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Ferromagnetic coupling and magnetic anisotropy in molecular Ni(II) squares
We investigated the magnetic properties of two isostructural Ni(II) metal
complexes [Ni4Lb8] and [Ni4Lc8]. In each molecule the four Ni(II) centers form
almost perfect regular squares. Magnetic coupling and anisotropy of single
crystals were examined by magnetization measurements and in particular by
high-field torque magnetometry at low temperatures. The data were analyzed in
terms of an effective spin Hamiltonian appropriate for Ni(II) centers. For both
compounds, we found a weak intramolecular ferromagnetic coupling of the four
Ni(II) spins and sizable single-ion anisotropies of the easy-axis type. The
coupling strengths are roughly identical for both compounds, whereas the
zero-field-splitting parameters are significantly different. Possible reasons
for this observation are discussed.Comment: 7 pages, 7 figure
Locality in GNS Representations of Deformation Quantization
In the framework of deformation quantization we apply the formal GNS
construction to find representations of the deformed algebras in pre-Hilbert
spaces over and establish the notion of local operators
in these pre-Hilbert spaces. The commutant within the local operators is used
to distinguish `thermal' from `pure' representations. The computation of the
local commutant is exemplified in various situations leading to the physically
reasonable distinction between thermal representations and pure ones. Moreover,
an analogue of von Neumann's double commutant theorem is proved in the
particular situation of a GNS representation with respect to a KMS functional
and for the Schr\"odinger representation on cotangent bundles. Finally we prove
a formal version of the Tomita-Takesaki theorem.Comment: LaTeX2e, 29 page
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