VOLUME 80, NUMBER 17 PHYSICAL REVIEW LETTERS 27 APRIL 1998 Common Phase Diagram for Antiferromagnetism in La 22x Sr x CuO 4 and Y 12x Ca x Ba 2 Cu 3 O 6 as Seen by Muon Spin Rotation Ch. Niedermayer, 1 C. Bernhard, 2 T. Blasius, 1 A. Golnik, 3 A. Moodenbaugh, 4 and J. I. Budnick 5 1 Fakultät für Physik, Universität Konstanz, D-78434 Konstanz, Germany 2 Max-Planck-Institut f ür Festkörperforschung, D-70569 Stuttgart, Germany 3 Institute of Experimental Physics, Warsaw University, PL-00-681 Warsaw, Poland 4 Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11977 5 Department of Physics and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269 (Received 19 September 1997) By zero field muon spin rotation we studied the antiferromagnetic correlations in the single layer system La 22x Sr x CuO 4 and the bilayer system Y 12x Ca x Ba 2 Cu 3 O 6 . We observe a common phase diagram as a function of hole doping per plane with two distinct transitions in the magnetic ground state. The first transition marks the border between the 3D antiferromagnetic state and a disordered state with short ranged correlations. The second transition marks a distinct change in the magnetic correlations at the onset of superconductivity. [S0031-9007(98)05990-0] PACS numbers: 74.25.Ha, 74.62.Dh, 76.75. + i A characteristic feature of the cuprate high-T c super- conductors is the strong dependence of their magnetic and superconducting (SC) properties on the number of holes doped into the CuO 2 planes. The undoped compounds La 2 CuO 4 and YBa 2 Cu 3 O 6 are insulators and exhibit long range 3D antiferromagnetic (AF) order, which is rapidly destroyed as holes are doped into the CuO 2 planes. Su- perconductivity occurs beyond a critical hole content of p sh  0.05 0.06, where p sh is the fraction of doped holes per Cu atom in the CuO 2 sheet. The critical temperature T c  p sh  follows a universal, approximately parabolic p sh dependence, which appears to be common to the high- T c cuprates, and all that varies is the optimal value T c,max [1,2]. In La 22x Sr x CuO 4 (La,Sr-214) a short range ordered AF state is known to persist at intermediate doping for 0.02 , p sh , 0.05. Previous muon spin rotation mSR studies on La,Sr-214 have indicated that this short range AF correlated state even coexists with SC in the strongly underdoped regime for 0.05 , p sh , 0.1 [3]. For the YBa 2 Cu 3 O 72d (Y-123) system, the regime of low dop- ing is not readily accessible since the hole transfer from the CuO chains to the CuO 2 planes is rather complex and depends critically on oxygen ordering and content. In this paper, we present the results of an extensive mSR reinves- tigation of the doping dependence of the AF correlation in polycrystalline La,Sr-214 samples. In addition, we stud- ied the bilayer compound Y 12x Ca x Ba 2 Cu 3 O 6 (Y,Ca-123) for which, because of the unoccupied chains, p sh can be adjusted in a controlled way through the substitution of Y 31 by Ca 21 . We obtain a common magnetic phase dia- gram as a function of one parameter, p sh , which suggests that we observe the intrinsic property of the electronic ground state of the CuO 2 planes. A series of powder La,Sr-214 samples was prepared using conventional ceramic techniques. The preparation of Y,Ca-123 samples has been described previously [2]. From neutron refinement, the occupancy of Ca on the Y site was found to be close to 100% up to x  0.15 [2] but somewhat reduced for higher Ca content, i.e., x eff  0.18 in the case of x  0.2. The substitution of Y 31 by Ca 21 produces holes in the CuO 2 planes giving p sh  x eff 2. This is indicated by the variation of T c with Ca content (for fixed oxygen content) and has been confirmed by optical studies [4], by measurements of the thermoelectric power and by bond-valence sum calculations [2]. The zero field muon spin rotation ZF-mSR technique [5] is especially suited for the study of weak and short range magnetic correlations, since the positive muon is an extremely sensitive local probe able to detect internal magnetic fields as small as 0.1 mT and covering a time window from 10 26 s to about 10 29 s. The mSR experiments were performed at the Paul-Scherrer-Institut in Villigen, Switzerland and at TRIUMF in Vancouver, Canada. Representative ZF-mSR time spectra are shown in Fig. 1. At low temperature and for p sh # 0.08, the time evolution of the muon spin polarization is well described by the ansatz: G z t   2 3 cosg m B m t 1F exp μ 2 1 2 g m DB m t  2 ∂ 1 1 3 exp2lt  , where g m  851.4 MHzT is the gyromagnetic ratio of the muon, B m the average internal magnetic field at the muon site, and DB its rms deviation. The two terms arise from the random orientation of the local magnetic field in a polycrystalline sample, which on average points parallel (perpendicular) to the muon spin direction with probability 1 3  2 3  [5]. In analogy to NMR the dynamic spin lattice relaxation rate l  1T 1 is given by 1 T 1  g 2 m B 2 t  t c 1 1 v m t c  2 . A slowing down of magnetic fluctuations typically causes a maximum of 1T 1 at v m t c  1, where v m is the 0031-9007 98 80(17) 3843(4)$15.00 © 1998 The American Physical Society 3843