Comment on “3DX-YScaling of the Specific Heat of YBa2

Abstract

In a recent article, Overend, Howson, and Lawrie [1], subsequently referred to as OHL, gave strong evidence that their specific heat data near T, in a magnetic field were better described by low field critical scaling laws than by the lowest Landau level (LLL) high field approximation, at least up to 8 Tesla. The critical exponents and amplitude ratios were found to be consistent with those observed in the A transition of He. OHL based their conclusion on the excellent scaling obtained using the 3D X-Y model, and the impossibility of scaling their data using the LLL approximation.OHL measured the specific heat C of a mg-size single crystal of YBa2Cu307 s (YBCO) in magnetic fields up to 8T, using an ac technique. Such methods yield only relative values. We have recently measured the specific heat of a much larger crystal (0.29g) of YBCO up to 16T, using a high precision adiabatic, continuous heating method.The weakest part of any scaling attempt is the approximation used for the nonsingular part of the specific heat, since the fluctuation component Cf1 is but a few percent of the total heat capacity Ct,t. OHL use a linear baseline (i.e., C", -Cri = a + bT) situatedfar above the specifi heat peak. To avoid such an arbitrary baseline subtraction, we suggest another way to scale the data. Since phonons, and more generally nonsingular contributions, are expected to be insensitive to the field, we have rlC, ",/r) lnB = r)Cfj/r) lnB. The quantity AC",/rl lnB obeys the same scaling laws as Cf& but is not blurred by a large background. The price to be paid for the derivation is a high accuracy of the thermometry versus field. The latter was verified in our case using the triple point of argon.Using the measured quantity r)Cr~j&3 lnB, we tested both the LLL [3] and 3D X-Y approximations [4], as attempted by OHL using Cri -Co. We define T, (B) as r)(C/T)/r)B(T = max. o 20 -QSII%+ IIII' --2O--60-037T 0.75 T 1.5 T Q 3 T o 12 T -0.05 -0.03 -0.01 0.01 0.03 0.05 {TTc) / (TcH ) [ T-0.763] FIG. 2. Scaling plot of B ' 't 'BCt~/6 lnB in the 3D X-I' model. u = -0.0066 and v = 0.664. The plot of r)Cf~/r) lnB vs the scaling variable x = [T-T, (B)]j/[BT] , / corresponding to the LLL approximation is given in Fig. 1. The curves collapse on a single one for average fields higher than 1 T. Below 1 T, as could be expected, either higher Landau levels contribute, making the LLL approximation invalid, or finite size and/or inhomogeneity effects limit the sharpness of the transition. The corresponding 3D X-Y scaling plot is given by B ' /~'r)Cr~/r) lnB vs [T -T,]j(tT, B'/ "] (Fig. 2). The result is somewhat less good but does not differ drastically from that obtained in the LLL scheme. This is due to the negligible variation of the prefactor B~/ (2'1 (0.986 & [B(T)]~/ (2'1 & 1.007 for 0.25 & B & 16 T, which is replaced by 1 in the LLL case, and to the small difference between I/2v = 0.753 and the LLL exponent of 3. 2Summarizing, we state that, based on a method that does not depend on an arbitrary baseline subtraction, one cannot decisively ru...

Thermal fluctuations and vortex melting in theNb3Snsuperconductor from high resolution specific heat measurements

“…A relevant length scale is the average length of vortex segments which are "straight" along the field direction 36 and it can be assumed that this length is closely related to the coherence length. We thus normalize the ⌬S value by the coherence length ͑ = 36 Å for Nb 3 Sn͒ which extends in Nb 3 Sn over a few lattice parameters ͑5.293 Å͒. 12 We find 0.3± 0.1 k B / vortex/ , comparable to the value of YBCO and thus a reasonable value for a vortex-melting transition.…”

“…We note that the exponents in the scaling variables of the 3d-XY and the 3d-LLL model are very similar and it is hard to determine from scaling alone which model is more suitable for describing the fluctuations, as has also been observed in HTSCs. 2,3 Nevertheless neither model can be used alone to describe the scaling over the whole range of fields which we take as an indication for a crossover from 3d-XY to 3d-LLL fluctuations in high fields. The fluctuations disappear in low fields in the vicinity of the Meissner phase.…”

“…In some HTSCs, the scaling of data taken in different fields has been successfully used to investigate fluctuations. 2,3,[5][6][7] The effect of a magnetic field on fluctuations is to induce a length scale which reduces the effective dimensionality. This magnetic length l = ͑⌽ 0 / B͒ 1/2 is related to the vortex-vortex distance in type-II superconductors.…”

“…In the layered compound YBCO values of ϳ0.4 k B /vortex/layer are reported in comparable fields applied perpendicular to the superconducting layers. 35 It is a delicate question how to compare the latent heat of a vortex in an isotropic system as Nb 3 Sn with that of a layered compound. A relevant length scale is the average length of vortex segments which are "straight" along the field direction 36 and it can be assumed that this length is closely related to the coherence length.…”

Magnetic field induced enlargement of the regime of critical fluctuations in the classical superconductor V3Si from high-resolution specific heat experiments

“…Secondorder phase transitions are usually strongly influenced by fluctuations in the degrees of freedom of the order parameter, represented here by the phase and amplitude of the superconducting wave-function. This is indeed the case for the superconducting transition of high-temperature superconductors (HTSCs) with their high critical transition temperatures and their small coherence volumes [1][2][3][4][5][6][7][8]. As a result, critical fluctuations have a strong impact on most physical quantities.…”