brief communications observed optical bumps. These arise photons in quantumspace-time should lead quadratic space-time birefringence could reverse that to a measurable difference in arrival time(of be tested experimentally in the future by form in the refreshed shocks the order of milliseconds)for photons with polarimetry of such GRBs Jonathan Granot, Ehud Nakart, Tsvi Pirant di I therefore conclude that either the nstitute for Advanced Study, Princeton GRB 021206 allows us to test another possi- n=1 should be below the level of x>10- fRacah Institute for Physics, The Hebrew ble effect of quantum space-time, which is or it should be quadratic(n=2), assuming University, Jerusalem 91904, Israel redicted for canonical quantum gravity in that the strong linear polarization of GRBs e-mail: udinieplys huji acil loop representation. In this case, space-time is confirmed by asecond measurement. xhibits the property of birefringence: two Igor G Mitrofan photons with opposite states of helicity, +1 search Institute, Profsojuznaya str 84/32, 3. Price pa.eaNa2844-847(20) . Rees, M. i& Meszaros, P. Astrophys. L. 196, L1-LA(1998). and -1, have different group velocities 117997 Moscow. Russia 5. Kumar, P& Piran, T. Astroplys J 532, 286-293(2000 V2=c(1±x(EFc 7. Granot, 1, Mille M. Piran. T. Suen, W M. Cnot.E. Frontera, The factor x is about 1 for loop z Jacobson, T, Liberati, D& Mattingly, D. Nature 121, E& Hjorth, J)312-314 (Springer, Berlin, 2001). tion of quantum gravity. A linear D. V. Sarkar S. Nature 393. 768 electromagnetic wave may be repi the superposition of two mon 5. Gonzalez, M. M. et al. Nature 124 749-751(20 ives with opposite circular polarizations COMMUNCATIONS ARISING When a linearly polarized wave propagates inside the substance with birefringence, the A constraint on canonical plane of polarizatic s ee m group velocity Condensed-matter physics quantum gravity? For the linear case n=i, the phase angle. Spurious magnetism in im ma ras fromthe y-ray burst (grb) sl, of a plane of linear polarization changes high-Tc superconductor strongly linearly polarized,with the ne challenge in condensed-matter estimated degree of polarization(80+20%) △q1(E=x(Dhd)E/Ec= ravel the interplay being close to the absolute maximum of 10x(E/0. 1 Mev) between magnetism and supercon tivity in copper oxides with a high critical onstrain models of quantum gravity, which This angle depends on the photon energy as temperature(To). Kang et al. claim to have has had 10 years to act on the photons as E. Linear polarization measured within a revealed a quantum phase transition from they travelled towards us. Here I show that if broad energy range should vanish, provided the superconducting to an antiferromagnetic the effects of quantum gravity are linearly that the difference in accumulated angles is state in the electron-doped material proportional to the ratio of the photon energy large for photons with different energies. Nd2-Ce, CuO,(NCCO)based on the obser- to the characteristic scale energy of quantum Two photons with energies of around 0.1 vation of magnetic-field-induced neutron- gravity, then the polarization of photons Mev and with a difference of energy of scattering intensity at (1/2, 1/2,0),(1/2, 0.0 with energies of about 0.1 Mev should be about 0.01% will therefore accumulate a and related reflections. Here we argue that pletely random, contrary to what is difference of Sp=x in polarization phase the observed magnetic intensity is due to observed. I conclude that, should the polar- angle after a year of propagation in spac condary phase of (Nd, Ce)2O, We therefor ization measurement be confirmed, quan- with birefringence(see equation(2)) contend that the effect is spurious and not tum gravity effects act with a power that is For cosmological GRBs, which havea travel intrinsic to superconducting NCCO greater than linearity, or that loop quantum distance of D=10 light years, the planes of To achieve superconductivity in NCCO, gravity is not viable. Compared with previ- linear polarization of photons with different a rather severe oxygen-reduction procedure ous methods and results(see ref 2, for exam- energies should be totally randomized. The has to be applied. We have discovered that ple), testing of the linear polarization of bulk linearpolarization of photonswithener- the reduction process decomposes a small cosmic y-ray bursts may substantially extend gies greater than 0.01 eV over a broad energy (0.01-0.10%)volume fraction of NCCO. The the observational windo the theory of range must become zero even if they were all resultant(Nd, Ce)O, secondary phase has the quantum gravity originally 100% polarized inasingle plane. complex cubic bixbyite structure, common GRBs are characterized by a highly vari- In the quadratic case of quantum space- among rare-earth(RE) sesquioxides, with a able flux of high-energy photons that propa- time birefringence with n=2, the rotation of lattice constant, a, that is about 2 v2 times the gate over cosmological distances. It has been a plane of linear polarization is rather small planar lattice constant of tetragonal NCCO suggestedthat they are the best candles in for photons with energy of around o 1 Mev(Nd, Ce)2O, is epitaxial with the host lattice, smological space, allowing us either to with long-range order parallel to the CuO2 study or to constrain the effects of quantum △q2(E= x(D/hc)E/Ec2= planes ofNCCO, butextending onlyabout5 gravity. These effects are knownto be pro- 10 x(EO. 1 Mev)'D perpendicular to the planes. Because of the portional to the ratio(E/Eoc)"of the phot relationship between the two lattice con ergy, E, to the Planck energy, EoG=10 However, the distance D-10 light years stants, certain structural reflections from the GeV, and to the distance, D, of the photon's is so large that even the quadratic case of impurity phase appear at seemingly com- propagation. The linear case(n=1)is the birefrigence could be tested by polarization mensurate NCCO positions-that is, the est studied, but the quadratic case(n=2) measurements of photons with energies cubic(2, 0,0), reflection can also be indexed as has also recently been considered(see greater than 100 MeV. The detection of (1/2, 1/2,0). However, there is roughly a 10% preprintathttp://xxx.lanlgov/ps_cachE/ahigh-energycomponentofGrb941017mismatchbetweena,andthec-latticecon gr-qc/pdf/0305/0305057. pdf). For n=1, the (energies up to 200 Mev), which dominates stant of NCCO, and therefore(0,0, 2) can also effect of the energy-dependent refraction of the total fluence of the event, suggests that beindexedas(0, 0, 2.2) NaturEvOl42613november2003www.nature.com/nature e 2003 Nature Publishing Group 139
brief communications NATURE|VOL 426 | 13 NOVEMBER 2003 |www.nature.com/nature 139 COMMUNICATIONS ARISING Astrophysics A constraint on canonical quantum gravity? G amma rays from the g-ray burst (GRB) 021206 have been reported to be strongly linearly polarized1 , with the estimated degree of polarization (80520%) being close to the absolute maximum of 100% — affording us the opportunity to constrain models of quantum gravity, which has had 1010 years to act on the photons as they travelled towards us. Here I show that if the effects of quantum gravity are linearly proportional to the ratio of the photon energy to the characteristic scale energy of quantum gravity, then the polarization of photons with energies of about 0.1 MeV should be completely random, contrary to what is observed. I conclude that, should the polarization measurement be confirmed, quantum gravity effects act with a power that is greater than linearity, or that loop quantum gravity is not viable. Compared with previous methods and results (see ref. 2, for example), testing of the linear polarization of cosmic g-ray bursts may substantially extend the observational window on the theory of quantum gravity. GRBs are characterized by a highly variable flux of high-energy photons that propagate over cosmological distances. It has been suggested3 that they are the best candles in cosmological space, allowing us either to study or to constrain the effects of quantum gravity. These effects are known3,4 to be proportional to the ratio (E/EQG) n of the photon energy, E, to the Planck energy, EQGö1019 GeV, and to the distance, D, of the photon’s propagation. The linear case (n41) is the best studied3,4, but the quadratic case (n42) has also recently been considered (see preprint at http://xxx.lanl.gov/PS_cache/ gr-qc/pdf/0305/0305057.pdf). For n41, the effect of the energy-dependent refraction of photons in quantum space-time should lead to a measurable difference in arrival time (of the order of milliseconds) for photons with different energies2 . The linear polarization of g-rays from GRB 021206 allows us to test another possible effect of quantum space-time, which is predicted for canonical quantum gravity in loop representation. In this case, space-time exhibits the property of birefringence4 : two photons with opposite states of helicity,&1 and 11,have different group velocities v54c(15x(E/EQG) n ) (1) The factor x is about 1 for loop representation of quantum gravity3 . A linearly polarized electromagnetic wave may be represented as the superposition of two monochromatic waves with opposite circular polarizations. When a linearly polarized wave propagates inside the substance with birefringence, the plane of polarization rotates along the path because of the difference in group velocity between the two circular components. For the linear case n41, the phase angle, w1, of a plane of linear polarization changes along a distance D(in light years) as Dw1(E)öx(D/hc)E2 /EQGö 104 x(E/0.1 MeV)2 D (2) This angle depends on the photon energy as E2 . Linear polarization measured within a broad energy range should vanish, provided that the difference in accumulated angles is large for photons with different energies. Two photons with energies of around 0.1 MeV and with a difference of energy of about 0.01% will therefore accumulate a difference of dwöx in polarization phase angle after a year of propagation in space with birefringence (see equation (2)). For cosmological GRBs,which have a travel distance of Dö1010 light years, the planes of linear polarization of photons with different energies should be totally randomized. The bulk linear polarization of photons with energies greater than 0.01 eV over a broad energy range must become zero even if they were all originally 100% polarized in a single plane. In the quadratic case of quantum spacetime birefringence with n42, the rotation of a plane of linear polarization is rather small for photons with energy of around 0.1 MeV Dw2(E)öx(D/hc)E3 /EQG 2 ö 10–19x(E/0.1 MeV)3 D (3) However, the distance Dö1010 light years is so large that even the quadratic case of birefrigence could be tested by polarization measurements of photons with energies greater than 100 MeV. The detection5 of a high-energy component of GRB941017 (energies up to 200 MeV), which dominates the total fluence of the event, suggests that quadratic space-time birefringence could be tested experimentally in the future by polarimetry of such GRBs. I therefore conclude that either the birefringence of quantum space-time with n41 should be below the level of x¤10114, or it should be quadratic (n42), assuming that the strong linear polarization of GRBs is confirmed by a second measurement. Igor G. Mitrofanov Space Research Institute, Profsojuznaya str. 84/32, 117997 Moscow, Russia e-mail: imitrofa@space.ru 1. Colburn, W. & Boggs, S. E. Nature 423, 415–417 (2003). 2. Jacobson, T., Liberati, D. & Mattingly, D. Nature 424, 1019–1021 (2003). 3. Amelino-Gamelia, G., Ellis, J., Mavromatos, N. E., Nanopoulos, D. V. & Sarkar, S. Nature 393, 763–765 (1998). 4. Gambini, R. & Pullin, J. Phys. Rev. D 59, 124021 (1999). 5. Gonzalez, M. M. et al. Nature 424, 749–751 (2003). observed optical bumps. These should arise from emission by the reverse shocks that form in the refreshed shocks. Jonathan Granot*, Ehud Nakar†, Tsvi Piran† *Institute for Advanced Study, Princeton, New Jersey 08540, USA †Racah Institute for Physics, The Hebrew University, Jerusalem 91904, Israel e-mail: udini@phys.huji.ac.il 1. Stanek, K. Z. et al. Astrophys. J. 591, L17–L20 (2003). 2. Hjorth, J. et al. Nature 423, 847–850 (2003). 3. Price, P. A. et al. Nature 423, 844–847 (2003). 4. Rees, M. J. & Mészáros, P. Astrophys. J. 496, L1–L4 (1998). 5. Kumar, P. & Piran, T. Astrophys. J. 532, 286–293 (2000). 6. Sari, R. & Mészáros, P. Astrophys. J. 535, L33–L37 (2000). 7. Granot, J., Miller, M., Piran, T., Suen, W. M. & Hughes, P. A. in Gamma-Ray Bursts in the Afterglow Era (eds Costa, E., Frontera, F. & Hjorth, J.) 312–314 (Springer, Berlin, 2001). Competing financial interests: declared none. COMMUNICATIONS ARISING Condensed-matter physics Spurious magnetism in high-Tc superconductor One challenge in condensed-matter physics is to unravel the interplay between magnetism and superconductivity in copper oxides with a high critical temperature (Tc). Kang et al.1 claim to have revealed a quantum phase transition from the superconducting to an antiferromagnetic state in the electron-doped material Nd21xCexCuO4 (NCCO) based on the observation of magnetic-field-induced neutronscattering intensity at (1/2,1/2,0), (1/2,0,0) and related reflections. Here we argue that the observed magnetic intensity is due to a secondary phase of (Nd,Ce)2O3. We therefore contend that the effect is spurious and not intrinsic to superconducting NCCO. To achieve superconductivity in NCCO, a rather severe oxygen-reduction procedure has to be applied2 . We have discovered that the reduction process decomposes a small (0.01–0.10%) volume fraction of NCCO.The resultant (Nd,Ce)2O3 secondary phase has the complex cubic bixbyite structure, common among rare-earth (RE) sesquioxides3 , with a lattice constant,ac,that is about 2£2 times the planar lattice constant of tetragonal NCCO. (Nd,Ce)2O3 is epitaxial with the host lattice, with long-range order parallel to the CuO2 planes of NCCO,but extending only about 5ac perpendicular to the planes. Because of the relationship between the two lattice constants, certain structural reflections from the impurity phase appear at seemingly commensurate NCCO positions — that is, the cubic (2,0,0)creflection can also be indexed as (1/2,1/2,0). However, there is roughly a 10% mismatch between ac and the c-lattice constant of NCCO,and therefore (0,0,2)c can also be indexed as (0,0,2.2). © 2003 Nature PublishingGroup
brief communications There are 32 rare-earth ions in the rEo nit cell, belonging to two crystallographically NCCOat(1/2. 1/2,0), Mang etal. argue that distinct sites with inequivalent saturated o Grant toour c-axis field-induced scattering our observed magnetic scattering is due oments. At the(2, 0,0), reflection, the con- entirely to(Nd, Ce)2O, We disagree, however. tributions from the two rare-earth sites inter There are three ways to resolve this impu in the observed scattering intensity in the206 rity problem. First, if the magnetic scattering at(1/2, 1/2,0)(ref. 2) is due entirely to paramagnetic phase if the moments saturate (Nd, Ce)2O,, one would expect the field- at different fields. Although the magnetic induced intensity to be identical when B is structure and spin hamiltonian of epitaxial arallel to the c-axis and when it is parallel to quasi-two-dimensional (Nd, Ce)2O3 are he [1, -1, 0] axis, as required by the cubic unknown, it is possible to devise simple mmetry of (Nd, Ce)2O,. Experimentally periments to test whetherthe field-induced we find that the field-induced effect at scattering is due to NCCO or(Nd, Ce)2O. (1/2, 1/2.0)is much larger when Bis parall Kang et al. find that at a temperature of to the c-axis which is inconsistent with the 5 K, the(1/2. 1/2.0)(that is, (2.0.0))intensity 0.8 cubic symmetry of(Nd, Ce)O, but consis- aches a peak at a field of about 6.5 T, and tent with the upper critical field of NCCO upper critical field B2 of NCCO. Figure la being much smaller in this geometry Second. as the latti summarizes the field dependence of an x=0.18 superconducting sample of ours in parameterof NCCo (ref 1), measurementsat the non-zero integer L cannot be contaminated era a with those of Kang et al. The figure by(Nd, Ce)2O,. Our experiments indicate shows that the intensity scales with B/Tand that the(1/2, 1/2, 3)peak shows an induced exhibits a peak consistent with two-moment antiferromagnetic component when the field paramagnetism. Furthermore, as the upper is along the c-axis and hence superconduct itical field of a superconductor increa tivityisstronglysuppressed, but not whenin withdecreasing temperature, thisimplies tha 06 the a-b plane and superconductivity is only thereported correspondence the peak posi- weakly affected. This is direct proof of the tion with b, at 5 K is coincidental. We do not connection between field-induced antiferro- observe spontaneous neodymium ordering agnetic order and suppression of super- of either(Nd, Ce)O, or NCCO down to 1.4K. onductivity in NCCO. We also note that the x=0.10 sample, both at the previously Figure 1 Fled and temperature dependence of magnet cater- the cubicsymmetry of (Nd cen g pi. ved igure 1b, c shows that the field effects qualitatively different behaviour observed reported by Kang et al. are also observable 3 when Bis perpendicular to c, in comparison with when it is parallel to c, direc reported positions and at positions that are ing. a, Arbitrarly scaled scattering intensity at (1/2. 1/2.0) for a Finally, an independent report confirms unrelated to the NCCO lattice but equivalent superconducting sample of NCCo (nominal cerium concentration ourprincipal findings instudies of annealed in the cubic lattice of(Nd, Ce)2O, Not only x=0.18: T =20 K) as a function of B/T with the field along superconducting PTag LaCea CuO(PLCCO). and(1/4, 1/4, 1. 1)unrelated to the proposed (=0.15: 7=5 K b, c, Comparison of the results of Kang et ad the cubic impurity (Pr, La, Ce)2O, has NCCO magnetic order, but the physical with data taken at T=4 K for a superconducting sample a non-magnetic ground state and no field situation of the magnetic field applied (=0.18)and a non-superconducting sample (x=0.10). Super- dependence below 7 T(our unpublished rallel (in the cases of the (0, 0, 2.2)and conductivity in NCCO can be achieved only for x>0.13. The mag- observations). For fields upto 5T, Fujitaetal. (1/4, 1/4, 1. 1))or perpendicular (in all other netic field is applied along [1, T, o] for(0. 0. 2. 2) and (1/4. 1/4. 1. 1) find enhanced antiferromagnetic order at ses)to the CuO2 planes is fundamentally and along 10. 0. 1) in all other cases Data were normalized by (1/2, 3/2,0)with increasing field in PLCCO different in that the upper critical fields for maximum intensity Fu details are avallable from the authors. Above 5T, this order decreases with increasing the two geometries differ significantly. Note field. which is consistent with the field that(1/2,0,0)and(1/4. 1/4, 1. 1)correspond Kang et al. reply- Mang et al. observe a dependence of (1/2. 1/2,0)of NCCo (ref 2) to(1, 1,0) and(1.0, 1) respectively. Care was cubic(Nd, Ce)2O, impurity phase grown The agreement between two different elec taken to ensure that in all cases the magnetic epitaxially in annealed samples of electron- tron-doped systems in two independent field was applied along a cubic axis of doped Nd2- Ce CuO, (NCCO). They claim experiments-confirms the quantum phase (Nd. Ce),O, and perpendicular to the scat- that this impurity phase has. \o oNClar hitierromagnetic state in electron-doped These simple experimental tests demon- but extending only about 4a. perpendicular high-T superconductors strate that the observed field effects in oxy- to the planes, thus forming a quasi-two- H I Kang, Pengcheng Dai', J W.Lynn, gen-reduced NCCO result from an epitaxial dimensional (Nd, Ce)2O3 lattice matched M. Matsuura, J. R. Thompson, Shou-Cheng ndary phase of(Nd, Ce)2O3 with the a-b plane of NCCO. Zhang, D N. Argyriou, Y. Onose, Y. Tokura P K Mang*, S Larochelle, M. Greven't Although we have confirmed the presence "Department of Physics and Astronomy. University Department of Applied Physics, tDepartment of of such an impurity phase, (Nd, Ce)2O3 in of Tennessee, Knoxville, Tennessee 37996-1200, an Physics, and t Stanford Synchrotron Radiation ur samples forms a three-dimensional Condensed Matter Sciences Division, Oak Ridge Laboratory, Stanford University, Stanford, long-range structural order'and is unrelated National Laboratory, Oak Ridge California 94305. USA the quasi-two-dimensional superlattice Tennessee 37831-6 393. e-mail: greven@stanford. edu reflections". In the paramagnetic state of e-mail: daipeornlgov 3Mm是 M, Koehler, W. C. Child, HI秦 on magnetic Nd. By animaly scaling the2M业Bl1s 2铷mH减H边5Cm33530m0 Nd, Ce),O,, a field will induce a net moment 1Ma impurity scattering at (0,0, 2.2) for fields less (n the press) 40 e2003NaturePublishingGroupNatUrevOl42613noVeMbeR2003www.naturE.cOm/nAtUrE
There are 32 rare-earth ions in the RE2O3 unit cell,belonging to two crystallographically distinct sites with inequivalent saturated moments3 . At the (2,0,0)c reflection, the contributions from the two rare-earth sites interfere destructively, which should lead to a peak in the observed scattering intensity in the paramagnetic phase if the moments saturate at different fields. Although the magnetic structure and spin hamiltonian of epitaxial, quasi-two-dimensional (Nd,Ce)2O3 are unknown, it is possible to devise simple experiments to test whether the field-induced scattering is due to NCCO or (Nd,Ce)2O3. Kang et al. find that at a temperature of 5 K, the (1/2,1/2,0) (that is, (2,0,0)c) intensity reaches a peak at a field of about 6.5 T, and argue that this peak is associated with the upper critical field Bc2 of NCCO. Figure 1a summarizes the field dependence of an x40.18 superconducting sample of ours in the temperature range 1.9–10 K. Our data agree with those of Kang et al. The figure shows that the intensity scales with B/T and exhibits a peak consistent with two-moment paramagnetism. Furthermore, as the upper critical field of a superconductor increases with decreasing temperature,this implies that the reported correspondence of the peak position with Bc2 at 5 K is coincidental. We do not observe spontaneous neodymium ordering of either (Nd,Ce)2O3or NCCO down to 1.4 K. Figure 1b, c shows that the field effects reported by Kang et al. are also observable in a non-superconducting, oxygen-reduced, x40.10 sample, both at the previously reported positions and at positions that are unrelated to the NCCO lattice but equivalent in the cubic lattice of (Nd,Ce)2O3. Not only are the incommensurate positions (0,0,2.2) and (1/4,1/4,1.1) unrelated to the proposed NCCO magnetic order, but the physical situation of the magnetic field applied parallel (in the cases of the (0,0,2.2) and (1/4,1/4,1.1)) or perpendicular (in all other cases) to the CuO2 planes is fundamentally different in that the upper critical fields for the two geometries differ significantly. Note that (1/2,0,0) and (1/4,1/4,1.1) correspond to (1,1,0)c and (1,0,1)c,respectively.Care was taken to ensure that in all cases the magnetic field was applied along a cubic axis of (Nd,Ce)2O3 and perpendicular to the scattering wavevector. These simple experimental tests demonstrate that the observed field effects in oxygen-reduced NCCO result from an epitaxial secondary phase of (Nd,Ce)2O3. P. K. Mang*, S. Larochelle†, M. Greven*‡ *Department of Applied Physics, †Department of Physics, and ‡Stanford Synchrotron Radiation Laboratory, Stanford University, Stanford, California 94305, USA e-mail: greven@stanford.edu 1. Kang, H. J. et al. Nature 423, 522–525 (2003). 2. Tokura, Y., Takagi, H. & Uchida, S. Nature 337, 345–347 (1989). 3. Moon, R. M., Koehler, W. C., Child, H. R. & Raubenheimer, L. J. Phys. Rev. 176, 722–731 (1968). Kang et al. reply — Mang et al. observe a cubic (Nd,Ce)2O3 impurity phase grown epitaxially in annealed samples of electrondoped Nd21xCexCuO4 (NCCO). They claim that this impurity phase has long-range order parallel to the CuO2 planes of NCCO but extending only about 4ac perpendicular to the planes, thus forming a quasi-twodimensional (Nd,Ce)2O3 lattice matched with the a–b plane of NCCO. Although we have confirmed the presence of such an impurity phase, (Nd,Ce)2O3 in our samples forms a three-dimensional long-range structural order1 and is unrelated to the quasi-two-dimensional superlattice reflections1,2. In the paramagnetic state of (Nd,Ce)2O3, a field will induce a net moment on magnetic Nd. By arbitrarily scaling the impurity scattering at (0,0,2.2) for fields less brief communications 140 NATURE|VOL 426 | 13 NOVEMBER 2003 |www.nature.com/nature Intensity 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 1.9 K x=0.18 4.2 K 0.18 10 K 0.18 5 K 0.15 0 1 2 3 0 0.2 0.4 0.6 0.8 1 B/T (1/2,0,0) x=0.10 (1/4,1/4,1.1) 0.10 (1/2,0,0) 0.15 0 0.2 0.4 0.6 0.8 1 (1/2,1/2,0) x=0.18 (1/2,1/2,0) 0.10 (0,0,2.2) (1/2,1/2,0) 0.15 I/Imaximum I/Imaximum a b 0.10 Figure 1 Field and temperature dependence of magnetic scattering. a, Arbitrarily scaled scattering intensity at (1/2,1/2,0) for a superconducting sample of NCCO (nominal cerium concentration x40.18; Tc420 K) as a function of B/T with the field along [0,0,1]. The results are compared with the data of Kang et al.1 (x40.15; T45 K). b, c, Comparison of the results of Kang et al. with data taken at T44 K for a superconducting sample (x40.18) and a non-superconducting sample (x40.10). Superconductivity in NCCO can be achieved only for x¤0.13. The magnetic field is applied along [1,11 ,0] for (0,0,2.2) and (1/4,1/4,1.1) and along [0,0,1] in all other cases. Data were normalized by maximum intensity. Full details are available from the authors. than 7 T to our c-axis field-induced scattering of NCCO at (1/2,1/2,0),Mang et al.argue that our observed magnetic scattering2 is due entirely to (Nd,Ce)2O3.We disagree,however. There are three ways to resolve this impurity problem.First,if the magnetic scattering at (1/2,1/2,0) (ref. 2) is due entirely to (Nd,Ce)2O3, one would expect the fieldinduced intensity to be identical when B is parallel to the c-axis and when it is parallel to the [1,11,0] axis, as required by the cubic symmetry of (Nd,Ce)2O3. Experimentally, we find that the field-induced effect at (1/2,1/2,0) is much larger when B is parallel to the c-axis1 , which is inconsistent with the cubic symmetry of (Nd,Ce)2O3 but consistent with the upper critical field of NCCO being much smaller in this geometry1,2. Second, as the lattice parameter of (Nd,Ce)2O3 does not match the c-axis lattice parameter of NCCO (ref.1),measurements at non-zero integer L cannot be contaminated by (Nd,Ce)2O3. Our experiments indicate that the (1/2,1/2,3) peak shows an induced antiferromagnetic component when the field is along the c-axis and hence superconductivity is strongly suppressed1 ,but not when in the a–b plane and superconductivity is only weakly affected2 . This is direct proof of the connection between field-induced antiferromagnetic order and suppression of superconductivity in NCCO. We also note that the qualitatively different behaviour observed when B is perpendicular to c, in comparison with when it is parallel to c, directly violates the cubic symmetry of (Nd,Ce)2O3. Finally, an independent report3 confirms our principal findings1,2 in studies of annealed superconducting Pr0.89LaCe0.11CuO4 (PLCCO), a similar electron-doped material in which the cubic impurity phase (Pr,La,Ce)2O3 has a non-magnetic ground state and no field dependence below 7 T (our unpublished observations).For fields up to 5 T,Fujita et al.3 find enhanced antiferromagnetic order at (1/2,3/2,0) with increasing field in PLCCO. Above 5T,this order decreases with increasing field, which is consistent with the field dependence of (1/2,1/2,0) of NCCO (ref. 2). The agreement between two different electron-doped systems in two independent experiments1–3 confirms the quantum phase transition from the superconducting to an antiferromagnetic state in electron-doped, high-Tc superconductors2 . H. J. Kang, Pengcheng Dai*, J. W. Lynn, M. Matsuura, J. R. Thompson, Shou-Cheng Zhang, D. N. Argyriou , Y. Onose, Y. Tokura *Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996-1200, and Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA e-mail: daip@ornl.gov 1. Matsuura, M. et al. Phys. Rev. B 68, 144503 (2003). 2. Kang, H. J. et al. Nature 423, 522–525 (2003). 3. Fujita, M., Matsuda, M., Katano, S. & Yamada, K. Physica B (in the press). © 2003 Nature PublishingGroup