May 17, 1993 - ofChemistry, Materials Research Center and Science and Technology Center for Superconductivity,. Northwestern. Unii ersity, Evanston ...
PH YSICAL REVIEW LETTERS
VOLUME 70, NUMBER 20
Spin Susceptibility
in the La2 —„Sr
to overdoped Regimes
K. R. Poeppelmeier,
and W. P. Halperin1'1 1Department of Physics and Astronomy, Materials Research Center and Science and Technology Center for Superconductivity, Northwestern University, F. I. anston, Illinois 60208 t21Department of Chemistry, Materials Research Center and Science and Technology Center for Superconductivity, Northwestern Unii ersity, Evanston, Illinois 60208 (Received 2 October 1992)
Y.-Q. Song,
1'
Cu04 System from Underdoped
17 MAY 1993
'
Mark A. Kennard,
Cu NMR Knight shifts were measured on La2 — Sr„Cu04 for x =0. 10, 0. 16, and 0.20 in the normal and superconducting states. These results, combined with magnetic susceptibility measurements, allow At temperatures just the separation of the carrier spin and orbital contributions to the susceptibility. above the superconducting transition, the conduction electron spin susceptibility increases dramatically with strontium doping. The analysis of the Knight shift at low temperature suggests that the spin susceptibility is zero and the superconducting state is a spin singlet. PACS nUmbers:
74.25. Nf, 74. 62. Dh, 74. 72. Dn, 76.60.Cq
The La2 — Sr Cu04 system has attracted a great deal owing to a rich electronic phase diagram [l]. transition temperature The maximum superconducting T, of 36-38 K occurs at a strontium or barium doping of x=0. 15 and T, decreases on either side. This behavior has evoked considerable discussion in the literature. For example, it was proposed that a van Hove singularity in the electronic density of states (DOS), obtained in a rigid band structure calculation [2], might be responsible for the maximum of T, . More recently, there has been concern that the overdoped materials, x 0. 15, are not inof the trinsically phase pure based on measurements Meissner fraction, muon spin rotation (p+SR) [3], neutron diffraction [4], and high resolution x-ray experiments [5]. Our results provide strong evidence that wellannealed samples, 0. 1 ~ x ~ 0.2, are electronically homogeneous. They also show that the spin susceptibility is a monotonic function of x and there is no evidence for a van Hove singularity in the DOS. are generally Antiferromagnetic spin correlations thought to be an important characteristic of the normal Phenomonological thestate of high T, superconductors. ories for N MR (nuclear magnetic resonance) Knight rates [6] have been shift and spin-lattice relaxation developed [7] to include the effects of antiferromagnetic fluctuations in Fermi liquid theory. We believe that the comparison of properties, such as the carrier spin susceptibility, of underdoped and overdoped materials is particHowever, contributions from the van ularly important. cannot be and core dimagnetism Vleck paramagnetism separated from the total susceptibility with susceptibility alone. We have achieved this separation measurements by combining NMR and dc susceptibility measurements ~0.2. Our results show that, on samples with 0. 1 upon increasing doping, there is a smooth evolution in the spin susceptibility from a regime of strong singlet correlations among carriers, to one where they are relatively weak. Powder samples were prepared by the solid-state reaction of a mixture of the appropriate high purity metal ox-
of' attention
)
~x
ides. The product phase was formed after initial reaction at 950 C for 48 h, and was characterized by x-ray powder diffraction. The products were annealed in air at 950 C for an additional month and then quenched in air For details of sample preparation, to room temperature. see Ref. [8]. The transition temperature of each sample was determined by observing the diamagnetic shielding signal at a magnetic field of 10 G. Measurements of the dc magnetic susceptibility, g, were made at a magnetic field of 1 T on the powder samples. Samples for NMR measurements were finely ground, mixed with an epoxy resin (Stycast l 266, Emerson and Cumming, Inc. ) at a nomiThe superconnal filling fraction of 15% by volume. ductor-epoxy composite was cured in a 8.5 T magnetic field. This procedure is expected to produce stable, predominantly c-axis-aligned crystallites. NMR and nuclear quadrupole resonance (NQR) exx on three compositions, were performed periments =0. 10, 0. 16, and 0.20, using a heterodyne pulsed spectrometer. A magnetic field of 8. 5 T was used for NMR with the field perpendicular to the average c axis of the crystallites, H&c. The spectra were recorded using a spin-echo sequence while scanning the spectrometer frequency through the spectrum. The delay time between the tr/2 and tr pulses was 20-30 ps. The temperature was established between 5 and 300 K to an accuracy of ~ 0. 1 K. Two Cu resonances were found in the NMR and NQR spectra, which we have called A and 8, consistent with our earlier work [8,9]. These resonances are well separated, at 98.4 and 100 MHz, respectively, and the Cu resonances were observed above 107 corresponding MHz. The B site appears to be intrinsic to the material and to depend on doping but its origin is not yet understood. In this Letter, we focus on the main resonance, the 8 copper site. The copper spin Hamiltonian, including the external magnetic field, Knight shift and quadrupolar coupling, determined from NQR, is solved exactly to obtain the Knight shift K.
l993 The American Physical Society
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Below T„ it is important to account for possible magnetic field shifts inside the superconductor due to the combined diamagnetic effects of shielding and the vortex state. We have measured the local magnetic field at 5 K using ' La as a spectator nucleus following the idea of Barrett et al. [10l who used Y for the same purpose to study YBa2Cu307. After measurement of the temperature dependence of the magnetic and quadrupole shifts of the ' La resonance, we have found that at 8. 5 T and at 5 K the diamagnetic field shifts in the La2 — Sr„CuO4 systern are negligible within 4- 0, 05%. The measured copper Knight shift is shown in Fig. 1 for three doping levels. The temperature dependence of the shift in the normal state is qualitatively different for each sample. However, at the lowest temperature measured, K converges to a composition independent value, K(0) =0. 17%+ 0.04%, for x =0. 1-0.2. For x =0. 10, K decreases as temperature decreases tending toward K(0) even above T, . We will argue later that the carrier spin contribution to K(0) is zero. For x =0. 16 and 0. 20, just above T„ the shift approaches a constant much larger than K(0). For x =0. 16, the temperature dependence of the shift is weak in the normal state. For x=0.20, K increases with decreasing temperature above T„ in contrast to x =0. 10, and 0. 16. The composition dependence of the shift is stronger at low temperature just above T, and much weaker at room temperature. In general, we have found that in the normal state, K increases as the doping increases from x =0. 10 to 0.20. The dc magnetic susceptibility, g, is shown in Fig. 2. Our measurements of g are in reasonable agreement with the literature [11,12]. It is clear that the dc susceptibility has the same temperature dependence as that of the AddiKnight shift for each of the three compositions. tional results for x =0. 18 are also shown. Since NMR is a microscopic probe of the electronic susceptibility and is insensitive to paramagnetic impurities [131, this result indicates that each of the three samples is free of paramag-
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I. IG. 1. Transverse Cu Knight shift as a function of temperature for x =0.20 (squares), x =0. 16 (circles), and x =0. 10 (diamonds), in an 8. 5 T magnetic field. The lines are guides to the eye. See text for the determination of K„b.
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It also shows unambiguously
netic impurities.
that the different from x =0. 16 since the Knight shift and susceptibility are consistent with each other and are different for these two compositions. The NMR spectrum of the x =0.20 compound is not broadened as compared to the x =0. 16 sample nor do we find evidence in the x =0.20 sample of any of the x =0. 16 compound through observation of a resonance at the frequency corresponding to x = 0. 16. For these reasons we believe our x =0.20 sample is homogeneous and intrinsically phase pure. The copper nuclei couple to the electronic susceptibility through hyperhne interactions of spin and orbital character: K = +s + Korb ~sos + ~ orb+orb gs and gorp are the spin and orbital susceptibility and 8, and A, „b are the corresponding hyperfine coupling constants. K, and K,„b are spin and orbital shifts, respectively. In a material where the carrier density changes continuously as a result of doping, the orbital shift remains constant while the spin shift varies. We show a plot of K vs g in Fig. 3 with the temperature and the composition as implicit parameters. All the normal state data for three compositions are included in this plot. As Sr doping increases the spin susceptibility increases monotonically from x =0. 10 to 0.20. This result is inconsistent with the notion that the electronic density of states, proportional to the spin susceptibility, has a peak as a function of doping owing to a van
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VOLUME 70, NUMBER 20
PHYSICAL REVIEW LETTERS
Hove singularity [2]. If one assumes that A, and K„b are independent of composition, the whole data set can be used to extract A, . Such an analysis would lead to an A, approximately 3 times as large as that for YBa2Cu307 [14]. On the other hand, if we determine A, from data for each sample individually, A, for x =0. 10 and 0. 16 would be approximately 280 kOe/pz and is close to the value for YBa2Cu307, however, with large errors. For x =0.20, we have found 2, =470 kOe/ps. Ishida et al. [15] have reported Cu for x =0. 15 with HJ e and Knight shift measurements determined A, =189 kOe/pa, consistent with that for YBa2Cu307 [14]. We note that it is unusual to have composition dependence for the hyperfine coupling con-
stant. In general, given the linear relationship between K and g, one cannot obtain the absolute spin shift without an independent determination of either K,„b and g, „b. Traditionally, a diamagnetic insulator from the same family of compounds is used as a reference sample for which the carrier contribution is zero. This is not possible for the La2 — Sr„Cu04 system since the insulating compositions, x &0.05, are antiferromagnetic. On the other hand, we have found that the shift decreases rapidly below T, and converges as the temperature goes to zero, as shown in Fig. 1. This convergence strongly supports the idea that K, (0) =0 and that the superconducting pairing in La2-Sr Cu04 is in a singlet state. The zero temperature limit of the shift is the orbital shift, K „b=0.17%. The excess shift at higher temperatures is attributed to the spin susceptibility, as indicated in Fig. 1. In the case of YBazCu307, Takigawa er al. [16] and Barrett et al. [10] have concluded that superconductivity Takiis a spin singlet from their NMR measurements. gawa et al. [16] examined the possible pairing states and concluded that triplet pairing was unlikely. Barrett et al. [10] based their conclusions on a model analysis of the anisotropy of the Cu orbital shifts. Similar effects have also been found in the TI2Ba2Cu06~& system [17]. On the basis of our result and that of previous work on other high T, materials [10,16, 17], we speculate that the ground state of all high T, copper oxide superconductors is a spin singlet. Having established this reference point in the Knight shift, let us examine the normal state behavior of the x =0. 10 sample in more detail. The spin susceptibility of this composition is significantly smaller than those with higher doping. K increases with temperature, indicating strong singlet correlations between the carriers. It is worth noting that the Knight shift just above T, would extrapolate to zero spin shift at zero temperature even without superconductivity. Consequently, an appropriate ground state model for the normal electrons should be a spin singlet state in the low doping regime. A similar effect was observed for the plane copper in YBa2Cu3067
[18]. Johnston
17 MAY 1993
with spin 2 to account Heisenberg antiferromagnetism for the composition and the temperature dependence of the dc susceptibility of La2 —„Sr Cu04. Such a local moment model predicts a broad maximum in the temperature dependence of g. The temperature of this maximum corresponds to the spin exchange coupling constant, J. Johnston [11] proposed that is a function of x and that becomes progressively smaller as x increases. The observed positive and negative slopes of g as a function of temperature correspond to the measurement temperature being below or above J. However, it is not clear how to adapt this model to include the contributions from the carriers. In contrast, our results demonstrate that the Cu + moments and the carrier spins are strongly coupled such that there is no independent local moment contribution to g. A more general approach, the "t-J" model [19] has been studied [20] to account for the eAects of doping in the normal state. The high temperature behavior [21] of this model is found qualitatively consistent with the measured g, however, calculations in the lower temperature range would be desirable for a comparison with experiment. In Fig. 4, we have replotted the data in the superconducting state for x =0. 16 and 0.20 with the temperature scaled to the T, of each sample and we have set K, =0 at 5 K. It is evident from Fig. 4 that in the superconducting state, K(T) for x =0. 16 and 0.20 do not scale with each other. We find that K, (T) for x =0.20 can be fitted by a weak coupling Yosida function for s-wave pairing, with the zero temperature gap parameter 2A(0)/k~T, =3.53. However, I'or x =0. 16, K, (T) has a much steeper reduction immediately below T„which can be accounted for with the larger value, 2A(0)/k TB, =7 ~ 1. This value is similar to that derived for the plane copper in YBa2-
J
J
Cu307 [10]. This different temperature dependence in the superconducting state can also be accounted for from Fermi liquid efrects on the spin susceptibility [22] within the weak coupling BCS theory. This requires a relatively strong Fermi liquid parameter Fo = —0.5 for x =0. 16 while
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FIG. 4. Spin shift in the superconducting state for x =0.20 0. 16. The lines are Yosida functions for curve a, 26(0)/ kaT, =3.53, and curve b, 2h(0)lksT, =7. and
[11] has
invoked a model for two dimensional
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PH YSICAL REVIEW LETTERS
F0=0 for x =0.2. This correction would also have a With dramatic effect on the normal state susceptibility. these values of Fo, the effective mass must be increased by a factor of 5 in going from x =0. 16 to x =0.20. Measurements of the heat capacity jump at T„as a rough measure of the eA'ective mass [23], do not support this hypothesis. It is our view that a strict application of Fermi liquid theory is inappropriate for La2 — Sr„Cu04 up to the doping level of x =0.2. In conclusion, we emphasize a comparison between the two compounds, YBa2Cu30b and Lap —„Sr Cu04. For Y Ba2Cu30q, upon changing the oxygen content 6 from 6.4 to 7.0, the carrier density increases. T, increases with 6 and reaches a maximum at 6=7.0. This is the extent of the underdoped regime. In the normal state, the Knight shift is temperature independent for 6=7 [10,16], for 6 =6.7 but increases with increasing temperature 15 is [18]. In this respect, the La2, Sr„Cu04 for very similar to YBa2Cu30b. The chemistry of the La2 Sr Cu04 system allows the doping to be increased further beyond that for a maximum T; and a progressive change in the spin susceptibility and its temperature dependence can be observed in the overdoped regime. Continuity of the change of the temperature dependence of g from the x =0. 1 to x =0.2 indicates that, qualitatively, enhancement of g at higher doping is related to the reduction of antiferromagnetic interactions and, correspondingly, singlet spin correlations. The weak temperature dependence of g around x =0. 16 should not be viewed as evidence for a conventional Fermi liquid picture, rather it is the result of a weakening in the singlet It is possible that the negative slope in spin correlations. the temperature dependence of g, which we observe in our measurement of the Knight shift at x =0.2, extends well into the overdoped regime, up to x =0.33 [12]. A correct theoretical picture should then include this nontrivial magnetic behavior for the heavily doped regime. It is also interesting to note that the highest T, occurs when the spin susceptibility is least temperature dependent in the normal state. This is also the case for YBa2Cu30p though only the underdoped regime can be explored. We thank Dr. J. Sauls, Dr. S. Yip, Dr. M. T. Rice, and Dr. M. Randeria for helpful discussions. This work was supported by the MRL program of the NSF at the Materials Research Center of Northwestern University under award No. DMR-9120521, and by the Science and Technology Center for Superconductivity supported by
x~0.
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NSF Cooperative Agreement No. DMR 91-20000.
[1] J. B. Torrance
er al. , Phys. Rev. Lett. 61, 1127 (1988). [2] J.-H. Xu et al. , Phys. Lett. A 120, 489 (1987). [3] D. R. Harshman et al. , Phys. Rev. Lett. 63, 1187 (1989). [4] J. D. Jorgensen er al. , Phys. Rev. B 38, 11337 (1988); J. D. Jorgensen et al. , in Advances in Superconductivity 111, edited by K. Kajimura and H. Hayakawa (Springer-
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[5] H. Takagi er al. , Phys. Rev. Lett. 68, 3777 (1992). [6] For a review, see C. H. Pennington and C. P. Slichter, in Physical Properlies of High Temperature Superconduc ror 11, edited by D. M. Ginsberg (World Scientific, Singapore, 1990), Chap. 5. [7] B. S. Shastry, Phys. Rev. Lett. 63, 1288 (1989); A. J. Millis, H. Monien, and D. Pines, Phys. Rev. B 42, 167 (1990); N. Bulut et al. , Phys. Rev. B 41, 1797 (1990). [8] M. A. Kennard et al. , Chem. Mat. 3, 672 (1991). [9] Y.-Q. Song et al. , Phys. Rev. B 44, 88 (1991), and reference therein.
[10] S. E. Barrett et al. , Phys. Rev. B 41, 6283 (1990). [11] D. Johnston, Phys. Rev. Lett. 62, 957 (1989). [12] J. B. Torrance et al. , Phys. Rev. B 40, 8872 (1989). [13] This is often evident in the dc susceptibility measurements in the form of a Curie-Weiss term which has to be to obtain intrinsic behavior. See, for example, Ref. [11]. H. Alloul, T. Ohno, and P. Mendels, Phys.
subtracted
Rev. Lett. 63, 1700 (1989). [14] H. Monien, P. Monthoux, and D. Pines, Phys. Rev. B 43,
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[15] K. Ishida et al. , J. Phys. Soc. Jpn. 60, 3516 (1991). [16] M. Takigawa er al. , Phys. Rev. B 39, 7371 (1989). [17] Y. Kitaoka et al. , Physica (Amsterdam) 179C, 107
(1991). [18] R. E. Walstedt et al. , Phys. Rev. B 41, 9574 (1990); M. Takigawa et al. , Phys. Rev. B 43, 247 (1991). and M. T. Rice, Phys. Rev. B 37, 3759
[19] F. C. Zhang (1989).
[20] A. J. Millis,
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11871 (1992). [22] T. Leggett, Rev. Mod. Phys. 47, 331 (1975). [23] N. Wada et al. , Physica (Amsterdam) 157C, 453 (1989). For a review of specific heat measurements, see N. E. Philips et al. , in Progress in Lo~ Temperature New Physics, edited by D. F. Brewer (North-Holland, York, 1992), Vol. 13, Chap. 5.
