A limiting factor in the ability to interpret isotope effect measurements in cuprates is the absence of sufficiently accurate data for the whole phase diagram; there is precise data for Tc, but not for the antiferromagnetic transition temperature TN. Extreme sensitivity of TN to small changes in the
amount of oxygen in the sample is the major problem. This problem is solved here by using the novel compound (Ca0.1La0.9)(Ba1.65La0.35)Cu3Oy for which there is a region where TN is independent of oxygen doping. Meticulous measurements of TN for samples with 16O and 18O find the absence of an oxygen isotope effect on TN with unprecedented accuracy. A possible interpretation of our finding and existing data is that isotope substitution affects the normal state charge carrier density.
Isotope substitution is a powerful experimental tool used to investigate complex systems. Ideally, the isotope substitution affects only one parameter, for example, a phonon frequency which is directly related to the nuclear mass. However, the strong coupling of many parameters in cuprates highly limit the ability to interpret isotope effect (IE) experiments. Even though the oxygen isotope substitution is known to affect the superconductivity transition temperatures Tc, it is unclear whether it primarily impacts phonons, polarons, magnons, doping, or other physical properties [1].
The isotope effect is usually described using the isotope coefficient α via the relation Tq∝M-αq,
where Tq is a phase transition temperature, M is the isotope mass and q=C,N, and g for the superconducting (SC), antiferromagnetic (AFM), and spin glass critical temperatures, respectively. In many conventional superconductors α was found to be very close to 0.5 [2, 3]. The explanation of this α in terms of Cooper pairs glued by phonons was one of the triumphs of the BCS theory for metallic superconductors [4].
In cuprates the isotope effect is much more complicated and α is not single valued and varies across the phase diagram. The consensus today for YBCO like compounds is that in the SC phase, close to optimal doping, αCod=0.018±0.005,
for oxygen substitution [5]. On the SC dome αC increases as the doping decreases [6, 7]. In the glassy state less data is available, but it seems that the isotope effect reverses sign and αg becomes negative. In extremely underdoped samples, where long range AFM order prevails at low temperatures, data is scarce, controversial, and has relatively large error bars [5, 8]. The most recent measurements with YyPr1-yBa2Cu3O7-δ show that αN=0.02(3) in the parent compound [5]. There are also several theories dealing with the variation of α along the phase diagram [9–14], but since αCod and αN are within an error bar of each other one cannot contrast these theories with experiments. In particular, it is impossible to tell whether the same glue that holds the spins together holds the cooper pair together, or not. Increasing the accuracy of the IE measurements of the Néel temperature will shed light on the role of isotope substitution.
As mentioned above, a major limitation on the measurements of αN is the strong dependence of TN on doping. For example, in YyPr1-yBa2Cu3O7-δ, TN decreases with increasing doping at a rate ΔTN=2.5 K per Δy=0.01. This strong temperature dependence is, of course, common to many other cuprates. As a consequence, it is very difficult to prepare two samples with exactly the same TN even with the same isotope. The smallest fluctuation in either y or δ may lead to a huge fluctuation in TN regardless of the isotope effect. This is not the case for (Ca0.1La0.9)(Ba1.65La0.35)Cu3Oy where TN is constant for oxygen density y<6.6, as can be seen in Figure 1 [15].
The (Ca0.1La0.9)(Ba1.65La0.35)Cu3Oy phase diagram [15]. The antiferromagnetic, spin glass, and superconducting phases are represented in red, green, and blue, respectively. For y<6.6 the Néel temperature does not depend on y. This enables accurate measurements of the oxygen isotope effect on the Néel temperature TN.
For our experiments, four sintered pellets were prepared using standard techniques [16]. Two of the pellets were enriched with O18 isotope and two with O16 isotope in the same procedure: the samples were placed simultaneously in two closed tubes, each with different isotope gas, and then they were heated to allow the isotope to diffuse into the sample. In order to achieve a higher percentage of gas, the enrichment was repeated several times.
The O18 isotope content in the samples was determined based on measurements of gas composition being in equilibrium with the sample during the exchange. Balzers Prisma mass spectrometer was used to analyze in situ isotopic composition of the atmosphere. After the exchange process was performed, the weight increase of the sample was also determined as the light O16 isotope was exchanged with the heavy O18. The isotope enrichment in the samples measured by both methods looked to be higher than 80%. Finally a Thermal Analysis (TA) experiment was performed for the investigated samples after all experiments described in this work were fulfilled in order to verify the isotope enrichment. The samples were heated up to 1200°C in the NETSCH STA 449C Jupiter analyzer in a stream of helium. During the TA experiments, ion current signals for the O218, 18O16O, and O216 molecules were measured using a mass spectrometer (ThermoStar Pfeiffer Vacuum). The results are shown in Figure 2. The isotope content deduced from these measurements (comparing peak areas for the signals of particular oxygen molecules) was larger than 70%.
Ion current signals for the O182, 18O16O, and O162 molecules (red, green, and blue color, resp.) obtained during heating of the sample in a stream of helium. This graph shows that the O18 isotope fraction in the samples is bigger than 70% (see text).
The oxygen IE was measured using zero-field muon spin rotation/relaxation (μSR). We particularly used the ISIS facility, which allows low muon relaxation rate and rotation frequency measurements. This is ideal for measurements near magnetic phase transitions where the muon signal varies on a long-time scale. μSR data at temperatures close to the phase transition are shown in Figure 3. As the temperature is lowered from 383.4 K, the relaxation rate increases. At T=378.5 K oscillations appear in the data indicating the presence of long range magnetic order. The frequency of oscillations and the relaxation rate increase as the temperature is further lowered. The formula Pz(t)=Pm(ae-λ1t+(1-a)e-λ2tcos(ωt))+Pne-Δt
was fitted to the muon polarization, where Pm, λ1, λ2 and ω are the polarization, relaxation rates, and frequency of muons spin in the fraction of the samples which is magnetic, and a is the weighting factor between the muons experiencing transverse field and longitudinal field. This factor is close to 2/3 and temperature independent. Pn and Δ are the polarization and relaxation of the spin of muons that stopped in the nonmagnetic volume of the sample. The solid lines in Figure 3(a) represent the fits.
(a) The μSR raw data at different temperatures and fits of (3) to the data in solid lines. (b) Comparison between three different methods used to describe the AFM phase transition: (i) the muon precession frequency ω obtained from (3). (ii) the magnetic volume fraction Pm determined by (3), and (iii) 𝒪𝒫 calculated by (4).
The AFM order parameter is determined by the frequency ω=γB, where B is the average magnetic field at muon site and γ is the muon gyromagnetic ratio. This frequency can be easily extracted from the μSR data well below the transition but is very difficult to determined near the transition. A second approach is to treat the magnetic volume fraction Pm as the order parameter [5, 17]. Pm can be followed more closely to TN, although this parameter also has large error bars when ω is not well defined. We used an alternative approach similar to [18]; we define an order parameter, which does not require a fit, via the relation OP(T)≡〈Pinf〉-〈P(T)〉〈Pinf〉-〈P(0)〉,
where 〈P(T)〉 is the average polarization at temperature T, and 〈Pinf〉 is the average polarization above the transition. The denominator normalizes 𝒪𝒫 to 1 at zero temperature. All three order parameters for one sample are shown in Figure 3(b). The transition temperatures determined using the different order parameters are in good agreement. The advantages of 𝒪𝒫 are clear: it is a model-free and has very small uncertainties.
In Figure 4, we present the 𝒪𝒫 for two samples with O16 and one with O18 around 380 K. A wide temperature range from 50 to 410 K is shown in the inset for an experiment done on separate occasion, in which two samples of O18 and one with O16 were examined. We determine TN by fitting a straight line to the data in the main panel of Figure 4 in the temperature range 378 to 382 K, for each sample, and taking the crossing with the temperature axis. We find that TN18=382.49(0.34) K and TN16=382.64(0.29) K. For 100% isotope substitution the isotope exponent is determined by αN=-Mo16TN16TN18-TN16Mo18-Mo16.
When taking into account the isotopic fraction in the samples we obtain αN=0.005±0.011.
This result indicates that αN<αCod (see (2)) beyond the error bars and is consistent with no isotope effect on TN.
The parameter 𝒪𝒫 (see (4)) versus temperature near TN for O18 and O16 rich samples. The solid lines are fits to the data near the phase transition used to determine TN. The inset shows a second experiment on the entire temperature range. No oxygen isotope effect of TN is observed within experimental error.
One possible interpretation of these results is that magnetic excitations are not relevant for superconductivity since the isotopes affect Tc without affecting TN. This approach was presented, for example, by Zhao et al. [9]. They found that samples enriched with O18 have longer penetration depth λ than samples enriched with O16 with the same amount of oxygen per unit cell. λ is related to the SC carrier density ns and effective mass m* by λ-2∝ns/m* so a priory both ns and m* can be affected by isotope substitution [19]. They ruled out the possibility that the number of carriers concentration varies by demonstrating that the thermal expansion coefficient of samples with different isotopes are the same. The authors therefore concluded that the IE changes the mass of the cooper pairs, which could be explained by polaronic supercarriers.
An alternative interpretation is that the isotopes affect the efficiency of doping, as suggested in [13]. To demonstrate this interpretation we present in Figure 5(a) the critical temperatures in YyPr1-yBa2Cu3O7-δ for the two different isotopes taken from [5]. TN18 seems to be a bit higher than TN16, but Tc18 is a bit lower than Tc16. However, if we define an efficiency parameter Ki which relates the number of holes p to the number of oxygen ions in the unit cell y via p=Kiy, where i stands for the isotope type, we can generate a unified phase diagram. This is demonstrated in Figures 5(b) and 5(c) for TN and Tc, respectively. In these graphs three different values of K18 are used to generate p while keeping K16=1. When using K18=0.98, both curves of TN and Tc versus p for the two different isotopes collapse to the same curve. Similar scaling of the doping axis was applied to the (CaxLa1-x) (Ba1.75-xLa0.25+x) Cu3Oy system [15] and was explained by NQR [20].
(a) Oxygen isotope effect of TN (left) and Tc (right) in YyPr1-yBa2Cu3O7-δ taken from [5]. The 18O and 16O samples are in filled red circles and empty black squares, respectively. Figures (b) and (c) are demonstration of the IE using charge carriers density p=Kiy, instead of oxygen content y. The values of Ki are given in the figures. Green triangles (Ki=0.98) represent reduction of 2% in the number of charge carriers in the 18O samples compared to the 16O sample. In this case both TN and Tc are functions of p regardless of the isotope.
Next we discuss the IE on the stiffness in the above scenario. We assume that the effective mass of the SC charge carrier m*, the critical p where superconductivity starts pcrit, and where Tc is optimal popt, are not affected by the isotope substitution. The stiffness can be measured by the muon transverse relaxation rate σ, and it is expected that [19] σi=C(pi-pcrit),
where C is a constant. Dividing the differential of σ from (7) by the relaxation at optimal doping yields dσσopt=dppopt-pcrit=y(K16-K18)popt-pcrit.
The expected change in the stiffness due to isotope substitution can be calculated from (8) using popt=1, pcrit=0.42 (which are extracted from Figure 5(c)), and σopt=3.0μs-1 [21]. For y=0.8, K16=1 and K18=0.98 we get dσ=0.083μs-1. This value is consistent with the experimental value of dσ=0.08μs-1 reported in [21]. In other words a 2% difference in the doping efficiency between the two isotopes can explain both the variations in the phase diagram and the variation in the stiffness.
Our experiment shows that oxygen isotope substitution does not affect the Néel temperature and therefore does not play a role in magnetic excitations. However, the isotope effect of Tc does not necessarily imply that phonons play a role in cuprate superconductivity. We show that an isotope-dependent doping efficiency can explain the variation in Tc and in the magnetic penetration depth between samples rich in O16 or O18.
Acknowledgments
The authors would like to thank the ISIS pulsed muon facility at Rutherford Appleton Laboratory, UK for excellent muon beam conditions. This work was funded by the Israeli Science Foundation, the joint German-Israeli DIP project, and the Posnansky research fund in high temperature superconductivity.
LeeP. A.From high temperature superconductivity to quantum spin liquid: progress in strong correlation physics200871101250110.1088/0034-4885/71/1/012501MaxwellE.Isotope effect in the superconductivity of mercury19507844772-s2.0-3614902124710.1103/PhysRev.78.477ReynoldsC. A.SerinB.WrightW. H.NesbittL. B.Superconductivity of isotopes of mercury19507844872-s2.0-3614902823010.1103/PhysRev.78.487BardeenJ.CooperL. N.SchriefferJ. R.Theory of superconductivity19571085117512042-s2.0-034719097910.1103/PhysRev.108.1175KhasanovR.ShengelayaA.Di CastroD.MorenzoniE.MaisuradzeA.SavićI. M.ConderK.PomjakushinaE.Bussmann-HolderA.KellerH.Oxygen isotope effects on the superconducting transition and magnetic states within the phase diagram of Y1−xPrxBa2Cu3O7−δ200810172-s2.0-4954909599710.1103/PhysRevLett.101.077001077001PringleD. J.WilliamsG. V. M.TallonJ. L.Effect of doping and impurities on the oxygen isotope effect in high-temperature superconducting cuprates2000621812527125332-s2.0-003431284410.1103/PhysRevB.62.12527KellerH.2005Berlin, GermanySpringerZhaoG. M.SinghK. K.MorrisD. E.Oxygen isotope effect on Néel temperature in various antiferromagnetic cuprates1994506411241172-s2.0-2444443831810.1103/PhysRevB.50.4112ZhaoG. M.HuntM. B.KellerH.MüllerK. A.Evidence for polaronic supercarriers in the copper oxide superconductors La2-XSrXCuO4199738566132362382-s2.0-003101838210.1038/385236a0BillA.KresinV. Z.WolfS. A.The isotope effect in superconductorshttp://arxiv.org/abs/cond-mat/9801222BaugherJ. F.TaylorP. C.OjaT.BrayP. J.Nuclear magnetic resonance powder patterns in the presence of completely asymmetric quadrupole and chemical shift effects: application to metavanadates19695011, article 49141210.1063/1.1670988FisherD. S.MillisA. J.ShraimanB.BhattR. N.Zero-point motion and the isotope effect in oxide superconductors19886144822-s2.0-424363776610.1103/PhysRevLett.61.482KresinV. Z.WolfS. A.Microscopic model for the isotope effect in the high-Tc oxides1994495365236542-s2.0-2444444780710.1103/PhysRevB.49.3652SerbynM.LeeP. A.Isotope effect on the superfluid density in conventional and high-temperature superconductors2011832802450610.1103/PhysRevB.83.024506OferR.BazalitskyG.KanigelA.KerenA.AuerbachA.LordJ. S.AmatoA.Magnetic analog of the isotope effect in cuprates20067422422050810.1103/PhysRevB.74.220508GoldschmidtD.ReisnerG. M.DirektovitchY.KnizhnikA.GartsteinE.KimmelG.EcksteinY.Tetragonal superconducting family (CaxLa1−x) (Ba1.75−xLa0.25+x)Cu3Oy: the effect of cosubstitution on the transition temperature19934815325422-s2.0-3454715097810.1103/PhysRevB.48.532OferR.KerenA.ChmaissemO.AmatoA.Universal doping dependence of the ground-state staggered magnetization of cuprate superconductors200878142-s2.0-5444909000610.1103/PhysRevB.78.140508140508ShayM.KerenA.KorenG.KanigelA.ShafirO.MarciparL.NieuwenhuysG.MorenzoniE.SuterA.ProkschaT.DubmanM.PodolskyD.Interaction between the magnetic and superconducting order parameters in a La1.94 Sr0.06 CuO4 wire studied via muon spin rotation2009801414451110.1103/PhysRevB.80.144511UemuraY. J.LukeG. M.SternliebB. J.BrewerJ. H.CarolanJ. F.HardyW. N.KadonoR.KemptonJ. R.KieflR. F.KreitzmanS. R.MulhernP.RisemanT. M.WilliamsD. LL.YangB. X.UchidaS.TakagiH.GopalakrishnanJ.SleightA. W.SubramanianM. A.ChienC. L.CieplakM. Z.XiaoG.LeeV. Y.StattB. W.StronachC. E.KosslerW. J.YuX. H.Universal correlations between Tc and ns/m∗ (Carrier density over effective mass) in High-Tc cuprate cuperconductors19896219231723202-s2.0-334295002610.1103/PhysRevLett.62.2317AmitE.KerenA.Critical-doping universality for cuprate superconductors: Oxygen nuclear-magnetic-resonance investigation of(CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy20108217417250910.1103/PhysRevB.82.172509KhasanovR.ShengelayaA.ConderK.MorenzoniE.SavićI. M.KarpinskiJ.KellerH.Correlation between oxygen isotope effects on transition temperature and magnetic penetration depth in high-temperature superconductors close to optimal doping2006746606450410.1103/PhysRevB.74.064504