Magnetic circular dichroism of transition metal ions in solids-I. MgO:Cr3+

Absorption and magnetic circular dichroism (MCD) spectra of MgO: Cr³⁺ have been studied over the temperature range 5–300 °K and with magnetic fields up to 77 kG. A theory for intensity calculation using a weak field coupling scheme is discussed. Spin-forbidden transitions to ²E and ²T₁, are observed in MCD and are interpreted as magnetic dipole zero-phonon lines. The spin allowed bands ⁴T₂ and ⁴T₁ are found to be vibration-induced electric dipole transitions in which the t_1u lattice modes are the dominant contributors to the intensity.     

Vibronic state and optical spectrum of the N i2+ impurity ion in CaO

The relative intensities of vibronic splitting components of the³A_2g→¹T_2g optical electronic dipole transition induced by odd local vibrations and spin-orbit interaction are calculated for an impurity center with O _h point-group symmetry. The polarization dependences and magnetic circular dichroism (MCD) are found for the vibronic components in an external magnetic field. In contrast with the previous works, the calculation is not confined to the nearest-term approximation. It is shown that measurements of the polarization dependences and MCD allow one to identify unambiguously the vibronic components. A comparison with the experiment is carried out for theNi ²⁺ ion in CaO. A. M. Gor'kii Ural State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 19–23, June, 1999.     

Electron-vibration splitting of the vibronic levels of the 1T2g state of MgO:Ni2+

Magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) measurements of the ${}^3\text{A}{}_{\mathrm{2g}}\text{→}{}^1\text{T}{}_{\mathrm{2g}}$ absorption band in MgO:Ni²⁺ are reported. It is shown that for the lowest energy vibrational peak there is considerable evidence of splitting of the T_2g × T_1u vibronic levels by the electron-vibration interaction.     

Linear and quadratic magneto-optical effects observed in La0.7Sr0.3MnO3 thin films in transmitted light

Magnetic linear dichroism (MLD) is observed in polycrystalline La_0.7Sr_0.3MnO₃ films in transmitted light. The spectral and temperature dependences of the MLD are determined for the energy E of the light wave ranging from 1.5 to 3.5 eV. The experimental spectra are fitted by a sum of Lorentzian curves. The MLD spectrum exhibits more features in comparison to the spectra of magnetic circular dichroism (MCD), which we measured earlier using the same film samples. Various temperature behaviors of the intensities of the Lorentzian components centered at different E values have been revealed. This can be related to the effect of the surface states on the magneto-optical characteristics of the samples.     

Magnetic resonance in relaxed excited states AX and AT of Ga+ in alkali halides

The optical detection technique is used to observe magnetic resonance in the excited states ³T_1u of Ga⁺ in KI, KC? and NaC?. The relaxed excited states A_X and A_T display trigonal and tetragonal symmetry respectively, as a result of a static Jahn-Teller effect. Furthermore the coupling to E_g and T_2g modes is found to be nearly equal in KI : Ga⁺, as already observed in KBr : Ga⁺.     

Exchange interactions in polynuclear complexes

We present detailed optical and magneto-optical data on Cs₃Cr₂Cl₉ as a single crystal containing only pairs of Cr³⁺ ions. Measurements have been carried out in a wide range of temperatures down to pumped helium and in the whole spectral region covering all singly and several doubly excited states. MCD helped considerably in resolving the absorption spectra into their numerous components, and proved especially useful in demonstrating the occurrence of a double excitation to ⁴ T ₂. It provides also parallel g factors for several excited terms.

The main conclusions of our work are: (i) all transitions are electric dipole allowed; (ii) transitions to singly excited doublet states are essentially promoted via a single ion mechanism; (iii) vibronic interaction must be invoked to understand the absorption data on sharp lines; (iv) the trigonal plus spin-orbit interaction competes favourably with exchange interaction to produce excited states splittings.

We present also a new non-phenomenological model to describe the splitting of the ⁴ A ₂Θ² E manifold under the combined effects of exchange, trigonal and spin-orbit interaction. This model includes no adjustable parameter. It leads to λ₀ ～ 180 cm^-1 and offers a good starting basis for a coherent interpretation of most of our experimental data.     

High resolution MCD spectroscopy of transition metal ions in fluoride crystals

Measurements of the MCD spectra of Ni²⁺ in KMgF₃ and KZnF₃ have confirmed and extended previous assignments of spin-orbit structure based on similarities of vibrational patterns. The measurements also reveal the presence of a ¹ A _1g (¹ G) state which interacts strongly with the ³ T _1g ^b (³ P) state. The MCD spectra of the tetragonal crystals K₃Ni₂F₇ and K₂NiF₄ have been measured for the transitions ³ A _2g →³ T _1g ^a , ¹ E_g . The spectrum of K₃Ni₂F₇ is characterized by the appearance of electric dipole zero phonon lines, consistent with the C _4v site symmetry of the Ni²⁺ in the paramagnetic phase. An analysis of the MCD spectrum allows a positive assignment of six of the seven states (from ³ T _1g ^a and ¹ E_g ) to which transitions are allowed by symmetry in the axial spectrum. A complete tetragonal crystal-field analysis has been made which shows that the distortion is an axial compression of the fluoride octahedron. The absorption spectrum of K₂NiF₄ shows much less vibrational structure, but the MCD spectrum allows a definitive assignment of six states (from ³ T _1g ^a and ¹ E_g ) through a _2u vibrations in the usual vibronic mechanism. False origins based on e_u phonons have not been identified. The tetragonal field is larger than for K₃Ni₂F₇ and corresponds to an axial compression, in agreement with the known crystal structure.     

Application of symmetry groups of four-dimensional space in spectroscopy of crystals

A method of classification of many-electron states that involves symmetry groups of four-dimensional space is developed. Taking into account the spatial and temporal symmetry, the selection rules for electric and magnetic dipole transitions are investigated. The reduction relations for the irreducible representations of the orthogonal group O ₄ and the group R ₄ of pure rotations of the four-dimensional space on the groups and O _h ⁴ and O ⁴ of the four-dimensional cube and of the octahedron on the three-dimensional groups O _h and D _6h of the cubic and hexagonal systems, respectively, are obtained. The four-dimensional classification of the levels of the spin-orbit interaction of rare earth ions for the intermediate reduction on the group of the four-dimensional cube is performed. With the help of the irreducible representations of the O ₄ group, the selection rules of magnetic and forbidden electric dipole transitions, as well as of intercombination transitions, are investigated.     

The magnetic circular dichroism spectra of matrix-isolated benzene

The magnetic circular dichroism (MCD) spectra of the ¹ B _2u ←¹ A _1g transition of benzene in nitrogen and argon matrices at 20 K have been measured in order to obtain a spectrum devoid of hot bands and complicating rotational structure. The spectrum is dominated by three progressions of B terms, two of positive sign and one of negative. One positive progression and the negative one can be definitely assigned to the e_2g modes v ₆ and v ₉ respectively, whilst the other positive progression may be the e _2g mode v ₈. This is in marked contrast with the absorption spectra of the same matrices which reveal only a single progression built upon v ₆. The MCD spectra are nicely accounted for in terms of a magnetic mixing between the ¹ B _1u and ¹ B _2u states, the electric dipole intensity arising from the mixing in of a ¹ E _1u state via e _2g vibrational modes.     

The magnetic circular dichroism spectrum of the hexaquocobalt (II) ion in the infra-red region

The magnetic circular dichroism (MCD) and absorption spectra in the range 5500–10 250 cm^-1 of a single cubic crystal of [Co(H₂O)₆](BrO₃)₂ have been measured at various temperatures between 5 and 300 K. An analysis of the temperature variation of the zeroth absorption and MCD moments shows that the intensity of the E′ (⁴αT _1g ) → ⁴ T _2g transition is provided mainly through the two cobalt-oxygen t _1u vibrations. The signs and magnitudes of the overall b and c term are in reasonable accord with previously published calculations. The low energy side of the MCD band exhibits some zerophonon lines and a complex vibronic structure which appears to involve low energy lattice vibrations as well as the cobalt-oxygen skeletal vibrations.     

Intensity of singlet-triplet transitions in C<Subscript>60</Subscript> fullerene calculated on the basis of the time-dependent density functional theory and taking into account the quadratic response

The singlet-singlet and triplet-triplet absorption spectra of C₆₀ fullerene are calculated using the density functional method and taking into account the theory of linear and quadratic responses. The B3LYP density functional and the 6–31G and 3–21G atomic basis sets are used. The calculations are performed using the D_2h and D_5d symmetry groups, although the real symmetry of the ground state is described by the I _h symmetry group. The matrix elements of the operator of the spin-orbit coupling are calculated and the probabilities of some singlet-triplet transitions are estimated. Taking into account the data in the literature on vibronic interactions of vibrations of the t_1u, t_2u, g _u , and h _u symmetry species, the radiative lifetime of the 1³T_2g → 1¹A _g phosphorescence was estimated to be 45 s. The fact that this time proved to be considerably greater than the experimentally observed total lifetime of the triplet testifies to a fast nonradiative deactivation of the lowest triplet state of C₆₀ fullerene and agrees with a low phosphorescence intensity. The zero-field splitting of some triplets and the intensities of magnetic dipole transitions are discussed.     

The magnetic circular dichroism spectrum of the 1 B 2u ←1 A 1g transition of benzene in the vapour phase

The magnetic circular dichroism (MCD) spectrum of the ¹ B _2u ←¹ A _1g transition of benzene has been measured in the vapour phase. Many of the bands due to transitions between single vibronic levels display A terms. It has been shown that the angular momentum arises by vibronic mixing both of the ¹ E _1u state with the ¹ B _1u state and of the ¹ E _2g states with the ¹ A _1g ground state by e _2g vibrations. The magnitudes and signs of the experimental and calculated ratios, A/D, for the A ₀ ⁰ vibronic origin are in excellent agreement. Two strong MCD progressions of opposite sign with B-term dispersion have been observed in regions of low absorption. These are identified with vibronic origins due to the v ₈ and v ₉ e _2g modes. By contrast the MCD spectrum of hexadeuterobenzene vapour has a much lower magneto-rotational strength and displays none of the striking features of the benzene MCD spectrum.     

Magnetic circular dichroism and the nature of ferromagnetism in colloidal gold nanoparticles

The spectra of optical absorption and of magnetic circular dichroism (MCD) have been measured in the 350–1150 nm wavelength range for a set of colloidal solutions containing Au nanoparticles with the average size of 6 nm having thiolate coatings with different degrees of chirality. The form of absorption and MCD spectra suggests the dipole character of interband transitions involving the 5d-6(sp) orbitals. The absence (within the experimental error) of the dependence of the MCD spectra on the coating type rules out the hypothesis on the orbital nature of the observed magnetism. We argue that the spin polarization plays the dominant role in the magnetism of gold nanoparticles with a thiolate coating.     

Inversion relations,phase transitions and transfer matrix excitations for special spin models in two dimensions

The infrared and Raman active phonons (k=0) of orthorhombic TbF₃ and of isomorphous HoF₃ have been observed and attributed to the different irreducible representations of the factor groupD _2h. Moreover we investigated crystal-field excitations of the 4f-configuration of the Rare-Earth-ions and effects of their interaction with optical phonons, especially as a function of an external magnetic field. The infrared reflection spectra of these materials not only display reststrahlen bands of electric dipolar but also of magnetic dipolar type with a characteristic shape of the latter bands.On entering the ferromagnetic ordered state pertinent symmetry reductions (D _{2hC 2h}) become evident in the system of electronic transitions and optical phonons in TbF₃ by a change of selection rules and a magnetization-induced transfer of transition intensities to new components of the transition dipole or of the Raman polarizability tensor. These observations are in accordance with general symmetry considerations.The delocalization of the crystal-field excitations results in a Davydov splitting of the single-ion transitions.     

Gamow-Teller transitions from 58Ni to discrete states of 58Cu

Under the assumption that isospin is a good quantum number, symmetry is expected for the transitions from the ground states of T = 1, T _z = ±1 nuclei to the common excited states of the T _z = 0 nucleus situated between the two nuclei. The symmetry can be studied by comparing the strengths of Gamow-Teller (GT) transitions obtained from a (p, n)-type charge-exchange reaction on a target nucleus with T _z = 1 with those from the β-decay of the T _z = - 1 nucleus. The A = 58 system is the heaviest for which such a comparison is possible. As a part of the symmetry study, we measured the GT transitions from ⁵⁸Ni (T _z = 1) to ⁵⁸Cu (T _z = 0) by using the zero-degree (³ He, t) reaction at 150 MeV/nucleon. With the achieved resolution of 50 keV, many hitherto unresolved GT states have been identified. The GT transition strengths were obtained for states up to 8 MeV excitation, i.e., near to the Q window limitation ( Q _EC = 9.37 MeV) of the β-decay from ⁵⁸Zn (T _z = - 1) to ⁵⁸Cu. The strength distribution is compared with that from shell-model calculations. Received: 24 November 2001 / Accepted: 30 January 2002     

Influence of spin-orbit coupling on vibronic spectra of metalocomplexes porphin: Manifestation of out-of-plane vibrations

In fine-structure phosphorescence spectra of metallocomplexes of porphin with ions of the Pd(II) and Pt(II) and their meso-deuterated derivatives additional lines have been detected which have no analogs in fluorescence and resonance Raman spectra of metalloporphyrins and in phosphorescence spectra of metallocomplexes of porphin with light ions of the Mg(II) and Zn(II). For Zn-porphin, quantum-chemical calculations of frequencies and forms of in-plane and out-of-plane vibrations have been performed. Based on experimental data and calculation results it has been found, that in vibronic phosphorescence spectra of metallocomplexes of porphin, out-of-plane gerade modes of the E _g symmetry (D _4h symmetry group) are manifested. The activity of out-of-plane vibrations increases with enhancing spin-orbital coupling upon changing to heavier chelated metal ions. Vibronic transitions with participation of out-of-plane gerade E _g vibrations manifest in the T ₁ → S ₀ transition through the vibronic intensity borrowing from the triplet-triplet ³ E _u -³ E _g transition.     

Forbidden vibrational-rotational transitions and Herman-Wallis factors in fundamental IR bands of symmetric-top molecules

Within the theory of coupled schemes of ordering of vibrational-rotational interactions, the operator of the effective dipole moment of single-quantum vibrational transitions is represented in the form of an infinite series in vibrational (normal coordinates and conjugate momenta) or rotational variables (components of the total angular momentum). Mechanisms of activation of infrared-inactive totally symmetric vibrations in molecules of the D _2a , D _3h , C _3h , D _n (n ≥ 3), S ₄, T, T _a , and O symmetries and forbidden vibrational-rotational transitions in IR bands of active vibrations have been studied. The group-theoretic analysis of tensor parameters in higher-order effective dipole moments of single-quantum vibrational transitions in axially symmetric molecules has been performed. The strengths of allowed transitions and forbidden transitions in fundamental and hot IR bands of axially symmetric molecules are calculated with allowance for the Herman-Wallis factors. For effective dipole moments of multiquantum transitions in molecules, models are developed in the form of infinite series in rotational variables and in the form of Padé approximants.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

nπ transitions in crystals of tetramethyl-1,3-cyclobutanedione-h12 and -d12

The polarized low-temperature crystal absorption spectra of tetramethyl-1,3-cyclobutanedione-h₁₂ and -d₁₂ have been measured from 25 000–40 000 cm⁻¹, and nπ^* excited states identified as follows: ³A_u with origin (-h₁₂/-d₁₂) at (25 720/25 780)cm⁻¹; ¹A_u at (27 130/27 173)cm⁻¹; two ¹B_1g states with origins near 32 000 cm⁻¹. Excitation is accompanied by distortion of the ring and a slight lengthening of the CO bonds, but the carbonyl groups remain planar. Surprisingly, CH/CD-stretching vibrations in the substituent methyl groups are active in intensity borrowing.