A Precise Measurement of the Oxygen Isotope Effect on the N\'{e}el temperature in Cuprates

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 T_N. Extreme sensitivity of T_N 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 (Ca 0.1 La 0.9)(Ba 1.65 La 0.35)Cu 3 O y for which there is a region where T_N is independent of oxygen doping. Meticulous measurements of T_N for samples with oxygen 16 and oxygen 18 find the absence of an oxygen isotope effect on T_N 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. Eventhough the oxygen isotope substitution is known to affect the superconductivity transition temperatures T c , 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 where T q 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, the oxygen IE is which is very small but non zero. [5] On the SC dome α C 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 α g becomes negative. In extremely underdoped samples, where long range AFM order prevails at low temperatures, data is scarce, controversial, * Electronic address: eranamita@gmail.com FIG. 1. 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 . and has relatively large error bars. [5,8] The most recent measurements with Y y Pr 1−y Ba 2 Cu 3 O 7−δ show that α N = 0.02(3) in the parent compound. [5] There are also several theories dealing with the variation of α along the phase diagram, [9][10][11][12][13][14] but since α od C and α N 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 α N is the strong dependence of T N on doping. For example, in Y y Pr 1−y Ba 2 Cu 3 O 7−δ , T N decreases with increasing doping at a rate ∆T N = 2.5 K per ∆y = 0.01. This strong temperature dependence is, of course, common to many other cuprates. As a conse-quence, it is very difficult to prepare two samples with exactly the same T N even with the same isotope. The smallest fluctuation in either y or δ may lead to a huge fluctuation in T N regardless of the isotope effect. This is not the case for the (Ca 0.1 La 0.9 )(Ba 1.65 La 0.35 )Cu 3 O y where T N is constant for oxygen density y < 6.6, as can be seen in Fig. 1. [15] For our experiments, four sintered pellets were prepared using standard techniques. [16] Two of the pellets were enriched with 18 O isotope and two with 16 O 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 18 O 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 16 O isotope was exchanged with the heavy 18 O. The isotope enrichment in the samples measured by both methods looked to be higher than 80%. Finally a Thermal Analysis experiment (TA) 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 18 O 2 , 18 O 16 O and 16 O 2 molecules were measured using a mass spectrometer (ThermoStar Pfeiffer Vacuum). The results are shown on Fig. 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 (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 Fig. 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 P z (t) = P m (ae −λ1t + (1 − a)e −λ2t cos(ωt)) + P n e −∆t (3) was fitted to the muon polarization, where P m , λ 1 , λ 2 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. P n 300 400 500 600 and ∆ are the polarization and relaxation of the spin of muons that stopped in the non-magnetic volume of the sample. The solid lines in Fig. 3(a) represent the fits. 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 P m as the order parameter. [5,18] P m can be followed more closely to T N , although this parameter also has large error bars when ω is not well defined. We used an alternative approach similar to Ref. [19]; we define an order parameter which, does not require a fit, via the relation where < P (T ) > is the average polarization at temperature T , and < P inf > 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 Fig. 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 Fig. 4 we present the OP for two samples with 16 O and one with 18 O around 380 K. A wide temperature range from 50 to 410 K is shown in the inset for an ex- Order Parameter  periment done on separate occasion, in which two samples of 18 O and one with 16 O were examined. We determine T N by fitting a straight line to the data in the main panel of Fig. 4 in the temperature range 378 to 382 K, for each sample, and taking the crossing with the temperature axis. We find that T 18 N =382.49(0.34) K and T 16 N =382.64(0.29) K. 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 α N < α od C (see Eq. 2) beyond the error bars, and is consistent with no isotope effect on T N .
One possible interpretation of these results is that magnetic excitations are not relevant for superconductivity since the isotopes affect T c without affecting T N . This approach was presented, for example, by Zhao et al.. [9] They found that samples enriched with 18 O have longer penetration depth λ than samples enriched with 16 O with the same amount of oxygen per unit cell. λ is related to the SC carrier density n s and effective mass m * by λ −2 ∝ n s /m * so a priory both n s and m * can be affected by isotope substitution. [17] 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 Ref. [13]. To demonstrate this interpretation we present in Fig. 5(a) the critical temperatures in Y y Pr 1−y Ba 2 Cu 3 O 7−δ for the two different isotopes taken from Ref. [5]. T 18 N seems to be a bit higher than T 16 N , but T 18 c is a bit lower than T 16 c . However, if we define an efficiency parameter K i which relates the number of holes p to the number of oxygens in the unit cell y via p = K i y, where i stands for the isotope type, we can generate a unified phase diagram. This is demonstrated in Fig. 5(b) and 5(c) for T N and T c , respectively. In these graphs three different values of K 18 are used to generate p while keeping K 16 = 1. When using K 18 = 0.98, both curves of T N and T c versus p for the two different isotopes collapse to the same curve. Similar scaling of the doping axis was applied to the (Ca x La 1−x )(Ba 1.75−x La 0.25+x )Cu 3 O y system [15] and was explained by NQR. [20]  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 p crit , and where T c is optimal p opt , are not affected by the isotope substitution as suggested by Fig. 5(c) and demonstrated in Ref. [20]. The stiffness can be measured by the muon transverse relaxation rate σ, and it is expected that: [17] where C is a constant. Dividing the differential of σ from Eq. 7 by the relaxation at optimal doping yields: The expected change in the stiffness due to isotope substitution can be calculated from Eq. 8 using p opt = 1, p crit = 0.42 (which are extracted from Fig. 5(b)) and σ opt = 3.0 µs −1 . [21] For y = 0.8, K 16 = 1 and K 18 = 0.98 we get dσ = 0.083 µs −1 . This value is consistent with the experimental value of dσ = 0.08(1) µs −1 reported in Ref. [21]. In other words a 2% difference in the doping efficiency between the two isotopes can explain both the variations in phase diagram in Fig. 5(a) 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 T c 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 T c and in the magnetic penetration depth between samples rich in 16 O or 18 O. We 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 and the Posnansky research fund in high temperature superconductivity.