In this thesis, anisotropic Heisenberg magnets with arbitrary spin are investigated within the second-order Green-function theory. Three models are considered.
First, the second-order Green-fuction theory for one-dimensional and two-dimensional Heisenberg ferromagnets with arbitrary spin S in a
magnetic field is developed. For the determination of the introduced vertex parameters sum rules, higher-derivative sum rules, and regularity conditions are derived, and the equality of the isothermal and the longitudinal uniform static Kubo susceptibilities is required. Thermodynamic quantities, such as the specific heat, magnetic susceptibility, transverse and longitudinal correlation lengths are calculated. Empirical formulas describing the dependence of the position and height of the susceptibility maximum on the magnetic field are given. An anomal behavior of the longitudinal correlation length is observed. The appearance of two maxima in the temperature dependence of the specific heat is discussed.
Further, as an example of a system with an anisotropy in the spin space, the S=1 ferromagnetic chain with easy-axis single-ion anisotropy is studied. Justified by the up-down symmetry of the model with respect to $S_i^z -> -S_i^z$, $\\langle S_i^z \\rangle=0$ is set. Two different ways of the determination of the introduced vertex parameters are presented. The transverse nearest-neighbor correlation function, spin-wave spectrum and longitudinal correlation length are analyzed. The effects of the single-ion anisotropy on the transverse and longitudinal uniform static
susceptibilities as well as on the appearance of two maxima in the temperature dependence of the specific heat are examined.
Finally, as examples of spatial anisotropic spin systems,layered Heisenberg
ferromagnets and antiferromagnets with arbitrary spin are studied within the rotation-invariant Green-function theory. The long-range order is described by the condensation term, which is determined from the requirement that in the ordered state the static susceptibility has to diverge at the ordering wave vector. For determination of the introduced vertex parameters, the sum rule and the isotropy condition are used and also assumptions regarding the temperature dependence of some parameters are made. The main focus is put on the calculation of the specific heat, the Curie temperature, and the Néel temperature in dependence on the interlayer coupling and the spin-quantum number. Empirical formulas describing the dependence of the transition temperatures on the ratio of interlayer and intralayer couplings are given.
For all three models, the results of the Green-function theory are compared to available results of exact approaches (Quantum Monte Carlo, exact diagonalization, Bethe-ansatz method) and to available experimental data.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:11228 |
| Date | 25 May 2011 |
| Creators | Juhász Junger, Irén |
| Contributors | Ihle, Dieter, Nolting, Wolfgang, Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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