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Some quantum effects of the magnon-photon interaction are investigated. A magnon life-time, arising from a radiative relaxation through the absorption and emission of one photon, is found. Multiple scattering of magnons and photons is indicated. The creation of a photon at one spin site and the resonant absorption of the same photon at a later time at a different site is found to lead to a spin-spin real radiation exchange interaction. The predicted effects are large enough to be experimentally observed.

The magnon-photon interaction is formulated for a direction of the magnetic vector of the electromagnetic wave perpendicular to the direction of the sublattice magnetization in an antiferromagnet, and from this the one-magnon self-energy is calculated. The linewidth predicted from the one-magnon one-photon process is in good agreement with the experimental value for Mn${\mathrm{F}}_{2}$. Higher-order magnon-photon scattering processes are indicated and the corrections arising from such multiple magnon-photon scattering processes are found to depend on temperature and microwave power.

Charge densities at 40K+ in KF, KCl, and KBr lattices are calculated from Hartree-Fock wavefunctions including the effect of overlap of core orbitals with the neighboring atoms. From the calculation of KF and KCl and the experimental measurements of Mossbauer centre of gravity shifts we estimate the relative change in nuclear charge radius upon emission of 29.4 keV γ-radiation to be in the limits of −6 × 10−4 ≦δ / ≦ 31 × 10−4. Die Ladungsdichten am 40K+ im KF-, KCl- und KBr-Gitter werden aus Hartree-Fock-Wellenfunktionen berechnet, wobei Uberlappungseffekte der Rumpforbitale mit Nachbaratom berucksichtigt werden. Aus der Berechnung fur KF und KCl und aus experimentellen Messungen der Schwerpunktsverschiebungen des Mosbauerzentrums wird berechnet, das die relative Anderung des Kernladungsradius nach Emission von 29,4 keV-Strahlung innerhalb der Grenzen von 6 × 10−4 ≦δ / ≦ 31 × 10−4 liegt.

The theory of transferred hyperfine interaction at the F - site in the mixed σ - and π - bonding Mn 2+ F - and Mn 2+ F - Mn 2+ systems is developed from first principles. The transfer of electrons from the occupied p and s orbitals of F - ion to the empty d orbits on the Mn 2+ ion is considered and all the integrals of the kinetic energy and the Coulomb interactions are evaluated using the Hartree-Fock wave functions. The spin density for 1s, 2s, 2p σ and 2p π orbits at the F - ion is calculated as a function of interatomic distance and from the hyperfine field is calculated. It is found that there are large cross terms between 1s and 2s functions. The order of magnitude of the hyperfine field at the F - site can be predicted only if the covalency is taken into account. There occurs considerable change in the spin density in going from the single magnetic ion to the magnetic ion pair as a result of a change redistribution effect associated with the electron transfer in the pair.

A theory of the spin–fracton interaction for paramagnetic ions in fractal structures is developed The interaction is exponentially damped by the self-similarity length of the fractal and by the range dimensionality dphiv;. The relaxation time of the spin due to the absorption and emission of the fracton is calculated for a general dimensionality called the Raman dimensionality dR, which for the fractons differs from the Hausdorff (fractal) dimensionality, D, as well as from the Euclidean dimensionality, d. The exponent of the energy level separation in the relaxation rate varies with dRdphiv;/D. Also the spin relaxation rate due to a new type of Raman process is calculated in which one fracton is absorbed to affect a spin transition from one electronic level to another and later another fracton is emitted along with a spin transition such that the difference in the energies of the two fractons is equal to the electronic energy level separation. The temperature and the dimensionality dependence of such a process is found in several approximations. In one of the approximations where the van Vleck relaxation rate for a spin in a crystal is known to vary with temperature as T9, the calculated variation for fractals turns out to be T6.6 whereas the experimental value for Fe3+ in frozen solutions of myoglobin azide is T6.3. Since dR = 4/3 is used and the fracton range dimensionality dphiv; = D/1.8, it is expected to measure the dimensionalities of the problem by measuring the temperature dependence of the relaxation times. Also calculated is the shift of the paramagnetic resonance transition for a spin in a fractal for general dimensionalities. Eine Theorie der Spin–Fracton–Wechselwirkung fur paramagnetische Ionen in Fractalstrukturen wird entwickelt. Die Wechselwirkung ist exponentiell gedampft durch die Selbst-Ahnlichkeitslange des Fractals und der Bereichsdimensionalitat dphiv;. Die Relaxationszeit des Spins infolge der Absorption und Emission des Fractons wird fur eine allgemeine Dimension, die Raman-Dimension, berechnet, die bezuglich der Fractonen sich von der Hausdorff (Fractal)-Dimension, D, sowie von der Euclidischen Dimension, d, unterscheidet. Der Exponent der Energieniveauseparation der Relaxationsrate andert sich mit dRdphiv;/D. Auch die Spin-Relaxationsrate wird berechnet, die durch einen neuartigen Ramanprozes verursacht wird, bei dem ein Fracton absorbiert wird und den Spinubergang von einem Elektronenniveau zum anderen beeinflust und darauf ein anderes Fracton emittiert wird, zusammen mit einem Spinubergang von der Art, das die Energiedifferenz der beiden Fractonen gleich dem Abstand der Elektronenenergieniveaus ist. Die Temperatur- und Dimensionsabhangigkeit eines solchen Prozesses wird in verschiedenen Naherungen gefunden. In einer der Naherungen, bei der die Van Vleck-Relaxationsrate fur einen Spin in einem Kristall mit der Temperatur wie T9 variiert, betragt die berechnete Variation der Fractale T6,6, wahrend der experimentelle Wert fur Fe3+ in eingefrorenen Losungen von Myoglobinazid T6,3 betragt. Da dR = 4/3 und eine Fracton-Bereichsdimension dphiv; = D/1,8 benutzt wird, wird erwartet, das die Dimensionen des Problems durch Messung der Temperaturabhangigkeit der Relaxationszeiten gemessen werden. Ebenfalls berechnet wird die Verschiebung des paramagnetischen Resonanzubergangs fur einen Spin in einem Fractal fur allgemeine Dimensionen.

The electron-phonon interaction for a paramagnetic impurity in an insulating crystal is derived and from that an electron-electron interaction in a higher order is considered. An attempt is made to provide a unified presentation of the effect of phonons on the parameters measured in an electron-paramagnetic resonance experiment. The phonon-induced corrections to the zero-field splitting, the hyperfine field, the superhyperfine splitting and line intensities is reviewed theoretically along with experimental data. Both the point charge and covalent models are discussed. The effect of local and resonance modes is calculated and discussed in terms of isotope effect. Some related problems of the energy levels, dispersion, screening and phonon force are also included in appendices.

The dependence of the recombination relaxation rate on the carrier concentration, n, is examined in detail. It is found that in polar indirect band gap semiconductors the phonon-induced recombination rate varies as n 4 3 at low temperatures. This is a new power law. On the other hand, in the non-polar materials, the relaxation rate varies as a linear combination of n2, n 5 3 and n 4 3 terms. We find the experimental evidence for the occurence of n 5 3 and n 4 3 contributions for the first time.

The mixed valence of ions causes the appearance of electrons at random sites in which the phonon-induced charge transfer from one site to another and the band hybridization give rise to electron pairing interaction, the coupling constant of which is larger than that of the ordinary electron-phonon interaction in metals. As the impurity band approaches the conduction band, the strength of the phonon-induced charge transfer from the impurity band to the conduction band increases. Insulating as well as superconducting pairs of electrons are predicted. The range of the one-electron states in which the interaction is attractive extends from −ϵi − ℏωD to ϵi + ℏωD where ϵi is the impurity band width and ℏωD is the Debye cutoff. Thus the transition temperature in the present theory is larger than in the BCS theory.

Mixed-valence compounds are divided into two classes. Class I includes materials in which charge transfer from a ligand orbital to one of the rare-earth atom valence orbitals occurs along with production of a soft phonon (via electron-phonon interaction) at a given transition temperature. In class II materials, the lattice is dynamically stable and the soft phonon does not occur.

The effect of dynamic phonon interaction on the hyperfine fields of ions with electronic configuration 3d3 has been examined theoretically. The zero-point vibrational contribution and the temperature dependent part is discussed for both the acoustical and the optical phonons in a covalent model. As the amplitude of phonon vibrations is thermally increased a net decrease in the V2+ hyperfine interaction in octahedrally coordinated environment is predicted the temperature dependence of which is in agreement with experimental measurements in V2+ doped MgO. Der Einflus einer dynamischen Phononenwechselwirkung auf die Hyperfeinfelder von Ionen mit der Elektronenkonfiguration 3d3 wurde theoretisch untersucht. Der Beitrag der Nullpunktsschwingungen und der temperaturabhangige Anteil wird sowohl fur akustische als auch optische Phononen in einem kovalenten Modell diskutiert. Da die Amplitude der Phononenschwingungen mit der Temperatur zunimmt, wird eine Gesamtabnahme in der V2+-Hyperfeinwechselwirkung bei oktaedrischer Umgebung vorhergesagt, deren Temperaturabhangigkeit mit experimentellen Ergebnissen an V2+-dotiertem MgO ubereinstimmt.

Phonon-induced contributions to the antibonding orbitals of an Mn2+ ion in octahedral crystalline fields are calculated by means of orbit-lattice interaction. The corrected orbitals are used to calculate the transferred hyperfine interaction, which is compared with the experimental measurements in Mn2+-doped LiF. Almost half of the observed variation of the transferred hyperfine interaction is interpreted in terms of implicit (thermal expansion) and half as explicit (lattice vibration) effects. The strength of variation of 19F hyperfine coupling with temperature when calculated from Hartree-Fock wave functions is found to agree with the measured one provided a 4% expansion of wave functions in going from the free ion to the solid state is assumed.

The theory of Raman relaxation is developed without the approximation of small wave vectors for the lattice phonons and it is shown that the accurate theory reduces into the known one if the expressions are expanded into infinite series and only the first term retained. The temperature dependence of electronic relaxation times is found to be more involved in the correct expressions than in the approximate ones. Eight different cases depending on the structure of energy levels are derived starting from a single formula. Four of these cases are new. Efforts are made to compare the theory with the experiments on Pr3+, Ce3+, Nd3+, Yb3+, and Mo5+ ions. A new T5 behaviour predicted for Kramers ions is apparently observed in Nd3+: LaCl3 and Mo5+:TiO2 and for the non-Kramers Pr3+: LaCl3 system. Faster temperature dependence than the usual T9 one is predicted and probable indications of the same are noted on Ce3+, Nd3+, and Yb3+ in CaWO4. Es wird die Theorie der Raman-Relaxation ohne die Naherung der kleinen Wellenvektoren fur die Gitterphononen entwickelt und es wird gezeigt, das die genaue Theorie sich auf die bekannte reduziert, wenn die Ausdrucke in unendliche Reihen entwickelt werden und nur der erste Term berucksichtigt wird. Es wird gefunden, das die Temperatur-abhangigkeit der elektronischen Relaxationszeiten in den korrekten Ausdruck mehr eingeht als in den Naherungsausdruck. Acht unterschiedliche Falle, die von der Struktur der Energieniveaus abhangen, werden aus einer einzigen Formel abgeleitet. Vier dieser Falle sind neu. Es werden Versuche gemacht, die Theorie mit Experimenten an Pr3+, Ce3+, Nd3+, Yb3+ und Mo5+-Ionen zu vergleichen. Ein neues T5-Verhalten, das fur Kramers-Ionen vorhergesagt wird, wird wahrscheinlich in Nd3+: LaCl3-, Mo5+: TiO2- und in nicht Kramersschen Pr3+: LaCl3-Systemen beobachtet. Starkere Temperaturabhangigkeit als normale T3-Ab-hangigkeit wird vorhergesagt und wahrscheinliche Anzeichen bei Ce3+, Nd3+ und Yb3+ in CaWO4 bemerkt.

A new shift in the nuclear magnetic resonance frequency of ligand nuclei in antiferromagnets above the Neel temperature is obtained as a direct consequence of inclusion of phonon-induced effects in the transferred hyperfine coupling. The shift has two parts, one of which has the same temperature dependence as the usual paramagnetic susceptibility chi (T). The other part at low temperature depends on T4 chi (T). Both the experimental and the theoretical evidence is produced for the 19F nuclei in MnF2.

Electron spin resonance studies of γ‐irradiated single crystals of semicarbazide hydrochloride and the deuterated form, ND2CONHND3+·Cl−, revealed the presence of the stably trapped ·N(α)H(α) − N(β)H(β)3+ radical obtained by C–N bond rupture of the parent molecule. The principal g values were gaa = 2.0041 ± 0.0003, gbb = 2.0023, and gcc = 2.0044. The principal elements of the hyperfine couplings were found to be N(α) = 4.8 ± 4.0, 34.2 ± 1.0, and 11.8 ± 4.0 G; H(α) = − 10.5 ± 4.0, −27.6 ± 1.0, and −36.7 ± 4.0 G; N(β) = − 4 G; H(β) = 15 ± 0.5 G. The N(β) coupling was estimated from the angular dependence of the linewidths. The direction cosines of the N(α)and H(α) couplings were evaluated with reference to the orthorhombic crystallographic axes (a, b, c). The direction cosines of the N–H bond calculated from the ESR spectra were found to agree with those obtained by x‐ray diffraction. The spin densities calculated for this radical indicate that the unpaired electron is highly localized on the α nitrogen, the...

Electron paramagnetic resonance spectra of crystals of NaCl: Mn show eight different well-resolved paramagnetic centres. The relaxation of the centres is studied by observing the time variation of the intensities of the resonance lines at different temperatures. The kinetics of the relaxation process has been established and a measurement of the activation energy for the various types of interactions is given.

For pt. I, see ibid., vol. 3, No. 3 538 (1970). The wave functions including nearest and next-nearest neighbours are developed in magnetic as well as non-magnetic systems. The hyperfine coupling at the F- and Mg2+ sites in the linear chain Mn2+-F--Mg2+ in a cubic crystal is calculated. Similar calculations are carried out for the two sublattice type ant ferromagnets, the cubic KMnF3 and the rutile structure MnF2. It is found that at the F- site there exists a new kind of field in addition to the usual transferred hyperfine field. The new field in MnF2 calculated for both the phases, above and below the Neel temperature, indicates a spin deviation of magnetic ions in the antiferromagnetic phase of approximately 4.5%.

The ground $^{6}S$ and excited $^{4}L$ states of the ${\mathrm{Mn}}^{2+}$ ion are perturbed by the cubic crystalline field and mixed by the spin-orbit coupling. A two-phonon Raman process, second order in the orbit-lattice interaction, is found to contribute to the ground-state splitting. The theory is developed within the framework of Van Vleck's small-wave-vector averaging procedure for acoustic phonons. Both the zero-point vibrational contribution and the temperature-dependent parts are calculated and compared with experimental measurements in ${\mathrm{Mn}}^{2+}$-doped MgO. Good qualitative agreement between the theory and experiment is found but quantitative agreement is not obtained.

We find that the imaginary part of the complex susceptibility as a function of magnetic field at a frequency of 9.2 GHz shows equally spaced lines indicating harmonic oscillator type of excitations. The maximum in d ξ″ d H is also found to be proportional to the life time of the electron in the normal state. The predictions are verified by using the microwave absorption in ErBa2Cu3O7−δ and YBa2Cu3O7−δ (δ ≃ 0.2).

Fractal phase in frozen solution of deoxygenated myoglobin has been deduced for the first time using the previously-reported Mossbauer data. The exponent of the Debye-Waller factor is found to vary with temperature as T 0.40±0.07 . This exhibits a scale invariance for a fractal dimension of 1.40 ± 0.07, and is consistent with the dimensionality obtained from computer-generated models.

The interaction of the spin-polarized hydrogen atoms in the bulk as well as on the surface of the superfluid helium with the third-sound ripplons is investigated. The dispersion relation is found to show a kink at a particular wave vector at which new quasiparticles appear.

The core and overlap contributions to the electronic charge density at the 107 Ag nucleus in AgF and AgCl lattices are calculated as a function of the interatomic distance.

The contribution of the ferroelectric soft-mode to the zero-field splitting is calculated and separated from the thermal contribution arising from the splitting due to the electron-phonon interaction. The predicted effect is compared with the measured values in Mn 2+ -doped NaNO 2 .

The superexchange in V 2+  O 2−  V 2+ pair in MgO is calculated including the orbit-lattice interaction into theone-electron. hamiltonian. Although the exchange by itself is ferromagnetic, the phonon-induced contribution is found to be dominantly antiferromagnetic.

Reduction of the constants of the form DS Z 2 and FS Z 4 in going from the para- to the ferroelectric transition in Mn 2+ doped (NH 4 ) 2 SO 4 is interpreted to arise from the spin-phonon interaction owing to the ferroelectric soft mode.

The two photon Bethe-Salpeter equation is written from the magnon-photon interaction in a ferromagnet excited by microwaves and from this a new quasi-particle which is a state of two photons magnetically bound to each other, is predicted for the first time.

The variation of the zero‐field splitting parameter D for Ni2+ in ZnSiF6⋅6H2O between 4 and 250 K has been used to calculate the temperature dependence of the Debye temperature θD(T) in ZnSiF6⋅6H2O. θD(T) was determined to be 143 K at a temperature of 30 K and 127 K at 250 K. There was a pronounced minimum of 105 K in θD(T) near 60 K. The behavior of θD(T) is qualitatively similar to that found for alkali halides from specific heat data.

The orbit-lattice interaction is found to lead to a biquadratic superexchange in linear T 2 g system V 2+ − F - − V 2+ in cubic KMgF 3 . This is the first time that the biquadratic superexchange related to magnetostriction is calculated for any system.

We find that the input light intensity as a function of electron and hole density in semiconductors shows nonlinearity which describes bistability of nonequilibrium fermion states. Our model can describe the hysteresis phenomenon observed in electron-hole droplets.

The bound state of one magnon with one photon is predicted to occur for the first time in a ferromagnet with the magnetic vector of the electromagnetic wave parallel to the direction of magnetisation. The binding energy is calculated as a function of the sample size and the possibility of observing the one-magnon one-photon bound state, in a well controlled parallel pumping experiment, is suggested.

A Lagrangian of a degenerate phonon mode is suggested, which describes a finite-mass phonon (optical mode) and a phonon of zero mass (soft mode) upon symmetry breaking. It is found that this effect is related to the reduction of constants of the spin Hamiltonian. It is shown that for a doubly degenerate electronic states the degeneracy is lifted upon symmetry breaking.

The evaporation is quantized in units of roton energy. Since the rotons can have velocity and wave vector in opposite directions, the evaporated atoms have energies equal to the thermal energy E of the helium atoms in the liquid, from which an integer multiple of the roton energy h ω r is either subtracted or added, E ± n h ω r (n = 0, 1, 2,…) .

A new Hamiltonian for the interaction of magnetic impurity spin with the conduction electrons is proposed. It is found that the conduction electrons may be condensed into the spin levels. For single impurity, the exact eigenstates are found. In the case of many impurities, virtual electron exchange is predicted for the first time. A single fermion and a single phonon operator interaction leads to hybrid interaction between bands of electrons along with some interesting effects.

The displacement of ions in magnetically ordered materials by the ultrasound creates a fluctuating field via the hyperfine field. This fluctuating field can produce an extraordinarily strong absorption of ultrasonic waves which has been observed experimentally in the antiferromagnetic RbMnF3.

A level shifting effect in relation to the coupling of degenerate electronic states with vibrations in crystals is discussed. In this effect a degenerate level interacting with the lattice-phonon spectrum is shifted without the removal of degeneracy. This phenomenon is compared with Jahn-Teller effect in which the degeneracy is statically or dynamically removed without a shift. While the Jahn-Teller effect is essentially a tunnel effect with the system either tunneling over a hill (dynamic) or staying in one well (static) so that the degenerate state is instable, the present level-shifting effect is entirely stable.

The optical energy levels of Mn2+ ion in solids are shown to be modified by the lattice vibrations. The spectral shift is calculated within the framework of covalent model treating only the acoustic phonons and the low energy part of the Debye lattice spectrum. Significant shift in the optical spectrum due to lattice vibrations is found.

We have calculated the transferred hyperfine interaction at the ${\mathrm{F}}^{\mathrm{\ensuremath{-}}}$ ion in ${\mathrm{PbF}}_{2}$ in which the distance between ${\mathrm{F}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{Pb}}^{2+}$ is 30% larger than the bond lengths in ${\mathrm{MnF}}_{2}$. The contributions arising from the overlap of wave functions and the charge transfer and the charge redistribution effects have been calculated from first principles and the s, ${p}_{\ensuremath{\sigma}}$, and ${p}_{\ensuremath{\pi}}$ spin densities have been found. The change in the transferred hyperfine coupling due to a soft-phonon mode which goes to zero at a temperature of ${T}_{c}$=50 K has been calculated and verified experimentally.

The crystal field hamiltonian Hc = B20Y20 + B22(Y22 + Y2−2) commonly used in the study of electron-spin resonance is employed to obtain new contributions to the 57Fe3+ isomer shift in the Mossbauer effect. A numerical estimate of the shift is also presented.

It is suggested that while evaluating contact charge densities from internal conversion coefficients it is important to consider overlap effects. Ratios of the internal conversion coefficients and are evaluated as a function of interatomic separation for Fe 3+ in an octahedral arrangement of Br − ions.

Line width in ferromagnetic resonance is found to consist of the magnon scattering, the superradiance, and a new effect due to the simultaneous presence of magnon scattering and the superradiance.

The measured increase in g∥ between 4 and 100 K for Ni2+ in ZnSiF6⋅H2O has been explained as a consequence of the dynamical phonon coupling between the spins and the lattice. The Debye temperature of θ=130 K previously determined from the zero‐field splitting has been found to agree with that obtained from the temperature dependence of the g value. The zero‐point vibrational correction to the g value has been deduced.

We have found energy states at a fraction of the frequency of the Landau levels. The fraction is in accord with the experimental measurements of fractionally quantized conductance.

In a magnon-phonon interaction an energy minimum is obtained in the one-magnon ground-state dispersion. The magnon momentum at the minimum is half the product of the mass of the magnon and the sound velocity, h k 0 = 1 2 h ν × (cD) -1 .