Research Article | Open Access

E. Amit, A. Keren, J. S. Lord, P. King, "A Precise Measurement of the Oxygen Isotope Effect on the Nรฉel Temperature in Cuprates", *Advances in Condensed Matter Physics*, vol. 2011, Article ID 178190, 5 pages, 2011. https://doi.org/10.1155/2011/178190

# A Precise Measurement of the Oxygen Isotope Effect on the Nรฉel Temperature in Cuprates

**Academic Editor:**Ashok Chatterjee

#### Abstract

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 , but not for the antiferromagnetic transition temperature . Extreme sensitivity of 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 ()() for which there is a region where is independent of oxygen doping. Meticulous measurements of for samples with and find the absence of an oxygen isotope effect on 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 , 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 via the relation where is a phase transition temperature, is the isotope mass and , and for the superconducting (SC), antiferromagnetic (AFM), and spin glass critical temperatures, respectively. In many conventional superconductors was found to be very close to 0.5 [2, 3]. The explanation of this 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 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, for oxygen substitution [5]. On the SC dome 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 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 show that in the parent compound [5]. There are also several theories dealing with the variation of along the phase diagram [9โ14], but since and 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 Nรฉel temperature will shed light on the role of isotope substitution.

As mentioned above, a major limitation on the measurements of is the strong dependence of on doping. For example, in , decreases with increasing doping at a rate โK per . 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 even with the same isotope. The smallest fluctuation in either or may lead to a huge fluctuation in regardless of the isotope effect. This is not the case for ()() where is constant for oxygen density , as can be seen in Figure 1 [15].

For our experiments, four sintered pellets were prepared using standard techniques [16]. Two of the pellets were enriched with isotope and two with 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 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 isotope was exchanged with the heavy . 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 1200ยฐC in the NETSCH STA 449C Jupiter analyzer in a stream of helium. During the TA experiments, ion current signals for the , OO, and 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%.

The oxygen IE was measured using zero-field muon spin rotation/relaxation (SR). 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. SR data at temperatures close to the phase transition are shown in Figure 3. As the temperature is lowered from 383.4โK, the relaxation rate increases. At 378.5โK 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 was fitted to the muon polarization, where , , and are the polarization, relaxation rates, and frequency of muons spin in the fraction of the samples which is magnetic, and is the weighting factor between the muons experiencing transverse field and longitudinal field. This factor is close to 2/3 and temperature independent. and 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)**

**(b)**

The AFM order parameter is determined by the frequency , where is the average magnetic field at muon site and is the muon gyromagnetic ratio. This frequency can be easily extracted from the SR data well below the transition but is very difficult to determined near the transition. A second approach is to treat the magnetic volume fraction as the order parameter [5, 17]. can be followed more closely to , although this parameter also has large error bars when 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 where is the average polarization at temperature , and is the average polarization above the transition. The denominator normalizes 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 are clear: it is a model-free and has very small uncertainties.

In Figure 4, we present the for two samples with and one with around 380โK. A wide temperature range from 50 to 410โK is shown in the inset for an experiment done on separate occasion, in which two samples of and one with were examined. We determine by fitting a straight line to the data in the main panel of Figure 4 in the temperature range 378 to 382โK, for each sample, and taking the crossing with the temperature axis. We find that โK and โK. For 100% isotope substitution the isotope exponent is determined by When taking into account the isotopic fraction in the samples we obtain This result indicates that (see (2)) beyond the error bars and is consistent with no isotope effect on .

One possible interpretation of these results is that magnetic excitations are not relevant for superconductivity since the isotopes affect without affecting . This approach was presented, for example, by Zhao et al. [9]. They found that samples enriched with have longer penetration depth than samples enriched with with the same amount of oxygen per unit cell. is related to the SC carrier density and effective mass by so a priory both and 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 for the two different isotopes taken from [5]. seems to be a bit higher than , but is a bit lower than . However, if we define an efficiency parameter which relates the number of holes to the number of oxygen ions in the unit cell via , where stands for the isotope type, we can generate a unified phase diagram. This is demonstrated in Figures 5(b) and 5(c) for and , respectively. In these graphs three different values of are used to generate while keeping . When using , both curves of and versus for the two different isotopes collapse to the same curve. Similar scaling of the doping axis was applied to the () () system [15] and was explained by NQR [20].

**(a)**

**(b)**

**(c)**

Next we discuss the IE on the stiffness in the above scenario. We assume that the effective mass of the SC charge carrier , the critical where superconductivity starts , and where is optimal , are not affected by the isotope substitution. The stiffness can be measured by the muon transverse relaxation rate , and it is expected that [19] where is a constant. Dividing the differential of from (7) by the relaxation at optimal doping yields

The expected change in the stiffness due to isotope substitution can be calculated from (8) using , (which are extracted from Figure 5(c)), and โ*ฮผ*s^{-1} [21]. For , and we get . This value is consistent with the experimental value of โ*ฮผ*s^{-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 Nรฉel temperature and therefore does not play a role in magnetic excitations. However, the isotope effect of 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 and in the magnetic penetration depth between samples rich in or .

#### 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.

#### References

- P. A. Lee, โFrom high temperature superconductivity to quantum spin liquid: progress in strong correlation physics,โ
*Reports on Progress in Physics*, vol. 71, no. 1, Article ID 012501, 2008. View at: Publisher Site | Google Scholar - E. Maxwell, โIsotope effect in the superconductivity of mercury,โ
*Physical Review*, vol. 78, no. 4, p. 477, 1950. View at: Publisher Site | Google Scholar - C. A. Reynolds, B. Serin, W. H. Wright, and L. B. Nesbitt, โSuperconductivity of isotopes of mercury,โ
*Physical Review*, vol. 78, no. 4, p. 487, 1950. View at: Publisher Site | Google Scholar - J. Bardeen, L. N. Cooper, and J. R. Schrieffer, โTheory of superconductivity,โ
*Physical Review*, vol. 108, no. 5, pp. 1175โ1204, 1957. View at: Publisher Site | Google Scholar - R. Khasanov, A. Shengelaya, D. Di Castro et al., โOxygen isotope effects on the superconducting transition and magnetic states within the phase diagram of ${\text{Y}}_{1-\text{x}}{\text{Pr}}_{\text{x}}{\text{Ba}}_{2}{\text{Cu}}_{3}{\text{O}}_{7-\delta}$,โ
*Physical Review Letters*, vol. 101, no. 7, Article ID 077001, 2008. View at: Publisher Site | Google Scholar - D. J. Pringle, G. V. M. Williams, and J. L. Tallon, โEffect of doping and impurities on the oxygen isotope effect in high-temperature superconducting cuprates,โ
*Physical Review B*, vol. 62, no. 18, pp. 12527โ12533, 2000. View at: Publisher Site | Google Scholar - H. Keller,
*Unconventional Isotope Effects in Cuprate Superconductors*, Springer, Berlin, Germany, 2005. - G. M. Zhao, K. K. Singh, and D. E. Morris, โOxygen isotope effect on Néel temperature in various antiferromagnetic cuprates,โ
*Physical Review B*, vol. 50, no. 6, pp. 4112โ4117, 1994. View at: Publisher Site | Google Scholar - G. M. Zhao, M. B. Hunt, H. Keller, and K. A. Müller, โEvidence for polaronic supercarriers in the copper oxide superconductors ${\text{La}}_{2-X}{\text{Sr}}_{X}{\text{CuO}}_{4}$,โ
*Nature*, vol. 385, no. 6613, pp. 236โ238, 1997. View at: Publisher Site | Google Scholar - A. Bill, V. Z. Kresin, and S. A. Wolf, โThe isotope effect in superconductors,โ http://arxiv.org/abs/cond-mat/9801222. View at: Google Scholar
- J. F. Baugher, P. C. Taylor, T. Oja, and P. J. Bray, โNuclear magnetic resonance powder patterns in the presence of completely asymmetric quadrupole and chemical shift effects: application to metavanadates,โ
*Journal of Chemical Physics*, vol. 50, no. 11, article 4914, 12 pages, 1969. View at: Publisher Site | Google Scholar - D. S. Fisher, A. J. Millis, B. Shraiman, and R. N. Bhatt, โZero-point motion and the isotope effect in oxide superconductors,โ
*Physical Review Letters*, vol. 61, no. 4, p. 482, 1988. View at: Publisher Site | Google Scholar - V. Z. Kresin and S. A. Wolf, โMicroscopic model for the isotope effect in the high-${T}_{c}$ oxides,โ
*Physical Review B*, vol. 49, no. 5, pp. 3652โ3654, 1994. View at: Publisher Site | Google Scholar - M. Serbyn and P. A. Lee, โIsotope effect on the superfluid density in conventional and high-temperature superconductors,โ
*Physical Review B*, vol. 83, no. 2, Article ID 024506, 8 pages, 2011. View at: Publisher Site | Google Scholar - R. Ofer, G. Bazalitsky, A. Kanigel et al., โMagnetic analog of the isotope effect in cuprates,โ
*Physical Review B*, vol. 74, no. 22, Article ID 220508, 4 pages, 2006. View at: Publisher Site | Google Scholar - D. Goldschmidt, G. M. Reisner, Y. Direktovitch et al., โTetragonal superconducting family (${\text{Ca}}_{x}{\text{La}}_{1-x}$) (${\text{Ba}}_{1.75-x}{\text{La}}_{0.25+x}$)${\text{Cu}}_{3}{\text{O}}_{y}$: the effect of cosubstitution on the transition temperature,โ
*Physical Review B*, vol. 48, no. 1, pp. 532โ542, 1993. View at: Publisher Site | Google Scholar - R. Ofer, A. Keren, O. Chmaissem, and A. Amato, โUniversal doping dependence of the ground-state staggered magnetization of cuprate superconductors,โ
*Physical Review B*, vol. 78, no. 14, Article ID 140508, 2008. View at: Publisher Site | Google Scholar - M. Shay, A. Keren, G. Koren et al., โInteraction between the magnetic and superconducting order parameters in a La1.94 Sr0.06 CuO4 wire studied via muon spin rotation,โ
*Physical Review B*, vol. 80, no. 14, Article ID 144511, 2009. View at: Publisher Site | Google Scholar - Y. J. Uemura, G. M. Luke, B. J. Sternlieb et al., โUniversal correlations between ${T}_{c}$ and ${n}_{s}/{m}^{\ast}$ (Carrier density over effective mass) in High-${T}_{c}$ cuprate cuperconductors,โ
*Physical Review Letters*, vol. 62, no. 19, pp. 2317โ2320, 1989. View at: Publisher Site | Google Scholar - E. Amit and A. Keren, โCritical-doping universality for cuprate superconductors: Oxygen nuclear-magnetic-resonance investigation of$({\text{Ca}}_{x}{\text{La}}_{1-x})({\text{Ba}}_{1.75-x}{\text{La}}_{0.25+x}){\text{Cu}}_{3}{\text{O}}_{y}$,โ
*Physical Review B*, vol. 82, no. 17, Article ID 172509, 4 pages, 2010. View at: Publisher Site | Google Scholar - R. Khasanov, A. Shengelaya, K. Conder et al., โCorrelation between oxygen isotope effects on transition temperature and magnetic penetration depth in high-temperature superconductors close to optimal doping,โ
*Physical Review B*, vol. 74, no. 6, Article ID 064504, 6 pages, 2006. View at: Publisher Site | Google Scholar

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Copyright © 2011 E. Amit et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.