Search results for "ZEE"
showing 6 items of 106 documents
Crystal field and magnetism with Wannier functions: Rare-earth doped aluminum garnets
2015
Using the recently developed method we calculate the crystal field parameters in yttrium and lutetium aluminum garnets doped with seven trivalent Kramers rare-earth ions. We then insert calculated parameters into the atomic-like Hamiltonian taking into account the electron-electron, spin-orbit and Zeeman interactions and determine the multiplet splitting by the crystal field as well as magnetic $\hat{g}$ tensors. We compare calculated results with available experimental data.
Eulerin summia
2014
Tämän tutkielman tarkoituksena on tarkastella menetelmiä joilla voidaan laskea niin kutsuttuja Eulerin summia. Eulerin summia ovat Riemannin zeeta-funktion arvoja parillisissa ja positiivisissa kokonaislukupisteissä. Vaikka kyseessä on ääretön joukko äärettömiä summia, niin Eulerin summien laskemiseksi on mahdollista johtaa eksplisiittinen kaava. Tämä kaava johdetaan tutkielmassa kahdella eri tavalla: Bernoullin lukuja ja toisaalta Fourier-analyysin tuloksia hyödyntäen. Lisäksi tutkielmassa tarkastellaan muutamia menetelmiä, joilla voidaan laskea yksittäisiä Eulerin summia. Huomionarvoinen maininta on, että vaikka mielivaltainen äärellinen Eulerin osasumma on rationaalinen, niin kaikki Eule…
Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta.
2011
In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demons…
Spin-lattice relaxation of deuterated methyl groups: Implications of the pauli principle
1999
The high-field spin-lattice relaxation of deuterated methyl groups undergoing rotational tunneling is investigated theoretically. It is found that for systems showing a tunneling frequency comparable to accessible Larmor frequencies the relaxation to equilibrium of the Zeeman energy does not follow a simple exponential time dependence even in powdered samples due to a finite coupling to the relaxation of the tunneling system. This finding contrasts to the high-temperature behavior of reorienting methyl groups which undergo simple exponential relaxation. The nonexponentiality has its origin in the statistical coupling of the three deuteron spins due to the Pauli principle.
Long-range spin accumulation from heat injection in mesoscopic superconductors with Zeeman splitting
2015
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