Derivation of the spin Hamiltonians for Fe in MgO

A method to calculate the effective spin Hamiltonian for a transition metal impurity in a non- magnetic insulating host is presented and applied to the paradigmatic case of Fe in MgO. In a first step we calculate the electronic structure employing standard density functional theory (DFT), based on generalized-gradient approximation (GGA), using plane waves as a basis set. The corresponding basis of atomic-like maximally localized Wannier functions is derived and used to represent the DFT Hamiltonian, resulting in a tight-binding model for the atomic orbitals of the magnetic impurity. The third step is to solve, by exact numerical diagonalization, the N electron problem in the open shell of the magnetic atom, including both effect of spin-orbit and Coulomb repulsion. Finally, the low energy sector of this multi-electron Hamiltonian is mapped into effective spin models that, in addition to the spin matrices S, can also include the orbital angular momentum L when appropriate. We successfully apply the method to Fe in MgO, considering both, the undistorted and Jahn-Teller (JT) distorted cases. Implications for the influence of Fe impurities on the performance of magnetic tunnel junctions based on MgO are discussed.Comment: 10 pages, 7 Figure

Electronic properties of transition metal atoms on Cu2_2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co and Ni) deposited on a Cu$_2$N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent Nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent Nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.Comment: 12 pages, 14 figures, regular articl

Electronic properties of transition metal atoms on Cu2_2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co and Ni) deposited on a Cu$_2$N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent Nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent Nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.Comment: 12 pages, 14 figures, regular articl

Enseñar matemáticas con recursos de ajedrez

This article synthesize two studies obove construction, validation and aplication of didactic material for maths teaching. Realitzed between 2006 and 2008, is centred various experiences of utilitzation of didactic material in the teaching of the maths in the stage of primary education. The aportation have how finality show a serie of manipulation materials, innovating and motivating to the maths teaching with the help of chess resources. Is characterized in this article, the didactic material is analized the game how resource and is especificated the make of chess resources in the maths teaching.El presente artículo sintetiza dos estudios realizados sobre la construcción, validación y aplicación de material didáctico para la enseñanza de las matemáticas. Realizados entre 2006 y 2008, se centraron en varias experiencias de utilización de material didáctico con recursos de ajedrez en la enseñanza de las matemáticas en la etapa de educación primaria. La aportación tiene como finalidad mostrar una serie de materiales manipulativos, innovadores y motivadores para la enseñanza de las matemáticas con recursos ajedrecísticos. Se caracteriza en este artículo el material didáctico, se analiza el juego como recurso y se especifica la utilización de recursos de ajedrez en la enseñanza de las matemáticas. Se describen, diseñan y fundamentan materiales con elementos de ajedrez que permitan una enseñanza de las matemáticas de una manera más amena, divertida, innovadora y educativa; también, se presentan los datos sobre su influencia en capacidades como el razonamiento lógico y el cálculo numérico. Finalmente, se presentan en forma de conclusiones y propuestas algunas indicaciones para la enseñanza

Descartes y el sueño

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¿Es que tiene la ciencia algún sentido?

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