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Superconductivity mediated by a soft phonon mode: Specific heat, resistivity, thermal expansion, and magnetization of YB6

R. Lortz, Y. Wang, U. Tutsch, S. Abe, C. Meingast, P. Popovich, W. Knafo, N. Shitsevalova, Yu. B. Paderno, and A. Junod
Phys. Rev. B 73, 024512 – Published 26 January 2006

Abstract

The superconductor YB6 has the second highest critical temperature Tc among the boride family MBn. We report measurements of the specific heat, resistivity, magnetic susceptibility, and thermal expansion from 2to300K, using a single crystal with Tc=7.2K. The superconducting gap is characteristic of medium-strong coupling. The specific heat, resistivity, and expansivity curves are deconvolved to yield approximations of the phonon density of states F(ω), the spectral electron-phonon scattering function αtr2F(ω), and the phonon density of states weighted by the frequency-dependent Grüneisen parameter γG(ω)F(ω), respectively. Lattice vibrations extend to high frequencies >100meV, but a dominant Einstein-like mode at 8meV, associated with the vibrations of yttrium ions in oversized boron cages, appears to provide most of the superconducting coupling and gives rise to an unusual temperature behavior of several observable quantities. A surface critical field Hc3 is also observed.

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  • Received 20 October 2005

DOI:https://doi.org/10.1103/PhysRevB.73.024512

©2006 American Physical Society

Authors & Affiliations

R. Lortz1,*, Y. Wang1, U. Tutsch1, S. Abe1, C. Meingast2, P. Popovich2,3, W. Knafo2,3, N. Shitsevalova4, Yu. B. Paderno4,†, and A. Junod1

  • 1Department of Condensed Matter Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
  • 2Forschungszentrum Karlsruhe, Institut für Festkörperphysik, D-76021 Karlsruhe, Germany
  • 3Physikalisches Institut, Universität Karlsruhe, D-76128 Karlsruhe, Germany
  • 4Institute for Problems of Materials Science NASU, 03680 Kiev, Ukraine

  • *Corresponding author. Electronic address: Rolf.Lortz@physics.unige.ch
  • Deceased.

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Vol. 73, Iss. 2 — 1 January 2006

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Images

  • Figure 1
    Figure 1
    Superconducting transition of the YB6 crystal observed by (a) resistivity, (b) ac susceptibility (8kHz, 0.01Grms), and (c) Meissner susceptibility (field cooled, 2.7G).Reuse & Permissions
  • Figure 2
    Figure 2
    Magnetic susceptibility of YB6 in the normal state as a function of the temperature. Solid line: fit (see text). Dashed line: non-Curie part of the fit.Reuse & Permissions
  • Figure 3
    Figure 3
    Total specific heat CT of YB6 in the superconducting state in zero field (solid symbols) and in the normal state in 1T (open symbols) vs the temperature squared.Reuse & Permissions
  • Figure 4
    Figure 4
    BCS plot of the electronic specific heat in the superconducting state normalized by the Sommerfeld constant γn, vs the inverse reduced temperature, data (symbols), and BCS weak-coupling limit (line). The residual contribution γ0T has been subtracted. Inset: deviation function of the thermodynamic critical field (symbols) and BCS weak-coupling limit (dashed line).Reuse & Permissions
  • Figure 5
    Figure 5
    Lattice-specific heat of YB6 vs the temperature up to room temperature. The long-dashed line shows the Debye-specific heat calculated using a constant Debye temperature equal to its minimum θD(16K)=278K, the short-dashed line using the effective value at room temperature θD(300K)=1088K. Inset: effective Debye temperature vs temperature.Reuse & Permissions
  • Figure 6
    Figure 6
    Lattice-specific heat divided by the temperature vs the temperature showing the decomposition into Einstein terms. The labels k correspond to Einstein temperatures ΘE,k=90K×1.75k—i.e. (from left to right), 51, 90, 158, 276, 482, 844, and 1477K.Reuse & Permissions
  • Figure 7
    Figure 7
    Normal-state resistivity of YB6 vs the temperature. Dashed line: residual resistivity. Crosses: residuals of the fit in %. Inset: expanded low-temperature data and polynomial fit. Superconductivity is quenched by a field of 1T.Reuse & Permissions
  • Figure 8
    Figure 8
    Linear thermal expansivity of YB6 vs temperature. Inset: Grüneisen parameter vs temperature, assuming a bulk modulus κT1=190GPa.Reuse & Permissions
  • Figure 9
    Figure 9
    Phonon density of states F(ω) deconvoluted from the specific heat, electron-phonon transport coupling function αtr2F(ω) deconvolved from the resistivity, and spectral anharmonicity function γG(ω)F(ω)(lnωlnV)F(ω) deconvoluted from the thermal expansion. Fits are performed with δ functions Fkδ(ωωk), (αtr2F)kδ(ωωk), and (γGF)kδ(ωωk), respectively, on a basis of Einstein frequencies ωk+1=1.75ωk (see Fig. 6). In order to reflect the spectral density, the δ functions of the PDOS are represented by rectangles having a width Δωk1.7512ωkωk1.75120.57ωk and a height FkΔωk. In a similar way, the δ functions of the αtr2F(ω) function are represented by solid circles at a height (αtr2F)kΔωk0.88λk and those of γG(ω)F(ω) by triangles at a height (γGF)kΔωk. The dashed lines are guides for the eye.Reuse & Permissions
  • Figure 10
    Figure 10
    Difference between the normal-state and superconducting-state linear thermal expansivity near Tc. The idealized jump is shown by a dotted line. Inset: expansivity in the normal and superconducting states.Reuse & Permissions
  • Figure 11
    Figure 11
    Resistivity of YB6 near Tc as a function of the temperature in different magnetic fields.Reuse & Permissions
  • Figure 12
    Figure 12
    Magnetization of YB6 as a function of the magnetic field for different temperatures, virgin curves with increasing field (M in emucm3, 4πM in G). Inset: sample hysteresis curve at 4K (similar curves are obtained from 2to6K).Reuse & Permissions
  • Figure 13
    Figure 13
    Detail of the previous plot at T=5K, expanded 100 times in the inset and 5000 times in the main frame. The normal-state magnetization Mn has been subtracted. Note the absence of any measurable diamagnetism at Hc3=1700G where the resistance drops to zero. Fluctuation diamagnetism sets in smoothly near 1500G. The upper critical field Hc2=1270G defined by the intersection of the extrapolated linear sections in the inset coincides with the position of the specific heat jump.Reuse & Permissions
  • Figure 14
    Figure 14
    Electronic specific heat of YB6 divided by the temperature vs the temperature for different magnetic fields.Reuse & Permissions
  • Figure 15
    Figure 15
    Specific heat difference [C(H,T)C(0,T)]T normalized by the Sommerfeld constant vs TTc in different magnetic fields. The value calculated within the Caroli–Matricon–de Gennes approximation is shown by solid lines at T0.Reuse & Permissions
  • Figure 16
    Figure 16
    Phase diagram of YB6 in the HT plane. From top to bottom: third critical field Hc3(T) defined by zero resistance for H parallel to the current and surface, second upper critical field Hc2(T) given by the position of the specific heat jump (closed diamonds) and the knee of the magnetization (open diamonds), thermodynamic critical field Hc(T) obtained by integration of the specific heat CT (open circles), and lower critical field Hc1(T) given by the position of the sharp minimum of the magnetization (solid circles). All lines are polynomial fits to the data, except for the Hc1(T) line, which is recalculated based on Hc(T) and the Maki parameter κ1(T) (see text). Inset: variation of κ1 with the temperature.Reuse & Permissions
  • Figure 17
    Figure 17
    Thermodynamic critical field Hc(T) of boron-rich (lower-Tc) and boron-deficient (higher-Tc) samples. In this plot, Hc(T) is obtained by integration of the magnetization curves.Reuse & Permissions
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