Fourfold oscillations and anomalous magnetic irreversibility of magnetoresistance in the non-metallic regime of Pr1.85Ce0.15CuO4
arXiv:cond-mat/0309144v1 [cond-mat.supr-con] 5 Sep 2003
P. Fournier, M.-E. Gosselin, S. Savard, J. Renaud, I. Hetel, P. Richard and G. Riou D?partement de Physique, Universit? de Sherbrooke, e e Sherbrooke, Qu?bec, CANADA, J1K 2R1 e
(Dated: February 2, 2008)
Using magnetoresistance measurements as a function of applied magnetic ?eld and its direction of application, we present sharp angular-dependent magnetoresistance oscillations for the electrondoped cuprates in their low-temperature non-metallic regime. The presence of irreversibility in the magnetoresistance measurements and the related strong anisotropy of the ?eld dependence for di?erent in-plane magnetic ?eld orientations indicate that magnetic domains play an important role for the determination of electronic properties. These domains are likely related to the stripe phase reported previously in hole-doped cuprates.
PACS numbers: 74.25.Fy,74.72.Jt,74.72.-h,74.20.Mn,75.30.Gw
In the low doping regime of high temperature superconductors (HTSC), resistivity crosses over most often from a high temperature metallic-like state to a low temperature non-metallic behavior. Interestingly, the crossover temperature observed by in-plane resistivity does not correspond to the N?el temperature (TN ), the onset of long range antiferromagnetic e order. In fact, there is no hint of this transition in ρxx (T ) as metallic-like behavior persists sometimes below TN [2, 3]. Ando and coworkers argued that this independence of ρxx (T ) from the underlying magnetic order is a sign of phase separation, probably with conducting stripes separated by antiferromagnetic domains. Such self-organized structures of the charge carriers was shown to lead to intriguing behaviors for several physical properties[4, 5, 6, 7]. An anisotropic twofold response to magnetic ?eld applied along the copper-oxygen (CuO2 ) planes was reported for instance using in-plane magnetoresistance (MR) in the non-metallic regime of YBa2 Cu3 O6.33 (YBCO) and in lightly doped La1.99 Sr0.01 CuO4 (LSCO). To avoid the possible contributions of orthorhombic distortions or phases (as in YBCO and LSCO), we have chosen the tetragonal electron-doped cuprates as good candidates to make a de?nitive test of anisotropic transport properties. We focus on the results obtained for magnetic ?elds always applied parallel to the CuO2 planes. In Figure 1, we present an example of raw in-plane and out-of-plane resistance data as a function of angle with respect to the in-plane crystal a-axis. These data were measured deep into the non-metallic regime of non-superconducting Pr1.85 Ce0.15 CuO4 (PCCO). We observe clear fourfold and symmetrical oscillations of the resistance with sharp maxima [minima] for Rxx [Rc ] for ?elds applied along the in-plane crystal axis (i.e. along the CuO bonds of the CuO2 planes) and broad minima [maxima] for ?eld applied along the diagonals. This e?ect can be emphasized using the polar plot of Fig. 1(c). In this Letter, we present this magnetoresistance anisotropy, for current along the CuO2 planes and along the c-axis (thickness) of non-superconducting electron-doped single crystals. We show for the ?rst time that sharp fourfold oscillations persist over the whole non-metallic regime for both in-plane (ρxx ) and out-of-plane (ρc ) resistivities. More importantly, the ?eld dependence of ρc presents irreversibilities which cannot be explained by conventional band theory. We ascribe the new transport signatures to the presence of magnetic domains. Their origin is probably related to the presence of stripe domains (order) in the cuprates. The single crystals of Re2?x Cex CuO4 (Re = Pr, Nd, Sm and Eu) used for this study were grown by the directional ?ux growth method in alumina and high purity magnesia 2
FIG. 1: Raw resistance data as a function of angle for non-superconducting Pr1.85 Ce0.15 CuO4 : (a) in-plane resistance Rxx , (b) out-of-plane resistance Rc and (c) Polar plot of the same data. 0o corresponds to the ?eld applied along the Cu-O bonds. The inserts in (a) and (b) show the contact con?gurations used for the measurements.
crucibles[9, 10]. The as-grown crystals are known to be non-superconducting even for x = 0.15, and only a reduction process allows them to become superconducting with a maximum transition temperature between 18 and 25K depending on the rare-earth ion. In the present work, we study only as-grown non-superconducting crystals with x = 0.15 in order to extend as much as possible the temperature range for which a non-metallic regime is observed. Silver epoxy contacts were applied directly onto the as-grown crystals (typical in-plane size : 2mm x 1 mm, and 30 ?m thickness along the c-axis) in two di?erent con?gurations insuring uniform current density for the measurement of the in-plane (ρxx ) and c-axis (ρc ) resistivity as shown in the inserts of Figs. 1(a) and (b). The samples were then mounted on sapphire supports and attached onto a specially designed Physical Property Measurement System (PPMS) rotator chip, such that the applied magnetic ?eld can be rotated over a
FIG. 2: (a) In-plane resistivity and c-axis resistivitity as a function of temperature for nonsuperconducting Pr1.85 Ce0.15 CuO4+δ crystals. (b) in-plane magnetoresistance as a function of ?eld for T = 5K and its anisotropy for ?eld applied along the c-axis (⊥) and along the CuO2 planes( ).
full 360? . The direction of the in-plane crystal axis (a-axis direction relative to the edge of the rectangular crystals) were determined using Laue x-ray di?raction and by Raman scattering. Several tests were performed to rule out contact con?guration, thermometry and misorientation problems. In Figure 2(a), we present the typical temperature dependence of in-plane and c-axis resistivity components for non-superconducting Pr1.85 Ce0.15 CuO4 single crystals. Both components show a non-metallic regime at low temperatures where the MR oscillations are observed. The in-plane resistivity ρxx is metallic-like at room temperature while it shows an upturn starting at Tmin,xx ≈ 125K which is very sensitive to the oxygen content. Below Tmin,xx , ρxx approaches a ln(T ) behavior (not shown), similar to that reported for non-superconducting NCCO and PCCO. This temperature behavior and the strong anisotropy illustrated in Fig. 2(b) have been interpreted as a signature of two-dimensional weak localization (2DWL) by disorder. For the c-axis resistivity ρc , a non-metallic trend is observed at room temperature for several crystals, followed by a maximum (at 4
FIG. 3: In-plane magnetoresistance as a function of angle (a) for several ?elds at 10K; (b) for several temperatures at 5T. The data has been moved vertically for clarity.
T ≈ 200K), then by a metallic-like regime. It is ?nally followed by a non-metallic regime, also approaching ln(T ) , below Tmin,c ≈ 70K . The ?eld dependence of the in-plane magnetoresistance oscillations at 10K are presented in Fig. 3(a). The MR oscillations evolve steadily from broad features at 2T to sharp maxima for 4T whenever the ?eld is applied along the Cu-O bonds. For ?elds approaching 9T, new maxima develop for ?elds applied approximately along the diagonal directions. The relative proportion of both oscillations varies also steadily with temperature as evidenced by the same 45? features barely appearing at 5T and 2K in Fig. 3(b) (see arrows). The amplitude of these oscillations in ρxx represents only a small fraction (?ρosc /ρ ? 0.05%) of the total negative MR [?ρtot /ρ ? 1% : see Fig. 2(b)]. Thus, unlike YBCO and LSCO, ρxx oscillations are very weak and have almost perfect fourfold symmetry. In Fig. 3(b), we present the evolution of these ρxx oscillations (at 5T) with temperature. A similar e?ect is obtained if one decreases the temperature or increases the applied ?eld. We observe that the weak oscillations disappear quickly with increasing temperature, vanishing close to Tmin,xx . This seems to imply that this anisotropic behavior can only be observed in 5
FIG. 4: Out-of-plane magnetoresistance as a function of angle: (a) for several ?elds at 5K; (b) and (c) for several temperatures at 5T. The data has been moved vertically for clarity.
the non-metallic regime of these materials (within our sensitivity). In Fig. 4(a), we present the angular dependence of ρc in several magnetic ?elds at 5K. We observe very sharp minima in the c-axis resistivity, developing particularly for intermediate ?elds (3 to 6T). These sharp cusps appear for magnetic ?elds applied along the Cu-O bonds. As the applied magnetic ?eld is further increased, these anomalies are gradually replaced by oscillations of smaller amplitude. In Figs. 4(b) and (c), we illustrate the strong temperature dependence of these features as they seem once again to vanish as the sample reaches temperatures close to the crossover to the metallic-like state. As will be shown below, the magnitude of the oscillations observed for ρc are comparable to the total positive MR, in sharp contrast with those observed with ρxx . Therefore, they are less sensitive to mis-orientation of the crystals and thus easily observed. In Figure 5 (a), we present the c-axis magnetoresistance at T = 5K as a function of in-plane magnetic ?eld applied along three di?erent directions (0, 15 and 45? ). Contrary to the in-plane resistivity, the c-axis magnetoresistance is positive and presents an unusual ?eld dependence. For the ?eld applied along the a-axis (at 0? ), the resistivity remains remarkably 6
FIG. 5: Out-of-plane magnetoresistance as a function of ?eld : (a) for 0, 15 and 45? at 5K; (b) same data magni?ed around 5T (arrows indicate ?eld sweeping rate); and (c) for several temperatures for ?eld along CuO bonds (θ = 0? ). The data has been moved vertically for clarity.
?at at low ?elds until a threshold ?eld is reached. At this point, the resistance varies sharply, as if the system was crossing a transition. Beyond this threshold, the magnetoresistance resumes a high ?eld ?B 2 behavior. As soon as the ?eld direction deviates from the aaxis [for 15 and 45? in Fig. 5(a)], the magnetoresistance presents a very sharp positive increase at low ?elds, quickly reaching the saturation ?B 2 regime. The large magnitude of the oscillations in ρc at about 4 - 5T in Fig. 4 (a) can easily be explained by the strong variations in resistance at 5T for di?erent ?eld orientations underlined by the dashed line in Fig. 5(a). We should emphasize here that ρxx displays its sharpest peaks in the same range of applied ?eld. Interestingly, upon decreasing the applied magnetic ?eld, the resistance for θ = 0? shows a similar transition-like pattern, but the resistance presents a clear sign of irreversibility observed in Fig. 5(b). The arising of magnetic hysteresis is a clear demonstration of the in?uence of magnetic history, i.e. the presence of magnetic domains. These domains (and their domain walls) are strongly a?ected by the direction and strength of the in-plane rotat7
ing ?eld, and in turn they a?ect the conductivity. We can interpret the data in Fig. 5(a) as evidence of easy magnetization axis along the diagonal directions, while the Cu-O bond directions (a and ”b” axis) correspond to hard axis. Since the c-axis resistivity is a measure of interplane tunneling between CuO2 planes, the alignment of magnetic domains at high ?elds is detrimental to interplane tunneling causing an increase of c-axis resistivity. This e?ect is present up to temperatures approaching Tmin,c [see Fig. 5(c)]. Inversely, in-plane resistivity ρxx presents peaks for ?elds applied along the hard axis and ?at minima for ?eld applied along the diagonal easy axis. The behavior of the magnetoresistance anisotropy for PCCO is signi?cantly di?erent from YBCO and LSCO. For YBCO, there is a clear sign change when magnetic ?eld is applied parallel and transverse to the applied in-plane current. In LSCO, no sign change, but the presence of four asymmetrical lobes was attributed to twinning. In our case, we never observe a sign change in the MR with angle (it always remains negative) and the oscillations are not sensitive to the direction of the applied current as they remain about the same height for the ?eld parallel [0? ] and transverse [90? ] to the current, except for the additional features observed at high magnetic ?elds in ρxx . The magnitude of the in-plane MR oscillations is much smaller for PCCO than for YBCO and LSCO. In both cases however, the oscillations disappear close the non-metal to metal crossover. We suspect that orthorhombic distortions could be a key player in promoting the di?erences in the magnitude and the anisotropy of these MR oscillations in YBCO, LSCO and PCCO. MR oscillations of c-axis resistivity in cuprates were ?rst reported in strongly overdoped Tl-based cuprates with Tc ≈ 25K. In this case, the fourfold oscillations are large (0.33% of the total resistance at 40K and 10T) and correspond to a doping region of the phase diagram where both ρxx and ρc remain metallic-like over the whole temperature range. Because the mean-free path (MFP) is fairly large in this strongly overdoped regime, Dragulescu et al. argued that the oscillations in Tl-based cuprates could be due to angular-dependent magnetoresistance oscillations. In our case, the very small MFP for this doping[18, 19] precludes such interpretation. Recent experiments indicate that the carriers injected into the cuprates through chemical substitution have a strong tendency to distribute non-uniformly in the copper-oxygen planes, segregating into phase-separated regions, clusters and stripes. Several experimental observations, including the MR oscillations obtained with YBCO and LSCO, ?t into this 8
possible scenario. However, only a recent report by Sun et al. indicates the possible presence of stripes in the electron-doped cuprates. Assuming their existence in the electron-doped cuprates, we should expect the c-axis resistivity to decrease whenever stripes in adjacent CuO2 planes are directly on top of each other and aligned in the same direction : in this particular case, electrons can tunnel more easily between planes, thus decreasing resistivity. However, our data show that ρc is higher when the ?eld is high (for well aligned domains). We suggest here that a low density of stripes in adjacent planes makes it more di?cult to have stripes on top of each other whenever domains are well aligned (high ?elds), in particular if domains on adjacent planes are not or weakly correlated (as in LSCO). At low ?elds, random orientation of stripe domains could lead to a better overlap from weakly correlated adjacent planes, and thus to a better conductivity. For in-plane MR [see Fig. 1(a)], the application of in-plane magnetic ?eld could promote a partial displacement of domain walls (the stripes), enough to change the resistivity and improve the channeling of electrons along longer conducting ”rivers of charges”. Because the in-plane MR oscillations are so small, the changes in domain wall con?gurations are probably scarse. Our data would suggest that such modi?cations of the wall con?guration are hard to develop only along the hard axis (the Cu-O bonds), leading to maxima in ρxx . We should mention that this simple scenario ignores completely the possibility of interaction with the underlying rare earth magnetic order (di?erent in PrCeCuO, NdCeCuO, SmCeCuO). Our preliminary data on NdCeCuO and SmCeCuO showed no signi?cant di?erence for the ?eld and angular dependence of ρab and ρc , thus ruling out a direct implication of rare earth magnetism. Moreover, it remains unclear how an electronic system could present at the same time signatures consistent with 2DWL by disorder and one dimensional features like stripes, unless the spin stripes induce only a partial charge density wave in the CuO2 planes. This aspect will need further exploration, possibly through the doping dependence of the observed oscillations. In summary, we presented anomalous magnetoresistance oscillations for nonsuperconducting electron-doped cuprates in their non-metallic regime for magnetic ?eld applied along the copper-oxygen planes. We showed that sharp fourfold oscillations persist over the whole non-metallic regime for both in-plane (ρxx ) and out-of-plane (ρc ) resistivities. The ?eld dependence of ρc presents irreversibilities which can be explained by the presence of magnetic domains. Their origin is probably related to the presence of stripe domains in 9
the cuprates. We thank A.-M. Tremblay, C. Bourbonnais, K. LeHur and M. Li for several discussions and S. Pelletier for technical assistance. We acknowledge the support of CIAR, CFI, NSERC and the Fondation of the Universit? de Sherbrooke. e
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