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High-magnetic-field study of high-Tc cuprates
Physica B 319 (2002) 310–320
High-magnetic-field study of high-Tc cuprates N. Miuraa,*, H. Nakagawaa, T. Sekitania, M. Naitob, H. Satob, Y. Enomotoc a
Institute for Solid States Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, 277-8581 Chiba, Japan b NTT Basic Research Laboratories, Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan c Superconductivity Research Laboratory, International Technology Center, Shinonome, Koto-ku, Tokyo 135-0062, Japan Received 11 March 2002
Abstract We present our recent studies of high-Tc superconductors in very high pulsed magnetic fields exceeding 100 T (megagauss fields). In YBa2Cu3O7d, the super to normal transition was observed in transport measurements for B8c under short pulse fields up to 120 T. A plot of the upper critical field Hc2 as a function of temperature demonstrates that the curve obeys the conventional relation well established in other type-II superconductors in the dirty limit. From the resistivity versus temperature curve at high magnetic fields above the super to normal transition, it was found that the hole system shows a metallic temperature dependence for B8c: In Nd2xCexCuO4 as electron-doped cuprate, a large magneto-resistance was observed above the transition field. It was also found that the temperature dependence of the resistivity above the critical field is insulator-like showing a prominent logarithmic up-turn at low temperatures. A similar logarithmic up-turn was observed in several other cuprates such as La2xSrxCuO4 (LSCO), La2xCexCuO, and Pr2xCexCuO4. The experimental results for thin-film samples of LSCO with different strains suggest that the Kondo effect plays an important role in these materials. A new phase diagram of LSCO is proposed on the basis of a viewpoint of the interplay between superconductivity and the Kondo effect. r 2002 Published by Elsevier Science B.V. PACS: 72.15.Gd; 74.72.Bk; 74.72.Jt; 74.76.Bz Keywords: High magnetic fields; High-Tc cuprates
1. Introduction The recent advances in the magnet technology have enabled us to produce very high magnetic fields up to several megagauss (>100 T) that can be applied to solid-state experiments [1]. At the Institute for Solid State Physics (ISSP) of the University of Tokyo, we have succeeded in *Corresponding author. Tel.: +81-471-36-33-41; fax: +81471-36-33-35. E-mail address: [email protected] (N. Miura).
producing very high magnetic fields up to 622 T by electromagnetic flux compression and up to 302 T by the single-turn-coil technique [2,3]. Nondestructive long pulse fields up to about 60 T were also generated by conventional wire-wound solenoids. These fields were applied in many different experiments such as magneto-optical spectroscopy [4,5], cyclotron resonance [6], magnetization [7], or magneto-transport measurements [8]. A variety of interesting experiments can be performed in the extreme limit of high magnetic fields in diverse research areas. As an example of experiments in
0921-4526/02/$ - see front matter r 2002 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 1 3 4 - 1
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very high magnetic fields, we present here a study of high-Tc cuprates in semi-destructive fields generated by the single-turn-coil technique and non-destructive pulse fields generated by wirewound magnets. Since its discovery [9], high-Tc superconductors have been one of the most important research subjects in solid-state physics. It has been pointed out that the electron system in this class of materials might have unusual properties unlike normal Fermi liquids. In order to investigate the origin of the unique properties of these materials and the mechanism of the high-Tc superconductivity, we need to investigate the normal-state properties at low temperatures. These materials have high critical temperatures and hence the upper critical field is also quite high. Therefore, in order to break their superconductivity at low temperatures, either chemical-doping or application of high magnetic fields above the upper critical field is an essential means to exploit. We investigated the super–normal transition and the normal-state conductivity by using very high magnetic fields. Measurement of the electrical resistance in a short pulse of megagauss fields is a difficult task, because of the large induction associated with the high and short magnetic field pulse. Some pioneering work on the measurements in very high fields has been reported on YBa2Cu3O7d (YBCO) [10,11]. In order to avoid the problems arising from the induction in the lead wire loop, we have developed a contactless technique to measure the AC field transmission through samples [12]. We have also developed a technique to measure magnetization hysteresis for determining the field of irreversible point as a function of temperature [13,14]. As regards the resistivity measurements with contacts on samples, we have succeeded in measuring the resistivity of high-Tc superconductors in megagauss fields by minimizing the loop involved in the sample and the lead wire, and by use of band path filters [8,15,16]. By using this technique, we found many new features in YBCO. Another technique is to utilize a strip line measuring the microwave transmission with a frequency of 0.5–1.0 GHz [17]. In collaboration with the group of National Pulsed Magnet Laboratory of the University of the
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New South Wales, the strip-line technique was successfully applied for experiments with the single-turn-coil technique [18] and explosive-driven flux compression [19]. In long pulse fields up to 60 T, the transport measurements can be more readily made and very accurate measurements are possible on 214-type high-Tc cuprates, such as hole-doped La2xSrxCuO4 (LSCO) and electrondoped La2xCexCuO4 (LCCO), Pr2xCexCuO4 (PCCO), and Nd2xCexCuO4 (NCCO) [20–22]. One of the important problems on high-Tc superconductors is the transition from the superconducting state (S) to the normal state (N) by a magnetic field. Previous studies of the S–N transition have been mostly limited to the vicinity of the critical temperature Tc ; since we need very high fields to extend the measurements to lower temperatures. In over-doped Tl or Bi compounds which have Tc lower than 20 K, the upper critical field determined from the resistivity measurements were found to increase abruptly at low temperatures down to the mK range [23,24]. This behavior is completely different from that of conventional type-II superconductors which is well described by the theory of Werthamer–Helfand–Hoenberg (WHH) [25]. In high-Tc cuprates, the fluctuation effect is very large due to the short coherence length and the two-dimensional character of the electron system. As a result, it is generally believed that Hc2 is not a phase transition point, but the cross-over point from the flux-liquid state to the normal state [26]. Therefore, the implication of Hc2 determined by resistivity measurements is not so clear. However, in order to clarify the nature of the S–N transition, it would certainly be very important to investigate the S–N transition at low temperatures in detail. Another important problem is the temperature dependence of the normal resistivity at low temperatures created by the S–N transition in high magnetic fields. In order to investigate the normal resistivity of high-Tc superconductors at low temperatures, we need to break the superconductivity either by chemical-doping or by application of high magnetic fields. The latter is much more preferable, since it allows measurements over a wide range of composition including the vicinity of the optimal-doping. Boebinger,
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Ando and coworkers reported results of experiments on the normal resistivity in the ab-plane and along the c-axis at low temperatures and high magnetic fields. They found in the temperature dependence of LSCO that, for nearly optimally doped samples, the c-axis resistivity is insulating whilst the ab-plane resistivity is metallic, but both become insulating at low temperatures [27,28]. In Bi2Sr2xLaxCuOy, however, the metallic behavior of the ab-plane resistivity is preserved down to low temperatures (0.66 K) keeping the insulating behavior of the c-axis resistivity [29]. It is of importance to study the temperature dependence of the normal resistivity in a wide range of materials.
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Fig. 1. Magneto-resistance of YBa2Cu3O7d thin film for B8c at different temperatures in long pulse fields up to 50 T. The temperatures are 40, 45, 50, 55, 60, 62.8, 65, 67, 69, 71, 73, 75, 77.5, 79, 80.4, 82, 84, 86, 88 and 90 K from bottom to top.
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The samples of YBCO thin film with a thickness ( were grown on a MgO substrate by the of 1000 A laser ablation technique. It is a slightly underdoped sample with a critical temperature Tc of 84 K. The samples were processed to make their shapes to either a meander-like or a simple bar-like shape with a length of about 500 mm. Four contacts method was employed with a DC (square pulse) and AC current. In the case of AC measurements, AC current of frequencies of 5–10 MHz was supplied to the sample. Fig. 1 shows the magneto-resistance of YBCO thin film for B8c at different temperatures in long pulse fields up to 50 T. Magneto-resistance curves with excellent signal-to-noise ratio were obtained with both up-rising and down-falling field slopes. It was confirmed that there was no heating effect from eddy currents in our experiments, since the two data obtained by both up- and down-sweep of the pulsed field coincided almost perfectly. In short pulses with peak field higher than 100 T produced by the single-turn-coil technique, the measurement of the resistivity involves much more difficult technical problems. Fig. 2 shows the typical wave forms of the magnetic field and the current of the single-turn-coil technique [2,3]. In this case, a peak field of 263 T was obtained in a bore of 6 mm. The maximum field depends on the bore of the coil. The duration of the magnetic field
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is about 7 ms. In such a short pulse, the induced voltage in the lead wires becomes enormous. If there is a loop with a radius of 2 mm in the circuit formed by the sample and the lead wire, the induced voltage reaches B800 V in a field up to 100 T, which is much larger than the bias voltage applied to the sample for measurements. By minimizing the cross-section and by making the lead wires parallel to the field as much as possible, the induced voltage was greatly reduced. Optimizing wirings, filters and compensation circuits, it
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has become possible to obtain the magnetoresistance curve with a reasonable signal-to-noise ratio [8,15,16]. The sample was cooled by flowing He liquid or gas around the sample, and the temperature was measured by a gold–iron Chromel thermocouple.
3. Results and discussion 3.1. YBa2Cu3O7d Fig. 3 shows the DC magneto-resistance of YBCO for B8c-axis measured with the singleturn-coil technique at various temperatures. An abrupt jump of the resistivity corresponding to the super–normal transition is clearly observed. At the start of the pulse, large noise is induced due to the extraordinary large dB=dt and the trigger noise. Except for the region at the first part of the pulse in the up-sweep (below B40 T), the signal was much deteriorated by the noise, but at about 40 T, the signal was in agreement with the data taken by a long pulse up to 40 T. In addition, the up-sweep trace and down-sweep trace taken in one pulse coincide with each other above 60 T. Below 60 T, therefore, we obtained just down-traces. In the down-trace we obtained reproducible data depending just on temperature.
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As the field-induced transition is gradual with several deflection points, there are many ways of the definition of the critical field for the S–N transition. The onset of the transition Honset ; that can be determined as a cross-point between the straight lines from the low field range and the transition range, the offset field Hhf where the nearly constant gradient of the resistance vs. field curve in the high-field range starts increasing in the transition at lower fields, the midpoint Hmidpoint determined by the midpoint where the resistivity is a half of that for Hhf ; etc. If we take Hhf ; the gradient of the Hc2 2T curve in the vicinity of Tc becomes B2 T/K which is in good agreement with the data reported by Welp et al. [30]. From such measurements, we can determine the phase diagram of YBCO. The diagram for Hhf is shown in Fig. 4. The phase diagram for B8c is well described by the WHH model of the dirty-limit superconductor [25] by choosing certain parameters of a and lSO : It implies that the system is featured by a phase diagram similar to those for conventional type-II superconductors for B8c: This is in sharp contrast to the case for B8c [18], where the upper critical field exceeds the paramagnetic limit suggesting the FFLO state [31,32]. Another interesting problem of high-Tc superconductors is the normal-state conductivity at low temperatures. Study of the low-temperature
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transport provides a rich source of information of the mechanism of the transport and the superconductivity itself. However, in order to realize the normal state at low temperatures, we have to dope impurities or apply high magnetic fields to destroy the superconductivity. By applying high magnetic fields exceeding the upper critical field, we investigated the normal state of YBCO at low temperatures. Fig. 5 shows the temperature dependence of the normal-state resistivity at different magnetic fields. At sufficiently high magnetic fields above 100 T, samples are considered to be in the normal state. It is clearly seen that the resistivity exhibits metallic behavior. Namely, the resistivity decreases with decreasing temperature. Boebinger et al. reported that in LSCO bulk, the in-plane resistivity shows metallic behavior near the optimum-doping but converts to insulating behavior when the doping is reduced [25]. In a very under-doped sample of YBCO (d ¼ 0:62), an insulating properties were observed [33]. The present sample is almost optimally doped but slightly under doped (dB0:1). Therefore, we can conclude that in YBCO, the metal–insulator transition occurs at a more over-doped region in comparison to LSCO. 3.2. Nd2xCexCuO4 and La2xSrxCuO4 The normal resistivity at low temperatures can be studied in detail at lower fields in the so-called ‘‘214’’-type cuprate compounds, such as hole-
doped LSCO and electron-doped LCCO, PCCO, and NCCO. Recently, the NTT group succeeded in growing high-quality film samples of these compounds whose residual resistance is significantly lower than in previous samples grown by MBE [34–37]. The c-axis-oriented films were grown on SrTiO3 (0 0 1) substrates and LaSrAlO4 (0 0 1) substrates. It was found that the properties of the films, such as the critical temperature, can be controlled significantly by choosing the lattice constant of the substrates. For LSCO, for instance, films on LaSrAlO4 (0 0 1) substrates, are compressively strained in plane (a-axis) and expansively strained out of plane (c-axis) by the Poisson effect, and have Tc B44 K, whereas films on SrTiO3 (0 0 1) substrates are strained in the opposite way, and have Tc B26 K. In the absence of magnetic fields, the in-plane (ab) resistivity of NCCO films on SrTiO3 (0 0 1) substrates showed roughly a T 2 dependence at high temperatures above B50 K. This seems to indicate that electron–electron scattering dominates in this region. Below 50 K, however, a very different r T relation was observed depending on the doping; T-linear dependence in over-doped samples, and insulating behavior in under-doped samples. Fig. 6 shows the resistivity as a function of magnetic field at various temperatures for an optimal-doped sample (x ¼ 0:146). In addition to positive magneto-resistance as a background, negative magneto-resistance appears at low temperatures just above the magnetic field (Hc2 ). It becomes more prominent with decreasing temperature, and diminishes at very high magnetic fields. The under-doped sample (x ¼ 0:131) shows behavior qualitatively similar to this optimaldoped sample (x ¼ 0:146). In over-doped samples (x ¼ 0:166), however, the negative magneto-resistance is discernible only at the lowest temperature region. Fig. 7 shows r2T curves for under-, optimal- and over-doped samples. All of them show a low-temperature up-turn at low magnetic fields. The up-turn follows a log T dependence below 50 K in the under-doped sample, below 10 K in the optimal-doped sample, and below 2 K in the over-doped sample. In the under-doped samples, this dependence appears already in zero magnetic field above Tc : In over-doped samples, the up-turn
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behavior of the resistivity is very weak and can be seen only at very low temperatures. The resistivity minimum shifts to lower temperature with increasing Ce-doping. Furthermore, it should be noted that in the lowest temperature region, the resistivity of all films tends to deviate from a simple log T dependence showing a tendency of saturation. This result is very similar to that for optimally doped PCCO [38]. With increasing magnetic field, the log T dependent up-turn is suppressed except for under-doped samples, where the up-turn behavior persists up to the highest magnetic field studied. In optimaldoped samples, the resistivity shows metallic behavior in high magnetic fields, except for very low temperatures, where the up-turn remains. In over-doped samples, the low-temperature resistivity turns to be completely metal-like in high magnetic fields. In optimal- and over-doped
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samples, an insulator–metal transition occurs by applying the magnetic field. Fig. 8 shows the magneto-resistance curve at different directions of magnetic field relative to the normal of the film for the optimal-doped sample. A striking finding is that the field gradient of the negative magnetoresistance is almost independent of the direction of the magnetic field, i.e. the negative magnetoresistance component is isotropic. In the ‘‘low-Tc ’’ LSCO film on a SrTiO3 (0 0 1) substrate (Tc B26 K), similar tendency was
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observed, whereas the ‘‘high-Tc ’’ film on a LaSrAlO4 (0 0 1) substrate (Tc B44 K) showed no up-turn even at the lowest temperature. The two LSCO films show quite different magnetotransport properties as shown Fig. 9 which displays raw magneto-resistivity data of the ‘‘high-Tc’’ and ‘‘low-Tc ’’ films taken by sweeping magnetic fields applied parallel to the c-axis at various temperatures. Even in these raw data, the contrast between the two films is prominent. With increasing magnetic field, the superconductivity is gradually suppressed, and the low-temperature normal behavior is unveiled accordingly. With decreasing temperature, the normal-state resistivity above Hc2 monotonically decreases in the ‘‘high-Tc ’’ whereas it increases in the ‘‘low-Tc ’’ film. Fig. 10 shows the temperature dependences of the resistivity in magnetic fields. The normal-state resistivity of the ‘‘high-Tc ’’ film is rather normal and metallic down to the lowest temperature. In contrast, the normal-state resistivity of the ‘‘lowTc ’’ film shows an anomalous semiconducting upturn (dr=dTo0) with a resistivity minimum at around 30 K. A low-temperature semiconducting up-turn with a resistivity minimum has frequently been observed in high-Tc cuprates [27,28,38–42], and they are common with those in electron-doped superconductors (Nd,Ce)2CuO4, (Pr,Ce)2CuO4, and (La,Ce)2CuO4 [20,22].
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Fig. 9. Comparison of the normal-state resistivity in high magnetic fields (B8c-axis) between the ‘‘high-Tc’’ and ‘‘lowTc ’’ LSCO films. The ‘‘high-Tc ’’ film is grown on a LaSrAlO4 substrate (lower panel), and the ‘‘low-Tc ’’ film is grown on a SrTiO3 substrate (upper panel). The temperature for each graph is 4.2, 6, 8, 10, 13, 15, 17, 21, 26, 30, 33, 36, 40, 43, 45, 50, 55 and 60 K (from bottom to top) in the lower panel; 1.5, 4.2, 5, 6, 8, 10, 13, 15, 17, 19, 21, 23, 25, 27, 30, 36, 45 and 50 K in the upper panel. The normal-state resistivity of the ‘‘high-Tc ’’ film is small, showing metallic behavior down to the lowest temperature, whereas that of the ‘‘low-Tc ’’ film is large, showing a semiconducting up-turn with a resistivity minimum around 30 K.
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One possible explanation of the observed log T dependence is in terms of simple two-dimensional weak localization [39]. However, this possibility is unlikely because it cannot explain the observed isotropic negative magneto-resistance as shown in Fig. 8. Moreover, in the two-dimensional weak localization, it is expected that the coefficient of the log T dependence of the conductivity per sheet should be always a common universal value irrespective of the doping. However, we found that the values of the coefficient of the optimaldoped films are almost one order of magnitude larger than that of under- and over-doped films. Therefore, the possibility of weak localization is discarded. Another candidate for the mechanism of the log T up-turn observed in 214 compounds is the Kondo scattering. As is well known, materials in which the Kondo effect predominates the transport exhibit the log T dependence of the up-turn caused by the localization effect due to singlet formation. They also show saturation of the up-turn at lower temperatures (unitarity limit of scattering), and suppression of the up-turn by high magnetic fields (delocalization effect due to singlet dissociation by magnetic field). The normal-state resistivity of the NCCO (x ¼ 0:13120:166) and the ‘‘low-Tc ’’ LSCO film follows log T behavior and saturates at lower temperatures. In addition, the negative magneto-resistance observed in these samples looks very similar to that observed in the typical Kondo material (La,Ce)B6 [43]. Recently, NMR experiments have revealed that in high-Tc cuprates, local magnetic moments are induced in the CuO2 plane by doping spinless impurities such as Li, Zn or Al [44–50]. These local moments can play a role as Kondo scatterers. The suppression of the up-turn by high magnetic fields (negative magneto-resistance) has not been observed in ‘‘high-Tc ’’ LSCO, most likely because the magnetic field of 50 T is not sufficient to dissociate the Kondo singlets, which seem to be more strongly bounded than in electron-doped superconductors. Experiments in higher magnetic fields of up to B100 T, which we are planning, may clarify this issue. Based on the Kondo-effect model, we give here a rough estimate for the Kondo temperature (TK )
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and the Kondo magnetic field (HK ). Following the procedure by Samwer and Winzer [43] to define TK as the temperature at the half-height of the Kondo resistivity step, the TK of ‘‘low-Tc ’’ LSCO is B20 K. Then the scaling relation, kB TK ¼ Sgeff mB HK ; gives m0 HK B30 T, assuming S ¼ 12 and geff ¼ 2: However, the actual value for m0 HK of ‘‘low-Tc ’’ LSCO seems to be much larger than B30 T. This discrepancy may partly be explained by supposing geff o2: However, it may be better to postpone quantitative discussions to later publications since a single-impurity-scattering approximation apparently does not apply to the present case. Given the Kondo effect as the origin for the lowtemperature up-turn, the question arises what is the origin of the Kondo scatterer. In the case of NCCO, we have to pay attention to the presence of the Nd3+ paramagnetic spin moment. However, we can exclude the possibility of the role of the Nd3+ spin moments as the Kondo scatterer, because similar phenomena are observed in LCCO, PCCO and LSCO which have no spin moments of Pr3+ or La3+ even at low temperatures [20–22]. So we have to resort to another mechanism, i.e. residual Cu2+ spins in the CuO2 plane. Actually, in LSCO, the existence of significant AF spin fluctuations is indicated by the incommensurate magnetic peaks in inelasticneutron-scattering experiments [51]. On the other hand, the neutron-scattering results on NCCO are controversial, partly due to the difficulty in removing interstitial apical oxygen homogeneously in single crystals to achieve good superconductivity [52,53]. In the early experiment by Matsuda et al. no well-defined AF magnetic correlation of Cu2+ spins was observed in high-quality superconducting samples, although random spins may exist. So, we speculate that there may exist much fewer or/and much weaker magnetic moments due to Cu2+ in NCCO than in LSCO. This may explain the weaker up-turn at low temperatures in NCCO than in LSCO. Furthermore, the less anomalous properties of the over-doped films can also be explained by the above scenario, assuming that the Cu-3d orbit becomes more itinerant and then the Cu2+ spin moments are reduced with doping.
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Our experimental observation of strained LSCO films indicates that the Kondo effect prevails in the ‘‘low-Tc ’’ film, while it is practically negligible in the ‘‘high-Tc ’’ film of LSCO. This seems to indicate that a stronger Kondo interaction lowers superconducting transition temperature Tc ; or in other words, Kondo-singlet formation hinders Cooper-pair formation. The interplay between the Kondo effect and superconductivity for lowTc superconductors has been extensively investigated theoretically and also experimentally [54]. However, it has not yet been considered seriously for high-Tc cuprates. Both the Kondo interaction HK and the superconducting pairing interaction Hpair are involved in this problem. In the case that HK dominates Hpair ; conduction electrons pair up with local spins, resulting in Kondo localization. In the other extreme where Hpair dominates, conduction electrons pair up with each other, resulting in superconductivity. In the present case for LSCO with xB0:15; HK and Hpair are both important and in competition, and thereby there is frustration for a conduction electron to pair up either with a local spin or with another conduction electron. Epitaxial strain seems to have a significant influence on this delicate balance. We assume that epitaxial strain dominantly affects the Kondo interaction HK ; while leaving Hpair nearly unchanged. Epitaxial strain changes only the lattice parameters (a0 and c0 ) of LSCO, leaving the doping level constant. The explicit dependence of HK on these lattice parameters requires microscopic calculations. Our experimental results indicate that shorter a0 and longer c0 reduces either the Kondo-coupling constant JK or the number and the magnitude of local spins [51]. We speculate that a longer Cu–Oapex distance reduces the Kondo interaction, and thereby raises Tc : This speculation is supported by the systematic Tc suppression by the induced Cu2+ local spins in (La1xPrx)1.85Sr0.15CuO4 with smaller c0 (and also smaller a0 ) [55]. Based on the above scenario, we propose a new electronic phase diagram for LSCO as shown in Fig. 11. The thin line represents a virtual Tc with no Kondo interaction, the bold line a real Tc ; and the broken line a Kondo cross-over temperature
Fig. 11. New electronic phase diagram proposed for LSCO. The thin line represents a virtual Tc with no Kondo interaction, the bold line a real Tc ; and the broken line a Kondo cross-over temperature TK : The gradation of the shadow schematically represents the development of the Kondo effect. The edge of the shadowed region is given roughly below the resistivity minimum temperature. The Kondo interaction shifts the virtual Tc to the real Tc : In-plane compressive epitaxial strain weakens the Kondo interaction, resulting in a smaller shift. In-plane expansive strain will act in an opposite way. The symbol em ¼ ek represents a Cooper pair, and Sm ¼ ek a Kondo singlet.
(TK ). The gradation of the shadow schematically represents the development of the Kondo effect. Without the Kondo interaction, the virtual Tc (Tc ) would keep increasing with decreasing x: The Kondo interaction, however, sets in below a certain x value and becomes stronger for lower x: This suppresses the virtual Tc to the real Tc ; with more significant reduction in Tc for lower x; and eventually leads to the disappearance of superconductivity. As regards the epitaxial strain effect, in-plane compressive strain weakens the Kondo interaction and thereby results in less Tc suppression. In-plane expansive strain will act in an opposite way. With over-doping, the Cu-3d orbit becomes more itinerant, resulting in reduction or eventually loss of spin moments. As a result, the Kondo interaction between a Cu2+ local spin and a conduction electron essentially diminishes. Nevertheless, against the above scenario, Tc decreases by over-doping. We speculate that the reduction of Tc by over-doping is caused by the weakening of the pairing interaction (Hpair ), although we have no microscopic explanation for this trend at present.
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4. Summary
References
In this paper, we present the study of high-Tc cuprates in pulsed high magnetic fields. In YBCO, the phase diagram of Hc2 as a function of temperature was determined for B8c: It was found to be very similar to that for conventional type-II superconductors. The resistivity vs. temperature curve demonstrates that the system is metallic at low temperatures. This indicates that the metallic region extends to the more under-doped region in comparison to LSCO. In LCCO, PCCO, NCCO and LSCO, we studied the temperature dependence of the normal resistivity in detail. We observed negative magneto-resistance in the normal state. In NCCO, the field gradient of the negative magnetoresistance was found to be independent of the direction of the magnetic field. All the samples showed prominent cross-over from insulating to metallic conduction by a magnetic field. The temperature dependence was found to exhibit a log T dependence at low temperatures. The log T dependence is suppressed at low temperatures and in high magnetic fields. These results were explained in terms of manifestation of the Kondo effect originating from the magnetic moments of Cu ions. Based on these results, we proposed a new scenario for the electronic phase diagram of LSCO:Kondo interaction suppresses superconducting Tc in the under-doped regime. Removing or weakening the Kondo interaction can raise the superconducting transition temperature Tc :
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Acknowledgements One of the authors (N.M.) is thankful to Professor J.J.M. Franse for his great contribution to the community of high-magnetic-field physics and personal companionship for many years. This work was partially supported by a GrantIn-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan and the New Energy and Industrial Technology Development Organization (NEDO).
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High-magnetic-field study of high-Tc cuprates N. Miuraa,*, H. Nakagawaa, T. Sekitania, M. Naitob, H. Satob, Y. Enomotoc a
Institute for Solid States Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, 277-8581 Chiba, Japan b NTT Basic Research Laboratories, Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan c Superconductivity Research Laboratory, International Technology Center, Shinonome, Koto-ku, Tokyo 135-0062, Japan Received 11 March 2002
Abstract We present our recent studies of high-Tc superconductors in very high pulsed magnetic fields exceeding 100 T (megagauss fields). In YBa2Cu3O7d, the super to normal transition was observed in transport measurements for B8c under short pulse fields up to 120 T. A plot of the upper critical field Hc2 as a function of temperature demonstrates that the curve obeys the conventional relation well established in other type-II superconductors in the dirty limit. From the resistivity versus temperature curve at high magnetic fields above the super to normal transition, it was found that the hole system shows a metallic temperature dependence for B8c: In Nd2xCexCuO4 as electron-doped cuprate, a large magneto-resistance was observed above the transition field. It was also found that the temperature dependence of the resistivity above the critical field is insulator-like showing a prominent logarithmic up-turn at low temperatures. A similar logarithmic up-turn was observed in several other cuprates such as La2xSrxCuO4 (LSCO), La2xCexCuO, and Pr2xCexCuO4. The experimental results for thin-film samples of LSCO with different strains suggest that the Kondo effect plays an important role in these materials. A new phase diagram of LSCO is proposed on the basis of a viewpoint of the interplay between superconductivity and the Kondo effect. r 2002 Published by Elsevier Science B.V. PACS: 72.15.Gd; 74.72.Bk; 74.72.Jt; 74.76.Bz Keywords: High magnetic fields; High-Tc cuprates
1. Introduction The recent advances in the magnet technology have enabled us to produce very high magnetic fields up to several megagauss (>100 T) that can be applied to solid-state experiments [1]. At the Institute for Solid State Physics (ISSP) of the University of Tokyo, we have succeeded in *Corresponding author. Tel.: +81-471-36-33-41; fax: +81471-36-33-35. E-mail address: [email protected] (N. Miura).
producing very high magnetic fields up to 622 T by electromagnetic flux compression and up to 302 T by the single-turn-coil technique [2,3]. Nondestructive long pulse fields up to about 60 T were also generated by conventional wire-wound solenoids. These fields were applied in many different experiments such as magneto-optical spectroscopy [4,5], cyclotron resonance [6], magnetization [7], or magneto-transport measurements [8]. A variety of interesting experiments can be performed in the extreme limit of high magnetic fields in diverse research areas. As an example of experiments in
0921-4526/02/$ - see front matter r 2002 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 1 3 4 - 1
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very high magnetic fields, we present here a study of high-Tc cuprates in semi-destructive fields generated by the single-turn-coil technique and non-destructive pulse fields generated by wirewound magnets. Since its discovery [9], high-Tc superconductors have been one of the most important research subjects in solid-state physics. It has been pointed out that the electron system in this class of materials might have unusual properties unlike normal Fermi liquids. In order to investigate the origin of the unique properties of these materials and the mechanism of the high-Tc superconductivity, we need to investigate the normal-state properties at low temperatures. These materials have high critical temperatures and hence the upper critical field is also quite high. Therefore, in order to break their superconductivity at low temperatures, either chemical-doping or application of high magnetic fields above the upper critical field is an essential means to exploit. We investigated the super–normal transition and the normal-state conductivity by using very high magnetic fields. Measurement of the electrical resistance in a short pulse of megagauss fields is a difficult task, because of the large induction associated with the high and short magnetic field pulse. Some pioneering work on the measurements in very high fields has been reported on YBa2Cu3O7d (YBCO) [10,11]. In order to avoid the problems arising from the induction in the lead wire loop, we have developed a contactless technique to measure the AC field transmission through samples [12]. We have also developed a technique to measure magnetization hysteresis for determining the field of irreversible point as a function of temperature [13,14]. As regards the resistivity measurements with contacts on samples, we have succeeded in measuring the resistivity of high-Tc superconductors in megagauss fields by minimizing the loop involved in the sample and the lead wire, and by use of band path filters [8,15,16]. By using this technique, we found many new features in YBCO. Another technique is to utilize a strip line measuring the microwave transmission with a frequency of 0.5–1.0 GHz [17]. In collaboration with the group of National Pulsed Magnet Laboratory of the University of the
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New South Wales, the strip-line technique was successfully applied for experiments with the single-turn-coil technique [18] and explosive-driven flux compression [19]. In long pulse fields up to 60 T, the transport measurements can be more readily made and very accurate measurements are possible on 214-type high-Tc cuprates, such as hole-doped La2xSrxCuO4 (LSCO) and electrondoped La2xCexCuO4 (LCCO), Pr2xCexCuO4 (PCCO), and Nd2xCexCuO4 (NCCO) [20–22]. One of the important problems on high-Tc superconductors is the transition from the superconducting state (S) to the normal state (N) by a magnetic field. Previous studies of the S–N transition have been mostly limited to the vicinity of the critical temperature Tc ; since we need very high fields to extend the measurements to lower temperatures. In over-doped Tl or Bi compounds which have Tc lower than 20 K, the upper critical field determined from the resistivity measurements were found to increase abruptly at low temperatures down to the mK range [23,24]. This behavior is completely different from that of conventional type-II superconductors which is well described by the theory of Werthamer–Helfand–Hoenberg (WHH) [25]. In high-Tc cuprates, the fluctuation effect is very large due to the short coherence length and the two-dimensional character of the electron system. As a result, it is generally believed that Hc2 is not a phase transition point, but the cross-over point from the flux-liquid state to the normal state [26]. Therefore, the implication of Hc2 determined by resistivity measurements is not so clear. However, in order to clarify the nature of the S–N transition, it would certainly be very important to investigate the S–N transition at low temperatures in detail. Another important problem is the temperature dependence of the normal resistivity at low temperatures created by the S–N transition in high magnetic fields. In order to investigate the normal resistivity of high-Tc superconductors at low temperatures, we need to break the superconductivity either by chemical-doping or by application of high magnetic fields. The latter is much more preferable, since it allows measurements over a wide range of composition including the vicinity of the optimal-doping. Boebinger,
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Ando and coworkers reported results of experiments on the normal resistivity in the ab-plane and along the c-axis at low temperatures and high magnetic fields. They found in the temperature dependence of LSCO that, for nearly optimally doped samples, the c-axis resistivity is insulating whilst the ab-plane resistivity is metallic, but both become insulating at low temperatures [27,28]. In Bi2Sr2xLaxCuOy, however, the metallic behavior of the ab-plane resistivity is preserved down to low temperatures (0.66 K) keeping the insulating behavior of the c-axis resistivity [29]. It is of importance to study the temperature dependence of the normal resistivity in a wide range of materials.
90 K
350 300 250 R (Ω)
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200 150 100 50 40 K
0 0
10
20
30 B (T)
40
50
Fig. 1. Magneto-resistance of YBa2Cu3O7d thin film for B8c at different temperatures in long pulse fields up to 50 T. The temperatures are 40, 45, 50, 55, 60, 62.8, 65, 67, 69, 71, 73, 75, 77.5, 79, 80.4, 82, 84, 86, 88 and 90 K from bottom to top.
3
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2
200
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1 B
B (T)
The samples of YBCO thin film with a thickness ( were grown on a MgO substrate by the of 1000 A laser ablation technique. It is a slightly underdoped sample with a critical temperature Tc of 84 K. The samples were processed to make their shapes to either a meander-like or a simple bar-like shape with a length of about 500 mm. Four contacts method was employed with a DC (square pulse) and AC current. In the case of AC measurements, AC current of frequencies of 5–10 MHz was supplied to the sample. Fig. 1 shows the magneto-resistance of YBCO thin film for B8c at different temperatures in long pulse fields up to 50 T. Magneto-resistance curves with excellent signal-to-noise ratio were obtained with both up-rising and down-falling field slopes. It was confirmed that there was no heating effect from eddy currents in our experiments, since the two data obtained by both up- and down-sweep of the pulsed field coincided almost perfectly. In short pulses with peak field higher than 100 T produced by the single-turn-coil technique, the measurement of the resistivity involves much more difficult technical problems. Fig. 2 shows the typical wave forms of the magnetic field and the current of the single-turn-coil technique [2,3]. In this case, a peak field of 263 T was obtained in a bore of 6 mm. The maximum field depends on the bore of the coil. The duration of the magnetic field
I (MA)
2. Experimental procedure
I
0
0
0
5
10 15 Time (µs)
20
Fig. 2. Pulse shapes of the current (I) and magnetic field (B) generated by the single-turn-coil technique. The bore and the length of the coil are 6.0 mm and its wall thickness is 3 mm. The maximum of the field 263 T is reached earlier than that of the current because of the deformation of the coil. The maximum field increases with decreasing bore.
is about 7 ms. In such a short pulse, the induced voltage in the lead wires becomes enormous. If there is a loop with a radius of 2 mm in the circuit formed by the sample and the lead wire, the induced voltage reaches B800 V in a field up to 100 T, which is much larger than the bias voltage applied to the sample for measurements. By minimizing the cross-section and by making the lead wires parallel to the field as much as possible, the induced voltage was greatly reduced. Optimizing wirings, filters and compensation circuits, it
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has become possible to obtain the magnetoresistance curve with a reasonable signal-to-noise ratio [8,15,16]. The sample was cooled by flowing He liquid or gas around the sample, and the temperature was measured by a gold–iron Chromel thermocouple.
3. Results and discussion 3.1. YBa2Cu3O7d Fig. 3 shows the DC magneto-resistance of YBCO for B8c-axis measured with the singleturn-coil technique at various temperatures. An abrupt jump of the resistivity corresponding to the super–normal transition is clearly observed. At the start of the pulse, large noise is induced due to the extraordinary large dB=dt and the trigger noise. Except for the region at the first part of the pulse in the up-sweep (below B40 T), the signal was much deteriorated by the noise, but at about 40 T, the signal was in agreement with the data taken by a long pulse up to 40 T. In addition, the up-sweep trace and down-sweep trace taken in one pulse coincide with each other above 60 T. Below 60 T, therefore, we obtained just down-traces. In the down-trace we obtained reproducible data depending just on temperature.
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As the field-induced transition is gradual with several deflection points, there are many ways of the definition of the critical field for the S–N transition. The onset of the transition Honset ; that can be determined as a cross-point between the straight lines from the low field range and the transition range, the offset field Hhf where the nearly constant gradient of the resistance vs. field curve in the high-field range starts increasing in the transition at lower fields, the midpoint Hmidpoint determined by the midpoint where the resistivity is a half of that for Hhf ; etc. If we take Hhf ; the gradient of the Hc2 2T curve in the vicinity of Tc becomes B2 T/K which is in good agreement with the data reported by Welp et al. [30]. From such measurements, we can determine the phase diagram of YBCO. The diagram for Hhf is shown in Fig. 4. The phase diagram for B8c is well described by the WHH model of the dirty-limit superconductor [25] by choosing certain parameters of a and lSO : It implies that the system is featured by a phase diagram similar to those for conventional type-II superconductors for B8c: This is in sharp contrast to the case for B8c [18], where the upper critical field exceeds the paramagnetic limit suggesting the FFLO state [31,32]. Another interesting problem of high-Tc superconductors is the normal-state conductivity at low temperatures. Study of the low-temperature
40
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R (Ω)
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µ0Hc2_h µ0 Hc2_h (DC)
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(α, λ SO ) = (1.055, 3.3) (α, λ SO ) = (1.055, 0)
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0 − 40
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0
− 20
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Fig. 3. Raw data of the magneto-resistance of YBa2Cu3O7d at different temperatures measured in short pulse fields generated by the single-turn-coil technique.
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T (K)
Fig. 4. Plot of Hc22h as a function of temperature. Data obtained with DC current and AC current are shown together with the theoretical curve calculated based on the WHH theory. Different values of (a; lSO ) are assumed, as shown in the figure.
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314 60 B // c 50
0T 10T 20T 30T 40T 60T 80T 100T 110T
ρab (µΩcm)
40 30 20 10 0 0
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40
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T (K)
Fig. 5. Temperature dependence of the resistivity at different magnetic fields for YBa2Cu3O7dU
transport provides a rich source of information of the mechanism of the transport and the superconductivity itself. However, in order to realize the normal state at low temperatures, we have to dope impurities or apply high magnetic fields to destroy the superconductivity. By applying high magnetic fields exceeding the upper critical field, we investigated the normal state of YBCO at low temperatures. Fig. 5 shows the temperature dependence of the normal-state resistivity at different magnetic fields. At sufficiently high magnetic fields above 100 T, samples are considered to be in the normal state. It is clearly seen that the resistivity exhibits metallic behavior. Namely, the resistivity decreases with decreasing temperature. Boebinger et al. reported that in LSCO bulk, the in-plane resistivity shows metallic behavior near the optimum-doping but converts to insulating behavior when the doping is reduced [25]. In a very under-doped sample of YBCO (d ¼ 0:62), an insulating properties were observed [33]. The present sample is almost optimally doped but slightly under doped (dB0:1). Therefore, we can conclude that in YBCO, the metal–insulator transition occurs at a more over-doped region in comparison to LSCO. 3.2. Nd2xCexCuO4 and La2xSrxCuO4 The normal resistivity at low temperatures can be studied in detail at lower fields in the so-called ‘‘214’’-type cuprate compounds, such as hole-
doped LSCO and electron-doped LCCO, PCCO, and NCCO. Recently, the NTT group succeeded in growing high-quality film samples of these compounds whose residual resistance is significantly lower than in previous samples grown by MBE [34–37]. The c-axis-oriented films were grown on SrTiO3 (0 0 1) substrates and LaSrAlO4 (0 0 1) substrates. It was found that the properties of the films, such as the critical temperature, can be controlled significantly by choosing the lattice constant of the substrates. For LSCO, for instance, films on LaSrAlO4 (0 0 1) substrates, are compressively strained in plane (a-axis) and expansively strained out of plane (c-axis) by the Poisson effect, and have Tc B44 K, whereas films on SrTiO3 (0 0 1) substrates are strained in the opposite way, and have Tc B26 K. In the absence of magnetic fields, the in-plane (ab) resistivity of NCCO films on SrTiO3 (0 0 1) substrates showed roughly a T 2 dependence at high temperatures above B50 K. This seems to indicate that electron–electron scattering dominates in this region. Below 50 K, however, a very different r T relation was observed depending on the doping; T-linear dependence in over-doped samples, and insulating behavior in under-doped samples. Fig. 6 shows the resistivity as a function of magnetic field at various temperatures for an optimal-doped sample (x ¼ 0:146). In addition to positive magneto-resistance as a background, negative magneto-resistance appears at low temperatures just above the magnetic field (Hc2 ). It becomes more prominent with decreasing temperature, and diminishes at very high magnetic fields. The under-doped sample (x ¼ 0:131) shows behavior qualitatively similar to this optimaldoped sample (x ¼ 0:146). In over-doped samples (x ¼ 0:166), however, the negative magneto-resistance is discernible only at the lowest temperature region. Fig. 7 shows r2T curves for under-, optimal- and over-doped samples. All of them show a low-temperature up-turn at low magnetic fields. The up-turn follows a log T dependence below 50 K in the under-doped sample, below 10 K in the optimal-doped sample, and below 2 K in the over-doped sample. In the under-doped samples, this dependence appears already in zero magnetic field above Tc : In over-doped samples, the up-turn
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behavior of the resistivity is very weak and can be seen only at very low temperatures. The resistivity minimum shifts to lower temperature with increasing Ce-doping. Furthermore, it should be noted that in the lowest temperature region, the resistivity of all films tends to deviate from a simple log T dependence showing a tendency of saturation. This result is very similar to that for optimally doped PCCO [38]. With increasing magnetic field, the log T dependent up-turn is suppressed except for under-doped samples, where the up-turn behavior persists up to the highest magnetic field studied. In optimaldoped samples, the resistivity shows metallic behavior in high magnetic fields, except for very low temperatures, where the up-turn remains. In over-doped samples, the low-temperature resistivity turns to be completely metal-like in high magnetic fields. In optimal- and over-doped
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samples, an insulator–metal transition occurs by applying the magnetic field. Fig. 8 shows the magneto-resistance curve at different directions of magnetic field relative to the normal of the film for the optimal-doped sample. A striking finding is that the field gradient of the negative magnetoresistance is almost independent of the direction of the magnetic field, i.e. the negative magnetoresistance component is isotropic. In the ‘‘low-Tc ’’ LSCO film on a SrTiO3 (0 0 1) substrate (Tc B26 K), similar tendency was
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observed, whereas the ‘‘high-Tc ’’ film on a LaSrAlO4 (0 0 1) substrate (Tc B44 K) showed no up-turn even at the lowest temperature. The two LSCO films show quite different magnetotransport properties as shown Fig. 9 which displays raw magneto-resistivity data of the ‘‘high-Tc’’ and ‘‘low-Tc ’’ films taken by sweeping magnetic fields applied parallel to the c-axis at various temperatures. Even in these raw data, the contrast between the two films is prominent. With increasing magnetic field, the superconductivity is gradually suppressed, and the low-temperature normal behavior is unveiled accordingly. With decreasing temperature, the normal-state resistivity above Hc2 monotonically decreases in the ‘‘high-Tc ’’ whereas it increases in the ‘‘low-Tc ’’ film. Fig. 10 shows the temperature dependences of the resistivity in magnetic fields. The normal-state resistivity of the ‘‘high-Tc ’’ film is rather normal and metallic down to the lowest temperature. In contrast, the normal-state resistivity of the ‘‘lowTc ’’ film shows an anomalous semiconducting upturn (dr=dTo0) with a resistivity minimum at around 30 K. A low-temperature semiconducting up-turn with a resistivity minimum has frequently been observed in high-Tc cuprates [27,28,38–42], and they are common with those in electron-doped superconductors (Nd,Ce)2CuO4, (Pr,Ce)2CuO4, and (La,Ce)2CuO4 [20,22].
80
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Fig. 9. Comparison of the normal-state resistivity in high magnetic fields (B8c-axis) between the ‘‘high-Tc’’ and ‘‘lowTc ’’ LSCO films. The ‘‘high-Tc ’’ film is grown on a LaSrAlO4 substrate (lower panel), and the ‘‘low-Tc ’’ film is grown on a SrTiO3 substrate (upper panel). The temperature for each graph is 4.2, 6, 8, 10, 13, 15, 17, 21, 26, 30, 33, 36, 40, 43, 45, 50, 55 and 60 K (from bottom to top) in the lower panel; 1.5, 4.2, 5, 6, 8, 10, 13, 15, 17, 19, 21, 23, 25, 27, 30, 36, 45 and 50 K in the upper panel. The normal-state resistivity of the ‘‘high-Tc ’’ film is small, showing metallic behavior down to the lowest temperature, whereas that of the ‘‘low-Tc ’’ film is large, showing a semiconducting up-turn with a resistivity minimum around 30 K.
0T 5T 10T 15T 20T 25T 30T 35T 40T 45T
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Resistivity (µΩcm)
Fig. 8. Magneto-resistance curve for different directions of the magnetic field relative to the normal-state of the film for an optimal-doped sample of NCCO at 4.2 K. The inset shows the angular dependence of the magnetic-field gradient A:
40
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N. Miura et al. / Physica B 319 (2002) 310–320
One possible explanation of the observed log T dependence is in terms of simple two-dimensional weak localization [39]. However, this possibility is unlikely because it cannot explain the observed isotropic negative magneto-resistance as shown in Fig. 8. Moreover, in the two-dimensional weak localization, it is expected that the coefficient of the log T dependence of the conductivity per sheet should be always a common universal value irrespective of the doping. However, we found that the values of the coefficient of the optimaldoped films are almost one order of magnitude larger than that of under- and over-doped films. Therefore, the possibility of weak localization is discarded. Another candidate for the mechanism of the log T up-turn observed in 214 compounds is the Kondo scattering. As is well known, materials in which the Kondo effect predominates the transport exhibit the log T dependence of the up-turn caused by the localization effect due to singlet formation. They also show saturation of the up-turn at lower temperatures (unitarity limit of scattering), and suppression of the up-turn by high magnetic fields (delocalization effect due to singlet dissociation by magnetic field). The normal-state resistivity of the NCCO (x ¼ 0:13120:166) and the ‘‘low-Tc ’’ LSCO film follows log T behavior and saturates at lower temperatures. In addition, the negative magneto-resistance observed in these samples looks very similar to that observed in the typical Kondo material (La,Ce)B6 [43]. Recently, NMR experiments have revealed that in high-Tc cuprates, local magnetic moments are induced in the CuO2 plane by doping spinless impurities such as Li, Zn or Al [44–50]. These local moments can play a role as Kondo scatterers. The suppression of the up-turn by high magnetic fields (negative magneto-resistance) has not been observed in ‘‘high-Tc ’’ LSCO, most likely because the magnetic field of 50 T is not sufficient to dissociate the Kondo singlets, which seem to be more strongly bounded than in electron-doped superconductors. Experiments in higher magnetic fields of up to B100 T, which we are planning, may clarify this issue. Based on the Kondo-effect model, we give here a rough estimate for the Kondo temperature (TK )
317
and the Kondo magnetic field (HK ). Following the procedure by Samwer and Winzer [43] to define TK as the temperature at the half-height of the Kondo resistivity step, the TK of ‘‘low-Tc ’’ LSCO is B20 K. Then the scaling relation, kB TK ¼ Sgeff mB HK ; gives m0 HK B30 T, assuming S ¼ 12 and geff ¼ 2: However, the actual value for m0 HK of ‘‘low-Tc ’’ LSCO seems to be much larger than B30 T. This discrepancy may partly be explained by supposing geff o2: However, it may be better to postpone quantitative discussions to later publications since a single-impurity-scattering approximation apparently does not apply to the present case. Given the Kondo effect as the origin for the lowtemperature up-turn, the question arises what is the origin of the Kondo scatterer. In the case of NCCO, we have to pay attention to the presence of the Nd3+ paramagnetic spin moment. However, we can exclude the possibility of the role of the Nd3+ spin moments as the Kondo scatterer, because similar phenomena are observed in LCCO, PCCO and LSCO which have no spin moments of Pr3+ or La3+ even at low temperatures [20–22]. So we have to resort to another mechanism, i.e. residual Cu2+ spins in the CuO2 plane. Actually, in LSCO, the existence of significant AF spin fluctuations is indicated by the incommensurate magnetic peaks in inelasticneutron-scattering experiments [51]. On the other hand, the neutron-scattering results on NCCO are controversial, partly due to the difficulty in removing interstitial apical oxygen homogeneously in single crystals to achieve good superconductivity [52,53]. In the early experiment by Matsuda et al. no well-defined AF magnetic correlation of Cu2+ spins was observed in high-quality superconducting samples, although random spins may exist. So, we speculate that there may exist much fewer or/and much weaker magnetic moments due to Cu2+ in NCCO than in LSCO. This may explain the weaker up-turn at low temperatures in NCCO than in LSCO. Furthermore, the less anomalous properties of the over-doped films can also be explained by the above scenario, assuming that the Cu-3d orbit becomes more itinerant and then the Cu2+ spin moments are reduced with doping.
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Our experimental observation of strained LSCO films indicates that the Kondo effect prevails in the ‘‘low-Tc ’’ film, while it is practically negligible in the ‘‘high-Tc ’’ film of LSCO. This seems to indicate that a stronger Kondo interaction lowers superconducting transition temperature Tc ; or in other words, Kondo-singlet formation hinders Cooper-pair formation. The interplay between the Kondo effect and superconductivity for lowTc superconductors has been extensively investigated theoretically and also experimentally [54]. However, it has not yet been considered seriously for high-Tc cuprates. Both the Kondo interaction HK and the superconducting pairing interaction Hpair are involved in this problem. In the case that HK dominates Hpair ; conduction electrons pair up with local spins, resulting in Kondo localization. In the other extreme where Hpair dominates, conduction electrons pair up with each other, resulting in superconductivity. In the present case for LSCO with xB0:15; HK and Hpair are both important and in competition, and thereby there is frustration for a conduction electron to pair up either with a local spin or with another conduction electron. Epitaxial strain seems to have a significant influence on this delicate balance. We assume that epitaxial strain dominantly affects the Kondo interaction HK ; while leaving Hpair nearly unchanged. Epitaxial strain changes only the lattice parameters (a0 and c0 ) of LSCO, leaving the doping level constant. The explicit dependence of HK on these lattice parameters requires microscopic calculations. Our experimental results indicate that shorter a0 and longer c0 reduces either the Kondo-coupling constant JK or the number and the magnitude of local spins [51]. We speculate that a longer Cu–Oapex distance reduces the Kondo interaction, and thereby raises Tc : This speculation is supported by the systematic Tc suppression by the induced Cu2+ local spins in (La1xPrx)1.85Sr0.15CuO4 with smaller c0 (and also smaller a0 ) [55]. Based on the above scenario, we propose a new electronic phase diagram for LSCO as shown in Fig. 11. The thin line represents a virtual Tc with no Kondo interaction, the bold line a real Tc ; and the broken line a Kondo cross-over temperature
Fig. 11. New electronic phase diagram proposed for LSCO. The thin line represents a virtual Tc with no Kondo interaction, the bold line a real Tc ; and the broken line a Kondo cross-over temperature TK : The gradation of the shadow schematically represents the development of the Kondo effect. The edge of the shadowed region is given roughly below the resistivity minimum temperature. The Kondo interaction shifts the virtual Tc to the real Tc : In-plane compressive epitaxial strain weakens the Kondo interaction, resulting in a smaller shift. In-plane expansive strain will act in an opposite way. The symbol em ¼ ek represents a Cooper pair, and Sm ¼ ek a Kondo singlet.
(TK ). The gradation of the shadow schematically represents the development of the Kondo effect. Without the Kondo interaction, the virtual Tc (Tc ) would keep increasing with decreasing x: The Kondo interaction, however, sets in below a certain x value and becomes stronger for lower x: This suppresses the virtual Tc to the real Tc ; with more significant reduction in Tc for lower x; and eventually leads to the disappearance of superconductivity. As regards the epitaxial strain effect, in-plane compressive strain weakens the Kondo interaction and thereby results in less Tc suppression. In-plane expansive strain will act in an opposite way. With over-doping, the Cu-3d orbit becomes more itinerant, resulting in reduction or eventually loss of spin moments. As a result, the Kondo interaction between a Cu2+ local spin and a conduction electron essentially diminishes. Nevertheless, against the above scenario, Tc decreases by over-doping. We speculate that the reduction of Tc by over-doping is caused by the weakening of the pairing interaction (Hpair ), although we have no microscopic explanation for this trend at present.
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4. Summary
References
In this paper, we present the study of high-Tc cuprates in pulsed high magnetic fields. In YBCO, the phase diagram of Hc2 as a function of temperature was determined for B8c: It was found to be very similar to that for conventional type-II superconductors. The resistivity vs. temperature curve demonstrates that the system is metallic at low temperatures. This indicates that the metallic region extends to the more under-doped region in comparison to LSCO. In LCCO, PCCO, NCCO and LSCO, we studied the temperature dependence of the normal resistivity in detail. We observed negative magneto-resistance in the normal state. In NCCO, the field gradient of the negative magnetoresistance was found to be independent of the direction of the magnetic field. All the samples showed prominent cross-over from insulating to metallic conduction by a magnetic field. The temperature dependence was found to exhibit a log T dependence at low temperatures. The log T dependence is suppressed at low temperatures and in high magnetic fields. These results were explained in terms of manifestation of the Kondo effect originating from the magnetic moments of Cu ions. Based on these results, we proposed a new scenario for the electronic phase diagram of LSCO:Kondo interaction suppresses superconducting Tc in the under-doped regime. Removing or weakening the Kondo interaction can raise the superconducting transition temperature Tc :
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