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Inelastic neutron scattering measurements by Okazaki, Tuberfield, and Stevenson (1964) of the antiferromagnetic spin wave energy, spectrum in manganese fluoride crystal at low temperatures, agree with the results predicted by a dispersion relation introduced without proof in their paper. In this thesis the question is considered in detail to what extent this dispersion relation is justified. The interaction between the manganese ions is described by the Heisenberg exchange Hamiltonian. Following Holstein and Primakoff's formalism the spin deviation operators are introduced and the part of the Hamiltonian ℋ[superscript B] containing all the terms up to those bilinear in the spin deviation operators is diagonalised by means of the Anderson transformation. A correction is next obtained by retaining the diagonal part of those terms which are quadrilinear in the spin deviation operators. Under certain conditions it is shown that ℋ[superscript B] together with the correction term give rise to, a dispersion relation which is identical with that used by Okazaki et al. (1964). Finally the validity of the approximations is also discussed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A single crystal neutron spectrometer using a copper crystal has been designed and constructed for the purpose of studying the low energy (<1 ev) neutron spectrum from the V.P.I. reactor. The basic theory necessary for the design, the details of the spectrometer, calibration data and method of operation are presented in this thesis. A relation between angle of diffraction and neutron energy is obtained from the known lattice spacing of the copper crystal. A measure of the total cross section of cadmium from 0.01 to 1.0 ev has been obtained from transmission data for a thin cadmium sheet. The position of the low energy resonance peak confirms the computed calibration. The resolution of the instrument and the intensity of the diffracted beam as a function of energy were studied in order to ascertain the usable range of the spectrometer. / Master of Science

The structural chemistry and magnetic properties of a number of manganese containing hexagonal perovskites have been studied by X-ray diffraction, neutron diffraction and magnetometry. Trends in the magnetic properties are investigated as a function of the hexagonal stacking sequence and manganese oxidation state. The synthesis of the series of BaMnO_3-x hexagonal perovskites is discussed. By varying both the partial pressure of oxygen and the firing temperature, stacking sequences with a range of hexagonal to cubic layer ratios can be synthesised. Factors which increase the structural tolerance factor are found to increase the proportion of hexagonal layers in the stacking sequence. The crystallographic properties of the BaMnO_3-x compounds are discussed, and the oxide vacancies are found to be exclusively located in the face-sharing hexagonal (h) layers, particularly those which are adjacent to two apex-sharing cubic (c) layers. The preferential localisation of oxide vacancies in chc sites can be used to rationalise the observed stacking sequences, as well as the limiting stoichiometries of BaMnO_3-x structures. The magnetic behaviour of the BaMnO_3-x phases is investigated, both individually and as a function of the stacking sequence. A strong direct exchange interaction between face-sharing cations couples all magnetic moments antiferromagnetically above ambient temperature. A slightly weaker interaction (utilising the 180° superexchange pathways between apex-sharing MnOe octahedra) results in three-dimensional antiferromagnetic order at a temperature in the range 230 ≤ T (K) ≤ 280. The strength of this interaction is found to be dependent on the length of the face-sharing chains. A third interaction occurs at T ~ 45K, believed to represent a canting transition. Low temperature neutron diffraction data reveal that the magnetic moments order in a simple antiferromagnetic manner. The magnitude of the ordered moment shows a dependence on the length of the face sharing chains, where phases with shorter chains have a larger ordered moment. Long-range magnetic order is disrupted by charge disorder in the mixed Mn(III)/Mn(IV) system 4H-BaMnO_{2.6 5(1)}. The hexagonal BaMn_1-zTi_z O_{3- x} and BaMn_1-zZr_z0_3-x systems were also studied. Synthesis under argon atmospheres allows a range of new phases to be accessed. These include a novel manganese-zirconium phase, 6H-BaMn_0.8Zr_0.2O_2.81(1), and BaMn_o.55Ti<sub>0.45,/sub>O_3-x, which adopts the rare 15R' stacking sequence. The BaMn_1-z Ti_zO_3-x system confirms that although the tolerance factor controls the proportion of cubic layers, it does not control the arrangement of these layers. This is controlled by the size of the B cations and the proportion of oxide vacancies. Partial cation order occurs in 6H-BaMn_o.8Zr_0.2O_2.81(1), which can be rationalised on the basis of the size difference between manganese and zirconium ions. Topotactic reductions using binary hydrides are carried out in order to decouple the manganese oxidation state from the adopted stacking sequence. Using hydride reductions, 4H-Ba_o.5Sr_o.5MnO_3-x can be topotactically reduced to 4H-Ba_o.5Sr_o.5MnO_2.o2(1). This increases the strength of the 180° superexchange interaction, and antiferromagnetic order is achieved above ambient temperature. Using the same techniques, 4H-BaMnO_3-x can be reduced to 4H-BaMnO_2.47(1) or 4H-BaMnO_2.o6(1). These phases undergo a distortion to an orthorhombic unit cell.

Powder neutron diffraction and magnetic susceptibility measurements of the antiferromagnetic phases of Mn_xNi_1-xO,Mn_xCo_1-xO, (Mn_xFe_1-x)_zO and (Co_xFe_1-x)_zO reveal that the magnetic moments of unlike ions are always effectively collinear, despite the presence of competing anisotropies. The magnetic moments of Mn_xNi_1-xO (x = 0.24,0.48 and 0.77) at 5K are confined to (111) planes by dipole-dipole forces, and the small trigonal exchangestrictions are the products of opposed antiferromagnetic Mn²⁺-Mn²⁺ and ferromagnetic Ni²⁺-Mn²⁺ nearest neighbour interactions. In Mn_xCo_1-xO (x = 0.05, 0.10, 0.25,0.36) at 5K, the orbital degener- acy of Co²⁺ is removed by both Jahn-Teller (J.T) and spin-orbit coupling (S.O) mechanisms, leading to orthorhombic or triclinic symmetries and partially quenched Co²⁺ moments. Monoclinic symmetry is observed for 0.51<x<0.67, and Jahn-Teller stabilisations and spin-only Co²⁺ moments are evident. The cobalt concentration is too small to support a cooperative J.T stabilisation in Mn_0.83Co_0.17O, where a magnetostriction (c/a < 1) is observed (in agreement with previous AFMR results). Previous results for Co_xNi_1-xO, and those for Mn_xCo_1-xO, (Mn_xFe_1-x)_zO (x = 0.05, 0.1, 0.12, 0.23, 0.36,0.56,0.66,0.89) and (Co_xFe_1-x)_zO (x = 0.04,0.12,0.50,0.63,0.81) at 5K indicate that the anisotropy order for the iron group monoxides is CoO>MnO»Fe_zO≈NiO. The weak trigonal anisotropy of Fe²⁺ correlates with the near-cubic symmetries of (Co_xFe_1-x)_z( (x = 0.04,0.12) and (Mn_xFe_1-x)_zO (0.1<x<0.66), and a tetragonal (c/a>1) magnetostriction of Fe²⁺ is observed in (Co_xFe_1-x)_zO with x > 0.5. Measurements of vacancy-ferric interstitial ratios for (Mn_xFe_1-x)_zO and (Co_xFe_1-x)_zO suggest that non-stoichiometry is accommodated by 6:2 or 8:3 defect clusters in the former, and by larger units in the latter. The observed magnetic moments of defective samples are normally larger than those calculated according to a previous model for Fe_zO, and require the postulation of partial antiferromagnetic order around the clusters. The room temperature Mossbauer effect parameters of (Mn_xFe_1-x)_zO (0<x<0.975,0.910<z<1.0) indicate that while Fe²⁺ and Mn²⁺ ions are randomly distributed over octahedral sites, ferric ions are localised around defect clusters.