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Colossal magnetoresistance of thin films of La0.66Ba0.33MnO3 as a function of film thickness
Materials Science and Engineering B56 (1998) 147 – 151
Colossal magnetoresistance of thin films of La0.66Ba0.33MnO3 as a function of film thickness G. Harzheim a, J. Schubert a,*, L. Beckers a, W. Zander a, D. Meertens b, C. Ostho¨ver b, Ch. Buchal a a
Institut fu¨r Schicht- und Ionentechnik, Forschungszentrum Ju¨lich GmbH, 52425 Ju¨lich, Germany b Institut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich GmbH, 52425 Ju¨lich, Germany
Abstract La0.66Ba0.33MnO3 shows a strong change of its resistivity if a magnetic field is applied. The strength of this colossal magneto resistance (CMR) effect depends of the thickness of epitaxial thin films prepared on MgO (100) and SrTiO3 (100). We have prepared films in a thickness range of 5 to 250 nm by pulsed laser deposition. The epitaxial La0.66Ba0.33MnO3 thin films were characterized by Rutherford backscattering spectrometry and channeling, X-ray diffraction measurements as well as by high resolution transmission electron microscopy (HRTEM). The high crystalline quality was proved by ion channeling (minimum yield of xmin :2%) and by HRTEM micrographs. By X-ray diffraction measurements, no additional phases were detected beside ˚ . The CMR effect of 10 nm thin films is enlarged by 45% as compared to 150 the cubic phase with a lattice constant a=3.915 A nm thick films on MgO (100) substrates. The saturation magnetization decreases with decreasing film thickness. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Pulsed laser deposition; Thin films; La0.66Ba0.33MnO3; Colossal magneto resistance
1. Introduction
2. Experimental
The colossal magneto resistance (CMR) effect of a large number of different materials as La0.66Ba0.33MnO3, La0.66Ca0.33MnO3 etc. has been investigated until now [1]. Device applications as magnetic reading heads or bolometers using these materials are under discussion. Heterostructures formed by CMR-materials combined with insulating materials are necessary for some of these devices. The CMR effect of epitaxial La0.66Ba0.33MnO3 films was published by Helmholt et al. [2]. The transition temperature of La0.66Ba0.33MnO3 is close to room temperature which makes this material especially attractive. In this paper we present our results on the thickness dependence of the resistivity, transition temperature and saturation magnetization of thin epitaxial La0.66Ba0.33MnO3 films.
The La0.66Ba0.33MnO3 (LBMO) films were grown by pulsed laser deposition (PLD) [3]. An excimer laser (LAMBDA LPX305) with a wavelength l=248 nm, a repetition rate of 20 Hz and an energy density of :8 J cm − 2 was used. The cylindrical target consists of sintered powder with the nominal stoichiometry La0.66Ba0.33MnO3. A typical deposition rate of 0.6 nm s − 1 was achieved. The single crystalline substrate materials MgO (100) and SrTiO3 (100) with dimensions of 10× 10×1 mm3 were placed on a resistive SiC-heater. Deposition temperatures in the range of Ts =950– 1100°C and an oxygen partial pressure of p=0.37 mbar were used to prepare optimized films. An annealing step of : 3 min in 1 bar oxygen at Ts = 900°C was performed directly after completion of the deposition process to improve the quality of the films. LBMO films were prepared with a thickness ranging from d=5 to 250 nm. The stoichiometry and the crystalline quality were characterized by X-ray diffraction (XRD), high resolution transmission electron microscopy (HRTEM) as well as Rutherford backscattering spectrometry and ion channeling (RBS/C).
* Corresponding author. Tel.: +49 2461 616379; fax: + 49 2461 614673; e-mail: [email protected]
0921-5107/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0921-5107(98)00243-8
148
G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
Fig. 1. RBS/ion channeling spectra of a 120 nm thick LBMO film on MgO (100). A simulation of the random spectrum is added, in order to demonstrate the good stoichiometry of the film.
3. Results and discussion
3.1. Structural characterization A typical RBS/C measurement of a 120 nm thick La0.66Ba0.33MnO3 film on MgO is shown in Fig. 1. The energy of the incident He + -beam was 1.4 MeV. The comparison between the simulation and the random spectrum confirms the stoichiometric transfer of the elements from the target to the substrate. The sharp drop at the left side of the Ba and La signal indicates a flat surface of the film and a sharp interface between substrate and film without detectable interdiffusion. Furthermore, the minimum yield xmin =2% measured at the La and Ba signal demonstrates clearly the high crystalline quality of the films grown on MgO (100)
substrates. The same results were achieved on SrTiO3 (100) substrates. To demonstrate the good epitaxial growth of thin LBMO films on MgO (100), 50 nm films were analyzed (Fig. 2). The minimum yield xmin =2.5% clearly show the good crystalline quality. All thinner films showed comparable channeling values. XRD investigations were performed to measure the lattice parameter of LBMO. In a conventional u−2u measurement of LBMO on SrTiO3(100) no additional diffraction peaks are visible compared to a measurement of a pure SrTiO3 (100) substrate. This suggests that the LBMO lattice exists in a cubic phase with a similar lattice parameter compared to SrTiO3 (100). Combined with the good minimum yield this points to the epitaxial growth of LBMO on SrTiO3 (100). On MgO (100) additional peaks belonging to LBMO are
Fig. 2. RBS/ion channeling spectra of a 50 nm thick LBMO film on MgO (100).
G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
149
Fig. 3. X-ray diffraction measurement of LBMO on MgO (100).
clearly separated (Fig. 3). No peaks corresponding to other crystalline phases than the cubic phase are visible. Only the (00n) reflexes of the cubic LBMO-phase corre˚ and sponding to a lattice parameter of a = 3.915 A peaks of the substrate MgO (100) were observed even down to a thickness of d = 10 nm. The amount of the mosaic spread of the LBMO on MgO (100) was estimated from the measurement of the full width at half maximum (FWHM) of the (002)-reflex of LBMO. The Dv (002)=0.65° which is not dependent on the thickness shows the good crystalline quality of the films. A pole figure measurement indicates the epitaxial growth of LBMO on MgO (100) with the same 4-fold symmetry as the MgO-substrate. To gain information about the microstructure and the lattice parameter of the LBMO thin film on SrTiO3 (100), HRTEM measurements were performed in a Philips CM20 FEG microscope at 200 keV. Fig. 4 shows a high resolution image in 100 orientation. The atomically sharp interface between the LBMO film and the SrTiO3 substrate is marked by arrows. No interdiffusion between film and substrate is detected in agreement with the RBS/C measurements. The epitaxial
Fig. 4. 100 cross-section HRTEM of a LBMO film on SrTiO3 (100). The arrows mark the interface.
growth of LBMO on the SrTiO3 substrate is clearly seen. Columnar growth which was observed by Gommert et al. [4] is not detectable for the LBMO films even at smaller magnifications. The comparison between the substrate and the LBMO lattice parameter parallel to ˚ , which the interface results in an a(LBMO)= 3.915 A confirms the cubic structure of the LBMO thin films on these substrates.
3.2. Electrical characterization Resistance measurements were performed using a conventional four probe technique in the temperature range from 77 to 350 K. A magnetic field up to H=4 T was applied during the resistance measurements. Typically the resistance curve of LBMO shows a metallic behavior at lower temperature and a semiconducting behavior at higher temperature. The transition occurs at temperature TP. The typical resistivity of samples with a thickness of d= 100 nm ranged between r=5 and 10 mVcm as shown in Fig. 5. The resistivity of LBMO at room temperature increases strongly for the thinnest films. On MgO (100) substrates, this increase of the resistivity starts at a thickness of d=50 nm, growing by a factor of 40. On SrTiO3 (100) substrates the onset is seen at d= 20 nm with a less pronounced effect. As mentioned before, we can exclude a loss of the crystalline perfection in the thinnest films as the reason for this observation. The CMR effect is measured by DR/R0 = (R0 − RH)/R0. RH is the resistance value of the sample measured in an applied magnetic field H, R0 correspondingly in the earth magnetic field. The temperature Tmax of the largest effect coincides with the transition temperature Tp. For fields up to 4 T, no field dependence of Tmax is observed. Thin films show a reduction of the characteristic temperature Tmax. This is plotted in Fig. 6. Comparing Fig. 5 and
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G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
Fig. 5. Room temperature resistivity measurements of LBMO-films on MgO (100) and SrTiO3 (100) as a function of film thickness.
Fig. 6, we observe, that the decrease in Tmax and the increase of the resistivity occur for the same samples at the same thickness, with the thinnest films showing the strongest effects. At thicknesses below d =50 nm on MgO (100) one notices a sharp drop in Tmax from 320 to 135 K and on SrTiO3 (100) below d = 20 nm from 320 to 210 K. (Fig. 6). Amazingly, the maximum CMR effect itself is enhanced at reduced thickness. This is seen in Fig. 7. On MgO (100) DR/R0 changes from 45 to 74% and on SrTiO3 (100) from 45 to 60% in a magnetic field of 4 T. An important information is the magnetic moment per Mn-atom. The theoretical estimate gives 3.67 mB/ Mn-atom, but in thin films typically a smaller value is measured. Gupta has pointed out, that La0.66Ca0.33MnO3 films show the highest magnetic moment per Mn-atom if they are polycrystalline with small grains [5]. The larger the grains are, the smaller the magnetic moment per Mn-atom becomes, with thin epitaxial films showing the lowest moments. Our films grown on SrTiO3 (100) show no characteristic
dependence of the magnetic moment on the film thickness. Within the scatter of the data a value of 2.8–3.0 mB/Mn-atom is found, see Fig. 8. In contrast, the films grown on MgO (100) show a clear anomaly, see Fig. 8. With decreasing film thickness, also the magnetic moment per atom decreases, reaching 1 mB/Mn at a film thickness of 10 nm. This unusually strong reduction is seen at the same samples, which show strong effects in the other properties, namely the CMR (DR/ R0, Fig. 7), the resistivity r (Fig. 5) and the characteristic temperature Tmax (Fig. 6).
4. Summary and conclusion High quality epitaxial thin films of LBMO have been grown on SrTiO3 (100) and MgO (100). The crystalline quality of all films has been analyzed and found to be excellent, even if investigated with high resolution TEM. Nevertheless we see a noticeable effect of resistivity, CMR-effect and characteristic tem-
Fig. 6. Temperature of the maximum CMR-effect of LBMO on MgO (100) and SrTiO3 (100) as a function of film thickness.
G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
151
Fig. 7. Maximum CMR-effect of LBMO on MgO(100) and SrTiO3(100) in an applied magnetic field of H =4 T as a function of film thickness.
Fig. 8. Saturation magnetization of LBMO on MgO (100) and SrTiO3 (100) measured at T =10 K as a function of film thickness.
perature, if the film thickness is lowered below 50 nm. All these effects are more pronounced on MgO substrates, if compared to SrTiO3 substrates. Very thin films grown on MgO show a strong increase of the CMR effect and at the same time remarkable decrease of the magnetic moment per Mn-atom. Although the influence of grains has been studied before, these observations are unexpected and surprising. They are a challenge for the theoretical understanding of these materials and open interesting perspectives for multilayered structures.
Acknowledgements We gratefully acknowledge the support from the
Tandetron facility and staff Forschungszentrum Ju¨lich.
at
the
IFF
of
References [1] H.Y. Hwang, S.W. Cheong, P.G. Radaelli, M. Marezio, B. Batlogg, Phys. Rev. Lett. 75 (1995) 914. [2] R.v. Helmolt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer, Phys. Rev. Lett. 71 (1993) 2331. [3] B. Stritzker, J. Schubert, U. Poppe, W. Zander, U. Kru¨ger, A. Lubig, Ch. Buchal, J. Less Common Metals 164/165 (1990) 279. [4] E. Gommert, H. Cwerva, A. Rucki, R.v. Helmolt, J. Wecker, C. Kuhrt, K. Samwer, J. Appl. Phys. 81 (1997) 5496. [5] A. Gupta, G.Q. Gong, G. Xiao, P.R. Duncombe, P. Lecoeur, P. Trouilloud, Y.Y. Wang, V.P. David, J.Z. Sun, Phys. Rev. B 54 (1996) 15269.
Colossal magnetoresistance of thin films of La0.66Ba0.33MnO3 as a function of film thickness G. Harzheim a, J. Schubert a,*, L. Beckers a, W. Zander a, D. Meertens b, C. Ostho¨ver b, Ch. Buchal a a
Institut fu¨r Schicht- und Ionentechnik, Forschungszentrum Ju¨lich GmbH, 52425 Ju¨lich, Germany b Institut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich GmbH, 52425 Ju¨lich, Germany
Abstract La0.66Ba0.33MnO3 shows a strong change of its resistivity if a magnetic field is applied. The strength of this colossal magneto resistance (CMR) effect depends of the thickness of epitaxial thin films prepared on MgO (100) and SrTiO3 (100). We have prepared films in a thickness range of 5 to 250 nm by pulsed laser deposition. The epitaxial La0.66Ba0.33MnO3 thin films were characterized by Rutherford backscattering spectrometry and channeling, X-ray diffraction measurements as well as by high resolution transmission electron microscopy (HRTEM). The high crystalline quality was proved by ion channeling (minimum yield of xmin :2%) and by HRTEM micrographs. By X-ray diffraction measurements, no additional phases were detected beside ˚ . The CMR effect of 10 nm thin films is enlarged by 45% as compared to 150 the cubic phase with a lattice constant a=3.915 A nm thick films on MgO (100) substrates. The saturation magnetization decreases with decreasing film thickness. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Pulsed laser deposition; Thin films; La0.66Ba0.33MnO3; Colossal magneto resistance
1. Introduction
2. Experimental
The colossal magneto resistance (CMR) effect of a large number of different materials as La0.66Ba0.33MnO3, La0.66Ca0.33MnO3 etc. has been investigated until now [1]. Device applications as magnetic reading heads or bolometers using these materials are under discussion. Heterostructures formed by CMR-materials combined with insulating materials are necessary for some of these devices. The CMR effect of epitaxial La0.66Ba0.33MnO3 films was published by Helmholt et al. [2]. The transition temperature of La0.66Ba0.33MnO3 is close to room temperature which makes this material especially attractive. In this paper we present our results on the thickness dependence of the resistivity, transition temperature and saturation magnetization of thin epitaxial La0.66Ba0.33MnO3 films.
The La0.66Ba0.33MnO3 (LBMO) films were grown by pulsed laser deposition (PLD) [3]. An excimer laser (LAMBDA LPX305) with a wavelength l=248 nm, a repetition rate of 20 Hz and an energy density of :8 J cm − 2 was used. The cylindrical target consists of sintered powder with the nominal stoichiometry La0.66Ba0.33MnO3. A typical deposition rate of 0.6 nm s − 1 was achieved. The single crystalline substrate materials MgO (100) and SrTiO3 (100) with dimensions of 10× 10×1 mm3 were placed on a resistive SiC-heater. Deposition temperatures in the range of Ts =950– 1100°C and an oxygen partial pressure of p=0.37 mbar were used to prepare optimized films. An annealing step of : 3 min in 1 bar oxygen at Ts = 900°C was performed directly after completion of the deposition process to improve the quality of the films. LBMO films were prepared with a thickness ranging from d=5 to 250 nm. The stoichiometry and the crystalline quality were characterized by X-ray diffraction (XRD), high resolution transmission electron microscopy (HRTEM) as well as Rutherford backscattering spectrometry and ion channeling (RBS/C).
* Corresponding author. Tel.: +49 2461 616379; fax: + 49 2461 614673; e-mail: [email protected]
0921-5107/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0921-5107(98)00243-8
148
G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
Fig. 1. RBS/ion channeling spectra of a 120 nm thick LBMO film on MgO (100). A simulation of the random spectrum is added, in order to demonstrate the good stoichiometry of the film.
3. Results and discussion
3.1. Structural characterization A typical RBS/C measurement of a 120 nm thick La0.66Ba0.33MnO3 film on MgO is shown in Fig. 1. The energy of the incident He + -beam was 1.4 MeV. The comparison between the simulation and the random spectrum confirms the stoichiometric transfer of the elements from the target to the substrate. The sharp drop at the left side of the Ba and La signal indicates a flat surface of the film and a sharp interface between substrate and film without detectable interdiffusion. Furthermore, the minimum yield xmin =2% measured at the La and Ba signal demonstrates clearly the high crystalline quality of the films grown on MgO (100)
substrates. The same results were achieved on SrTiO3 (100) substrates. To demonstrate the good epitaxial growth of thin LBMO films on MgO (100), 50 nm films were analyzed (Fig. 2). The minimum yield xmin =2.5% clearly show the good crystalline quality. All thinner films showed comparable channeling values. XRD investigations were performed to measure the lattice parameter of LBMO. In a conventional u−2u measurement of LBMO on SrTiO3(100) no additional diffraction peaks are visible compared to a measurement of a pure SrTiO3 (100) substrate. This suggests that the LBMO lattice exists in a cubic phase with a similar lattice parameter compared to SrTiO3 (100). Combined with the good minimum yield this points to the epitaxial growth of LBMO on SrTiO3 (100). On MgO (100) additional peaks belonging to LBMO are
Fig. 2. RBS/ion channeling spectra of a 50 nm thick LBMO film on MgO (100).
G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
149
Fig. 3. X-ray diffraction measurement of LBMO on MgO (100).
clearly separated (Fig. 3). No peaks corresponding to other crystalline phases than the cubic phase are visible. Only the (00n) reflexes of the cubic LBMO-phase corre˚ and sponding to a lattice parameter of a = 3.915 A peaks of the substrate MgO (100) were observed even down to a thickness of d = 10 nm. The amount of the mosaic spread of the LBMO on MgO (100) was estimated from the measurement of the full width at half maximum (FWHM) of the (002)-reflex of LBMO. The Dv (002)=0.65° which is not dependent on the thickness shows the good crystalline quality of the films. A pole figure measurement indicates the epitaxial growth of LBMO on MgO (100) with the same 4-fold symmetry as the MgO-substrate. To gain information about the microstructure and the lattice parameter of the LBMO thin film on SrTiO3 (100), HRTEM measurements were performed in a Philips CM20 FEG microscope at 200 keV. Fig. 4 shows a high resolution image in 100 orientation. The atomically sharp interface between the LBMO film and the SrTiO3 substrate is marked by arrows. No interdiffusion between film and substrate is detected in agreement with the RBS/C measurements. The epitaxial
Fig. 4. 100 cross-section HRTEM of a LBMO film on SrTiO3 (100). The arrows mark the interface.
growth of LBMO on the SrTiO3 substrate is clearly seen. Columnar growth which was observed by Gommert et al. [4] is not detectable for the LBMO films even at smaller magnifications. The comparison between the substrate and the LBMO lattice parameter parallel to ˚ , which the interface results in an a(LBMO)= 3.915 A confirms the cubic structure of the LBMO thin films on these substrates.
3.2. Electrical characterization Resistance measurements were performed using a conventional four probe technique in the temperature range from 77 to 350 K. A magnetic field up to H=4 T was applied during the resistance measurements. Typically the resistance curve of LBMO shows a metallic behavior at lower temperature and a semiconducting behavior at higher temperature. The transition occurs at temperature TP. The typical resistivity of samples with a thickness of d= 100 nm ranged between r=5 and 10 mVcm as shown in Fig. 5. The resistivity of LBMO at room temperature increases strongly for the thinnest films. On MgO (100) substrates, this increase of the resistivity starts at a thickness of d=50 nm, growing by a factor of 40. On SrTiO3 (100) substrates the onset is seen at d= 20 nm with a less pronounced effect. As mentioned before, we can exclude a loss of the crystalline perfection in the thinnest films as the reason for this observation. The CMR effect is measured by DR/R0 = (R0 − RH)/R0. RH is the resistance value of the sample measured in an applied magnetic field H, R0 correspondingly in the earth magnetic field. The temperature Tmax of the largest effect coincides with the transition temperature Tp. For fields up to 4 T, no field dependence of Tmax is observed. Thin films show a reduction of the characteristic temperature Tmax. This is plotted in Fig. 6. Comparing Fig. 5 and
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G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
Fig. 5. Room temperature resistivity measurements of LBMO-films on MgO (100) and SrTiO3 (100) as a function of film thickness.
Fig. 6, we observe, that the decrease in Tmax and the increase of the resistivity occur for the same samples at the same thickness, with the thinnest films showing the strongest effects. At thicknesses below d =50 nm on MgO (100) one notices a sharp drop in Tmax from 320 to 135 K and on SrTiO3 (100) below d = 20 nm from 320 to 210 K. (Fig. 6). Amazingly, the maximum CMR effect itself is enhanced at reduced thickness. This is seen in Fig. 7. On MgO (100) DR/R0 changes from 45 to 74% and on SrTiO3 (100) from 45 to 60% in a magnetic field of 4 T. An important information is the magnetic moment per Mn-atom. The theoretical estimate gives 3.67 mB/ Mn-atom, but in thin films typically a smaller value is measured. Gupta has pointed out, that La0.66Ca0.33MnO3 films show the highest magnetic moment per Mn-atom if they are polycrystalline with small grains [5]. The larger the grains are, the smaller the magnetic moment per Mn-atom becomes, with thin epitaxial films showing the lowest moments. Our films grown on SrTiO3 (100) show no characteristic
dependence of the magnetic moment on the film thickness. Within the scatter of the data a value of 2.8–3.0 mB/Mn-atom is found, see Fig. 8. In contrast, the films grown on MgO (100) show a clear anomaly, see Fig. 8. With decreasing film thickness, also the magnetic moment per atom decreases, reaching 1 mB/Mn at a film thickness of 10 nm. This unusually strong reduction is seen at the same samples, which show strong effects in the other properties, namely the CMR (DR/ R0, Fig. 7), the resistivity r (Fig. 5) and the characteristic temperature Tmax (Fig. 6).
4. Summary and conclusion High quality epitaxial thin films of LBMO have been grown on SrTiO3 (100) and MgO (100). The crystalline quality of all films has been analyzed and found to be excellent, even if investigated with high resolution TEM. Nevertheless we see a noticeable effect of resistivity, CMR-effect and characteristic tem-
Fig. 6. Temperature of the maximum CMR-effect of LBMO on MgO (100) and SrTiO3 (100) as a function of film thickness.
G. Harzheim et al. / Materials Science and Engineering B56 (1998) 147–151
151
Fig. 7. Maximum CMR-effect of LBMO on MgO(100) and SrTiO3(100) in an applied magnetic field of H =4 T as a function of film thickness.
Fig. 8. Saturation magnetization of LBMO on MgO (100) and SrTiO3 (100) measured at T =10 K as a function of film thickness.
perature, if the film thickness is lowered below 50 nm. All these effects are more pronounced on MgO substrates, if compared to SrTiO3 substrates. Very thin films grown on MgO show a strong increase of the CMR effect and at the same time remarkable decrease of the magnetic moment per Mn-atom. Although the influence of grains has been studied before, these observations are unexpected and surprising. They are a challenge for the theoretical understanding of these materials and open interesting perspectives for multilayered structures.
Acknowledgements We gratefully acknowledge the support from the
Tandetron facility and staff Forschungszentrum Ju¨lich.
at
the
IFF
of
References [1] H.Y. Hwang, S.W. Cheong, P.G. Radaelli, M. Marezio, B. Batlogg, Phys. Rev. Lett. 75 (1995) 914. [2] R.v. Helmolt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer, Phys. Rev. Lett. 71 (1993) 2331. [3] B. Stritzker, J. Schubert, U. Poppe, W. Zander, U. Kru¨ger, A. Lubig, Ch. Buchal, J. Less Common Metals 164/165 (1990) 279. [4] E. Gommert, H. Cwerva, A. Rucki, R.v. Helmolt, J. Wecker, C. Kuhrt, K. Samwer, J. Appl. Phys. 81 (1997) 5496. [5] A. Gupta, G.Q. Gong, G. Xiao, P.R. Duncombe, P. Lecoeur, P. Trouilloud, Y.Y. Wang, V.P. David, J.Z. Sun, Phys. Rev. B 54 (1996) 15269.