Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.

Some defects in two-dimensional spin-1/2 Heisenberg antiferromagnets: a numerical study of magnetic effects

En del av de intressantaste fenomenen inom dagens materialfysik uppstår ur ett intrikat samspel mellan myriader av elektroner. Högtemperatursupraledare är det mest berömda exemplet. Varken klassiska teorier eller modeller där elektronerna är oberoende av varandra kan förklara de häpnadsväckande effekterna i de starkt korrelerade elektronsystemen. I vissa kopparoxider, till exempel La2CuO4, är det känt att valenselektronerna till följd av en stark ömsesidig växelverkan lokaliseras en och en till kopparatomerna i föreningens CuO2 plan. Laddningarnas inneboende magnetiska moment—spinnet—får då en avgörande roll för materialets elektriska och magnetiska egenskaper, vilka i exemplets fall kan beskrivas med Heisenbergmodellen som är den grundläggande teoretiska modellen för mikroskopisk magnetism. Men exakt varför föreningarna kan bli supraledande då de dopas med överskottsladdningar är än så länge en obesvarad fråga. Min avhandling undersöker orenheters inverkan på Heisenbergmodellens magnetiska egenskaper—ett problem av både experimentell och teoretisk relevans. En etablerad numerisk metod har använts—en kvantmekanisk Monte Carlo teknik—för att utföra omfattande datorsimuleringar av den matematiska modellen på två dedikerade Linux datorkluster. Arbetet hör till området beräkningsfysik. De teoretiska modellerna för starkt korrelerade elektronsystem, däribland Heisenbergmodellen, är ytterst invecklade matematiskt sett och de kan inte lösas exakt. Analytiska utredningar bygger för det mesta på antaganden och förenklingar vars inverkningar på slutresultatet är ofta oklara. I det avseende kan numeriska studier vara exakta, det vill säga de kan behandla modellerna som de är. Oftast behövs bägge tillvägagångssätten. Den röda tråden i arbetet har varit att numeriskt testa vissa högaktuella analytiska förutsägelser rörande effekterna av orenheter i Heisenbergmodellen. En del av dem har vi på basen av mycket noggranna data kunnat bekräfta. Men våra resultat har också påvisat felaktigheter i de analytiska prognoserna som sedermera delvis reviderats. En del av avhandlingens numeriska upptäckter har i sin tur stimulerat till helt nya teoretiska studier.

Études de l’effet tunnel des spins quantiques macroscopiques

Dans cette thèse, nous présentons quelques analyses théoriques récentes ainsi que des observations expérimentales de l’effet tunnel quantique macroscopique et des tran- sitions de phase classique-quantique dans le taux d’échappement des systèmes de spins élevés. Nous considérons les systèmes de spin biaxial et ferromagnétiques. Grâce à l’approche de l’intégral de chemin utilisant les états cohérents de spin exprimés dans le système de coordonnées, nous calculons l’interférence des phases quantiques et leur distribution énergétique. Nous présentons une exposition claire de l’effet tunnel dans les systèmes antiferromagnétiques en présence d’un couplage d’échange dimère et d’une anisotropie le long de l’axe de magnétisation aisé. Nous obtenons l’énergie et la fonc- tion d’onde de l’état fondamentale ainsi que le premier état excité pour les systèmes de spins entiers et demi-entiers impairs. Nos résultats sont confirmés par un calcul utilisant la théorie des perturbations à grand ordre et avec la méthode de l’intégral de chemin qui est indépendant du système de coordonnées. Nous présentons aussi une explica- tion claire de la méthode du potentiel effectif, qui nous laisse faire une application d’un système de spin quantique vers un problème de mécanique quantique d’une particule. Nous utilisons cette méthode pour analyser nos modèles, mais avec la contrainte d’un champ magnétique externe ajouté. La méthode nous permet de considérer les transitions classiques-quantique dans le taux d’échappement dans ces systèmes. Nous obtenons le diagramme de phases ainsi que les températures critiques du passage entre les deux régimes. Nous étendons notre analyse à une chaine de spins d’Heisenberg antiferro- magnétique avec une anisotropie le long d’un axe pour N sites, prenant des conditions frontière périodiques. Pour N paire, nous montrons que l’état fondamental est non- dégénéré et donné par la superposition des deux états de Néel. Pour N impair, l’état de Néel contient un soliton, et, car la position du soliton est indéterminée, l’état fondamen- tal est N fois dégénéré. Dans la limite perturbative pour l’interaction d’Heisenberg, les fluctuations quantiques lèvent la dégénérescence et les N états se réorganisent dans une bande. Nous montrons qu’à l’ordre 2s, où s est la valeur de chaque spin dans la théorie des perturbations dégénérées, la bande est formée. L’état fondamental est dégénéré pour s entier, mais deux fois dégénéré pour s un demi-entier impair, comme prévu par le théorème de Kramer

Absence of collective effects in Heisenberg systems with localized magnetic moments

Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF3, K2NiF4, NiO, and La2CuO4. Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved.

Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.

Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Observation of two-magnon bound states in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl2-4SC(NH2)(2)

Results of systematic tunable-frequency ESR studies of the spin dynamics in NiCl2-4SC(NH2)(2) (known as DTN), a gapped S = 1 chain system with easy-plane anisotropy dominating over the exchange coupling (large-D chain), are presented. We have obtained direct evidence for two-magnon bound states, predicted for S = 1 large-D spin chains in the fully spin-polarized (FSP) phase. The frequency-field dependence of the corresponding excitations was calculated using the set of parameters obtained earlier [S.A. Zvyagin, et al., Phys. Rev. Lett. 98 (2007) 047205]. Very good agreement between the calculations and the experiment was obtained. It is argued that the observation of transitions from the ground to two-magnon bound states might indicate a more complex picture of magnetic interactions in DTN, involving a finite in-plane anisotropy. (C) 2007 Elsevier B.V. All rights reserved.

Spin-density functional for exchange anisotropic Heisenberg model

Ground-state energies for anti ferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains. (C) 2009 Elsevier B.V. All rights reserved.

THE PYROCHLORE SUPERGROUP OF MINERALS: NOMENCLATURE

A new scheme of nomenclature for the pyrochlore supergroup, approved by the CNMNC-IMA, is based on the ions at the A, B and Y sites. What has been referred to until now as the pyrochlore group should be referred to as the pyrochlore supergroup, and the subgroups should be changed to groups. Five groups are recommended, based on the atomic proportions of the B atoms Nb, Ta, Sb, Ti, and W. The recommended groups are pyrochlore, microlite, romite, betafite, and elsmoreite, respectively. The new names are composed of two prefixes and one root name (identical to the name of the group). The first prefix refers to the dominant anion (or cation) of the dominant valence [or H(2)O or rectangle] at the Y site. The second prefix refers to the dominant cation of the dominant valence [or H(2)O or rectangle] at the A site. The prefix "" keno-"" represents "" vacancy"". Where the first and second prefixes are equal, then only one prefix is applied. Complete descriptions are missing for the majority of the pyrochlore-supergroup species. Only seven names refer to valid species on the grounds of their complete descriptions: oxycalciopyrochlore, hydropyrochlore, hydroxykenomicrolite, oxystannomicrolite, oxystibiomicrolite, hydroxycalcioromite, and hydrokenoelsmoreite. Fluornatromicrolite is an IMA-approved mineral, but the complete description has not yet been published. The following 20 names refer to minerals that need to be completely described in order to be approved as valid species: hydroxycalciopyrochlore, fluornatropyrochlore, fluorcalciopyrochlore, fluorstrontiopyrochlore, fluorkenopyrochlore, oxynatropyrochlore, oxyplumbopyrochlore, oxyyttropyrochlore-(Y), kenoplumbopyrochlore, fluorcalciomicrolite, oxycalciomicrolite, kenoplumbomicrolite, hydromicrolite, hydrokenomicrolite, oxycalciobetafite, oxyuranobetafite, fluornatroromite, fluorcalcioromte, oxycalcioromite, and oxyplumboromite. For these, there are only chemical or crystalstructure data. Type specimens need to be defined. Potential candidates for several other species exist, but are not sufficiently well characterized to grant them any official status. Ancient chemical data refer to wet-chemical analyses and commonly represent a mixture of minerals. These data were not used here. All data used represent results of electron-microprobe analyses or were obtained by crystal-structure refinement. We also verified the scarcity of crystal-chemical data in the literature. There are crystalstructure determinations published for only nine pyrochlore-supergroup minerals: hydropyrochlore, hydroxykenomicrolite, hydroxycalcioromite, hydrokenoelsmoreite, hydroxycalciopyrochlore, fluorcalciopyrochlore, kenoplumbomicrolite, oxycalciobetafite, and fluornatroromite. The following mineral names are now discarded: alumotungstite, bariomicrolite, bariopyrochlore, bindheimite, bismutomicrolite, bismutopyrochlore, bismutostibiconite, calciobetafite, ceriopyrochlore-(Ce), cesstibtantite, ferritungstite, jixianite, kalipyrochlore, monimolite, natrobistantite, partzite, plumbobetafite, plumbomicrolite, plumbopyrochlore, stannomicrolite, stetefeldtite, stibiconite, stibiobetafite, stibiomicrolite, strontiopyrochlore, uranmicrolite, uranpyrochlore, yttrobetafite-(Y), and yttropyrochlore-(Y).

Preparation of pyrochlore-free PMN by an alternative chemical method

This work reports the synthesis of the MgNb(2)O(6) and the ferroelectric lead magnesium niobate Pb(Mg(1/3)Nb(2/3))O(3) (PMN) using fine precursor powders obtained from a chemical Oxide Precursor Method (OPM). To obtain pyrochlore-free PMN ceramics, the synthesis of the precursor MgNb(2)O(6) powders was studied for 2-25 mol% excess of MgO and 10 mol% excess of PbO. Structural and microstructural properties of the sintered ceramics obtained by the cited method and by the classical columbite method were studied and compared. Results lead to good quality, pyrochlore-free PMN ceramic prepared by OPM, presenting greater grain size if compared with ceramic prepared by columbite method.

BORN-INFELD ELECTRODYNAMICS and EULER-HEISENBERG-LIKE MODEL: OUTSTANDING EXAMPLES of THE LACK of COMMUTATIVITY AMONG QUANTIZED TRUNCATED ACTIONS and TRUNCATED QUANTIZED ACTIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)