New Perspective on the Phase Diagram of Cuprate High-Temperature Superconductors
Damian Rybicki, Michael Jurkutat, Steven Reichardt, Czesław Kapusta, Jürgen Haase
11 New Perspective on the Phase Diagram of Cuprate High-TemperatureSuperconductors
Damian Rybicki ∗ University of Leipzig, Faculty of Physics and Earth Sciences, Linn´estr. 5, 04103 Leipzig, Germany, andAGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of SolidState Physics, al. A. Mickiewicza 30, 30-059 Krakow, PolandEmail: [email protected]: +48.12.6172946
Michael Jurkutat
University of Leipzig, Faculty of Physics and Earth Sciences, Linn´estr. 5, 04103 Leipzig, GermanyEmail: [email protected]: +49.341.9732605
Steven Reichardt
University of Leipzig, Faculty of Physics and Earth Sciences, Linn´estr. 5, 04103 Leipzig, GermanyEmail: [email protected]: +49.341.9732605
Czes law Kapusta
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of SolidState Physics, al. A. Mickiewicza 30, 30-059 Krakow, PolandEmail: [email protected]: +48.12.6172554
J¨urgen Haase
University of Leipzig, Faculty of Physics and Earth Sciences, Linn´estr. 5, 04103 Leipzig, GermanyEmail: [email protected]: +49.341.9732601 a r X i v : . [ c ond - m a t . s up r- c on ] N ov (a) Structure x -y σ CRCuO CRCuO (b) Phase Diagram
La-214Hg-1201Tl-2201 Y-123Y-124CLBLCO_0.4CLBLCO_0.1 Bi-2212Tl-2212Tl-2223Hg,Tl-1223 Pr-214 Nd-214 μ SR NMR
Uemura et al. [1] T c [ K ] Planar oxygen hole density, n p doping x O NMR splitting, ν Q [MHz]Muon relaxation rate [ μ s -1 ] La-214Y-123 T c [ K ] (c) Triplelayer (d) n d + 2 n p = 1 parent: T N -0.1-0.2 0.2 0.1 T holeselectrons T * T c SCAFSC n d + 2 n p = 1+ x doping: h + e - FIG. 1. (a) top: the cuprates layered structure has CuO planes and charge reservoir (CR) layers; (a) bottom: the bondingorbitals in the CuO plane, i.e., Cu 3d x − y and O 2p σ , share the nominal Cu 3 d hole of the Cu + ion (indicated filling measuredwith NMR); (b) top: schematic electronic phase diagram of the cuprates for electron ( left ) and hole ( right ) doping x , withantiferromagnetic (AF) and superconducting (SC) phases; at low doping the pseudogap reigns below T ∗ ; (b) bottom: dopedelectrons go to the 3d x − y orbital almost exclusively, while doped holes predominantly go to the 2p σ orbital; (c) solid red: Uemura plot [1], i.e., T c vs. muon spin relaxation rate (upper abscissa); black symbols: T c vs. planar oxygen quadrupolesplitting ν Q (lower abscissa). For triple layer Tl-2223 and Hg,Tl-1223 the pairs connected with a dotted line belong to thesame sample and correspond to planar O sites of inner and outer layer (smaller splitting corresponds to underdoped inner CuO layer). (d) T c vs. planar O hole density n p calculated from ν Q for all available data (see text). Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity such an early influential relation showed that the critical temperatureof superconductivity ( T c ) correlates with the density of the superfluid measured at low temperatures.This famous Uemura relation has been inspiring the community ever since. Here we show that thecharge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO plane, accessiblewith nuclear magnetic resonance (NMR), is tied to the Uemura scaling. This charge distributionbetween copper and oxygen varies between cuprate families and with doping, and it allows us to drawa new phase diagram that has different families sorted with respect to their maximum T c . Moreover,it also shows that T c could be raised substantially if we were able to synthesize materials in whichmore oxygen charge is transferred to the approximately half filled copper orbital. I. INTRODUCTION
The cuprates’ essential building blocks are the CuO plane and charge reservoir layers that separate the planes,cf. Fig. 1(a). While the square-planar CuO plane with a Cu 3 d x − y orbital bonding to four O 2 p σ orbitals is quiteuniversal, the charge reservoir chemistry can vary widely. The antiferromagnetic parent compound can be doped withholes or electrons by alteration of the charge reservoir layers so that the static magnetism vanishes and new electronicphases emerge, cf. Fig. 1(b).The original plot by Uemura et al. [1] depicted in Fig. 1(c) (in red) shows T c correlated with the muon spinrelaxation rate σ (extrapolated to T = 0 K), which is proportional to the superfluid density divided by the effectivemass ( σ ∝ n s / m ∗ ). This relation holds for the underdoped materials and nicely orders different cuprate families.This and subsequent scaling laws have remained stimulating up to now, and some were shown to be valid for othersuperconductors as well [2–10]. Also shown in Fig. 1(c) (in black) is the planar O NMR quadrupole splitting ( ν Q )that measures the O 2 p σ hole content. The resemblance of this temperature independent charge density at the planaroxygen, set by material chemistry, and σ , the density of the superfluid at very low temperatures, is striking. A F M S C S C ho l e s e - -dopedLa-214Y-123, Y-124Bi,Hg,Tl based n p n d T [ K ] T FIG. 2. (Color online) T c as a function of oxygen (2 n p ) and copper ( n d ) hole content for electron-doped Pr-214 and Nd-214,hole-doped La-214, Y-123 and Bi-, Hg-, Tl-based compounds. The commonly used phase diagram ( T vs x ) appears as aprojection (upper left). Black dashed bold line is for the undoped case ( x =0), thin black lines correspond to doping x changingwith a step of 0.1. II. RESULTS AND DISCUSSION
Nuclear magnetic resonance (NMR) as a versatile local bulk probe revealed various trends among certain parametersfor the cuprates. [11] However, NMR spin shifts, nuclear relaxation, or local electric field gradients do not lendthemselves easily to simple physical pictures. For example, early work related T c to the planar O and Cu splittings[12], but it did not attract as much interest as the Uemura plot. Subsequent work [13] showed that the splittings aredue to the hole content of the Cu 3 d x − y ( n d ) and O 2 p σ ( n p ) orbitals, and that they measure the chemical hole-doping x (as in La − x Sr x CuO ), i.e., x = ∆ n d + n p . Here, n d and n p are measured with NMR based on calibratingthe quadrupole splittings with atomic spectroscopy data, in contrast to the earlier model [12]. Very recently [14], itwas found that even electron-doping is quantitatively accounted for with n d and n p from NMR. In addition, it wasfound that the parent materials differ substantially in n d and n p , however, the relation n d + n p = plane share the nominal d-shell Cu + hole differently. This results in thesorting of the families as shown in Fig. 1(d), and one recognizes that a large n p is a prerequisite for a high maximum T c (i.e. for optimal doping).While the knowledge of ν Q is sufficient for calculating n p , determination of n d requires the splittings measuredat both nuclei [13, 14]. Since NMR can only measure O enriched samples, the number of reports on ν Q is muchlower compared with ν Q (see Supplementary). Therefore, we could convert all the planar oxygen splittings fromthe literature, but only the corresponding subset of copper splittings. Although the plot of T c vs. n p in Fig. 1(d) issimilar to Fig. 1(c), it additionally includes non-superconducting and overdoped compounds. We also recognize inFig. 1(d) a parabolic-like dependence of T c on the oxygen charge n p , which resembles the typical phase diagram thatshows a dome-like dependence of T c on x . Since there is no superfluid in non-superconducting materials (parents, andfor doping outside the T c dome), they cannot be shown in the Uemura plot. Furthermore, the correlation between σ and ν Q is lost in the overdoped regime where σ decreases with increasing doping [15, 16] (which was attributed toa decrease of n s [17]).In Fig. 1(d) we also included results for the electron doped materials that we have obtained very recently.[14] Forelectron-doped Nd . Ce . CuO the muon relaxation rate and the superfluid density were reported to be very similarto that of hole-doped YBa Cu O + y . [4, 18, 19] We find that µ SR data for electron doped compounds are also inagreement with ν Q splittings (see Supplementary) and corresponding hole contents for those families, cf. Fig. 1(d).Electron-doping appears to be less efficient in providing a high T c , but the rather high oxygen hole content of theparent materials Pr(Nd) CuO suggests that hole-doping should result in much higher T c . Clearly, a large n p is onlya prerequisite for a high T c , but is not sufficient, as expected for such a material chemistry parameter. We also do notknow whether this empirical relation remains valid for higher oxygen hole content. If it does, the T c of the cupratesmight be raised by the proper chemistry substantially (we estimate 300 K to 400 K per oxygen hole from the straightline in Fig. 1(d)). Since the charge transfer between Cu and O is governed by 1 = n d + n p for the parent materials,we also conclude that compounds with the highest T c favor a smaller Cu hole content.These findings suggest a different kind of cuprate phase diagram that we present in Fig. 2. It does not use theaverage doping ( x ) as abscissa, but distinguishes between the oxygen and copper charges. The ordinary phase diagram( T vs. x ), cf. Fig. 1(b), appears as a projection that has x = n d + n p − J varies as a functionof n d and n p , the exchange between the CuO planes and with it the Ne´el temperature will depend on the chargereservoir layers, and correspondingly, T N shows no simple trend. The parent materials of the electron-doped cupratespromise a large T c upon hole doping.Doping appears essential for unlocking the maximum T c , and it changes n d and n p in a family-specific manner.While hole-doping changes mostly n p , electron-doping almost exclusively affects n d . According to our analysis, allfamilies show optimal doping near x = n d + n p − ≈ ± .
15. This suggests that optimal doping is related to the parentmagnetism rather than the distribution of charges between Cu and O. Electron-doping is less effective in unlockingthe maximum T c . The hole-doped compounds appear in three separate groups: (1) La − x Sr x CuO , (2) YBa Cu O + y and other cuprates of that structure, as well as YBa Cu O , and (3) Bi, Tl and Hg based families, which have thehighest T c values.Another important issue concerns the heterogeneity of the cuprates. We know from NMR that the static chargeand spin density can vary drastically within the CuO plane, in particular between different cuprate families [20].For example, the charge density in terms of the total doping x may easily vary by ∆ x ≈ . T c isnot in a simple relation to this static inhomogeneity, only the average n d and n p appear to matter. From this, onewould conclude that inhomogeneity is either not important for the maximum T c , or it is ubiquitous and dynamicallyaveraged for NMR, depending on the chemical environment. [20]Pressure has profound effects on T c and probably on n d and n p . This would be very revealing, and some of us areengaged with new high-pressure NMR experiments [24] and pursue this issue currently.Concerning the electronic fluid: it is beyond doubt now that the susceptibility of a single electronic spin componentcannot explain the cuprate NMR shifts [25, 26]. Instead, one needs at least a Fermi-liquid-like spin component thathas a temperature-independent spin polarization above T c , and a pseudogap-like spin component that is temperature-dependent far above T c for lower doping levels. A third, doping-dependent NMR shift term was recently identified[27], and it may represent the expected coupling between the two components. Therefore, it will be of great interestto see how the different spin components vary across the new phase diagram.To conclude, NMR measures the charge distribution in the bonding orbitals in the CuO plane quantitatively, andsince it reproduces the Uemura plot, i.e., it finds the same ordering of families with respect to their maximum T c ,we now have material chemistry parameters that are responsible for setting the highest T c and superfluid density.These findings inspired a new perspective on the cuprate phase diagram and it is very likely that the complex cuprateproperties might be better understood when discussed in the context of the charge distribution in the CuO plane. ACKNOWLEDGMENTS
Acknowledgement
We are thankful to O.P. Sushkov, C. P. Slichter, G. V. M. Williams for helpful discussions,and acknowledge financial support by the University of Leipzig, the DFG within the Graduate School Build-MoNa,the European Social Fund (ESF) and the Free State of Saxony. [1] Y. J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F.Kiefl, S. R. Kreitzman, P. Mulhern, T. M. Riseman, D. L. Williams, B. X. Yang, S. Uchida, H. Takagi, J. Gopalakrishnan,A. W. Sleight, M. A. Subramanian, C. L. Chien, M. Z. Cieplak, G. Xiao, V. Y. Lee, B. W. Statt, C. E. Stronach, W. J.Kossler, and X. H. Yu, Phys. Rev. Lett. , 2317 (1989).[2] S. V. Dordevic, E. J. Singley, D. N. Basov, S. Komiya, Y. Ando, E. Bucher, C. C. Homes, and M. Strongin, Phys. Rev.B , 134511 (2002).[3] A. T. Savici, Y. Fudamoto, I. M. Gat, T. Ito, M. I. Larkin, Y. J. Uemura, G. M. Luke, K. M. Kojima, Y. S. Lee, M. A.Kastner, R. J. Birgeneau, and K. Yamada, Phys. Rev. B , 014524 (2002).[4] C. C. Homes, S. V. Dordevic, M. Strongin, D. A. Bonn, R. Liang, W. N. Hardy, S. Komiya, Y. Ando, G. Yu, N. Kaneko,X. Zhao, M. Greven, D. N. Basov, and T. Timusk, Nature , 539 (2004).[5] J. L. Tallon, J. R. Cooper, S. H. Naqib, and J. W. Loram, Phys. Rev. B , 180504 (2006).[6] C. C. Homes, Phys. Rev. B , 180509 (2009).[7] S. V. Dordevic, D. N. Basov, and C. C. Homes, Sci. Rep. , 1713 (2013). [8] D. Wu, N. Barii, N. Drichko, P. Kallina, A. Faridian, B. Gorshunov, M. Dressel, L. Li, X. Lin, G. Cao, and Z. Xu, PhysicaC , S399 (2010).[9] C. C. Homes, Z. J. Xu, J. S. Wen, and G. D. Gu, Phys. Rev. B , 144530 (2012).[10] A. Shengelaya and K. A. Mller, EPL , 27001 (2015).[11] C. P. Slichter, Handbook of High-Temperature Superconductivity, edited by J. R. Schrieffer (Springer, 2007).[12] G. Zheng, Y. Kitaoka, K. Ishida, and K. Asayama, J. Phys. Soc. Jpn. , 2524 (1995).[13] J. Haase, O. P. Sushkov, P. Horsch, and G. Williams, Phys. Rev. B , 0945041 (2004).[14] M. Jurkutat, D. Rybicki, O. P. Sushkov, G. V. M. Williams, A. Erb, and J. Haase, Phys. Rev. B , 140504 (2014).[15] Y. J. Uemura, A. Keren, L. P. Le, G. M. Luke, W. D. Wu, Y. Kubo, T. Manako, Y. Shimakawa, M. Subramanian, J. Cobb,and J. Markert, Nature , 605 (1993).[16] C. Niedermayer, C. Bernhard, U. Binninger, H. Gl¨uckler, J. L. Tallon, E. J. Ansaldo, and J. I. Budnick, Phys. Rev. Lett. , 1764 (1993).[17] J. L. Tallon, C. Bernhard, and C. Niedermayer, Supercond. Sci. Technol. , A38 (1997).[18] A. Shengelaya, R. Khasanov, D. G. Eshchenko, D. Di Castro, I. M. Savi´c, M. S. Park, K. H. Kim, S.-I. Lee, K. A. M¨uller,and H. Keller, Phys. Rev. Lett. , 127001 (2005).[19] C. C. Homes, B. P. Clayman, J. L. Peng, and R. L. Greene, Phys. Rev. B , 5525 (1997).[20] J. Haase, Phys. Rev. Lett. , 189701 (2003).[21] D. Rybicki, J. Haase, M. Greven, G. Yu, Y. Li, Y. Cho, and X. Zhao, J. Supercond. Nov. Magn. , 179 (2009).[22] M. Jurkutat, J. Haase, and A. Erb, J. Supercond. Nov. Magn. , 2685 (2013).[23] P. M. Singer, A. W. Hunt, and T. Imai, Phys. Rev. Lett. , 047602 (2002).[24] T. Meissner, S. K. Goh, J. Haase, G. V. M. Williams, and P. B. Littlewood, Phys. Rev. B , 220517 (2011).[25] J. Haase, C. P. Slichter, and G. V. M. Williams, J. Phys.: Condens. Matter , 455702 (2009).[26] J. Haase, D. Rybicki, C. P. Slichter, M. Greven, G. Yu, Y. Li, and X. Zhao, Phys. Rev. B , 104517 (2012).[27] D. Rybicki, J. Kohlrautz, J. Haase, M. Greven, X. Zhao, M. K. Chan, C. J. Dorow, and M. J. Veit, arXiv:1505.01725v1. Supplement to: New Perspective on the Phase Diagram of CuprateHigh-Temperature Superconductors
Damian Rybicki ∗ University of Leipzig, Faculty of Physics and Earth Sciences, Linnestr. 5, 04103 Leipzig, Germany, andAGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of SolidState Physics, al. A. Mickiewicza 30, 30-059 Krakow, PolandEmail: [email protected]: +48.12.6172946
Michael Jurkutat
University of Leipzig, Faculty of Physics and Earth Sciences, Linnestr. 5, 04103 Leipzig, GermanyEmail: [email protected]: +49.341.9732605
Steven Reichardt
University of Leipzig, Faculty of Physics and Earth Sciences, Linnestr. 5, 04103 Leipzig, GermanyEmail: [email protected]: +49.341.9732605
Czes law Kapusta
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Department of SolidState Physics, al. A. Mickiewicza 30, 30-059 Krakow, PolandEmail: [email protected]: +48.12.6172554
J¨urgen Haase
University of Leipzig, Faculty of Physics and Earth Sciences, Linnestr. 5, 04103 Leipzig, GermanyEmail: [email protected]: +49.341.9732601 a r X i v : . [ c ond - m a t . s up r- c on ] N ov doping T c r[ K ] r[MHz] ν Q doping Bi-2212Hg-1201Hg-1212Hg-1223
Hg-1245
Tl-2201TlSr-1212rTl-2212Ba-0212F rHg-1234
La-214Y-123Y-124Y,Ca-123CLBLCO_0.4CLBLCO_0.1Pr-214La-112TlBa-1212Nd-214
Hg,Tl-1223
Tl-2223 r[MHz] ν Q FIG. 1. (Color online) Phase diagrams of cuprates based on quadrupole splittings of the planar copper ( left panel ) and oxygen( right panel ). Black and blue symbols and arrows (indicating increase of doping x ) are for hole and electron doped systems,respectively. Dotted lines are guides to the eye and connect different doping levels for one family. For compounds with threeor more CuO layers there are two different planar Cu and O sites, which have different quadrupole splittings, hence thehorizontally connected data points belong to the same sample. A detailed analysis of the planar oxygen and copper electric field gradient tensors in the cuprates is presentedelsewhere [1]. Here we only present collected literature values of the quadrupole splittings of planar copper ( ν Q ) and oxygen ( ν Q ) (table 1 and 2, respectively). All O and most of Cu splittings are also plotted in Fig. 1. Inthe case of the CLBLCO family there are ν Q data for more dopings.[2] Since all show the same behaviour in thetables we show only two families, for which both ν Q and ν Q are available. There are also ν Q results for cupratescontaining Bi, e.g. for single layer Bi-2201 family.[3] However, the Cu NQR spectra are very broad with at leastfour peaks (ranging from 27 MHz to 35 MHz), despite the fact that all Cu sites are equivalent in the ideal Bi-2201structure without the modulation in the Bi-O layer. Very broad Cu NQR spectra are a general feature of cuprateswith this type of modulation [4], and we only quote one ν Q obtained from NMR on Bi-2212 single crystals,[5] forwhich also ν Q is available.The hole contents of the oxygen 2 p σ ( n p ) and copper 3 d x − y ( n d ) orbitals, which are shown in the main paper, arecalculated using the following formulas [6]: n p = ν Q − .
39 MHz2 .