A comparison of µsr and thermopower in Hg 1:2:0:1 high-t c cuprates

Transcription

1 Hyperfine Interactions 105 (1997) A comparison of µsr and thermopower in Hg 1:2:0:1 high-t c cuprates B. Nachumi a,a.keren a, K. Kojima a,m.larkin a, G.M. Luke a,j.merrin a, W.D. Wu a,y.j.uemura a,y.xue b,f.chen b,q.xiong b,z.huang b,z.he b, Q. Lin b, J. Clayhold b and C.W. Chu b a Department of Physics, Columbia University, 538 W. 120th St., New York, NY 10027, USA b Texas Center for Superconductivity at the University of Houston, Houston, TX , USA We present the results of µsr measurements of the transverse field relaxation rate below T c for seven samples of HgBa 2CuO 4+δ, spanning the underdoped, optimally doped, and nominally overdoped regions of the superconducting phase. On comparison with the anomalous thermopower data for these compounds, we find that nominally overdoped Hg 1:2:0:1 resembles underdoped compounds in certain respects. The transverse field relaxation rate σ for polarized muons in the vortex state of a superconductor is proportional to the width of the magnetic field distribution of the flux lattice. Maxwell s equations, in the London gauge, show that the field distribution width is, in turn, proportional to the inverse square of the London penetration depth, λ 2 London = m /(4πn s e 2 ),wherem is the effective mass of a superconducting charge carrier, and n s is the density of these carriers. Hence, σ n s /m directly measures the superfluid density: effective mass ratio [1 3]. In the normal state, the thermopower S(T > T c ) measures the ratio p/m, where p is the normal-state carrier density. These two sets of measurements allow comparison between the normal state and superconducting charge transport properties. Previous µsr studies have shown that n s /m for all cuprates scales linearly with T c [1,2] in the underdoped regime, where T c increases with δ. Presland et al. have shown that, for many cuprates, T c varies quadratically with both the stoichiometric doping, δ, andp, calculated from bond-valence summation and thermopower [4]. For underdoped cuprate superconductors, n s /m measured with µsr, and p, the number of holes per planar copper, measured by thermopower, behaves similarly as functions of the chemical doping δ: asδand p increase, n s /m follows suit. Work was supported by NSF grant no. DMR and NEDO (Japan). Work was supported by NSF grant DMR J.C. Baltzer AG, Science Publishers

2 120 B. Nachumi et al. / A comparison of µsr and thermopower in Hg cuprates The opposite situation seems to obtain in the far overdoped regime. µsr measurements on the overdoped Tl 1:2:0:1 and Tl 2:2:0:1 cuprates [2,3] established that, while T c in these compounds varies approximately quadratically with δ and p as in the underdoped samples, the plot of T c vs. n s /m becomes double-valued, tending to revert to the universal line observed for the underdoped cuprates. n s /m did not scale with p, δ in the extremely overdoped limit. Because few superconductors are stable with substantial overdoping, the data in the overdoped regime remains sparse, and the normal and superconducting states of the overdoped cuprates are not well understood. In this context, the mercury compounds, which admit continuous doping from the underdoped through the far overdoped regime of the superconducting phase, become especially important experimental subjects. Here, we present the results of µsr measurements on Hg 1:2:0:1 (HgBa 2 CuO 4+δ )for seven ceramic samples spanning the entire doping range. We find the behavior which is qualitatively consistent with µsr measurements on other overdoped cuprates. However, because the behavior of Hg 1:2:0:1 in thermopower measurements [7] differs from that of the other overdoped cuprates [6,7], we are led to question whether the nominally overdoped (i.e. high-δ) compounds are actually overdoped superconductors. The δ values for five of the seven samples were determined by refinement from the c-axis lattice constant measured by X-ray diffraction. The other two were then interpolated from a parabolic fit to T c (δ) following [8]. The decaying muon asymmetry signal was fit to the functional from A(t) =A 1 cos(ω 1 t + φ) exp( σ 2 t 2 /2)+A 2 cos(ω 2 t + φ). Here the A 1 term is the signal from the superconductor, while A 2 is the amplitude of a nonrelaxing tail observed in the signals for some of the samples, which originates from muons which miss the sample entirely, or from nonsuperconducting regions of the sample. In all such instances, A 2 /A 1 0.1, so the signals are fairly homogeneous. As stated above, the relaxation rate σ is proportional to the inverse width of the magnetic field distribution in the sample. The T>T c background relaxation rate is subtracted, so the plotted σ measures the change in the field distribution due to the screening supercurrents: σ λ 2 London n s/m [2]. The temperature at which the relaxation rate rises significantly above zero marks the onset of the superconducting transition. σ for T 0 indicates the ground state behavior of n s /m : the low-temperature behavior of σ(t ) diagnoses the structure of the superconducting gap. In fig. 1, we plot σ as a function of temperature. As a function of δ, T c rises, saturates at Tc max 99 K, and falls to 29 K in the high-δ sample. n s /m similarly rises and falls as δ increases, although the n s /m and T c maxima occur at different values of δ. The T 0 behavior of σ is increasingly linear with doping; this may indicate the presence of line nodes in the superconducting gap [5]. Figure 2 shows that, for the underdoped samples, the plot of T c vs. n s /m follows the universal line for underdoped cuprates (dashed line). The overdoped samples follow a trajectory similar to those of the other overdopable cuprates: above the

3 B. Nachumi et al. / A comparison of µsr and thermopower in Hg cuprates 121 Fig. 1. The transverse-field muon spin relaxation rate, σ n s/m, in a transverse field of 4 kg, as a function of temperature. Fig. 2. Comparison of n s/m vs. T c plots for three overdoped cuprates. Arrows indicate increasing chemical doping δ. Dashed line: the universal relation for the underdoped cuprates of Uemura et al. [1,2].

4 122 B. Nachumi et al. / A comparison of µsr and thermopower in Hg cuprates Fig. 3. T c plotted against p, the hole density per planar copper. The p values are interpolated from the measurements in ref. [7]. Arrows indicate increasing δ. critical doping, the scaling between T c and n s /m breaks, and the plot of T c vs. n s /m returns to the universal underdoped line [2,3]. The thermopower data suggests that, while all the samples behave similarly in µsr experiments below T c, in the normal-state Hg 1:2:0:1 differs substantially from the other overdoped cuprates. Obertelli, Cooper, and Tallon [6] have shown that plots of the normal state thermopower S(290 K)vs. (1 T c /Tc max ) 1/2 for many of the cuprates, including the overdoped thallium compounds, describe another universal curve. For underdoped samples, S(290 K) is large and positive, while in the overdoped regime, it is small and negative. All of the samples which obey this relationship also obey the relation T c = Tc max (1 82.6(p 0.16) 2 ) [4,6]: the thermopower seems to be an accurate measure of the normal state carrier density. Hence, the thermopower allows another experimental distinction between underdoped and overdoped cuprates. Recently, Chen et al. [7] have shown that high-δ, nominally overdoped mercury cuprates deviate from the predicted linear behavior. Chen et al. have also associated the anomalous thermopower with the departure of T c (p) in overdoped Hg 1:2:0:1 from the parabolic dependence seen in the other cuprates. The fact that T c (δ) remains parabolic led these authors to hypothesize the existence of a second oxygen doping site in Hg 1:2:0:1. In fig. 3, we plot T c vs. p interpolated from the comprehensive graph in reference [7], where p is deduced from measurements of S(290 K). The T c vs. p plot for Hg 1:2:0:1 bears a strong resemblance to the T c vs. n s /m plot shown in fig. 2. Combining the thermopower data with the µsr data, we may establish a comparison between the overdoped Hg 1:2:0:1 and other cuprates which do follow the universal thermopower relation of reference [6]. Since, for underdoped Hg 1:2:0:1, T c depends quadratically [8] on both p and δ, p δ for the underdoped samples. For an

5 B. Nachumi et al. / A comparison of µsr and thermopower in Hg cuprates 123 Fig. 4. σ(t 0) n s/m from µsr, versus p from thermopower [7] for Hg 1:2:0:1. For comparison, we plot n s/m from µsr [2,3] and p deduced from the T c [2,4] for Tl 2:2:0:1 (asterisks). Arrows indicate increasing δ. underdoped cuprate, which follows the universal µsr behavior, a plot of n s /m T c against p will have a positive slope. If p δ in the overdoped regime where n s /m decreases with increasing δ, the apparent slope should change sign. In fig. 4, we plot n s /m vs. p for all of the Hg 1:2:0:1 samples measured. The nominally overdoped 1:2:0:1 samples remain close to the line n s /m p even for the highest values of δ. On the same graph, we plot the n s /m of Tl 2:2:0:1 [2], against values of p deduced from the T c (p) parabola for the cuprates which fall on the universal thermopower curve [6]. The overdoped thallium compound shows the expected negative slope. The anomalous behavior occurs when p, instead of following the chemical doping δ, follows σ n s /m. If the thermopower relation is an accurate measurement of p for the overdoped cuprates, then Hg 1:2:0:1 is not overdoped in the same sense as the thallium compounds, for increasing δ does not increase the normal state carrier density p. Whether this implies a fundamental difference between their respective superconducting states and their overdoped superconducting behavior is unresolved. While it is tempting to draw conclusions about all overdoped cuprates from the similarities in the µsr data, until the anomalous thermopower is explained, the mercury compounds must be regarded as suspect. References [1] Y.J. Uemura et al., Phys. Rev. Lett. 62 (1989) [2] Y.J. Uemura et al., Nature 364 (1993) 605. [3] C. Niedermayer et al., Phys. Rev. Lett. 71 (1993) 1764.

6 124 B. Nachumi et al. / A comparison of µsr and thermopower in Hg cuprates [4] M.R. Presland et al., Physica C 176 (1991) 95. [5] D.A. Bonn et al., Phys. Rev. B 50 (1994) [6] S.D. Obertelli et al., Phys. Rev. B Rapid Commun. 46 (1995) [7]F.Chenetal.,T csuh Preprint 96:006, by permission, submitted to Phys. Rev. B Rapid Commun. (1996). [8] Q. Xiong et al., Phys. Rev. B 50 (1994)