Physica C 162-164 (1989) 474-475 North-Holland
ORIGIN OF THE NUCLEAR SPECIFIC HEATS IN H I G H - T c SUPERCONDUCTORS R. CASPARY, M. WlNKELMANN AND F. STEGLICH Institut fiar Festk6rperphysik, Technisclae Hochschule Darmstadt, and SFB 252, D-6100 Darmstadt, Federal Republic of Germany Published B = 0 data of the nuclear specific heats of Bi2Sr2CaCu208 (T c = 85K) and Lal.85Sr0.15CUO4 originate from quadrupolar interactions only, implying that fluctuation rates of any intrinsic Cu moments have to exceed 107s ~1. Results up to B = 8 T for Bi2Sr2CaCu20 8 and YBa2Cu306.87 can be explained by a superposition of quadrupolar and hyperfine splittings. In this paper we discuss the origin of the lowtemperature (T < 0.5 K) specific heats of high-T c superconductors showing pronounced upturns in C / T v s T plot s [1], apparent ly result ing from a split t ing of nuclear levels. We will focus on results at B _< 8T for Bi2Sr2CaCu20 8 (BSCCO) [2] and YBa2Cu306.87 (YBCO) [3]. Published data for Lal.85Sr0.15CuO4 (LSCO) [4] will also be commented. As discussed in [2,3], the low-T specific heats of BSCCO and YBCO contain "spinglass"--derived 7(B)T terms which are strongly depressed by an external B---field. The stralghtiine behavior in plots CT2 vs T 3 (Fig. la) proves the existence of an additioual~ (B)T-2contribution, i.e. thehigh-T tail of a nuclear Schottky anomaly. The coefficients ~ are displayed as ~/~ v..ssB for both YBCO [3] and BSCCO [2] in Figs. 2aandb. B = 0 results.The ~T - 2 term found for BSCCO is consistent with pure quadrupolar splitting (~ =~Q) of
[7] on Gd substituted for Ba (7oo,Gd ~- 7oo,Ba) in YBCO, we obtain aQ = 17 pdK/mole f u " Since aex]~ = 54 #JK/molef.u. [3], the major coutrit;ution stems trom hyperfine splitting of the nuclear Zeeman states via (Tn: gyromagnetic ratio): 0,hf = R(TnBhf/21rkB)2I(I+1)/3. There are two probable extrinsic sources for hyperfine splitting in YBCO already at B = 0: (1) Antfferromagnetically ordered Cu 2+ moments in BaCuO 2 precipitates of ~ lwt%and (2) about 0.4 at%of paramagnetic Cu 2+ moments (S = 1/2) freezing into a spin-glass state [3]. Fermi contact at alloft hese magnetic Cu sites (Bhf = 12.2T [5]) yields ~ hf-~ 19 pJK/molef.u.. The remaining ~--(CXQ+~hf) ~ 18 p2K/molef.u, might indicate the inadequacy of our analysis, for which we assumed (i) the quadrupolar splitting to be small compared to the hyperfine splitting and (ii) Bhf to be parallel to the EFG (0 = 0). However, both effects are of the same order of magnitude, NMR studies [8] reveal
(209Bi) and l(63Cu,65C'u).
0=900 and the splitting depends in detail on 0 [9]. In contrast to YBCO, but similar to BSCCO, the analysis of the LSCO data [4] is not seriously impeded by extrinsic magnetic specific-heat contributions. We estimate CCQ ~- 17 pdK/mole f.u. which explains, within the experimental and analytical uncertainties, the measured
The experimental result O,ex p = 430 pJK/molef.u, is verified [2], if 700 = 77 is chosen for the Sternheimer factor
value of 19 pdK/molef.u. [4]. B > 0 results. Fig. lb shows the nuclear level splitting
of 209Bi, a typical value for heavy atoms [5]. Utilizing NQR results [6] for the nuclear quadrupolar splitting at the Cu(1)-and Cu(2)---sit es as well as Moessbauer results
for the exemplary case of I = 3/2(63Cu,65Cu), obtained from a (highly simplifying) model in which the Zeeman splitting by the external field (Bhf = B) is treated as a
209Bi, 63Cu and 65Cu nuclear states (spin I) by the action of an electricfield gradient (ext) on the nuclear quadrupole moment Qvia (R = k B. NA):~ Q = R[7oo(eq)eQ/4kB ]2" f and f = [3/I(2I-1)]2[I(I + 1)(21+3)(21-1)/45] = 11/30
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
475
R. Caspary et al. I Nuclear specific heats in high-To superconductors
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0 Fig. l.a: Specific heat of Bi2Sr2CaCu208 in various B-fields as C T 2 vs T 3 for T < OAK. Solid lines: guide to the eye. b: Nuc~tr level splitting of Cu(I = 3/2) due to quadrupolar and Ze, mau effects, see text.
perturbation of the quadmpolar splitting (0 = 0). Calculated~/= (B) values are compared with the experimental ones in Figs. 2a and b. We state satisfactory agreement for BSCCO, while for YB CO the extrinsic magnetic contributions lead to a systematic discrepancy at B < 4T. To condude, the int riusie nuclear spedfieheat at B = 0, =T -2, of superconducting BSCCO, YBCO and LSCO is dominated by quadrupolar interactions. This poses a lower bound for the fluctuation rates of any intrinsic magnetic moments residing on the Cu lattice sites [10]: r -1 > rh~--- 107s-1 [3]. In fact, #SR results on LSCO [11] suggested magnetic fluctuations of order 108s-1 at 3 K. The presence of extrinsic magnetic contributions in YBCO still prevents us to rule out even slower fluctuations: The unexplained part (,2 18/dK/molef.u. ) of the experimental= value would correspond to an average Cu moment of 0.1/%. Finally, static (i.e. slow) moments of the correct size (0.5 and 0.6#B/CU ) are derived from the =T- 2 terms observed for the antfferromagnetie reference compoundsYBa2Cu306.01[3] and La2CuO4 [4]. We acknowledge illuminating discussions with H. Rietschel, H. Schmidt and N.E. Phillips, to whom one ofus (R. C. ) is grateful for his warm hospit alit y at UCB.
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Fig. 2. 4= vs B for YBa2Cu306.87 (a) and Bi2Sr2CaCu208 (b). Dashed lines: 4=Q(B) for pure quadrupolar splitting and 4=z(B) for pure Zeernan splitting of nuclear Ba/Cu (YBCO) or Bi/Cu (BSCCO) states..: Measured data; A: model data, as explained in the text. Solid lines: guide to the eye.
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