field induces additional transparency peaks in the spectral characteristic of the system and causes the colossal magnetoresistance effect.     

Effect of spin-flip processes on the Pauli susceptibility

The reduction of the Pauli susceptibility due to a perturbing Hamiltonian which allows for spin-flip processes is calculated. The results are applied to the spin-orbit coupling in liquid metals, and the exchange interaction in magnetic metals at high temperatures and near the Curie point. The corrections are small.     

Optical absorption spectra of I3 - molecular ions in KI crystals and aqueous solutions

A semiempirical molecular orbital method including spin-orbit interaction is used to study optical absorption spectra of I₃ ^- molecular ions in (KI + I₂) aqueous solutions and in KI crystals coloured additively or electrolytically. The splitting of two strong absorption bands observed for these specimens is considered to be due to the spin-orbit interaction in the iodine atoms. The values of the spin-orbit coupling constants for I₃ ^- in aqueous solutions and coloured KI crystals are estimated to be 0·56 and about 0·47 eV, respectively. The oscillator strengths of the two strong bands for these specimens is also discussed.     

On the properties of the 1s-forms of TaSe2 and TaS2

The 1s-forms of TaSe₂ and TaS₂ with octahedral coordination of the metal are diamagnetic; 1s-TaS₂ is a semiconductor at low temperature. The diamagnetism is explained by taking account of spin-orbit coupling which leads to a ground state with zero magnetic moment (g = 0). This spin-orbit coupling stabilizes the d¹ configuration of the metal with respect to d² + d⁰. Thus, it can be understood that 1s−TaS₂ is semiconducting, while isostructural VSe₂ is metallic. Similarly, BaTaS₂ and BaTaSe₃ are semiconductors, but BaVS₃ is metallic.     

Energy level scheme and the effect of magnetic order on the optical transitions in europium chalcogenides

The optical constants of Eu-chalcogenide single crystals have been determined at room temperature for photon energies from 1 to 6 eV. In the same energy range the transmission of thin evaporated films (except for EuO) has been measured with polarized light above and below the magnetic ordering temperature. The observed polarization-dependent splittings of the two main absorption maxima in the region of magnetic order suggest transitions from the 4f⁷-level into the crystal field split 5dt_2g- and 5de_g-states. An attempt has been made to relate the maxima of the absorption coefficient to interband transitions and transitions from the localized 4f-states. With this assumption we derived a consistent energy level scheme of the four Eu-chalcogenides. From the scheme we gained useful information about the width of the 5d-states, the crystal field splitting and the possible type of conductivity. Finally we tried to explain theoretically the splittings observed in the region of magnetic order. For this purpose a one-particle model has been used to calculate the transition probabilities for the 4f⁷?4f⁶(⁷F _J ) 5dt_2g and the 4f⁷?4f⁶(⁷F _J ) 5de_g transition, taking into account an exchange interaction as well as a spin-orbit coupling. Although this simple model can explain the splittings of the excited 4f⁶(⁷F _J ) 5de_g-state, a complete explanation of the effect of magnetic order on the 4f⁶(⁷F _J ) 5dt_2g-state fails up to now.     

Spin-flip Raman scattering from electrons in localized donor states in n-InSb

We report the first observation of spin-flip Raman scattering from electrons localized in shallow donor states in InSb. For a non-degenerate n-InSb sample (8×10¹³ cm^-3) measurements of the spin-flip Raman gain and the effective g-value as a function of the magnetic field show lineshapes and magnetic field dependences completely different to that of an InSb sample with the electron gas being in a degenerate regime (1.35×10¹⁵ cm^-3). For the 8×10¹³ cm^-3 InSb sample, at magnetic fields greater than 11.5 kG, a splitting of the spin-flip Raman line into two lines is observed which may be an indication that two shallow donor states with different effective g-values are concerned.     

Relativistic multiple scattering theory of electrons by ferromagnets

In view of investigating for 3d- and 4f-ferromagnetic crystals the elastic scattering and the emission of polarized low-energy electrons as well as the bulk electronic structure, a relativistic multiple scattering theory has been developed, in which the exchange interaction with the magnetic ground state electrons is treated in a local density functional approximation. In a layer-KKR-type approach, the Dirac equation, which contains an effective magnetic field term, is first solved for a single crystal atom and subsequently for a monoatomic layer and for a semi-infinite crystal. Spin-orbit coupling and magnetic exchange interaction are thus simultaneously taken into account.     

Ground state properties of CsCoCl3

The electronic spectra of CsCoCl₃ are fit to a Hamiltonian that includes terms for interelectron repulsion, octahedral and trigonal crystal fields, and spin-orbit coupling. The fit adequately accounts for both the optical spectrum and the electronic Raman spectrum. The fitted parameters give empirical estimates of the radial expectation values 〈r^?1〉 and 〈r^?3〉 as well as the charge on the cobalt. The ground state wave functions generated from the fit are used to calculate the following properties: parallel and perpendicular g factors, Co hyperfine field, ⁵⁹Co quadrupole splitting, anisotropy of magnetic exchange, the magnetic moment of Co²⁺, and the spin flop field. The agreement between calculated values and observed values for this variety of independently obtained properties is reasonable in all cases.     

A matrix method for the calculation of nonlocal exchange potential and spin-orbit coupling in the first-principles calculation method

Adequate treatment of exchange interaction and inclusion of spin-orbit coupling are important in obtaining reliable electronic structures of semiconductors and magnetic materials. Here, a matrix method has been derived to calculate nonlocal exchange potential and spin-orbit coupling within a muffin-tin-orbital based first-principles calculation method. Good agreement between calculated and experimental band gaps for various zinc-blende and wurtzite semiconductors demonstrated that direct calculation of nonlocal exchange potential is feasible. This method may be an improvement over the currently used LSDA  +  U or LSDA  +  GGA  +  U method, which uses an adjustable U parameter, for wide-band-gap semiconductors and magnetic materials. In this method, the use of an extended Hamiltonian matrix, which contains off-diagonal matrix elements between up- and down-spin states due to spin-orbit coupling, enables mutual adjustment of the occupation of up- and down-spin states through atomic orbitals. In contrast, in the conventional spin-polarized calculation method up- and down-spin sub-matrices are diagonalized separately. The calculated spin-orbit splitting for the triplet states at the Γ point for GaAs and ZnS are in good agreement with experimental data.     

Spontaneous spin-flip Raman linewidth and nonlinear processes in InSb

A small-signal gain technique has been used to measure the lineshape of spontaneous spin-flip Raman scattering as a function of magnetic field (H = 0.5–10 kG) for an electron concentration n = 10¹⁵ cm^-3 at T = 2°K with both photons propagating normal to H. Four-wave mixing processes have been observed for varying carrier concentrations together with an interference between the resonant spin-flip nonlinearity and the nonresonant nonlinearity resulting from conduction electron nonparabolicity.     

Magnetooptik und elektronische Struktur der magnetisch ordnenden Europiumchalkogenide

The absorption coefficient and the interband Faraday rotation of EuS, EuSe and EuTe thin films have been measured as function of the photon energy (1–6 eV), the temperature (2.7–300 K) and the applied magnetic field (0–11.5 kOe). In addition a magnetic field modulation technique has been developed, with a resolution of 2 ? 10^?4 deg. This allows the measurement of the Faraday rotation in fields of only 100 Oe, which is important for metamagnetic samples with low critical fields. A Kramers-Kronig transformation of the Faraday rotation leads to the circular dichroism and from these two quantities and the optical constants the off-diagonal elements of the conductivity tensor have been computed. From a comparison of this experimental result with values obtained from a modified atomic model, we deduce the character of the involved transitions and the spin polarization of the occupied ground states (4f ⁷,p(anion)). In addition the ratio of exchange splitting to band width of the empty 5d final state can be evaluated. The fine structure of the first main peak is discussed in terms of Kasuya's coupling scheme between the 4f ⁶ multiplett and the excited 5d electron. In the antiferromagnetic EuTe the temperature dependence of the Faraday rotation does not follow the net magnetization of the sample for all photon energies, but some transitions show a “ferromagnetic” behavior. This is interpreted in Slater's model of the magnetic Brillouin zone.     

Energy Structure of an Individual Mn Acceptor in GaAs : Mn

The energy structure of the Mn acceptor, which is a complex of Mn²⁺ ion plus valence band hole, is investigated in the external magnetic field and under presence of an uniaxial stress has been studied. The spin-flip Raman spectra are studied under resonant excitation of exciton bound to the Mn acceptor. The gfactors of the ground F = 1 and the first excited F = 2 states are determined and selection rules for the optical transitions between the acceptor states are described. The value of the random field (stress or electric field) acting on manganese acceptor and the deformation potential for the exchange interaction constant of the Mn²⁺ + hole complex are obtained. A theoretical model is developed that takes into account the influence of random internal and uniaxial external stress and magnetic field. The proposed model describes well the lines of spin-flip Raman scattering of Mn acceptor.     

Electronic structure and magnetic properties of the compound CeCuIn

Magnetization, magnetic susceptibility, electrical resistivity, thermoelectric power and X-ray photoemission measurements were performed on a polycrystalline sample of CeCuIn. This compound crystallizes in a hexagonal structure of the ZrNiAl type. The magnetic data indicate that CeCuIn remains paramagnetic down to 1.9 K with a paramagnetic Curie temperature of −13 K and an effective magnetic moment equal to 2.5 μ_B. The electrical resistivity has metallic character, yet in the entire temperature range studied here, it is a strongly nonlinear function of temperature. The temperature dependence of the thermoelectric power is dominated by a small positive maximum near 76 K and a deep negative minimum at about 16 K. Above 150 K the thermopower exhibits a Mott's type behavior. The positive sign of the Seebeck coefficient in this temperature region indicates that the holes are dominant charge and heat carriers. The structure of Ce 3d_5/2 and Ce 3d_3/2 XPS spectra has been interpreted in terms of the Gunnarsson-Schönhammer theory. Three final-state contributions f⁰, f¹ and f² are clearly observed, which exhibit a spin-orbit splitting Δ_SO≈18.7 eV. The appearance of the 3d⁹f⁰ component is a clear evidence of the intermediate valence behavior of Ce. From the intensity ratio I(f⁰)/[I(f⁰)+I(f¹)+I(f²)] the 4f-occupation number is estimated to be 0.95. In turn, the ratio I(f²)/[I(f¹)+I(f²)]=0.08 yields a measure of the hybridization energy that is equal to 45 meV.     

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd ³⁺ ions in Y ₃Fe ₅O ₁₂ garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f ³ and 4 f ²5d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd ³⁺ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed. Received 8 November 2000     

Electronic structure and magnetic properties of PuMGa5 compounds within the LDA + U + SO method

The electronic structure and magnetic properties of PuMGa₅ compounds (M = Co, Fe, Ni, Rh, Ir) have been calculated within the LDA + U + SO method taking into account the strong electron-electron correlations and the spin-orbit coupling in the 5f shell of the actinide metal. The features of the electronic structure, coupling type, electron configuration, and magnetic state of the plutonium ion have been considered depending on the type of transition metal in PuMGa₅. The estimates of the effective magnetic moment of the plutonium ion agree well with the known experimental values. It has been shown that the occupancy of d states of the transition metal correlates with the appearance of superconductivity in the compounds of this class, providing the optimum doping regime in the electronic subsystem.     

Energy levels,luminescence and electronic structure of ZnS:Tm3+

Energy levels, densities of states, electronic densities, electrostatic interaction integral parameters F_k and spin-orbit coupling parameters ζ_4f for ZnS: Tm³⁺ are calculated self-consistently, using both one-electron local density discrete variational non-relativistic Hartree-Fock-Slater (HFS) and relativistic Dirac-Slater (DS) cluster models. In these calculations, both spin-restricted and spin-polarized models are considered. The finite clusters calculated include TmS₄ and TmS₄Zn₁₂ clusters for cubic ZnS, which are embedded in the crystal environment. The spin-orbit coupling parameter ζ_4f derived from DS cluster calculations is equal to 2689 cm^-1, rather near the result of the relativistic Hartree-Fock free ion model. The parameters F_k and ζ_4f are further calculated from the 4f radial wave function obtained by solving the HFS and the DS atomic equations. It is shown that by decreasing the effective exchange-correlation potential, these parameters can be reduced to approximately match empirical values. A comparison of the excited energy level scheme of ZnS:Tm derived from the calculated parameters and the experimental spectra is presented.     

On the origin of the exchange interaction in EuO and EuS

The indirect magnetic interaction in semiconductors is used to evaluate the exchange parameters for EuO and EuS respectively which yields J_eff(EuO)?(0.06 ± 0.02) eV and J_eff(EuS)?(0.08 ± 0.04) eV.     

Luminescence study of the 4f5d configuration of Nd in LiYF4, LiLuF4 and BaY2F8 crystals

Ultraviolet fluorescence of Nd³⁺ ions induced by triphotonic excitation process was studied in Nd-doped LiYF₄, LiLuF₄ and BaY₂F₈ crystals using a technique of time-resolved spectroscopy. The observed ultraviolet luminescence was due to transitions between the bottom of 4f²5d configuration and 4f³ states of Nd³⁺ ions. Narrow emission lines superposed to the broadband emissions were observed. A detailed analysis of luminescence spectrum revealed that the narrow emissions are due to parity and spin allowed radiative transitions from the Stark levels of ⁴K_11/2(5d) state created by the electrostatic interaction between the 5d electron and the two electrons of the 4f² configuration. The narrow emissions are related to the high spin state (S=3/2) which gives f-f characteristics to the f-d broadband emissions. The narrow emissions superposed to the wide emission correspond to 18%, 34% and 43% of the integrated broadband emission at 262 nm observed in LiYF₄, LiLuF₄ and BaY₂F₈ crystals, respectively. Although the 5d-4f² interaction is observed to be weaker than 5d-crystal field interaction, it is stronger enough to select only the radiative transitions from 4f²5d configuration to 4f³ states that preserves the total spin S=3/2.     

Electronic structure and magnetic susceptibility of monoclinic α-plutonium

The electronic structure of the α-phase of plutonium has been calculated by the band methods with allowance for the spin-orbit interaction and Coulomb correlations in the complete matrix form (the LDA + U + SO method). The strong spin-orbit interaction of the 5 f electrons is manifested in the splitting of the calculated density of the 5f states, which makes a small contribution at the Fermi level on the order of the contribution from the 6d states. Using the results of the ab initio calculations, the spin and orbit contributions to the magnetic susceptibility of α-plutonium have been determined. Along with the impurity contribution, they describe well the experimental data on the susceptibility of this plutonium phase to a temperature of 300 K.