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Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects
Authors:
Andreas Alvermann,
Achim Basermann,
Hans-Joachim Bungartz,
Christian Carbogno,
Dominik Ernst,
Holger Fehske,
Yasunori Futamura,
Martin Galgon,
Georg Hager,
Sarah Huber,
Thomas Huckle,
Akihiro Ida,
Akira Imakura,
Masatoshi Kawai,
Simone Köcher,
Moritz Kreutzer,
Pavel Kus,
Bruno Lang,
Hermann Lederer,
Valeriy Manin,
Andreas Marek,
Kengo Nakajima,
Lydia Nemec,
Karsten Reuter,
Michael Rippl
, et al. (8 additional authors not shown)
Abstract:
We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highl…
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We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.
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Submitted 4 June, 2018;
originally announced June 2018.
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Lack of coupling between superconductivity and orthorhombic distortion in stoichiometric single-crystalline FeSe
Authors:
A. E. Böhmer,
F. Hardy,
F. Eilers,
D. Ernst,
P. Adelmann,
P. Schweiss,
T. Wolf,
C. Meingast
Abstract:
The coupling between superconductivity and othorhombic distortion is studied in vapor-grown FeSe single crystals using high-resolution thermal-expansion measurements. In contrast to the Ba122-based (Ba122) superconductors, we find that superconductivity does not reduce the orthorhombicity below Tc. Instead we find that superconductivity couples strongly to the in-plane area, which explains the lar…
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The coupling between superconductivity and othorhombic distortion is studied in vapor-grown FeSe single crystals using high-resolution thermal-expansion measurements. In contrast to the Ba122-based (Ba122) superconductors, we find that superconductivity does not reduce the orthorhombicity below Tc. Instead we find that superconductivity couples strongly to the in-plane area, which explains the large hydrostatic pressure effects. We discuss our results in light of the spinnematic scenario and argue that FeSe has many features quite different from the typical Fe-based superconductors.
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Submitted 8 March, 2013;
originally announced March 2013.
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Magnetic properties of single-crystalline CeCuGa3
Authors:
Devang A. Joshi,
P. Burger,
P. Adelmann,
D. Ernst,
T. Wolf,
K. Sparta,
G. Roth,
K. Grube,
C. Meingast,
H. v. Löhneysen
Abstract:
The magnetic behavior of single-crystalline CeCuGa3 has been investigated. The compound forms in a tetragonal BaAl4-type structure consisting of rare-earth planes separated by Cu-Ga layers. If the Cu-Ga site disorder is reduced, CeCuGa3 adopts the related, likewise tetragonal BaNiSn3-type structure, in which the Ce ion are surrounded by different Cu and Ga layers and the inversion symmetry is lost…
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The magnetic behavior of single-crystalline CeCuGa3 has been investigated. The compound forms in a tetragonal BaAl4-type structure consisting of rare-earth planes separated by Cu-Ga layers. If the Cu-Ga site disorder is reduced, CeCuGa3 adopts the related, likewise tetragonal BaNiSn3-type structure, in which the Ce ion are surrounded by different Cu and Ga layers and the inversion symmetry is lost. In the literature conflicting reports about the magnetic order of CeCuGa3 have been published. Single crystals with the centrosymmetric structure variant exhibit ferromagnetic order below approx. 4 K with a strong planar anisotropy. The magnetic behavior above the transition temperature can be well understood by the crystal-field splitting of the 4f Hund's rule ground-state multiplet of the Ce ions.
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Submitted 19 April, 2012;
originally announced April 2012.
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Thermal expansion and Grüneisen parameters of Ba(Fe1-xCox)2As2 - a thermodynamic quest for quantum criticality
Authors:
Christoph Meingast,
Frédéric Hardy,
Rolf Heid,
Peter Adelmann,
Anna Böhmer,
Philipp Burger,
Doris Ernst,
Rainer Fromknecht,
Peter Schweiss,
Thomas Wolf
Abstract:
Thermal expansion data are used to study the uniaxial pressure dependence of the electronic/magnetic entropy of Ba(Fe1-xCox)2As2. Uniaxial pressure is found to be proportional to doping and, thus, also an appropriate tuning parameter in this system. Many of the features predicted to occur for a pressure-tuned quantum critical system, in which superconductivity is an emergent phase hiding the criti…
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Thermal expansion data are used to study the uniaxial pressure dependence of the electronic/magnetic entropy of Ba(Fe1-xCox)2As2. Uniaxial pressure is found to be proportional to doping and, thus, also an appropriate tuning parameter in this system. Many of the features predicted to occur for a pressure-tuned quantum critical system, in which superconductivity is an emergent phase hiding the critical point, are observed. The electronic/magnetic Grüneisen parameters associated with the spin-density wave and superconducting transitions further demonstrate an intimate connection between both ordering phenomena.
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Submitted 22 December, 2011;
originally announced December 2011.
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Doping evolution of superconducting gaps and electronic densities of states in Ba(Fe1-xCox)2As2 iron pnictides
Authors:
F. Hardy,
P. Burger,
T. Wolf,
R. A. Fisher,
P. Schweiss,
P. Adelmann,
R. Heid,
R. Fromknecht,
R. Eder,
D. Ernst,
H. v. Loehneysen,
C. Meingast
Abstract:
An extensive calorimetric study of the normal- and superconducting-state properties of Ba(Fe1-xCox)2As2 is presented for 0 < x < 0.2. The normal-state Sommerfeld coefficient increases (decreases) with Co doping for x < 0.06 (x > 0.06), which illustrates the strong competition between magnetism and superconductivity to monopolize the Fermi surface in the underdoped region and the filling of the hol…
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An extensive calorimetric study of the normal- and superconducting-state properties of Ba(Fe1-xCox)2As2 is presented for 0 < x < 0.2. The normal-state Sommerfeld coefficient increases (decreases) with Co doping for x < 0.06 (x > 0.06), which illustrates the strong competition between magnetism and superconductivity to monopolize the Fermi surface in the underdoped region and the filling of the hole bands for overdoped Ba(Fe1-xCox)2As2. All superconducting samples exhibit a residual electronic density of states of unknown origin in the zero-temperature limit, which is minimal at optimal doping but increases to the normal-state value in the strongly under- and over-doped regions. The remaining specific heat in the superconducting state is well described using a two-band model with isotropic s-wave superconducting gaps.
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Submitted 13 July, 2010;
originally announced July 2010.
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Phonon spectrum and soft-mode behavior of MgCNi_3
Authors:
R. Heid,
B. Renker,
H. Schober,
P. Adelmann,
D. Ernst,
K. -P. Bohnen
Abstract:
Temperature dependent inelastic neutron-scattering measurements of the generalized phonon density-of-states for superconducting MgCNi_3, T_c=8 K, give evidence for a soft-mode behavior of low-frequency Ni phonon modes. Results are compared with ab initio density functional calculations which suggest an incipient lattice instability of the stoichiometric compound with respect to Ni vibrations ort…
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Temperature dependent inelastic neutron-scattering measurements of the generalized phonon density-of-states for superconducting MgCNi_3, T_c=8 K, give evidence for a soft-mode behavior of low-frequency Ni phonon modes. Results are compared with ab initio density functional calculations which suggest an incipient lattice instability of the stoichiometric compound with respect to Ni vibrations orthogonal to the Ni-C bond direction.
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Submitted 24 October, 2003;
originally announced October 2003.
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High-Resolution Thermal Expansion of MgB2
Authors:
R. Lortz,
C. Meingast,
D. Ernst,
B. Renker,
D. D. Lawrie,
J. P. Franck
Abstract:
The thermal expansion of polycrystalline MgB2 from 5-300 K is studied using high-resolution capacitance dilatometry. The thermal expansivity exhibits a small jump of -5.8x10-8 K-1 at Tc (in accord with expectations from the Ehrenfest relationship and published specific heat and pressure data) and a negative peak-like feature close to 5 K. No indications of any structural instabilities are observ…
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The thermal expansion of polycrystalline MgB2 from 5-300 K is studied using high-resolution capacitance dilatometry. The thermal expansivity exhibits a small jump of -5.8x10-8 K-1 at Tc (in accord with expectations from the Ehrenfest relationship and published specific heat and pressure data) and a negative peak-like feature close to 5 K. No indications of any structural instabilities are observed.
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Submitted 8 July, 2003;
originally announced July 2003.
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Lattice dynamics and electron-phonon coupling in transition metal diborides
Authors:
R. Heid,
B. Renker,
H. Schober,
P. Adelmann,
D. Ernst,
K. -P. Bohnen
Abstract:
The phonon density-of-states of transition metal diborides TMB2 with TM = Ti, V, Ta, Nb and Y has been measured using the technique of inelastic neutron scattering. The experimental data are compared with ab initio density functional calculations whereby an excellent agreement is registered. The calculations thus can be used to obtain electron-phonon spectral functions within the isotropic limit…
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The phonon density-of-states of transition metal diborides TMB2 with TM = Ti, V, Ta, Nb and Y has been measured using the technique of inelastic neutron scattering. The experimental data are compared with ab initio density functional calculations whereby an excellent agreement is registered. The calculations thus can be used to obtain electron-phonon spectral functions within the isotropic limit. A comparison to similar data for MgB2 and AlB2 which were subject of prior publications as well as parameters important for the superconducting properties are part of the discussion.
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Submitted 20 February, 2003;
originally announced February 2003.
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Superconducting energy gap distribution of MgB$_2$ investigated by point-contact spectroscopy
Authors:
F. Laube,
G. Goll,
J. Hagel,
H. v. Löhneysen,
D. Ernst,
T. Wolf
Abstract:
We performed point-contact spectroscopy on the binary superconductor MgB$_2$. The differential conductance shows gap-related structures which vary in width and position from contact to contact. The distribution of energy gaps shows a distinct accumulation around 1.7 and 7 meV which is associated with the occurrence of a small and a large energy gap in MgB$_2$. While with increasing $T$ the struc…
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We performed point-contact spectroscopy on the binary superconductor MgB$_2$. The differential conductance shows gap-related structures which vary in width and position from contact to contact. The distribution of energy gaps shows a distinct accumulation around 1.7 and 7 meV which is associated with the occurrence of a small and a large energy gap in MgB$_2$. While with increasing $T$ the structure in $dI/dV$ associated with the small gap is present up to $T_C$, in magnetic field it is suppressed well below $B_{c2}$.
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Submitted 20 June, 2001;
originally announced June 2001.