Table of contents

Calculations of the temperature dependence of the coercivity of a random array of non-interacting single domain particles of uniaxial anisotropy are presented. The extent of the coercivity variation in a given temperature range is found to depend upon the particle volumes, as well as on the anisotropy energy. Under special circumstances, these variations may be regarded as being approximately linear.

The cubic anharmonic contribution to the Helmholtz free energy of a face-centred cubic crystal has been evaluated for a nearest-neighbour central force model. The results are expressed in terms of the derivatives of an arbitrary interatomic potential and three sums S_m(a₁, T_R), (m = 1, 2, 3). Here T_R is an appropriate reduced temperature and a₁ is essentially the ratio of the first to the second radial derivative of the interatomic potential.

The three sums S_m(a₁, T_R) are tabulated for a representative range of volumes and temperatures as well as T_R = 0 and the high temperature limit. For these two limiting cases our results are compared with similar calculations by Flinn and Maradudin and Feldman and Horton.

Once the interatomic potential is specified our results yield both the volume and temperature dependence of the cubic anharmonic contribution to the Helmholtz free energy. The temperature dependence of S_m(a₁, T_R) is discussed in some detail since this determines the cubic anharmonic contribution to the entropy and specific heat.

The concept of saturation island density (i.e. numbers of discrete groups of atoms) is critically examined. Equations for nucleation and growth are derived, taking into account the random nature of evaporation and the competition of the processes consuming atoms, and it is shown that saturation never occurs. The concept of fractional nucleation rate is introduced; this is defined as the quotient of the nucleation rate and the island density. This parameter can be used experimentally to find values of the energy parameters which govern the nucleation and growth processes.

Measurements on polarized absorption and fluorescence of a single crystal of trans-stilbene are reported. Vibrational analysis is also reported for them. The a:b polarization ratio in the absorption of a pure trans-stilbene crystal deviates greatly from the oriented gas model value. The fluorescence origin of the pure crystal at 300 °K is 340 cm⁻¹ to the long-wavelength side of the 0-0 absorption band. On lowering the temperature to 90 °K the intensity of fluorescence near the origin decreases and a red shift of 50 cm⁻¹ to 100 cm⁻¹ is found. It is suggested that the fluorescence is due to a trapped exciton located at some lattice imperfection and that, at low temperature, a part of the fluorescence originates from a lower defect level.

A comparison is made between the spin-lattice relaxation times calculated in various ways from continuous saturation measurements and those obtained using the conventional pulse saturation method at 9·27 GHz, over the temperature range 1·7-4·2 °K. The material investigated was [(C₄H₉)₄N]₂ Cu[S₂C₂(CN)₂]₂ for which pulse saturation measurements were available.

The conclusion is drawn that, whereas relative measurements compare very favourably, it is difficult to ascribe an absolute value to T₁ because of the uncertainty inherent in the values of ancillary parameters (e.g. H₁ and T₂) and the assumptions made concerning the spin system. The forms of the saturation curves obtained using this material are found to agree closely with those calculated from the steady state solutions to the bottlenecked rate equation. The difficulties involved in the interpretation of such data under bottleneck conditions are discussed.

A point charge electrostatic model is used to explain the sudden increase in electron paramagnetic resonance linewidth at critical temperatures T_c and the low temperature entropy anomalies exhibited by hexammine nickel halides. It is suggested that these results are due to hindered rotation of the H₃ groups between different equilibria arrangements of H₃ protons within the solids. Barriers within the crystals are computed by assigning charges β|e| to each proton site, and summing the β²e²/r_ij terms between protons i and j on the same and on neighbouring Ni(NH₃)₆ clusters. Low and high energy arrangements of protons within each cluster are obtained.

The model explains the electron paramagnetic resonance results by predicting that the nickel ion experiences a change from trigonal to cubic symmetry, occurring when the nearest neighbour electrostatic interaction between protons on neighbouring clusters is thermally overcome. The entropy anomalies, corresponding to a depopulation of one member of a ground state split by rotation of individual H₃ groups, give values for β|e|. Reasonably consistent values for the three halides (similar ¼|e|) lend support to the validity of the main predictions.

The spin polarization due to the static part of the s-d interaction is derived exactly. It is shown that it leads to s wave resonant type of polarization which is larger than Yosida polarization but smaller than Friedel d-virtual level polarization. The resultant formulae predict both charge density and spin density oscillations unlike the usual Yosida result.

Electron spin resonance studies have been made of trapped hole centres with an F₂^- molecular ion structure in CaF₂. x-irradiation of CaF₂ at 77 °K produces self-trapped hole centres. These become mobile at higher temperatures and may be trapped at special sites in the lattice to form other, relatively stable, F₂^- molecular ions with axes near <100>, <111> and <110> directions. The <100> molecular ion which is stable at room temperature has a symmetry which is lower than that of the self-trapped hole and this is shown to be consistent with the hole being trapped adjacent to the site of a substitutional Na⁺ ion. The <111> case is treated in detail and is found to give an axially symmetric F₂^- molecular ion in which the probabilities of locating the hole near each of the two nuclei are unequal. This is shown to be consistent with the hole being trapped at the site of an interstitial anion. Activation energies for thermal annealing of these centres and for the self-trapped holes have been found by pulse annealing to be, respectively, 0·55 ± 0·10 and 0·13 ± 0·02 ev.

The temperature dependence of the low-frequency dielectric response of CaF₂, SrF₂ and BaF₂ over the range 2-350 °k is reported, together with the pressure dependence, for hydrostatic pressures up to 5 kbar, at selected temperatures in the range 60 to 350 °k. The low-temperature data are used to assess the nature and extent of the electronic structure and interionic forces of the alkaline earth fluorides. The temperature dependence of the dielectric response is found to be due principally to intrinsic volume changes in the crystals rather than to intrinsic temperature changes in the anharmonic contribution. The temperature dependence under constant volume of the anharmonic contribution to the dielectric constant of all three salts exhibits a maximum value near 0·25 θ_D, where θ_D is the characteristic Debye temperature. The quasi-harmonic contributions are analysed to determine values for the κ similar, equals 0 longitudinal and infra-red active transverse optic phonon Gruneisen constants.

A group-theoretic technique for simplifying spin-wave calculations in complicated magnetic structures is developed in this paper. The technique gives the free spin-wave energies exactly at the centre of the Brillouin zone and at certain other symmetry points. By simplifying the canonical transformation to magnon operators, it reduces the labour required to analyse magnon interaction effects, and brings complex crystals within the scope of the Green function method.

The group-theoretic technique described in an earlier paper is used to calculate the free spin wave energies for both magnetic phases of haematite. It is shown that the optic modes may have unusually low energy in α-Fe₂O₃, and that molecular field theory gives correct results for magnetic resonance.

Recent optical experiments have shown that the two-magnon spectra of antiferromagnets cannot be properly understood using simple non-interacting spin-wave theory. In these experiments two magnons are created close together in real space where they interact strongly to produce large observable effects. They therefore provide an excellent opportunity to study magnon-magnon interactions. A general theory of the two-magnon states using Green function methods is developed and the results applied to the spin-only antiferromagnet RbMnF₃ and to CoF₂ where the orbital contribution to the magnetic moment is important. The predicted optical properties are in good agreement with experiment.

A perturbation theory derivation of the energy shifts of spin-wave modes is used to clarify the nature of the approximations and the results obtained by Jacobsen and Stevens and Elliott and Parkinson for the coupled spin-phonon dispersion curve. It is emphasized that the cancellation of energy shifts for modes of large wave number κ is a consequence of the particular choice of coupling constant. The upward shift of the κ = 0 mode is interpreted in terms of phonon induced spin-spin interactions.

The magnetic equation of state proposed by Kouvel and Comly for nickel near T_c is applied to the calculation of the specific heat in a magnetic field and the magnetocaloric effect. An expansion about the critical isotherm is used for similar calculations at T_c. The experimental results for nickel are compared with those calculated. The difference in specific heats in two high fields agrees well with observation, but the specific heat in zero field does not agree so well, perhaps because of experimental difficulties. The calculated magnetocaloric effect agrees very well with observation, whereas it differs very markedly from the results based on molecular field theory.

To interpret either magnetic or recoil-free nuclear resonance experiments in metals and alloys, one requires knowledge of the valence electron densities at nuclear sites. An electron diffraction theory is developed which enables such information to be derived in terms of calculable parameters. The latter data are then computed for the monovalent metal ions from potentials previously used with fair success in calculating pseudopotentials. The approach represents a generalization of the method of orthogonalized plane waves, improving on the latter in that it recognizes the dynamical response, via a Schrödinger equation, of valence electrons to the ion core potentials. The chief new feature is a renormalization of the valence electron wave functions due to the attractive core fields and this is qualitatively different from the orthogonal plane wave method which expels charge from the cores. The data are used to account for the observed Knight shifts in lithium and sodium.

A first-principles calculation of the volume dependence of the Knight shift in monovalent metals is made. For each case, the susceptibility and the nuclear contact terms are obtained from a common source, namely the solution of a single Schrödinger equation for a screened ion potential. Semi-quantitative agreement with experiment is obtained. For the heavier alkalis, the increasing importance under pressure of the d character of the valence electrons emerges and provides a link with an explanation previously offered of the pressure dependence of the resistivities.

The Rudermann-Kittel interaction between spins centred on two impurity atoms in a crystal is examined by a Green function method. Since the impurity atoms have different spin-independent potentials the local charge density is changed and this modifies the R-K interaction. In general there is a change in amplitude and a phase change in the oscillations. Calculations have been made using the free electron model and the tight-binding model for a simple cubic lattice, assuming that the defects cause a change of potential which is short range. It is found that large enhancements of the interaction can occur if the defect gives a resonance close to the Fermi energy. Possible experiments whose interpretation is affected by these effects are discussed.

Using a Green function formalism, the calculation of the density of states for a one-dimensional liquid model is considered. In the weak binding case, and small disorder, a complex effective mass is defined, which gives rise to band tails in the density of states. For larger disorder, a two-band Green function is considered. The model is extended to three dimensions.

It is shown that the existing theories of large paramagnon contribution in nearly ferromagnetic metals imply a breakdown of the quasi-particle picture. A more sophisticated theory is outlined here to overcome this.

The theoretical moment functions of the Caesium halides based on the ragid-ion model, the polarization dipole model, and the two variations of the dipole model have been compared with the experimental ones.