A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site and also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped out for all values of the exchange interactions. Six distinct phases are identified. Monte Carlo simulations have been used to obtain the order parameter and the values for the energy and entropy in the ground state and also the transition temperatures. Excellent agreement is found between the simulated and analytic results. We find one region where there are two phase transitions with the lines meeting in a triple point. The orbital ordering that occurs in LaMnO3 occurs as one of the ordered phases.
An elastic anomaly, observed in the heavy fermi liquid state of Ce alloys (for example, CeCu$_6$ and CeTe), is analyzed by using the infinite-$U$ Anderson lattice model. The four atomic energy levels are assumed for f-electrons. Two of them are mutually degenerate. A small crystalline splitting $2\Delta$ is assumed between two energy levels. The fourfold degenerate conduction bands are also considered in the model. We solve the model using the mean field approximation to slave bosons, changing the Fermi energy in order to keep the total electron number constant. The nonzero value of the mean field of the slave bosons persists over the temperatures much higher than the Kondo temperature. This is the effect of the constant electron number. Next, the linear susceptibility with respect to $\Delta$ is calculated in order to obtain the renomalized elastic constant. The resulting temperature dependence of the constant shows the downward dip. We point out the relation of our finding with the experimental data.
The in-plane magnetization of a two-dimensional film may be stabilized by either dipolar interactions or by an in-plane anisotropy in the absence of an external field. We have calculated the conditions for either of these effects to dominate and show that there is only a restricted range of q values in which dipolar effects are important before the exchange dominates. We report measurements of all relevant anisotropy fields for an epitaxial Ag/2 ML Co/Ag(001) film structurally characterized by angle-resolved Auger spectroscopy and low-energy electron diffraction, together with a measurement of the ground state moment per Co atom (enhanced from the bulk value) using polarized neutron reflection. The results allow us to extend our previous study of the temperature dependence of the magnetization by including the perpendicular fields and the field dependence of the magnetization at 300 K. We show that the field dependence of the magnetization is not consistent with a spin wave gap due to dipolar interactions but is consistent with an anisotropy-induced spin wave gap, confirming the results of a preliminary study.
The forms of the birefringence change at phase transitions are discussed for four types of phase transition: (i) ferrodistortive, (ii) cubic systems with an n-dimensional soft mode and order parameter, (iii) cubic systems with a one-dimensional soft mode occurring at n q0 points, and (iv) tetragonal magnetic systems (in which there is no crystallographic symmetry change at the phase transition). The birefringence is shown to vary as ( pi ) for case (i); as the secondary parameter ( pi alpha pi alpha )-(1/n) sigma alpha ( pi alpha pi alpha ) for case (ii); as ( pi )2 for case (iii); and as the energy for case (iv). The advantage of birefringence is that it is not sensitive to fluctuations, while the disadvantages are that one must work with a single-domain single crystal of a transparent substance.
The use of the relativistic and spin-polarized real-space Korringa-Kohn-Rostoker (KKR) method is limited to small systems (less than 100 atoms). This is due to the prohibitively large CPU times needed for the inversion of the KKR matrix. To study systems of more than a thousand atoms, we have implemented the concept of a screened reference medium, within the fully relativistic spin-polarized version of the real-space locally self-consistent multiple-scattering method (LSMS). The LSMS method makes use of a local interaction zone (LIZ) for solving the quantum mechanical problem, while the Poisson equation is solved in the whole space. The screened reference medium gives rise to sparse KKR matrices and using state-of-the-art sparse matrix technology a substantial reduction in the CPU times is obtained, enabling applications of the method to systems whose LIZ consists of more than a thousand atoms. The method is benchmarked by application to the elemental transition metals, the fcc (face-centred-cubic) Co and Ni, and the bcc (body-centred cubic) Fe, and compared to the results of the conventional k-space methods. The convergence in real space of the magnetic moments, the magnetocrystalline anisotropy energy and the orbital moment anisotropy is discussed in detail.
For pt.I see ibid., vol.10, p.2937 (1977). The authors have measured changes in linear birefringence ( Delta n) associated with the cooperative Jahn-Teller phase transition of DyVO4 near 14K as a function of temperature and magnetic fields, B, between 0.024 and 0.095 T. Theoretical arguments show that Delta n is directly proportional to the order parameter of the transition and that B2 is equivalent to the conjugate ordering field. By extrapolation to zero field they obtain the temperature dependence of the order parameter and the susceptibility. The data are compared with calculations based on a mean-field 'compressible' Ising model. For a reasonable choice of adjustable parameters this classical description gives a good fit to the data close to TD consistent with general theoretical arguments and more detailed calculations, but it deviates progressively away from TD presumably because of the known importance of short-range interactions in the system.
The co-operative Jahn-Teller effect is a phase transition which is driven by the interaction between localized orbital electronic states and the crystal lattice. The possible origins, symmetries and properties of the electron-lattice interactions and how they lead to possible hamiltonians for the coupled system are discussed. The relation of these interactions with quadrupolar interactions and magnetostriction is included. The methods of solution of the hamiltonians lead to an understanding of the electronic states, the phonon spectrum and the mixed normal modes. The wide variety of experimental techniques used on this problem are reviewed in detail and the results are compared with theoretical expressions whenever possible. The application of external stress and magnetic field is of particular significance in the case of the rare earth compounds, because they can product effects which are larger than the low-temperature spontaneous effects.
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