Fermi liquid behavior and weakly anisotropic superconductivity in electron-doped cuprate Sr{}_{1-x}La{}_{x}CuO{}_{2}

Fermi liquid behavior and weakly anisotropic superconductivity in electron-doped cuprate SrLaCuO

Kohki H. Satoh ksatoh@post.kek.jp    Soshi Takeshita    Akihiro Koda    Ryosuke Kadono    Kenji Ishida    Sunsen Pyon    Takao Sasagawa [    Hidenori Takagi Department of Materials Structure Science, The Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801, Japan
Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
July 25, 2019

The microscopic details of flux line lattice state studied by muon spin rotation is reported in an electron-doped high- cuprate superconductor, SrLaCuO (SLCO, –0.15). A clear sign of phase separation between magnetic and non-magnetic phases is observed, where the effective magnetic penetration depth [] is determined selectively for the latter phase. The extremely small value of and corresponding large superfluid density () is consistent with presence of a large Fermi surface with carrier density of , which suggests the breakdown of the “doped Mott insulator” even at the “optimal doping” in SLCO. Moreover, a relatively weak anisotropy in the superconducting order parameter is suggested by the field dependence of . These observations strongly suggest that the superconductivity in SLCO is of a different class from hole-doped cuprates.

74.72.-h, 76.75.+i, 74.25.Qt
preprint: APS/123-QED

Present affiliation: ]Materials and Structures Laboratory, Tokyo Institute of Technology

The question whether or not the mechanism of superconductivity in electron-doped (-type) cuprates is common to that in hole-doped (-type) cuprates is one of the most interesting issues in the field of cuprate superconductors, which is yet to be answered. This “electron-hole symmetry” has been addressed by many experiments and theories since the discovery of -type cuprate superconductors.asy () In the theoretical models assuming strong electronic correlation where the infinitely large on-site Coulomb interaction () leads to the Mott insulating phase for the half filled band, the correlation among the doped carriers is projected into the - model in which the mechanism of superconductivity does not depends on the sign of charge carriers.tjmodel (); zgrc () This is in marked contrast to the models starting from Fermi liquid (= normal metal) state, where such symmetry is irrelevant to their basic framework.frmlqd () Experimentally, recent advent in crystal growth techniques and that in experimental methods for evaluating their electronic properties triggered detailed measurements on -type cuprates, reporting interesting results suggesting certain differences from -type ones, such as the observation of a commensurate spin fluctuations in neutron scattering study or the nonmonotonic -wave superconducting order parameter in ARPES measurement.neutron (); ARPES ()

The effective magnetic penetration depth () is one of the most important physical quantities directly related with the superfluid density (),


which is reflected in the microscopic field profile of the flux line lattice (FLL) state in type II superconductors. Considering that the response of against various perturbations strongly depends on the characters of the Cooper pairing, the comparison of between two types of carriers might serve as a testing ground for the electron-hole symmetry. However, the study of FLL state in -type cuprates such as T’-phase CuO compounds (= Nd, Pr, Sm, etc.), is far behind that in -type cuprates because of strong random local fields from rare-earth ions which mask information of CuO planes regarding both superconductivity and magnetism against magnetic probes such as muon. In this regard, infinite-layer structured SrLaCuO (SLCO) is a suitable compound for detailed muon spin relaxation and rotation (SR) study of electron-doped systems, as it is free from magnetic rare-earth ions.

A recent SR study on SLCO with ( K) reported a relatively large [116 nm] as compared to -type cuprates,PSI () strongly suggesting that -type cuprates belong to a different class in view of the versus relation.Uemura:91 () On the other hand, another SR study showed appearance of a spin glass-like magnetism over a wide temperature range including superconducting phase,Kojima () which might have also affected the result of Ref. PSI, . In this report, we demonstrate by SR measurements under both zero and high transverse field that SLCO exhibits a phase separation into magnetic and non-magnetic phases, where the superconductivity occurs predominantly in the latter. Our measurement made it feasible to evaluate reliably as it was selectively determined for the non-magnetic phase of SLCO.

Meanwhile, the paring symmetry of order parameter, which is one of the most important issues in discussing the electron-hole symmetry, still remains controversial in -type cuprates. A number of groups reported -wave symmetry in SLCO,STM (); SHeat () which is in marked contrast to the symmetry well established in -type cuprates. The pairing symmetry can be examined by measuring the temperature/field variation of () as an effective value observed by SR: it reflects the change of due to quasiparticle excitation and/or nonlocal effect associated with anisotropic order parameter.Kadono:07 (); Kadono:07_2 () Here, we show evidence that the order parameter in SLCO is not described by simple isotropic -wave pairing nor that of pure .

Powder samples of SLCO ( = 0.10, 0.125, and 0.15) were prepared by high pressure synthesis under 6 GPa, 1000 C. They were confirmed to be of single phase by powder X-ray diffraction, where a small amount of LaCuO phase (LCO2.5, less than a few %) was identified. The length of and axes showed almost linear change with , indicating successful substitution of Sr with La for carrier doping.GEr () As displayed in Fig. 1(a), the susceptibility () measured by SQUID magnetometer implies that the onset of superconductivity is nearly 42 K and least dependent on , whereas the bulk determined by the maximum of varies with [see Fig. 1(b)], which reproduces earlier results.kawashima (); karimoto () The dependence of bulk suggests that the sample is close to the optimal doping for .

Figure 1: (Color online) (a) Magnetic susceptibility of SLCO with =0.10, 0.125 and 0.15 under 20 G. (b) La concentration dependence of . Closed symbols show , and open symbols show , respectively. An earlier resultkawashima () (triangles) is also quoted for comparison. Dashed line is guide to eyes.

The SR experiment was performed on the M15 beamline at TRIUMF (Vancouver, Canada), where measurements under zero and longitudinal field (ZF and LF) were made to investigate magnetic ground state of SLCO. Subsequently, those under a high transverse field (HTF, up to 6 T) were made to study the FLL state in detail. In ZF and LF measurements, a pair of scintillation counters (in backward and forward geometry relative to the initial muon polarization that was parallel to the beam direction) were employed for the detection of positron emitted preferentially to the muon polarization upon its decay. In HTF measurements, sample was at the center of four position counters placed around the beam axis, and initial muon spin polarization was perpendicular to the muon beam direction so that the magnetic field can be applied along the beam direction without interfering with beam trajectory. A veto counter system was employed to eliminate background signals from the muons that missed the sample, which was crucial for samples available only in small quantities such as those obtained by high-pressure synthesis. For the measurements under a transverse field, the sample was field-cooled to the target temperature to minimize the effect of flux pinning.

Fig. 2(a) shows ZF-SR spectra for the sample with =0.125, where no spontaneous muon precession is observed as sample is cooled down to 2 K. Instead, fast muon spin depolarization can be identified between 00.2 s, which develops with decreasing temperature. LF-SR spectra in Fig. 3(a) shows that the depolarization is quenched in two steps as a function of field strength, at first near a few mT due to nuclear magnetic moments and secondly around 10 mT. The asymptotic behavior of under random local fields (with an isotropic mean square, ) as a function of external magnetic field is approximately given by the follows equation,


and we estimated the magnitude of from the behavior of as 39(3) mT [the best fit with Eq. (2) is shown in Fig. 3(b)]. This is consistent with the fast initial depolarization rate estimated by MHz (where MHz/T is the muon gyromagnetic ratio). The origin of can be uniquely attributed to the localized moments Cu atoms, where the effective moment size is 0.15(1) . The almost negligible depolarization for the asymptotic component implies that spin fluctuation rate is much smaller than at 50 K. Thus, ZF/LF-SR results strongly suggest that the sample that exhibits superconductivity has also static magnetic phase. The magnetic region enlarges to a halfway partition at low temperature (as seen in Fig. 2(b)). We note that a common tendency was observed for =0.10 and 0.15.

Figure 2: (Color online) (a) ZF-SR spectra in the sample with =0.125. Inset (b) is temperature dependence of the volume fraction of magnetic and non-magnetic phase.

In HTF-SR, each pair of counters (right-left, upward-downward) observes time-dependent muon spin polarization, , projected to or axis perpendicular to the beam direction (with a relative phase shift of ). Inhomogeneity of magnetic field distribution leads to depolarization due to the loss of phase coherence among muons probing different parts of . Using a complex notation, is directly provided using the spectral density distribution for the internal field, ,


where is defined as a spatial average () of the delta function,


and is the initial phase of muon spin rotation. Then, the real part of fast Fourier transform (FFT) of SR time spectrum corresponds to , namely,


Fig. 4 shows the real amplitudes obtained by the FFT of HTF-SR spectra, which contain information on . The narrow central peak (labeled A) is the signal from muons stopped in a non-magnetic (and/or non-superconducting) phase where the frequency is equal to that of the external field ( T) with a linewidth determined by random nuclear dipolar fields besides the effect of limited time window ( s). A broad satellite peak (labeled B) appears on the positive side of the central peak, when temperature is lowered below 300 K. This corresponds to the fast depolarization in time domain. The ZF/LF-SR spectra in Figs. 2,3 demonstrates that this satellite comes from a magnetic phase in which quasistatic random magnetism of Cu electron spins develops.

Figure 3: (Color online) (a) LF-SR spectra in the sample with =0.125. (b) Two kinds of decoupling behavior at 50 K. The dashed line is fitting curb by Eq. (2)

While the FFT spectra were useful to examine the overall feature of ), the actual data analysis was carried out in time domain using the -minimizing method. As inferred by Fig. 4, the SR spectra in the normal state can be reproduced by a sum of two Gaussian dumping signals,


where is the relative yield proportional to the fractional volume of each phase, is the linewidth, and = with being the mean value of local magnetic field following a Gaussian distribution,

It is inferred from the -minimizing fit of the time spectra by Eq. (6) that the volume fraction of magnetic phase increases toward low temperature monotonously in place of non-magnetic phase and becomes nearly a half at 50 K. This is clearly not due to the LCO2.5 impurity phase, considering the small volume fraction of LCO2.5 and its known Nel temperature (125 K).Ladder () The magnetic volume fraction is independent of at 50 K where the sample is in the normal state. Thus, the appearance of the satellite peak demonstrates the occurrence of a phase separation into magnetic and non-magnetic domains in the normal state of SLCO.

Taking the result in the normal state into consideration, we analyzed the SR spectra in the superconducting phase. In the FLL state of type II superconductors, one can reasonably assume that muon stops randomly over the length scale of vortex lattice, and serves to provide a random sampling of inhomogeneity due to FLL formation. In the modified London (m-London) model, is approximated as a sum of magnetic inductions from isolated vortices,

Figure 4: (Color online) Fast Fourier Transform of HTF-SR spectra under 6 T [after filtering the artifacts due to a finite time window for transform ( s)]. The peaks labeled A, B and C correspond to non-magnetic/non-superconducting, magnetic, and FLL phases, respectively.

where are the vortex reciprocal lattice vectors, () is the average internal field, is the effective London penetration depth depending on temperature and field, and is a nonlocal correction term with () being the cutoff parameter for the magnetic field distribution; the Gaussian cutoff generally provides satisfactory agreement with data. The density distribution in this case is characterized by the Van Hove singularity originating from the saddle points of with a negative shift primarily determined by , and that corresponds to the peak (seen as a shoulder) labeled C in Fig. 4. Thus, the signal from the FLL state can be readily separated from other phases at large as they exhibit different frequency shifts with each other. The FFT spectra below also indicate that the domain size of the superconducting phase is much greater than that determined by .

It is known that the m-London model is virtually identical to the Ginzburg-Landau (GL) model for large ( is the GL coherence length) and at low magnetic fields (, with being the upper critical field).Brandt (); SonierRev () Meanwhile, according to a reported value of the upper critical field for SLCO (=12 T, in Ref.Hc2, ), the field range of the present measurements ( T) might exceed the above mentioned boundary, and thus the use of the GL model would be more appropriate. However, the m-London model has certain advantages over the GL model in practical application to the analysis: for example, we can avoid further complexity of analysis due to introduction of the field-dependent effective coherence length.Kadono:07 () We also stress that the discrepancy in the analysis results has been studied in detail between these two models, and now it is well established that m-London model exhibits a systematic tendency of slight overestimation of at higher fields due to a known cause.Kadono:07 (); SonierRev () The discussion on the present result will be made below considering this tendency.

Another uncertainty comes from the fact that the FLL symmetry in SLCO is not known at this stage, and it might even depend on the magnitude of external field as has been found in some other cuprates.Brown (); Gilardi () However, since we do not observe any abrupt change of lineshape nor the increase of in the fits (irrespective of model) associated with the alteration of FLL symmetry with varying field,Nb3Sn (); YNBC () we can reasonably assume that the FLL symmetry remains the same throughout entire field range. Moreover, the observed lineshape is perfectly in line with the hexagonal FLL, without showing any sign of squared FLL (e.g., a large spectral weight at the lower field side of the central peak in the absence of nonlocal effectAegerter:98 (), or an enhanced weight at the central peak associated with the strong nonlocal effectYNBC ()). Therefore, the FLL symmetry has been assumed to be hexagonal in the following analysis.

The SR spectra in the FLL state were analyzed by fit analysis using


where is the volume fraction of FLL phase, represents the contribution from the distortion of FLL due to vortex pinning and that due to nuclear random local fields, and is that defined in Eq. (6). The parameters including , , , , , and were determined by the -minimization method with good fits as inferred from the value of reduced close to unity. (More specifically, in order to reduce the uncertainty for the analysis of data below , was fixed to the value determined by the data above .) The magnitude of line broadening due to vortex pinning () was relatively small (typically 30–40% of the frequency shift for the shoulder C in Fig. 4). This was partly due to relatively short and associated large asymmetry in , and thereby the correlation between these parameters turned out to be small except at lower fields ( T) where the spectra exhibit stronger relaxation due to greater linewidth of and stronger vortex pining (leading to larger ).

Figure 5: (Color online) Field dependence of cutoff parameter (a) and volume fraction of each phase (b) at 2 K for the sample with =0.125, where dashed curves are guide to eyes. (c)–(e): Field dependence of effective penetration depth at 2 K for =0.10, 0.125 and 0.15, respectively. Dashed lines are a linear fit (see text).

Fig. 5(a) shows a decreasing tendency of with increasing field, which is understood as a shrinkage of vortex core due to vortex-vortex interaction.SonierRev () Fig. 5(b) shows the field dependence of fractional yield for each phase at 2 K. With increasing field, the FLL phase appears to be transformed into the magnetic phase. However, it must be noted that there is a discontinuous change between ZF (%) and HTF-SR (–80%). Since no field dependence is observed for the volume fraction in the normal state (50 K), the reduction of the magnetic fraction at lower fields is attributed to the overlap of magnetic domains with vortex cores: the magnetic domains would serve as pinning centers for vortices more effectively at lower fields due to the softness of FLL. The increase of magnetic fraction with increasing field is then readily understood as a result of decreasing probability for vortices to overlap with random magnetic domains at higher fields, because the relative density of vortices as well as the rigidity of FLL would increase. This also suggests that the mean domain size of the magnetic phase is considerably smaller than the FLL spacing ( nm at 0.5 T).

Fig. 5 (c)–(e) show the field dependence of in each compounds. While the London penetration depth is a physical constant uniquely determined by local electromagnetic response, in our definition [Eq. (1)] is a variable parameter, as depends on temperature () and external magnetic field (). Therefore, we introduce an effective penetration depth, with an explicit reference to and dependence. It is clear in Fig. 5 (c)–(e) that tends to increase with increasing external field. Here, one may further notice a tendency that increases more steeply below 2 T in the case of and . However, these points at lower fields are also associated with larger error bars probably because of the stronger depolarization in the time domain. The value extrapolated to [] is estimated by a linear fit with a proper consideration of the uncertainty associated with these errors, and the result is indicated in Fig. 5. These values (104–119 nm) turn out to be significantly shorter than the earlier resultPSI () (hereafter, the inplane penetration depth is approximated by an equation , according to Ref. lmdab, ). In qualitative sense, however, our result supports the earlier suggestion of a large discrepancy for SLCO from the quasi-linear relation between and observed over a wide variety of -type cuprates.Uemura:91 () The anomaly becomes more evident when they are mapped to the vs plot, as shown in Fig. 6. They are far off the line followed by the data of -type cuprates, suggesting that -type SLCO belongs to a class of superconductors different from that of -type cuprates.

Figure 6: (Color online) vs for various cuprate superconductors. Closed circles represent our result, whereas open circle is that of Ref. PSI, . Open squares and triangles are for other -type cupratesPCCO_Homes (); NCCO_Nugroho (); NCCO_Homes (), closed upward triangles for LaSrCuO (Ref. LS15_Luke, ; LS15_Aeppli, ; LS_Schneider, ; LS_Pana, ) and downward ones for YPrBaCuO (Ref. Seaman_YPBCO, ). Square symbols for YBaCuO and diamond for BiSrCaCuO (Ref. YBCO_Hardy, ; YBCO_Sonier, ; Uemura_YBCO, ; Keller_YBCO, ).

It is well established that the carrier concentration, , of -type cuprates nearly corresponds to that of the doping value while 0.20.Fukuzumi () In contrast, a recent ARPES measurement on an -type cuprate, NdCeCuO, have revealed that small electron pockets () observed for =0.04 sample is replaced by a large Fermi surface (corresponding to ) for =0.10 and 0.15 samples.Armitage () When is assumed to be comparable with that of -type cuprate (), can be estimated using Eq. (1), yielding in SLCO with =0.125 [where is determined with the best accuracy]. This corresponds to , and an order of magnitude larger than that of -type cuprates.LS15_Aeppli (); SonierRev () A better correspondence to would be attained when . Thus, the present result is yet another evidence for a large Fermi surface in SLCO. This is also in line with some recent experimental results for -type superconductors. For example, resistivity () in the normal state shows a Fermi liquid-like temperature dependence () common to ordinary metals,rhoT () and a metallic Korringa law has been revealed by NMR study under high magnetic fields.Korringa () These observations coherently suggest that the -type cuprates cannot be regarded as the doped Mott-insulators, but they might be better understood as in the normal Fermi liquid state already at the optimal doping (0.1).

The increase of with increasing external field is a clear sign that the superconducting order parameter is not described by that of simple isotropic -wave paring for single-band electrons.Kadono:07 () One of the possible origins for the field dependent is the presence of nodal structure in the order parameter [ at particular ] that leads to the field-induced quasiparticle excitation due to the quasiclassical Doppler shift.Volovik () The quasiparticle energy spectrum is shifted by the flow of supercurrent around vortex cores to an extent , where and are the Fermi velocity and superfluid velocity, respectively. This gives rise to the pair breaking for and associated reduction of . The presence of nodes also leads to a nonlocal effect in which is affected by the modification of supercurrent near the nodes where the coherence length exceeds the local London penetration depth.Amin:98 () For the comparison of magnitude for the field-induced effect, we use a dimensionless parameter deduced by fitting data in Fig. 5 using with . Provided that is dominated by the presence of gap nodes, the magnitude of at lower fields is roughly proportional to the phase volume of the Fermi surface where . As seen in Fig 5, in SLCO is definitely greater than zero irrespective of , taking values between 1.2–1.7. It is noticeable that these values are considerably smaller than () observed in YBaCuO (YBCO) that has a typical -wave gap symmetry. The situation remains true even when one considers i) the nonlocal effect that tend to reduce at high magnetic fields ( for  T),nonlocal () and ii) a possible overestimation of at higher fields due to the extended use of the m-London model that also leads to the overestimation of [e.g., based on the m-London model is greater than that on the GL model by 0.23(7) in NbSe (Ref. SonierRev, ), and 0.6(2) in YB (Ref. Kadono:07, )].

Interestingly, the relatively small value of is in line with the recent suggestion by ARPES measurement on another -type superconductor, PrLaCeCuO (PLCCO), that the order parameter has a steeper gradient at the nodes along azimuthal () direction than that for the symmetry.ARPES () Since the phase volume satisfying is inversely proportional to at the node, we have


Assuming a situation similar to PLCCO and that observed in YBCO represents a typical value for -wave gap, our result suggests that the gradient in SLCO is 1.2(3)–5.0(3) times greater than that at the node of -wave gap. However, it is clear that further assessment by other techniques that are more sensitive to the symmetry of the order parameters are necessary to discuss the details of gap structure in SLCO.

In conclusion, it has been revealed by the present SR study that a phase separation occurs in an electron-doped cuprate superconductor, SrLaCuO (=0.10, 0.125 and 0.15), where nearly half of the sample volume exhibits magnetism having no long-range correlation while the rest remains non-magnetic. The superconductivity occurs predominantly in the non-magnetic domain, where the effective magnetic penetration depth evaluated by using a modified-London model is much shorter than that of other -type cuprates. This suggests a large carrier density corresponding to and accordingly the breakdown of the Mott insulating phase in SLCO and other -type cuprates even at their optimal doping. The field dependence of suggests that the superconductivity of SLCO is not described by single-band -wave pairing. The magnitude of the dimensionless parameter, (), is qualitatively in line with nonmonotonic -wave superconducting gap observed in other -type cuprates.

We would like to thank the staff of TRIUMF for technical support during the SR experiment and Takano-group of ICR-Kyoto Univ. (M. Takano, Y. Shimakawa, M. Azuma, I. Yamada and K. Oka) for useful advice concerning sample preparation. This work was partially supported by the Grant-in-Aid for Creative Scientific Research and the Grant-in-Aid for Scientific Research on Priority Areas by the Ministry of Education, Culture, Sports, Science and Technology, Japan.


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