Search results for "Isotropy"
showing 10 items of 1099 documents
Orbitally dependent kinetic exchange in cobalt(II) pairs: origin of the magnetic anisotropy
2003
Abstract A comprehensive theoretical study of the magnetic exchange between Co 2+ ions is reported. Using the microscopic background we deduce the general Hamiltonian for a corner-shared bioctahedral system involving kinetic exchange, spin–orbit coupling and low-symmetry local crystal field. This Hamiltonian acting within orbitally degenerate ground manifold 4 ( T 1g ) A ⊗ 4 ( T 1g ) B of the cobalt pair is expressed in terms of orbital and spin operators. We elucidate the major electronic factors controlling the exchange anisotropy in the Co(II) pairs. The degree of the magnetic anisotropy is shown to depend on the strength of the cubic crystal field and on the relative efficiency of two k…
Colloidal layers in magnetic fields and under shear flow
2005
The behaviour of colloidal mono- and bilayers in external magnetic fields and under shear is discussed and recent progress is summarized. Superparamagnetic colloidal particles form monolayers when they are confined to a air–water interface in a hanging water droplet. An external magnetic field allows us to tune the strength of the mutual dipole–dipole interaction between the colloids and the anisotropy of the interaction can be controlled by the tilt angle of the magnetic field relative to the surface normal of the air–water interface. For sufficiently large magnetic field strength crystalline monolayers are found. The role of fluctuations in these two-dimensional crystals is discussed. Fur…
Magnetic Exchange between Orbitally Degenerate Metal Ions: The Problem of Magnetic Anisotropy
2001
Abstract In this paper we show that a strong magnetic anisotropy appears in exchange mixed–valence clusters containing orbitally degenerate metal ions. Combining an effective Hamiltonian approach with the technique of the irreducible tensor operators (ITO) and pseudoangular momentum representation we have solved the problem of magnetic exchange in localized and delocalized (mixed–valence) systems with different overall symmetries ( D 2 h , D 3 h , D 4 h ). The energy pattern as well as the character of the magnetic anisotropy is closely related to the ground term of the ions, electron transfer pathways, and overall symmetry of the system being affected also by the local crystal fields, spin…
Anomalies in low-temperature lattice parameters of ErFeO3 and ErAlO3 single crystals: correlation with magnetic properties
2005
Abstract The paper presents the results of an experimental study of thermal expansion of isostructural orthorhombic ErFeO3 and ErAlO3 single crystals. Changes of lattice parameters have been investigated by X-ray measurements in the 10–300 K temperature range. Above ∼150 K, experimental results correspond well to the phonon mechanism. At low temperatures distinct anisotropic anomalies were observed in both compounds; and a correlation with the magnetic properties of the relevant ions is noted.
Magnetic properties of six-coordinated high-spin cobalt(II) complexes: Theoretical background and its application
2008
Abstract In this contribution we study and analyse the influence of the different parameters involved in the magnetic susceptibility of six-coordinated high-spin Co(II) complexes. We propose an empirical expression to fit the magnetic susceptibility of polycrystalline samples of mononuclear Co(II) complexes with an axial distortion, the variable parameters being Δ (axial distortion), α (orbital reduction factor) and λ (spin–orbit coupling). This expression avoids solving the 12 × 12 matrix associated to the distortion of the 4 T 1g term. In order to take into account the magnetic coupling ( J ) in the polynuclear Co(II) complexes, a perturbational approach is proposed to describe their magn…
Lattice and electronic contributions to the refractive index of CuWO4
2014
We report an investigation of the refractive index dispersion and anisotropy in CuWO4 by means of interference measurements in two extinction directions from mid infrared to the visible region of the energy spectrum. The analysis of the refractive index dispersion yields ϵ(∞) = 4.5(1) for light polarization parallel to the c-axis and ϵ(∞) = 5.3(1) with respect to the other extinction axis. In addition, we report reflectance measurements carried out from the far infrared to the near ultraviolet to study the lattice and electronic contributions to the refractive index of CuWO4. We have determined the wavenumbers of nine infrared active lattice modes and compared them with previous ab initio c…
Observing the anisotropic optical response of the heavy-fermion compound UNi2 Al3
2010
The optical conductivity of heavy fermions can reveal fundamental properties of the charge carrier dynamics in these strongly correlated electron systems. Here we extend the conventional techniques of infrared optics on heavy fermions by measuring the transmission and phase shift of THz radiation that passes through a thin film of UNi 2 Al 3 , a material with hexagonal crystal structure. We deduce the optical conductivity in a previously not accessible frequency range, and furthermore we resolve the anisotropy of the optical response (parallel and perpendicular to the hexagonal planes). At frequencies around 7 cm -1 , we find a strongly temperature-dependent and anisotropic optical conducti…
Phonon Scattering through a Local Anisotropic Structural Disorder in the Thermoelectric Solid Solution Cu_2Zn_(1−x)Fe_xGeSe_4
2013
Inspired by the promising thermoelectric properties of chalcopyrite-like quaternary chalcogenides, here we describe the synthesis and characterization of the solid solution Cu(2)Zn(1-x)Fe(x)GeSe(4). Upon substitution of Zn with the isoelectronic Fe, no charge carriers are introduced in these intrinsic semiconductors. However, a change in lattice parameters, expressed in an elongation of the c/a lattice parameter ratio with minimal change in unit cell volume, reveals the existence of a three-stage cation restructuring process of Cu, Zn, and Fe. The resulting local anisotropic structural disorder leads to phonon scattering not normally observed, resulting in an effective approach to reduce th…
Magnetic exchange between metal ions with unquenched orbital angular momenta: basic concepts and relevance to molecular magnetism
2010
This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…
The onset of convection in a two-layered porous medium with anisotropic permeability
2019
We consider convection in a horizontal porous layer of uniform thickness which is heated from below and which is composed of two anisotropic sublayers with principal axes lying in the three coordinate directions. The aim is to determine criteria for the onset of convection by finding the critical Rayleigh number, wavenumber and roll orientation relative to the coordinate axes. The full set of nondimensional parameters has at least six members even when the sublayers are considered to be thermally isotropic, and therefore, we select some special cases in order to illuminate the type of qualitative behaviour which may be expected. One such case is where the anisotropic sublayers are identical…