Inelastic neutron scattering experiments were performed to study manganese(II) dimer excitations in the diluted one-, two-, and three-dimensional compounds CsMn(x)Mg(1-x)Br(3), K(2)Mn(x)Zn(1-x)F(4), and KMn(x)Zn(1-x)F(3) (x<0.10), respectively. The t
ransitions from the ground-state singlet to the excited triplet, split into a doublet and a singlet due to the single-ion anisotropy, exhibit remarkable fine structures. These unusual features are attributed to local structural inhomogeneities induced by the dopant Mn atoms which act like lattice defects. Statistical models support the theoretically predicted decay of atomic displacements according to 1/r**2, 1/r, and constant (for three-, two-, and one-dimensional compounds, respectively) where r denotes the distance of the displaced atoms from the defect. The observed fine structures allow a direct determination of the local exchange interactions J, and the local intradimer distances R can be derived through the linear law dJ/dR.
We present results of inelastic neutron scattering experiments performed for the compound Magnetic and neutron spectroscopic properties of the tetrameric nickel compound $[Mo_{12}O_{28}(mu_2-OH)_9(mu_3-OH)_3{Ni(H_2O)_3}_4] $cdot$ 13H_2O$, which is a
molecular magnet with antiferromagnetically coupled Ni2+ ions forming nearly ideal tetrahedra in a diamagnetic molybdate matrix. The neutron spectroscopic data are analyzed together with high-field magnetization data (taken from the literature) which exhibit four steps at non-equidistant field intervals. The experimental data can be excellently described by antiferromagnetic Heisenberg-type exchange interactions as well as an axial single-ion anisotropy within a distorted tetrahedron of Ni2+ ions characterized by X-ray single-crystal diffraction. Our analysis contrasts to recently proposed models which are based on the existence of extremely large biquadratic (and three-ion) exchange interactions and/or on a strong field dependence of the Heisenberg coupling parameters.
In a previous article we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler manifolds. In the present article we study the limiting case, i. e. manifolds where the lower bound is attained as an eigenvalue. We give an
equivalent formulation in terms of a quaternionic Killing equation and show that the only symmetric quaternionic Kaehler manifolds with smallest possible eigenvalue are the quaternionic projective spaces.
