Geometrical frustration in an elemental solid: An Ising model to explain the defect structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-rhombohedral boron

Ogitsu, Tadashi; Gygi, François; Reed, John; Udagawa, Masafumi; Motome, Yukitoshi; Schwegler, Eric; Galli, Giulia

doi:10.1103/physrevb.81.020102

Cited by 45 publications

(60 citation statements)

References 24 publications

(33 reference statements)

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“…for the extraordinary strong correlation is probably the interaction of 3d atoms with the unique system of the antiferromagnetically organized, partially occupied regular boron sites B(16)-B(20), as recently described by Ogitsu et al [54,55] A systematic Raman study on the changes in the intraand inter-icosahedral force constants upon the interstitial accommodation of foreign atoms in β-rhombohedral boron is in progress.…”

Section: Force Constantsmentioning

confidence: 99%

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Raman effect in icosahedral boron-rich solids

Werheit¹,

Филипов

Kuhlmann

et al. 2010

Science and Technology of Advanced Materials

130

116

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We present Raman spectra of numerous icosahedral boron-rich solids having the structure of α-rhombohedral, β-rhombohedral, α-tetragonal, β-tetragonal, YB 66 , orthorhombic or amorphous boron. The spectra were newly measured and, in some cases, compared with reported data and discussed. We emphasize the importance of a high signal-to-noise ratio in the Raman spectra for detecting weak effects evoked by the modification of compounds, accommodation of interstitial atoms and other structural defects. Vibrations of the icosahedra, occurring in all the spectra, are interpreted using the description of modes in α-rhombohedral boron by Beckel et al. The Raman spectrum of boron carbide is largely clarified. Relative intra-and inter-icosahedral bonding forces are estimated for the different structural groups and for vanadium-doped β-rhombohedral boron. The validity of Badger's rule is demonstrated for the force constants of inter-icosahedral B-B bonds, whereas the agreement is less satisfactory for the intra-icosahedral B-B bonds.

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Section: Force Constantsmentioning

confidence: 99%

“…Ogitsu et al [54,55]. describe the partial occupancies of the sites B (13) The claimed purity of our samples (Wacker, Munich) is 99.9999% for any contaminant except carbon (typically 60 ppm).…”

Section: β-Rhombohedral Boron Structure Groupmentioning

confidence: 99%

Raman effect in icosahedral boron-rich solids

Werheit¹,

Филипов

Kuhlmann

et al. 2010

Science and Technology of Advanced Materials

130

116

View full text Add to dashboard Cite

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“…Frustration is most commonly associated with spin systems [1], where its consequences can be particularly well identified, but is by no means limited to magnetism. Frustrated interactions are also relevant in certain structural problems [2][3][4][5][6] Interest in frustrated spin systems stems from the idea that conventional order will be suppressed by the frustration, and an unconventional state will appear in its place. For example, Anderson proposed that in high temperature superconductors, antiferromagnetic Néel ordering would be replaced by a resonating valence bond state (RVB) [17], which would host the superconductivity on doping.…”

Section: Preamblementioning

confidence: 99%

“…Frustration is most commonly associated with spin systems [1], where its consequences can be particularly well identified, but is by no means limited to magnetism. Frustrated interactions are also relevant in certain structural problems [2][3][4][5][6], colloids and liquid crystals [7], spin glasses [8], stripe phases [9,10], Josephson junction arrays [11], stellar nuclear matter [12,13], social dynamics [14], origami [15], and protein folding [16], to name a few.…”

Section: Preamblementioning

confidence: 99%

Neutron scattering studies of spin ices and spin liquids

Fennell

2014

Journées de la Neutronique

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Abstract. In frustrated magnets, competition between interactions, usually due to incompatible lattice and exchange geometries, produces an extensively degenerate manifold of groundstates. Exploration of these states results in a highly correlated and strongly fluctuating cooperative paramagnet, a broad classification which includes phases such as spin liquids and spin ices. Generally, there is no long range order and associated broken symmetry, so quantities typically measured by neutron scattering such as magnetic Bragg peaks and magnon dispersions are absent. Instead, spin correlations characterized by emergent gauge structure and exotic fractional quasiparticles may emerge. Neutron scattering is still an excellent tool for the investigation these phenomena, and this review outlines examples of frustrated magnets on the pyrochlore and kagome lattices with reference to experiments and quantities of interest for neutron scattering. PREAMBLEIn physics, a frustrated system is one in which all interactions cannot be simultaneously minimized, which is also to say that there is competition amongst the interactions. Frustration is most commonly associated with spin systems [1], where its consequences can be particularly well identified, but is by no means limited to magnetism. Frustrated interactions are also relevant in certain structural problems [2][3][4][5][6] Interest in frustrated spin systems stems from the idea that conventional order will be suppressed by the frustration, and an unconventional state will appear in its place. For example, Anderson proposed that in high temperature superconductors, antiferromagnetic Néel ordering would be replaced by a resonating valence bond state (RVB) [17], which would host the superconductivity on doping. If the RVB state could be promoted by enhancing frustration, a route to high(er)-T c materials might appear. This has never been realized, and understanding the character of the "unconventional" states, particularly the quantum spin liquid, which emerge in frustrated magnets is usually the objective of current studies.Extensive reviews of topics in frustrated magnetism can be found in the books edited by Lacroix, Mendels and Mila [1], and by Diep [18]. Topics recently reviewed in the literature include quantum spin liquids [19,20]; various aspects of spin ice [21][22][23]; rare earth pyrochlores [24], spinels [25]; and spin ices and kagome spin liquids have their own chapters in Ref. [1]. In the following, I present a brief This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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“…Given the very small energy differences (per atom) among competing structures, it is not certain that DFT is of sufficient accuracy to correctly address the relative stabilities. In fact, the situation is reminiscient of a frustrated system [28]. To further test the reliability of our energy calculations requires climbing the "ladder of density functionals" [29].…”

Section: A Structural Stabilitymentioning

confidence: 99%

VASP on a GPU: Application to exact-exchange calculations of the stability of elemental boron

Hutchinson

Widom

2012

Computer Physics Communications

142

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General purpose graphical processing units (GPU's) offer high processing speeds for certain classes of highly parallelizable computations, such as matrix operations and Fourier transforms, that lie at the heart of first-principles electronic structure calculations. Inclusion of exact-exchange increases the cost of density functional theory by orders of magnitude, motivating the use of GPU's. Porting the widely used electronic density functional code VASP to run on a GPU results in a 5-20 fold performance boost of exact-exchange compared with a traditional CPU. We analyze performance bottlenecks and discuss classes of problems that will benefit from the GPU. As an illustration of the capabilities of this implementation, we calculate the lattice stability α-and β-rhombohedral boron structures utilizing exact-exchange. Our results confirm the energetic preference for symmetrybreaking partial occupation of the β-rhombohedral structure at low temperatures, but does not resolve the stability of α relative to β.

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Geometrical frustration in an elemental solid: An Ising model to explain the defect structure ofβ-rhombohedral boron

Cited by 45 publications

References 24 publications

Raman effect in icosahedral boron-rich solids

Raman effect in icosahedral boron-rich solids

Neutron scattering studies of spin ices and spin liquids

VASP on a GPU: Application to exact-exchange calculations of the stability of elemental boron

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