Complex magnetism in ultra-thin films: atomic-scale spin structures and resolution by the spin-polarized scanning tunneling microscope

In this paper we present a density functional theory investigation of complex magnetic structures in ultra-thin films. The focus is on magnetically frustrated antiferromagnetic Cr and Mn monolayers deposited on a triangular lattice provided by a Ag (111) substrate. This involves non-collinear magnetic structures, which we treat by first-principles calculations on the basis of the vector spin-density formulation of the density functional theory. We find for Cr/Ag (111) a coplanar non-collinear periodic 120° Néel structure, for Mn/Ag (111) a row-wise antiferromagnetic structure, and for Fe/Ag (111) a ferromagnetic structure as magnetic ground states. The spin-polarized scanning tunneling microscope (SP–STM) operated in the constant-current mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent atoms. We discuss a recent application of this operation mode of the SP–STM on Mn/W (110), which led to the first observation of a two-dimensional antiferromagnet on a non-magnetic metal. The future potential of this approach is demonstrated by calculating SP–STM images for different magnetic structures of Cr/Ag (111). The results show that the predicted non-collinear magnetic ground state structure can clearly be discriminated from competing magnetic structures. A general discussion of the application of different operation modes of the SP–STM is presented on the basis of the model of Tersoff and Hamann. Received: 07 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators.     

THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Heterobimetallische phosphanido-verbrückte Zweikern-Komplexe - Synthese von cis-rac-[(η-C5H4R)2Zr{μ-PH(2,4,6−iPr3C6H2)}2M(CO)4] (RMe,MCr,Mo; RH,MMo)

Heterobimetallic Phosphanido-bridged Dinuclear Complexes - Syntheses of cis-rac-[(η-C₅H₄R)₂Zr{μ-PH(2,4,6-ⁱPr₃C₆H₂)}₂M(CO)₄] (R?Me, M?Cr, Mo; R?H, M?Mo) The zirconocene bisphosphanido complexes [(η-C₅H₄R)₂Zr{PH(2,4,6-ⁱPr₃C₆H₂)}₂] (R?Me, H) react with [(NBD)M(CO)₄] (NBD?norbornadiene, M?Cr, Mo) to give only one diastereomer of the phosphanido-bridged heterobimetallic dinuclear complexes cis-rac-[(η-C₅H₄R)₂Zr{μ-PH(2,4,6-ⁱPr₃C₆H₂)}₂M(CO)₄] [R?Me, M?Cr ( 1 ), Mo ( 2 ); R?H, M?Mo ( 3 )]. However, no reaction was observed between [(η-C₅H₅)₂Zr{PH(2,4,6-^tBu₃ C₆H₂)}₂] and [Pt(PPh₃)₄]. 1—3 were characterised spectroscopically. For 1—3 , the presence of the racemic isomer was shown by NMR spectroscopy. No reaction was observed at room temperature for 3 and CS₂, (NO)BF₄, Me₃NO or PH(2,4,6-Me₃C₆H₂)₂. With Et₂AlH or PhC?CH decomposition of 3 was observed.     

Formation of Zn(1-x)MnxS nanowires within mesoporous silica of different pore sizes

Arrays of highly ordered Zn(1-x)MnxS quantum wires with x ranging from 0.01 to 0.3 and with lateral dimensions of 3, 6, and 9 nm were synthesized within mesoporous SiO2 host structures of the MCM-41 and SBA-15 type. The hexagonal symmetry of these arrays (space group p6m) and the high degree of order was confirmed by X-ray diffraction and transmission electron microscopy (TEM) studies. Physisorption measurements show the progressive filling of the pores of the SiO2 host structures, while TEM and Raman studies reveal the wire-like character of the incorporated Zn(1-x)MnxS nanostructures. X-ray absorption near-edge structure, extended X-ray absorption fine structure, photoluminescence excitation (PLE), and electron paramagnetic resonance studies confirm the good crystalline quality of the incorporated Zn(1-x)MnxS guest species and, in particular, that the Mn2+ ions are randomly distributed and are situated on tetrahedrally coordinated cation sites of the Zn(1-x)MnxS wires for all x up to 0.3. The amount of Mn2+ ions loosely bound to the surface of the Zn(1-x)MnxS nanowires is less than 4% of the total Mn content even for the 3 nm nanostructures up to the highest Mn content of x = 0.3. The effects of the reduction of the lateral dimensions on electronic properties of the diluted magnetic semiconductor were studied by PLE spectroscopy. Due to the quantum confinement of the excitons in the wires an increase of the direct band gap with decreasing particle size is observed.