MBE growth of (La,Sr)2CuO4 and (Nd,Ce)2CuO4 thin films

PHYSICA ELSEVIER

PhysicaC 293 (1997) 36-43

MBE growth of (La,Sr)2CUO4 and (Nd,Ce)2CUO4 thin films Michio Naito *, Hisashi Sato, Hideki Yamamoto NTT Basic Research Laboratories, Atsugi-shi, Kanagawa 243-01, Japan

Abstract

The growth of (La, Sr)2CuO4 and (Nd,Ce)zCuO4 thin films by reactive coevaporation is reviewed. By (1) careful adjustment of the cation stoichiometry, (2) optimum oxidation, and (3) appropriate choice of substrates, we have successfully grown c-axis and non-c-axis oriented high-quality thin films of (La,Sr)2CuO4 and (Nd,Ce)2CuO4. The key points for thin film growth and the characterization of grown films are discussed. © 1997 Elsevier Science B.V.

1. Introduction

2. Growth of thin films

T-(La,Sr)2CuO4(LSCO) and T'-(Ln,Ce) 2CuOa(LnCCO) (Ln = Pr, Nd, Sm, and Eu) are the prototype p-type and n-type cuprate superconductors. Because they have the simplest crystal structure, they provide the best opportunity for understanding the "physics" of high-T~ superconductors. Hole-doped LSCO appears (although not established) to be a d-wave exotic superconductor, while electron-doped LnCCO seems to be an s-wave conventional BCS superconductor. A comparison of them may provide clues to the superconducting mechanism of high-T~ cuprates. LSCO and LnCCO are also the most fundamental systems in thin film growth, so their growth will elucidate key requirements for thin film growth of high-Tc superconductors. In this article we describe the growth and characterization of high-quality LSCO and NCCO((Nd,Ce)eCuO 4) thin films [1].

We have been growing thin films of oxide superconductors by reactive coevaporation. The growth conditions for LSCO and NCCO are summarized in Table 1. The key requirements to obtain high-quality films are (1) precise stoichiometry control of evaporation beam fluxes, (2) optimum oxidation, and (3) appropriate substrate materials.

* Corresponding author. Fax: +81 462 70 2364; e-mail: [email protected].

2.1. Stoichiometry control

Growth of epitaxial films of cuprate superconductors by multi-source deposition techniques requires careful control of the beam flux of each source. The control must be stringent because the sticking coefficient is not self-limited as GaAs. Our approach to adjusting the cation stoichiometry involves two steps [2]. The first is a rough adjustment made by electron impact emission spectrometry (EIES). Although EIES has fairly high sensitivity for most of the elements used for growth of cuprate films and also has good short-time stability, it has a problem of long-term drift. The second step is fine tuning to overcome this

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M. Naito et al./Physica C 293 (1997) 36-43

37

Table 1 Growth conditions for thin films of LSCO and N C C O

LSCO NCCO

Tgrowth

Gas f l o w / D "

Total rate ( , ~ / s )

650-700°C 720-750°C

~ 2 sccm/30-35 mm ~ 1.5 s c c m / 1 5 - 2 0 m m

3 1.5

Reaction gas is ozone gas (not distilled, 5 to 10% ozone concentration), D is the nozzle-substrate distance.

drift problem. This is done by reflection high-energy electron diffraction (RHEED) observation during growth to detect precipitated impurity phases on the surface of the films. This method is based on the fact that the species of the impurity phases tell us the type of off-stoichiometry of the evaporation beam fluxes, namely whether the fluxes are copper rich or lanthanoid rich. Thereby, it becomes possible to adjust the cation ratio [Cu/(La + Sr) or C u / ( N d + Ce)] within 1-2%. 2.2. Oxidation

Most of the films were grown using ozone gas (not distilled, 5 to 10% ozone concentration) as oxidation gas. In the early era, it is asserted that strong oxidation is the most important requirement for growing cuprate films in a vacuum chamber since Cu is a difficult element to oxidize. However, our experience over the past 7 years in growing several cuprate films tells us that this assertion must be revised somewhat. The amount of oxidation gas must be sufficient for the fight phase to be formed. But stronger oxidation does not always produce better quality of films. An excessive amount of oxidaTable 2 Lattice constants of LSCO, NCCO, and substrates

Lal.85 Sr0.15CUO2 Nd 1.85Ce 015 CuO4 NdCaAIO~ YA103 LaSrAIO~ NdAIO 4 ~ LaAIO3 a NdGaO 3 ~ LaSrGaO 4 SrTiO 3

a (A)

c (A)

3.777 3.945 3.688 3.715 3.756 3.763 3.793 3.842 3.843 3.905

13.23 12.08 12.15 12.62

tion gas suppresses the surface migration of cation elements [3], resulting in a tendency toward island growth and also in the degradation of electrical properties. Our empirical law is that the optimum amount of oxidation gas is 2-3 times the lower limit for the right phase to be formed. 2.3. Substrate

Table 2 summarizes the lattice constants of commercially available perovskite substrates. It also lists the lattice constants of LSCO and NCCO. As expected from the viewpoint of lattice matching, the best results are obtained for LSCO (001) on LaSrA104(LSAO)(001) substrates and for NCCO (001) on SrTiO3(STO)(001) substrates. For (100) and (110) film growth, lattice matching is more difficult to achieve since both lattice constants, a and c, have to match. The data in Table 2 show there is no lattice-matched combination of commercially available substrates and LSCO/NCCO. The best approach is homoepitaxial growth. However, the size of LSCO and NCCO single crystals available for substrates is limited, and the superconductivity of substrates makes an evaluation of film quality difficult. These limitations are somewhat relaxed by using single crystals of the end members, La2CuO 4 and Nd2CuO 4. LSAO (100) and (110) substrates offer another choice for growing fairly good LSCO (100) and (110) films. On the other hand, the choice of substrates is more limited for NCCO (100) and (110) film growth. Any substrate other than Nd 2CuO4 does not seem to produce superconducting NCCO (100) and (110) films.

3. Properties of thin films 12.68

a NdA103" LaAIO3 ' and NdGaO 3 are indexed as pseudo-cubic systems.

3. I. (La, Sr) 2CuO 4 thin films

Fig. 1 shows the temperature dependences of the resistivity ( D - T ) of LSCO (001) films. The film

38

M. Naito et al. / Physica C 293 (1997) 36-43 . . . .

i

,..80

. . . . .

i .

.

. . . . .

i

. . . . ~

i

. . . .

i , , ,

,

~.

E95088

~t. 200

4o

50

e',,

o

1oo T (K) 200

300

Fig. 1. p-T of three LSCO (001) thin films: E95229 is a 1800 ~t film with x=0.15 on LSAO, E95331 a 4500 /k film with x = 0.31 on LSAO, and E95~8 a 1800 A film with x = 0.15 on STO. The inset shows the superconducting transition in E95229.

with x = 0.15 on an LSAO (001) substrate shows a superconducting transition at temperatures higher than 43.5 K. Our best T~( p -- 0) is 44.0 K, which is about 7 K higher than that reported for bulk materials under ambient pressure, as shown in Table 3. Noteworthy is that the film shows an almost linear p--T cmwe which extrapolates to a value lower than 10 VLfl crn at T = 0 K. Fig. 1 also shows the resistivity of an overdoped film on LSAO with x = 0 . 3 1 , which is as low as 6 i~ll cm at 4.2 K and 60 VLfl cm at 300 K. The results for STO substrates exhibit a clear contrast with those for LSAO substrates. The film with x = 0.15 on an STO substrate shows T~ = 29 K and a saturating temperature dependence of resistivity at low temperatures. X-ray diffraction measurements show that the crystal structure of LSCO films on both LSAO and STO substrates is distorted from that of bulk materials (Table 3). In 1800 .~ films on LSAO, the a-axis lattice (a) is compressed by 0.4% and the c-axis lattice constant (c) is expanded by 0.5%. On the other hand, in films of the same thickness on STO, a is expanded by 1.6% and c is compressed by 0.4%.

The changes in a show a clear correlation with the lattice mismatch between the films and the substrates, indicating that the changes are due to stress generated by the lattice mismatch. The stress is of a plane type because a film has no restriction in the direction perpendicular to the surface. This results in the respective expansion and shrinkage of c in the films on LSAO and STO due to the Poisson effect. The strain caused by the lattice mismatch tends to be relieved when the thickness exceeds 2000 ,~. This conclusion is based on the observation that the difference in the lattice constants between the films on LSAO and STO vanishes for a thickness of 4500 ,~. A Tc higher than bulk LSCO by about 7 K and the observed distortion of the crystal structure in LSCO (001) films on LSAO substrates are consistent with the uniaxial pressure studies by other groups [4]. Recently, Gugenberger et al. [5] deduced the uniaxial strain coefficients dTc/de i ( i = a , b, and c) for LSCO from high-resolution dilatometry experiments using the Ehrenfest relationship. Their result gave positive d T J d ~ a and d T J d ~ b and a negative d T J d ¢ c, which quantitatively explain the observed increase in Tc. The initial growth behavior of LSCO (001) films on LSAO (001) substrates was investigated in various ways, including RHEED, AFM, XPS/UPS, and p - T . Fig. 2 shows the evolution of the RHEED pattern in the initial stage of film growth, which indicates that the growth of LSCO thin films pro-

Table 3 LSCO films on LSAO and STO substrates as compared with bulk LSCO

LSCO/LSAO LSCO/STO Bulk LSCO

3.756 3.905

3.762 3.837 3.777

13.29 13.18 13.23

43.8 ")7.4 36.7

Fig. 2. Evolution of the ~ image in the initial stage of LSCO film growth on LSAO (001): (a) 0.5 unit cells, (b) 1 unit cell, (c) 2 unit cells, and (d) 140 unit cells.

M. Naito et a l . / Physica C 293 (1997) 36-43 0.15

I

~'I

\'

'

'

I\\\

ups

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olo

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He I

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.-~ 0.05

o

o

\

~

o

-~

0.5 - UCT

0

2

o J_'EF ' 1' Binding Energy (eV)

-

Fig. 3. Evolution of the UP spectrum in the initial stage of LSCO film growth on L S A O (001).

ceeds smoothly on LSAO substrates 1. It should be recalled that one unit cell contains two molecules of LSCO. The RHEED intensity oscillates during the growth with a period of 2.1 s, corresponding to the accumulation of 0.5 unit cells ( = 1 molecular layer). This indicates that the growth of LSCO (001) films on LSAO substrates proceeds molecular layer by molecular layer in a two-dimensional nucleation growth mode. This conclusion is also supported by AFM observations, which shows in most cases that the surface of ultrathin films consists of two-dimensional growtoh nuclei with molecular-layer height and 500-1000 A in size. In some cases, however, the surface consists of steps and flat terraces with no apparent growth nucleus. This suggests that step-flow growth may be possible for LSCO (001) films on LSAO substrates with an adequate incline. Fig. 3 shows the corresponding results for in situ UPS on LSCO ultrathin films. The Fermi edge structure is apparent for the whole thickness range. The height of the density of states at the Fermi level

I This result is unique for L S A O substrates with small lattice mismatch. LSCO ultrathin films on STO substrates show very broad streaks in the R H E E D pattern, which are remarkably different from those for thicker films.

39

(DOS(EF))for the 4-unit-cells-thick (4-UCT) film is identical to that for the 140-UCT film. The height slightly decreases with decreasing thickness down to 1 unit cell, and then shows a significant reduction for the 0.5-UCT film. This suggests that an electronic band structure is already well developed at 1-unit-cell thickness to a level similar to thick films. Fig. 4 shows the results for p-T of LSCO ultrathin films. The p-T for the 4-UCT film is comparable to that for the 140-UCT film. As the film thickness is reduced further, the resistivity increases and Tc decreases noticeably. However, it is rather surprising that the 2-UCT LSCO film without any buffer layer and cap layer still exhibits the onset of superconductivity at around 35 K and To( p = 0) at 10 K. There is large scattering in the p - T data for films less than 2-UCT, indicating that the morphology of the substrate surface strongly affects p--T behavior for ultrathin films. Even at best so far, 1-UCT films have electrical connection with no indication of superconductivity, and 0.5-UCT films have no electrical connection. Now we move to the results for LSCO (100) and (! 10) films. As mentioned above, the best choice for the substrate is LSCO or LCO. However, because of the limitations in the size and in the number of these substrates, the growth of LSCO (100) and (110) films have so far been examined extensively on LSAO substrates. Fig. 5 shows the p - T data (both of Pab and Pc) for LSCO (100) and (110) films on

2

50

100

150

200

250

300

T (K) Fig. 4. p - T of LSCO (001) ultrathin films.

40

M. Naito et a l . / Physica C 293 (1997) 36-43 1.5 . . . . i . . . . ~. . . . ~. . . . ~. . . . i . . . .

~, , , ,

300

10°

....

~1

F

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~ 300

(100) p~

250i

10 "1

©

(110) Pc

o

~

~00

I 250 b~ 1 0 0

a

"7

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LaLssSr0AsCuO4Thin Films on LaSrA104 (1800 A)

7-

10 -2 o

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C

.~;~150 2o 10-3 "~ 0.5

.<. -2

g

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.~i

5

lO

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0 0

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..2_(~)P~ I,

100

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~ , 1 ~ 1

150 200

~

250

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,,, 50

10,5 300

Temperature (K) Fig. 5. p - T of LSCO (100) and (110) thin films on LSAO (100) and (110) substrates. P,b is the resistivity parallel to CuO 2 planes, and Pc the resistivity perpendicular to CuO 2 planes. As a reference, p - T of an LSCO (001) thin film on LSAO is included.

LSAO substrates. The P,b is metallic and Pc is slightly semiconducting, leading to the anisotropy value (Pab/Pc) of 10(O300. This anisotropy is comparable to that obtained for bulk single crystals with x = 0 . 1 5 , indicating that the crystallinity is good. However, the (100) and (110) films have lower T~ and higher Pab than the (001) film 2. Although we have not done X-ray diffraction measurements on the c-axis lattice constant for the LSCO (100) and (110) films, it can be speculated that the shorter c of LSAO than LSCO may have a detrimental effect on T~. The RHEED patterns of LSCO (100) and (110) films on LSAO substrates are fairly streaky in spite of the intrinsic tendency for island growth for these orientations.

3.2. (Nd, Ce)2CuO4 thin films Fig. 6 plots the p--T data for NCCO (001) films grown on STO (001) substrates. It shows the systematic Ce doping dependence of p--T. The optimum

2 Nevertheless the pab-T curves of the (100) and (110) films have the same slope as that of the (001) film.

0 0

50

100

150

200

250

0 IOO

Temperature (K) Fig. 6. p - T of 900 ,~ NCCO (001) thin films with various Ce-doping concentrations on STO substrates: x = 0 (a), x = 0.128 (b), x = 0 . 1 3 1 (c), x = 0 . 1 3 7 (d), x = 0 . 1 5 0 (e), x = 0 . 1 6 6 (f), and x = 0.187 (g). The inset shows the superconducting transitions.

doped films typically shows Tc( p = 0) of 23-24 K, and p(300 K) of 150-200 txl~ cm, p(30 K) of 20-30 Ixll cm. When the Ce doping level decreases from x = 0.15, the Tc decreases and the resistivity increases, exhibiting slight semiconducting behavior at low temperatures (underdoped regime). When the Ce doping level increases from x = 0 . 1 5 , the Tc decreases and the resistivity decreases, exhibiting a strange "T-linear" dependence at low temperatures (overdoped regime). Superconductivity disappears below x = 0.12 and above x = 0.20. These results are roughly consistent with those reported for bulk materials. However, it seems that thin films have better quality than bulk specimens in that the superconducting transition is sharper and the resistivity is lower. In the case of bulk single crystals and ceramics, good superconducting properties are rather difficult to obtain for electron-doped NCCO. The reason, we now believe, is the difficulty involved in the reduction process required for achieving superconductivity in NCCO. There is now accumulated evidence that the presence of interstitial

M. Naito et al. / Physica C 293 (1997) 36--43

Film

I0 ~

B ~

1200 1000 800 700 60t) 500 I . I . I, J . I I . I. , . I . .

10:

i

i

T[°Cl

..... i ....

,o, S L\: i~,x'lla~e , ..... L~lmxt ... •~ o~aumty

___i 10-'

00.6

: \::1 N, I I

0.8

1

1.2

1.4

1000/T[KI Fig. 7. Phase stability diagram of NCCO. The chemical stability limit is from Kim and Gaskell [8]. The dark-shaded areas show the growth and reduction phase field for thin films, while the lightshaded areas show those for bulk specimens. Note that the phase field for bulk reduction is outside the phase stable field.

apical oxygens in as-grown NCCO specimens destroys the superconductivity [6,7]. Therefore, redaction to remove apical oxygens is a prerequisite. The reduction has to be made without phase decomposition, or more strictly speaking even without introduction of oxygen deficiencies at the regular sites, which may disrupt CuO 2 networks. Fig. 7 is a phase stability diagram for NCCO. The solid line represents the chemical stability limit reported by Kim and Gaskell [8]. This stability line is obtained by a thermogravimetric analysis of bulk ceramics, and is fairly consistent with our phase stability experiments on thin films using RHEED. In our experiments, the surface of thin films was observed by RHEED as the films were slowly heated under constant Po2' The decomposition temperature under this Po2 can be known by the appearance of impurity phases in the RHEED pattern. For example, at Po2 = 1 - 2 × 10 -8 Torr, the T' phase starts to decompose at around 640°C. In order to find the optimum reduction route, an oxygen nonstoichiometry phase diagram, constructed by taking into account the presence of three different oxy-

41

gen sites 0(1), 0(2), and apical 0(3), is required, but not available at present. Hence, we empirically optimized the reduction phase field, which is indicated by the darkly shaded area in Fig. 7. Because of sluggish oxygen diffusion in this phase field, it takes 5-10 min to reduce 1000 ,~ films homogeneously. Fig. 7 also shows the reduction phase field commonly used for bulk specimens, as indicated by the lightly shaded area. Bulk reduction is apparently performed outside the phase stable field, which leads to inhomogeneity, namely the phase decomposes near surface and is superconducting well inside as shown in the top of Fig. 7. If bulk specimens are reduced in the phase field optimized for films, it will take a very long time to obtain homogeneous oxygen distribution. Consequently, thin films have an advantage over bulk specimens for NCCO. NCCO ultrathin films were also grown, but they were not as good as LSCO ultrathin films. At best, 6-UCT films showed Tc,oase t --- 15 K and Tc( p --- 0) = 11 K. It seems that the growth of NCCO is intrinsically more awkward than that of LSCO in spite of their similar crystal structures. This is supported by the fact that NCCO film growth requires a higher growth temperature and stronger oxidation than LSCO film growth (Table 1). We have extensively investigated the surface and interface of MBE-grown NCCO thin films [9]. The results of this investigation have been helpful in improving the quality of tunnel junctions fabricated on NCCO thin lYdms. Fig. 8 shows the d l/dV characteristics of one such tunnel junction. This tunnel junction was fabricated by depositing Pb ex situ on an NCCO film. According to our surface and interface studies for NCCO, the following reaction occurs at ex situ Pb/NCCO interface: when NCCO surface is exposed to air, oxygens are adsorbed at interstitial apical sites (0(3)) on the NCCO surface, accompanied with H 2 0 / C O 2 adsorption. The deposition of Pb on this surface extracts most of these adsorbed oxygens and also a few regular oxygens 3. This is a redox reaction between NCCO and Pb. Consequently, the tunnel barrier of this type of junction is

3 Pb deposition without exposing NCCO surface to air extracts regular oxygens, leading to destruction of superconductivity at NCCO surface.

M. Naito et al. / Physica C 293 (1997) 36-43

42 0.5

Pb/NdL s sC eo. 15CUO4/SrTiO3(001)

0.4

~

7.5K

0.3 4.2K

0.2

0.1

0

-80

-60

.40

-20

0

20

40

60

80

Bias Voltage (mY) Fig. 8. Tunneling spectra of an P b / N C C O junction. For the details, see the text.

thought to be mainly PbO x. The favorable situation that only adsorbed oxygens are removed with regular oxygens mostly preserved will occur for a limited range of counter metals with mild reduction strength. One of the semiquantitative measures of reduction strength may be the standard reduction potential (E°). For example, Cu2++ e ¢* Cu ÷ ( E ° = +0.153 V) and p b 2 ÷ + e c ~ P b ( E ° = - 0 . 1 2 6 V). Metals such as Au or Ag with E ° much higher than +0.153 V do not extract any oxygen, while metals such as Sn or A1 with E ° much lower than +0.153 V extract all oxygens, including regular ones at the surface. The tunnel spectrum at 7.5 K in Fig. 8 clearly shows the superconducting gap structure of NCCO with a reasonable gap value (4-5 meV). The gap structure completely disappears above 25 K. It can also be seen that the dominant electron transport process in this junctions is elastic tunneling since the superconducting gap and the phonon structures of Pb are superimposed in the dl/dV at 4.2 K (broken line). However, the high zero-bias conductance above 7.3 K (our best: 20-25% of the normal conductance) and the smeared and strange shape of dI/dV imply the presence of a normal-metal region and the distribution of the magnitude of the superconducting gap.

This indicates nonuniform oxygen distribution at the interface, Namely, even with Pb counterelectrodes, a few apical oxygens remain and a few regular oxygens are removed. Finally, one comment should be made on the structures indicated by arrows at high biases (20-25 meV and 50-55 meV) in Fig. 8. These structures are reproducibly observed for tunnel junctions in which the NCCO superconducting gap structure is apparent. And they disappear above 25 K. Although we have not made the McMillan-Rowell gap inversion, these structures seem to correspond to the strong minima around 25 and 55 meV in the a2F(to) deduced from the NCCO point-contact spectra obtained by Huang et al. (see Ref. [10], fig. 4). It has been claimed, although not well established, that there is some correspondence between the a 2 F ( t o ) and the generalized phonon density of states deduced from the inelastic neutron scattering [1 l]. Further improvement in fabricating good tunnel junctions is required to verify this claim.

4. Summary Recent progress in growing thin films of high-T~ cuprates by reactive coevaporation enables us to produce thin films that are better in quality than bulk materials. (1) In the case of LSCO films, the choice of substrates is important. An increase in T~ can be achieved by the use of LSAO substrates. The increase is due to strain generated by the lattice mismatch, as indicated by our structural analysis. The best T~ obtained so far is 44 K, which is higher by 7 K than that for bulk materials. (2) In the case of NCCO films, reduction for homogeneous removal of interstitial apical oxygens is important. The reduction has to be made without phase decomposition, or more strictly speaking even without introduction of oxygen deficiencies at the regular sites, which may disrupt CuO 2 networks. Significant improvement in p-T can be achieved by low-temperature reduction, which may not be applicable for bulk specimens because of sluggish oxygen diffusion. These high-quality thin films have been used for photoemission spectroscopy and tunnel spectroscopy, the preliminary results of which demonstrate the

M. Naito et al. / Physica C 293 (1997)36--43

possibility of significant progress in surface and interface investigations for cuprates toward understanding the electronic structure and also obtaining accurate information on the complicated surface and interface reaction.

Acknowledgements The authors would like to thank A. Matsuda and T. Yamada for their helpful discussions, and N. Matsumoto and T. Izawa for their support and encouragement throughout the course of this study.

References [1] H. Sato, M. Naito, Physica C 274 (1997); H. Sato, H. Yamamoto, M. Naito, Physica C 274 (1997).

43

[2] M. Naito, H. Sato, Appl. Phys. Lett. 67 (1995) 2557. [31 R.H. Hammond, R. Bormann, Physica C 162-164 (1989) 703. [4] Y. Tajima, Y. I-ljdaka. unpublished; Y. Motoi, IC Fujimoto, H, Uwe, T. Sakudo, J. Phys. Soc. Jpn. 60 (1991) 384. [5] F. Gugenberger, C. Memgast, G. Roth, K. C_wube,V. Breit, T. Weber, H. Wiihl, Phys. Rev. B 49 (1994) 131377. [6] H. Oyanagi, Y. Yokoyama, H. Yamaguchi, Y. Kuwahara, T. Katayarna, Y. Nishihara, Phys. Rev. B 42 (1990) 10136; N.A. Fortune, K. Murata, M. Ishibashi, Y. Yokoyama, Y. Nishihara, Phys. Rev. B 43 (1991) 12930. [7] Y.T. Zhu, A. Mnnthiram, Physica C 224 (1994) 256. [8] J.S. Kim, D.R. Gaskell, Physica C 209 (1993) 381. [9] H. Yamamoto, M. Naito, H. Sato, Phys. Rev. B 56 (1997) 2852. [10] Q. Huang, J.F. Zasadzinski, N. Tralshawala, K.E. Gray, D.G. Hinks, J.L. Peng, R.L. Greene, Nature 347 (1990) 369. [11] I.W. Sumarlin, J.W. Lynn, D.A. Neumann, J.J. Rush, C-K. Loong, J.L. Peng, Z.Y. Li, Phys. Rev. B 48 (1993) 473.