Yukito Tanabe

Absorption Spectra of Cr3+ in Al2O3 Part A. Theoretical Studies of the Absorption Bands and Lines

In the frame-work of the crystalline field theory, the excited states of Cr 3+ in Al 2 O 3 and the optical transitions to these states are studied taking into account the effect of trigonal field and spin-orbit interaction. Initial splittings and optical anisotropies of the broad band (transitions to quartet states) and the sharp lines (transitions to doublet states) are examined. For the sharp lines, the Zeeman effect is also examined and the Zeeman patterns are predicted. Comparing these theoretical results with those of the experimental ones given in Part B, the assignments of U , Y bands and R 1 , R 2 , B 1 , B 2 lines have been established. It is shown that the g -shifts of the excited doublets observed in the Zeeman patterns can also be explained under such assignments. It is also shown that the experimental data of the optical absorption can be reasonably connected to those of the paramagnetic resonance absorption.

The Effects of Exchange Interactions in the Spectra of Octahedral Manganese. II. Compounds

Earlier experimental work (J. Ferguson, H.J. Guggenheim and Y. Tanabe, J. appl. Phys. 36 (1965) 1046, Phys. Rev. Letters 14 (1965) 737) on the Mn pair spectrum of KZnF 3 :Mn and the spectrum of KMnF 3 has been extended. The narrow bands of KMnF 3 and RbMnF 3 have been assigned and their abnormally high intensities established. The transition is an electric dipole one and oscillator strength (∼9.5×10 -7 for the 4000 A absorption) is temperature independent, corresponding to an allowed transition. The experimentally observed features of the pair absorption suggest a possible form of interaction between radiation and paramagnetic ion pair. The origin of this interaction is discussed and an order of magnitude argument is given to support the proposed mechanism. Related problems such as exchange interaction in excited states and the spectra of the concentrated materials are also considered.

On the Absorption Spectra of Complex Ions IV. The Effect of the Spin-orbit Interaction and the Field of Lower Symmetry on d electrons in Cubic Field

It is shown that the matrix elements of the crystalline field of lower symmetry than cubic and of the spin-orbit interaction for d -electrons in octahedral complex ions can be easily evaluated by the method of tensor operators, and the tables necessary to evaluate these elements by this method are given. It is also pointed out that the effective Hamiltonian which plays the same role as the spin Hamiltonian for the non-degenerate states can be constructed for the degenerate orbital states and will be useful for the analysis of line spectra of these complexes.

A Note on the Theory of Superexchange Interaction

The expressions of the coefficients appearing in the interaction \(\mathscr{J}_{ij,kl}(\textbf{\itshape s}_{i}{\cdot}\textbf{\itshape s}_{j})\) ( s k · s l ) between unpaired spins have been derived together with the expressions for the ordinary superexchange integral J i j . The latter expressions include some new terms which have been overlooked in previous derivations. Consideration of the former interaciton seems to solve, at least qualitatively, the difficulties encountered before. The results were also applied in the derivation of the expressions of the coupling constant in the interaction between a paramagnetic ion pair and an electric field. Finally, an attempt is made to calculate the superexchange integral in the three center four electron problem by using the values obtained in the calculation on KMnF 3 . The relation between Andersons recent theory and the older based upon Heitler-London model is studied. Numerical results are given and analyzed from both points of view.

Photonic Band Using Vector Spherical Waves : I. Various Properties of Bloch Electric Fields and Heavy Photons

The calculation is presented for the photonic bands for the fcc array of dielectric spheres, using the vector spherical-waves as basis functions. It is shown that the dimension of the secular determinant is less than 100, or less than one tenth of that of the plane-wave basis functions. Based upon the calculated eigenvectors, the symmetry properties of the electric-field vectors, the angle between the electric- and displcement-field vectors and the orthonormality of the Bloch states are investigated. Also the convergence of the plane-wave expansion is examined. Furthermore, we have demonstrated the existence of the modes appropriately called heavy photons, whose origin is exactly identical to the electronic analogues, heavy fermions.

Intensity of Magnon Sidebands

A general formula is derived for the integrated intensity of magnon sidebands in a two-sublattice antiferromagnet. The integrated intensity variation with temperature is calculated under the (random phase) decoupling approximation. Predicted values of the integrated intensity coincide with that obtained in the spin wave theory at low temperatures and that in the pair spectra theory at high temperature limit. The theory is applied to the rutile type antiferromagnets and numerical calculations are presented for magnon sidebands in MnF 2 .

Absorption of Light by Pairs of Exchange‐Coupled Manganese and Nickel Ions in Cubic Perovskite Fluorides

The absorption of light by exchange‐coupled pairs of manganese and nickel ions in KZnF3 is reported. Three absorption regions are discussed, of which two (4000 and 3300 A) are associated with electronic excitation of the manganese and the third (6600 A) corresponds to electronic excitation of the nickel ion. The lines can be analyzed by means of an exchange interaction of the type JS·S and a value of J = 18 cm−1 for the manganese—nickel pair in its electronic ground state has been obtained. The mechanism of the electronic transitions has been discussed using the theory developed for like pairs in an earlier paper and reasons for the greater intensity of absorption by unlike pairs are considered. Corresponding effects of exchange interaction have also been observed in the spectra of KMnxNi1−xF3 crystals. The energies and intensities of the absorption bands have been measured as a function of x and a theoretical analysis of the main results has been given. The main features of these spectra can be interpret...

Covalency in Ionic Crystals: KNiF3

Within the framework of the self-consistent field molecular orbital theory, studies are made of the covalency and the cubic field splitting parameter in ionic crystals, with a particular reference to KNiF 3 . It is pointed out that the effect of the rearrangement among the virtually transfered electron and d -electrons is essential in obtaining proper values of the covalency. By using the Heitler-London theory with an admixed excited configuration, in which atomic orbitals of the metal and ligand ions are different from those in the ground configuration, this effect of the rearrangement can be taken into account to some extent, and a reasonable value of the covalency may be obtained. Finally, by making a one to one correspondence between the expressions in the generalized Heitler-London theory and a simple molecular orbial theory, it is shown that the simple molecular orbital theory could successfully be used if an appropriate effective Hamiltonian is assumed.

Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field

For the fcc arrays of dielectric spheres, the reflectivity of a light and the local field excited by it are calculated exactly by applying the layer doubling method developed in LEED. It is shown that, when the number of the layers of a system is more than 4 or 5, the reflectivity reproduces the band gaps fairly well and 15 layers are enough for the stop bands to develop to match precisely with the band-gap widths, with one exception of the lowest stop band which requires a much larger thickness. Also, the good coherence and strong confinement effect of heavy photon are shown by demonstrating the well-defined interference fringes in the reflectivity and the very high intensity of the excited local-fields.

Spin Wave Sidebands in MnF2

It is shown that the observed features of the spinwave sideband structures in MnF 2 can be understood by assuming the transition mechanism proposed earlier and led to a successful interpretation of the infrared two magnon absorption. Selection rules of the magnon induced optical transition are discussed taking explicitly the symmetry of the crystal and orbitals into account. The results predict that the line shapes of the σ and π absorption should be opposite to those of the infrared absorption as is really the case. Calculated line shapes are in qualitative agreement in the case of σ1 (σ-polarized, at 18477.1 cm -1 ) and π1(π-polarized, at 18460.8 cm -1 ), but not with σ2 (at 18485.3 cm -1 ). Sidebands in FeF 2 are also discussed.