By Cu NMR we studied the spin and charge structure in
Nd_{2-x}Ce_{x}CuO_{4-delta}. For x=0.15, starting from a superconducting
sample, the low temperature magnetic order in the sample reoxygenated under 1
bar oxygen at 900^0 C, reveals a peculiar modulation of the internal field,
indicative for a phase characterized by large charge droplets ('Blob'-phase).
By prolonged reoxygenation at 4 bar the blobs brake up and the spin structure
changes to that of an ordered antiferromagnet (AF). We conclude that the
superconductivity in the n-type systems competes with a genuine type I
Mott-insulating state

A. A. Nugroho

H. B. Brom

I. M. Abu-Shiekah

I. P. McCulloch

J. Zaanen

M. Kato

O. N. Bakharev

English

arXiv

Crossref

NMR Evidence for a Two-Step Phase Separation in
                    
                      
                        
                          N

Quantum Matter and OpticsTheoretical Physic

Bakharev, O.

Abu-Shiekah, I.M.

Brom, H.B.

Nugroho, A.A.

McCulloch, I.P.

Zaanen, J.

Leiden University Scholary Publications

P H Y S I C A L R E V I E W L E T T E R S week ending16 JULY 2004VOLUME 93, NUMBER 3NMR Evidence for a Two-Step Phase Separation in Nd1:85Ce0:15CuO4O. N. Bakharev,1 I. M. Abu-Shiekah,1 H. B. Brom,1 A. A. Nugroho,2,* I. P. McCulloch,3 and J. Zaanen31Kamerlingh Onnes Laboratory, Leiden University, POB 9504, 2300 RA Leiden, The Netherlands2Van der Waals-Zeeman Institute, University of Amsterdam, 1018 XE Amsterdam, The Netherlands3Instituut Lorentz for Theoretical Physics, Leiden University, POB 9506, 2300 RA Leiden, The Netherlands(Received 15 January 2004; published 15 July 2004)037002-1By Cu NMR we studied the spin and charge structure in Nd2xCexCuO4. For x  0:15, startingfrom a superconducting sample, the low temperature magnetic order in the sample reoxygenated under1 bar oxygen at 900 C reveals a peculiar modulation of the internal field, indicative of a phasecharacterized by large charge droplets (‘‘blob’’ phase). By prolonged reoxygenation at 4 bars the blobsbreak up and the spin structure changes to that of an ordered antiferromagnet. We conclude that thesuperconductivity in the n-type systems competes with a genuine type I Mott-insulating state.DOI: 10.1103/PhysRevLett.93.037002 PACS numbers: 74.72.Dn, 75.30.Ds, 75.40.Gb, 76.60.–kand the strong pinning phase there is yet another phase.By reoxygenating a superconducting Nd2xCexCuO4applied external magnetic field Bappl. An example for x 0:15 withBappljjc is shown in Fig. 1(a) at high temperatureAt present an important issue in cuprate superconduc-tivity is the nature of the electronic state(s) competingwith the superconducting state (see [1,2] and referencestherein). In the hole doped cuprates evidence has beenaccumulating that at low dopings this competitor is astripe phase [3]. It is believed that these stripe phasesfind their origin in the microscopic incompatibility be-tween the metallic- and Mott-insulating states [4,5].Stripes are a priori not a unique way of resolving thisincompatibility. This was sharply formulated recently interms of the analogy with superconductivity [6]; stripescan be viewed as the analogue of the type II supercon-ductor while a type I behavior is also imaginable. In thelatter the Mott insulator and the metal/superconductor areimmiscible, and one expects a state characterized bydroplets of the metal/superconductor in a Mott-insulatingbackground. The electron doped (n-type) superconductorsare microscopically [7] quite different from the holedoped ones, while macroscopic properties also seem dis-tinct [8]. So far, no incommensurate spin fluctuationshave been found by neutron scattering in this system[9–11], arguing against stripe phases. Instead, recentlyit was reported that field induced commensurate antifer-romagnetism reemerges in the superconducting state inthe presence of an Abrikosov vortex lattice [12], suggest-ing that the superconductivity competes with a conven-tional antiferromagnet.Different from the p-type systems, the n-type systemsstay insulating up to quite high dopings while the anti-ferromagnetism of half filling degrades quite slowly. Infact, Vajk et al. [10] showed that the behavior of thisantiferromagnet can be understood in detail assuming arandom dilution of the Heisenberg quantum antiferro-magnet, suggesting that the individual carriers staystrongly bound to impurity sites. Is the field inducedantiferromagnet of a similar kind? Using NMR wepresent here evidence that between the superconductor0031-9007=04=93(3)=037002(4)$22.50 (NCCO) sample with x  0:15 up to the point that super-conducting diamagnetism has disappeared, we have de-tected a phase in a very small oxygen-doping rangelocated between the superconductor and the site dilutedantiferromagnet. This phase is extremely sensitive tofurther oxygenation. Approximately one oxygen atomper 100 [13] unit cells suffices to destroy this phase,allowing a site-dilution antiferromagnet to take over.With NMR one can measure the amplitude distributionof the magnetic moments. These show a double-peakdistribution in this special phase. Extensive Monte Carlo(MC) simulations on a representative model show thatsuch a distribution only arises in either a stripe phase or asituation where large droplets are formed. Since the neu-tron scattering appears to rule out the former, we con-clude that the superconductivity in the n-type systemscompetes with a genuine type I Mott-insulating state [6].Experimental.—The experiments were performed onsingle crystals with x  0:15, 0.12, and 0.08. For x 0:15 the oxygen reduced sample (NCCOp) had a super-conducting transition temperature of Tc  21 K. Half ofthe crystal (2  1  0:2 mm) was reoxygenated in air at900 C until no superconductivity could be detected inthe SQUID-susceptibility measurement (sample NCCO1).After performing the full set of NMR measurements, thesame sample was oxygenated further under 4 bars ofoxygen at 850 C for 20 h (sample NCCO2), and NMRscanned again. Sample preparation and characterizationare described elsewhere [14]. The Cu NMR spectrawere obtained with conventional phase coherent pulsedNMR between 4 and 350 K by sweeping the magneticfield at various constant frequencies. The NMR lineshift was determined by using a gyromagnetic ratio of1:1285 MHz=kOe for 63Cu and K  0:238% of metallicCu as a reference.The Cu NMR spectra were studied for two orientations(Bappljjc and Bappljjab) of the crystals with respect to2004 The American Physical Society 037002-1FIG. 1. Cu NMR spectra for x  0:15 in NCCOp (for com-parison scaled down from 78 to 43 MHz) at 100 K (at thistemperature the spectra for NCCO1 and NCCO2 are identicalto that of NCCOp) and NCCO1 at 5 K. The broadening andshifts at low temperature are clearly visible.FIG. 2. (a) Amplitude distribution of the internal field forNCCO1 at 5 K. The solid line gives the profile of the hyperfinefield, as deduced from B k c. From the data for B ? c theantiferromagnetic alignment of the electron spins in the 	a; bplane appears to be strongly disordered (see text). (b) Simplereconstruction of the internal field distribution for a one- andtwo-dimensional spin structure. In 1D the radial coordinate rand (incommensurate) wave vector kr have to be read as x andkx. In 2D cylindrical symmetry is assumed.P H Y S I C A L R E V I E W L E T T E R S week ending16 JULY 2004VOLUME 93, NUMBER 3(100 K). The two narrow lines correspond to the centraltransitions of the two copper isotopes 63Cu and 65Cu andare superposed on a relatively broad background thatlikely originates from quadrupole satellites with smallquadrupole frequencies. For characterization of thesamples, we measured the T dependencies of the normal-ized product of the line intensity (I) (corrected for T2effects) and T, the NMR line shift 63K, and the funda-mental relaxation probability W1 [15–18]. Here we con-centrate on the low temperature field profiles on the Cusites only; the internal field effects are so large that therole of the Nd moments can be neglected.Analysis of the low temperature profiles.—In the pres-ence of the static hyperfine magnetic field Bhf on thecopper nuclei produced by ordered Cu2 spins, one shouldobserve two Cu NMR lines at B  B2appl  B2hf 2BapplBhf cos0:5, where  is the angle between the di-rections of Bappl and Bhf . It is known from neutron scat-tering experiments on Nd1:85Ce0:15CuO4 [9] that the Cu2spins are ordered antiferromagnetically in the ab plane.Therefore, for Bappljjc (  90) only one Cu NMRresonance is expected at a lower value than the fieldcalculated from the gyromagnetic ratio, B0. For thosenuclei, where for some reason the internal field is can-celed, the resonance is unshifted. The Cu NMR spectrarecorded for Bappljjc for x  0:08, 0.13, and 0.15 canindeed be qualitatively explained in this way: for x 0:15 [see Fig. 1(b)], part of the nuclei mainly feel theexternal field [resonate at the fields of Fig. 1(a)] and theremainder experiences an internal field in addition. Atlower doping the line shifts are larger. The spectra forBappljjab [see Fig. 1(c)] seem to be composed out of atleast two lines of different intensities. This difference isnot due to T2 or different =2 conditions, because theseare similar for both peaks [T12  23	1  103 s1 and=2  2 s].For a quantitative analysis, the low-temperature copperNMR spectra of NCCO1 at 5 K were simulated by exact037002-2diagonalization of the nuclear spin Hamiltonian H witheffective spin I  1=2 (the quadrupolar interaction isweak compared to the magnetic interaction) for bothisotopes 63Cu and 65Cu. For B k c, H can be writtenas H hBapplIzhBhfIxcos’Iy sin’hB1Ix,where the z direction is along the crystallographic caxis and ’ is the angle between Bhf and the rf field B1(along the x axis); for B ? c, Iz has to be replaced by Iy.Bappl ? B1 in all experiments and the antiferromagnetic(AFM) coupled electron spins are assumed to be alwaysin the 	a; b plane. The amplitude distribution of theinternal field P	Bhf was obtained via Monte Carlo opti-mization to reproduce the data for B k c [see Fig. 2(a)].Analysis of the B ? c data [Fig. 1(c)] with this pure in-plane AFM spin model indicates that the alignment ofthe electron spins is rather disordered in the 	a; b planeand, on average, shows a field induced canting of some20, which does not influence significantly the distribu-tion P	Bhf in Fig. 2(a). In the x  0:12; 0:08 samples thecomputations give a single peak at a field 3 T, consistentwith a simple commensurate antiferromagnet. However,in the slightly oxygenated x  0:15 sample this spin-amplitude distribution is quite structured: the peak at2.4 T (corresponding with a reduced moment of0:14B) is asymmetric, showing a slow decrease onthe smaller moment side, while a second peak at thevanishing internal field corresponds with sites where theinternal fields have completely disappeared.Interpretation.—If the internal-field distribution wouldarise from a stripelike spin structure with wave vector kx,we would have P	B  d	kxx=dB and hence x /RB=Bmax0 P	B dB. Using the experimental outcome forP	Bhf the integration leads to the 1D wave depicted inFig. 2(b); note that, because the Cu nuclei that experience037002-2FIG. 3 (color). A 2D map of the blob (a) and stripe (b) resultsfrom thermalized averaged MC simulations, obtained with theHamiltonian discussed in the text. The spin-orientational dis-order in the 	a; b plane is represented by a difference in color(complementary colors correspond to opposite aligned spins),while the color intensity corresponds to the spin value. Thespin-zero regions (black), as also seen in experiment, are foundin the stripe simulations, but are almost absent for small blobs.The parameters for the blob and stripe panels are (J  1,VC  0): J1  0:2, Q  0:2, VS  0:2, R  10, T  0:4 andJ1  1, Q  0:4, VS  0:2, R  10 with T  0:3.FIG. 4 (color). Blob results from the MC simulations: a ther-malized result for larger blobs than in the previous figure. Onlyif blobs are sufficiently large, can zero field sites be generatedin the presence of the transferred hyperfine interaction. For stilllarger blobs the zero field contribution further increases.Parameter values are J  1, T  0:3, J1  0, Q  0:04, VS 0:2 with R  10 and VC  1:5.P H Y S I C A L R E V I E W L E T T E R S week ending16 JULY 2004VOLUME 93, NUMBER 3Bhf have regular lattice positions, the wave vector needs tobe incommensurate to realize such a field distribution atthe Cu sites. The peak of P	Bhf at zero internal field inFig. 2(a) then corresponds with the nodes. However, thefield profile for a radially symmetric two-dimensionalspin profile can be generated similarly via 	krr2 /RB=Bmax0 P	B dB and is given in the same figure. Thesesimple calculations are meant to show only that bothstripelike structures (comparable to the 1D case) andcharge blobs (2D case) are compatible with the experi-mental data. Furthermore, the needed zero field region in2D is larger than in 1D (because of the transferred hyper-fine interaction, the size of the blobs with zero spinexceeds the zero field region).The size enters into the problem even stronger becauseof the specific form of the Hamiltonian. The internal fieldhas not only an on-site contribution A, but also the trans-ferred hyperfine interaction B  A=4, which gives a fieldof opposite sign, and hence in a droplet a nonzero field isgenerated on zero-spin sites (in a stripe configuration zerofield states are easier to generate because it is an anti-domain boundary). To make this case more persuasive weperformed Monte Carlo simulations on a classical modeldesigned to interpolate smoothly between stripelike anddropletlike ground state textures [19]. This is a classical,spin-full lattice gas model, which is similar to themodel introduced by Stojković et al. [20]. It builds inthe quantum-physical ingredient that electrons or holes[‘‘charge,’’ 	1  ni] cause antiphase boundaries inthe spin system by a ‘‘charge mediated’’ exchange inter-action [21] coupling the spins antiferromagneticallyacross the charge, Hspin  JPx;ySx;y	Sx;y1  Sx1;y J1Px;ySx;y	1  nx;y1Sx;y2  	1  nx1;ySx2;y withJ; J1  0. The frustration in the spin system is releasedby the formation of charged domain walls. The frustratedphase separation motive is built in by balancing the spin-mediated attractive charge-charge interactions with arepulsive 1=r Coulomb interaction of strength Q betweenthe charges, which we cut off at ten sites (beyond theinterstripe distance) for reasons of numerical efficiency[22]. We take an XY spin system, and the spin-orienta-tional disorder is built in by a spin pinning potential,breaking the ground-state degeneracy by choosing a di-rection (up to spin reflection) for the antiferromagneticbackground, as well as providing an inhomogeneouscharge potential. It has the form HPot VSjPx;ySx;yPx;yj, where Px;y Px0;y0Ax0;y0ei&x0 ;y0 exp	x x02  	y y02p=R with R the correlationlength over which the antiferromagnetic background isallowed to rotate. The angle &x0;y0 is chosen randomlywith a uniform distribution and amplitude Ax0;y0 random0; 1. Finally we also incorporate a quencheddisorder potential acting on the charge in the form ofVC  random0; 1.Despite its simplicity, this simple model is capable ofgenerating quite complex ground states, ranging from037002-3highly disordered droplet patterns (J1 ! 0) to very or-derly stripe patterns J1; J Q;VS. In the simulations weused small but finite temperatures and thermal annealing,mimicking the effects of quantum fluctuations in smear-ing the sharp textures [23] in this classical model. Twotypical outcomes are illustrated in Figs. 3 and 4. We haveextensively scanned the parameter space of this model.Invariably, we find that a double peak structure is easilyassociated with stripelike patterns [Fig. 3(b)], but theseconfigurations invariably lead to incommensurate scatter-ing amplitudes, which are not observed experimentally.037002-3FIG. 5. Copper NMR spectra (the intensity in arbitrary unitsalong the vertical axis is plotted against the magnetic fieldvalue in tesla) at 5 K for NCCO1 and NCCO2 (a). The linesin (b) are fits with an optimized internal field distribution(see text).P H Y S I C A L R E V I E W L E T T E R S week ending16 JULY 2004VOLUME 93, NUMBER 3When droplets are formed instead, the zero-moment peakis always lacking for small droplets (Figs. 3 and 4). Onlydroplets of 2 nm or more (25 sites or larger) mimic thepeculiarities of the NMR spectra. This adds confidence toour claim that the double peak structure in the localmoment distribution is the NMR fingerprint signalingthe presence of large charge blobs.How can we reconcile our findings with the neutronscattering evidences favoring the site-diluted antiferro-magnet? The NMR sample has a volume of 1 mm3, muchsmaller than typical neutron targets, and we found thelarge droplet phase by almost continuously monitoringthe disappearance of the superconducting state while thesample was oxygenated. Apparently, the large dropletphase in the NCCO1 sample is linked to the presence ofa tiny amount of apical oxygens ( 0:005 for NCCO1)[13]. The result for continuing the oxygenation of NCCO1in 4 bars of oxygen as used in other studies [11] is given inFig. 5. The data clearly show that in NCCO2 the phase ofNCCO1 is suppressed in favor of a new phase [24].Applying a similar analysis as before, we find that thisnew phase is characteristic of an antiferromagnet with aninternal field of 3 T, the phase seen in the neutron data.Although it is hard to arrive at precise numbers, it seemsthat one extra oxygen per roughly 100 unit cells suffices tofracture the droplets and to favor a state where the chargecarriers are strongly bound to impurities. As the super-conductor, the large droplet insulating phase shows anextreme sensitivity to oxygen concentration explainingwhy this phase has been missed in the neutron scatteringstudies.In summary, we have presented evidence demonstrat-ing that the n-type cuprate superconductor is in a direct037002-4competition with a phase where the charge carriers formlarge droplets in a commensurate antiferromagneticbackground. This phase is in turn extremely sensitive tothe chemical conditions. Tiny amounts of excess oxygensuffice to destroy both superconductivity and the largedroplet phase in favor of a phase where the charge carriersare strongly bound to the impurities.We acknowledge fruitful discussions with MartinGreven (Stanford) and the financial support of FOM/NWO. Some of the numerical calculations were per-formed at the APAC National Facility via a grant fromthe Australian National University Supercomputer TimeAllocation Committee.*Present address: MSC, University of Groningen,Neijenborg 4, 9747 AG Groningen, The Netherlands.[1] S. Sachdev, Rev. Mod. Phys. 75, 913 (2003).[2] S. A. Kivelson et al., Rev. Mod. Phys. 75, 1201 (2003).[3] J. M. Tranquada et al., Nature (London) 375, 561 (1995).[4] J. Zaanen and O. Gunnarsson, Phys. Rev. B 40, 7391(1989); M. Kato et al., J. Phys. Soc. Jpn. 59, 1047 (1990).[5] V. J. Emery and S. A. Kivelson, Physica (Amsterdam)209C, 597 (1993).[6] D. H. Lee and S. A. Kivelson, Phys. Rev. B 67, 024506(2003).[7] J. Zaanen, G. A. Sawatzky, and J.W. Allen, Phys. Rev.Lett. 55, 418 (1985).[8] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.70, 1039 (1998).[9] K. Yamada et al., J. Phys. Chem. Solids 60, 1025 (1999).[10] O. P. Vajk et al., Science 295, 1691 (2002).[11] P. K. Mang et al., cond-mat/0307093.[12] H. J. Kang et al., Nature (London) 423, 522 (2003).[13] Y. Onose et al., Phys. Rev. Lett. 82, 5120 (1999).[14] A. A. Nugroho et al., Phys. Rev. B 60, 15 379 (1999).[15] N. J. Curro et al., Phys. Rev. Lett. 85, 642 (2000).[16] I. M. Abu-Shiekah, O. Bakharev, H. B. Brom, andJ. Zaanen, Phys. Rev. Lett. 87, 237201 (2001).[17] A.W. Hunt, P. M. Singer, A. F. Cederström, and T. Imai,Phys. Rev. B 64, 134525 (2001).[18] Details of the NMR relaxation and line shift data will bepublished elsewhere and are available on request.[19] K. Pijnenburg, Master’s thesis, Leiden University, 1996.[20] B. P. Stojković et al., Phys. Rev. Lett. 82, 4679 (1999).[21] J. Zaanen, J. Phys. Chem. Solids 59, 1769 (1998).[22] Using cutoffs larger than the typical length scale of thehighly structured solutions did not change the picture.[23] J. Zaanen et al., Philos. Mag. B 81, 1485 (2001).[24] Prolonged oxidation is expected to turn the crystalcompletely to the AFM phase; we decided to keepthe sample in its present mixed state to allow furtherinspection.037002-4

NMR evidence for two-step phase-separation in Nd1.85Ce0.15CuO4-δ

By Cu NMR we studied the spin and charge structure in Nd2-xCexCuO4-delta. For x=0.15, starting from a superconducting sample, the low temperature magnetic order in the sample reoxygenated under 1 bar oxygen at 900 degreesC reveals a peculiar modulation of the internal field, indicative of a phase characterized by large charge droplets ("blob" phase). By prolonged reoxygenation at 4 bars the blobs break up and the spin structure changes to that of an ordered antiferromagnet. We conclude that the superconductivity in the n-type systems competes with a genuine type I Mott-insulating state

Bakharev, ON

Abu-Shiekah, IM

Brom, HB

Nugroho, AA

McCulloch, IP

Zaanen, J

University of Queensland eSpace

NMR evidence for a two-step phase separation in Nd1.85Ce0.15CuO4-delta

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