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MOKE investigation of silicide films ion-beam synthesized in single-crystal silicon
Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
MOKE investigation of silicide films ion-beam synthesized in single-crystal silicon G.G. Gumarov a,b,⇑, V.Yu. Petukhov a,b, A.I. Gumarov b, R.A. Khalikov a, D.A. Konovalov a, V.F. Valeev a, R.I. Khaibullin a,b a b
Zavoisky Physical-Technical Institute of RAS, Sibirsky tract 10/7, 420029 Kazan, Russia Kazan (Volga Region) Federal University, Kremlyovskaya St. 18, 420008 Kazan, Russia
a r t i c l e
i n f o
Article history: Available online 2 February 2011 Keywords: Ion implantation Magnetic nanoparticles MOKE
a b s t r a c t Magnetic-field-assisted ion-beam synthesis was used to produce thin magnetic films. Si wafers were implanted with 40 keV Fe+ ions with a fluence of 3 1017 cm2 in the external magnetic field of 9.6 104 A/m. The samples were investigated by scanning magneto-optical Kerr effect magnetometry, inductive magnetometry and reflection high-energy electron diffraction. The main synthesized phase was ferromagnetic Fe3Si. In some regions of the samples the deviations of the easy magnetic axis near the applied magnetic field were revealed. These local changes can be caused by various reasons: the presence of mechanical stresses in a silicon substrate during the ion bombardment, the appearance of temperature gradients, inhomogeneous sputtering and the appearance of small magnetic fields in the chamber of the accelerator. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The study of the induced magnetic anisotropy in ferromagnetic thin films is of significant importance both for fundamental science and for practical applications. Usually the uniaxial anisotropy in ferromagnetic alloys is induced by applying magnetic saturation fields during film deposition or by subsequent thermomagnetic treatment. Recently, the alteration of magnetic properties in magnetic thin films by ion irradiation in external magnetic field has gained increased attention [1–7]. This technique is especially useful as it also can be used to locally alter magnetic properties like saturation magnetization, magnetic anisotropy and etc. [7]. Earlier we used magnetic-field-assisted ion-beam synthesis to produce thin films of ferromagnetic silicide Fe3Si in single-crystal silicon substrates [8]. The samples were investigated by Mössbauer spectroscopy, X-ray diffraction and autodyne method. The obtained thin films consisted of ferromagnetic Fe3Si and a small amount of nonmagnetic FeSi phases. Other phases were not detected. It was shown that application of the magnetic field during the high-dose Fe ion implantation led to the pronounced in-plane magnetic anisotropy in the synthesized films. The observed anisotropy was a superposition of the magnetocrystalline anisotropy of cubic Fe3Si and induced uniaxial anisotropy. The observed angular ⇑ Corresponding author at: Zavoisky Physical-Technical Institute of RAS, Sibirsky tract 10/7, 420029 Kazan, Russia. Tel.: +7 843 272 12 41; fax: +7 843 272 50 75. E-mail addresses: [email protected] (G.G. Gumarov), [email protected] (V.Yu. Petukhov), [email protected] (A.I. Gumarov), [email protected] (R.A. Khalikov), [email protected] (D.A. Konovalov), [email protected] (V.F. Valeev), [email protected] (R.I. Khaibullin). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.01.043
dependence of in-plane magnetic susceptibility measured by autodyne method was described on the basis of the Stoner–Wohlfarth model. The general features of the calculated curves are in good agreement with the experiment but the obtained results should be averaged over the sizes and the orientations of different clusters in the films. The goal of the present work is to closely investigate the magnetic properties of thin silicide films ion-beam synthesized in single-crystal silicon in external magnetic field using the magneto-optical Kerr effect (MOKE). In addition, this method allows studying local magnetic in-plane characteristics.
2. Experimental 40 keV Fe ions were implanted into (1 1 1) single-crystal silicon wafers at room temperature. The implantation fluence was 3 1017 cm2, the ion current density being about 4 lA/cm2. The external magnetic field Hi of 9.6 104 A/m was applied parallel to the sample surface during implantation. Reflection high-energy electron diffraction (RHEED) was used for investigation of the phase composition and the texture of the synthesized films. The RHEED gun was operated at 75 kV primary voltage, the pattern was recorded at room temperature. The integral magnetic properties of the films were investigated using an induction magnetometer. A dependence of the magnitude of the induced magnetic moment on the value of the magnetic field applied in the sample plane was registered at the magnetic field sweep up to 500 mT. While processing the results of magnetic
G.G. Gumarov et al. / Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
109
measurements, a diamagnetic contribution from the silicon substrate was subtracted. The local magnetic properties of samples were investigated by scanning Kerr polarimeter in the longitudinal mode. The measuring part of the polarimeter is constructed on the basis of an optical PCSA-ellipsometer LEF-3M-1 and has a computer-controlled goniometer for obtaining the azimuthal dependences. For investigation of local magnetic characteristics the polarimeter was equipped with an automated system for the sample movement relative to the probing laser beam and with a focusing system. Within the frames of the present research, a laser spot on the sample surface with a diameter of about 200 lm at the beam incidence angle of 45° was used.
3. Results and discussion Fig. 1 show the RHEED pattern obtained for Si implanted with Fe+ ions with a fluence of 3 1017 cm2. The pattern consists of diffraction rings which are typical for polycrystalline films. Small thickenings (brighter areas) are observed on the diffraction rings pointing to a weak texture. Identification of the diffraction rings represented in Fig. 1 has shown that the reflexes correspond to polycrystalline silicide a0 -Fe3Si. It agrees with the results of the phase analysis obtained earlier by methods of grazing angle Xray diffraction and Mossbauer spectroscopy of conversion electrons [8]. From magnetic measurements it has been revealed that all samples synthesized at specified regimes of implantation are ferromagnetic at room temperature. The control samples implanted in the absence of the magnetic field are isotropic (Figs. 3 and 4). Azimuthal dependences of the remanence measured both with inductive magnetometer (Fig. 2 and MOKE (Fig. 5) showed that all samples implanted in the applied magnetic field possess uniaxial anisotropy. However, directions of the easy magnetization axis (EMA) in various sections of the sample surface differ. For some regions the EMA direction does not coincide with that of the magnetic field applied during implantation. More detailed information about EMA directions on the surface was obtained by a scanning MOKE method. The greatest deviation of the EMA direction is observed in the regions closest to the sample clips (Fig. 6). The rectangular hysteresis loop and anhysteretic magnetization curve are observed in the easy and the hard magnetization axes, respectively (Fig. 7). Since the thickness of the synthesized layer does not exceed 50 nm we consider that particles in the synthesized layer are one-domain.
Fig. 2. Polar plot of the Jr/Ji ratio measured by a inductive magnetometer for 2.5 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m. Jr – remanent magnetic moment, Ji – induced magnetic moment.
Fig. 3. Polar plot of the Mr/Ms ratio measured by MOKE for Si implanted with 3 1017Jr Fe+/cm2 without magnetic field.
Fig. 4. Normalized hysteresis loop of Si implanted with 3 1017 Fe+/cm2 without applied magnetic field (MOKE). The loop shape remains unchanged for various azimuthal directions.
Fig. 1. RHEED pattern of Si implanted with 2.5 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m.
Azimuthal dependence of the normalized remanence in all regions of the surface is typical for uniaxial anisotropy – it has
110
G.G. Gumarov et al. / Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
Fig. 5. Polar plot of the Mr/Ms ratio for Si implanted with 3 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m measured by MOKE).
well-expressed dependence of the sin2 u type. Magnetic measurements on the inductive magnetometer allowed us to estimate the saturation magnetization of 4.7 105 A/m for the ferromagnetic layer synthesized with an implantation fluence of 3 1017 cm2. From Mossbauer spectroscopy data the filling factor was assumed to be equal g = 0.85 [8]. The volume saturation magnetization for stoichiometric compound Fe3Si is 9.7 105 A/m [9]. The difference can be explained by the deviation from stoichiometry towards the less iron concentration. Considering the anisotropy field Hk = 1100 A/m (see Fig. 7), the constant of the induced anisotropy equals to 330 J/m3. This value significantly exceeds those calculated earlier from autodyne curves. However, it is necessary to consider that the method of autodyne generator gives integral characteristics averaged over the sample. In the case of EMA deviations over the sample surface the method gives decreased values of anisotropy constants. In the samples the deviation of the EMA direction from that of the magnetic field Hi applied during implantation can be caused by several reasons. It can be due to the presence of mechanical stresses in a silicon substrate during the ion bombardment (Fe1xSix alloys have negative magnetostriction k 6 106 at x = 0.25 [10]), the appearance of temperature gradients, inhomogeneous sputtering and the appearance of small magnetic fields in the
Fig. 7. Normalized magnetization curves for Si implanted with 3 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m (MOKE). During measurements magnetic field was directed along the easy magnetization axis (blue) and the hard magnetization axis (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
chamber of the accelerator. It should be noted that mechanical stresses can be induced by clipping of samples and/or due to ionbeam irradiation. 4. Conclusion In summary, we carried out the detailed investigations of local magnetic characteristics of samples obtained by high-dose Fe+ implantation into single-crystal silicon at applied magnetic field. In some regions of the samples the deviations of EMA near the applied magnetic field were revealed by using a scanning magnetooptical Kerr polarimeter. These local changes can be caused by the presence of mechanical stresses in a silicon substrate during the ion bombardment, the appearance of temperature gradients, inhomogeneous sputtering and the appearance of small magnetic fields in the chamber of the accelerator. Acknowledgment The work was supported by the Grant of Presidium of RAS No. B60.
Fig. 6. Scanning Kerr polarimetry image of Fe-implanted Si. For each point of the surface the anisotropy direction is specified by the azimuthal dependence of the normalized remanence measured with an angle step of 9° and with a coordinate step of 1 mm. During the ion-beam synthesis the magnetic field Hi has been directed vertically. The gray rectangle in the left lower corner specifies the layout of the sample fixing to the holder.
G.G. Gumarov et al. / Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
References [1] K. Zhang, K.P. Lieb, P. Schaaf, M. Uhrmacher, W. Felsch, M. Munzenberg, Nucl. Instr. Meth. Phys. Res., Sec. B 161–163 (2000) 1016. [2] G.S. Chang, Y.P. Lee, J.Y. Rhee, J. Lee, K. Jeong, C.N. Whang, Phys. Rev. Lett. 87 (2001) 067208. [3] G.G. Gumarov, V.Yu. Petukhov, I.B. Khaibullin, E.P. Zheglov, E.N. Dulov, N.G. Ivoilov, Abstract Book of International Conf. on ‘‘Modern Development of Magnetic Resonance’’, August 15–20th, 2004, Kazan, Russia, p. 247. [4] R. Gupta, K.P. Lieb, G.A. Muller, P. Schaaf, K. Zhang, Hyperfine Interact. 160 (2005) 107–121.
111
[5] G.S. Chang, A. Moewes, S.H. Kim, J. Lee, K. Jeong, C.N. Whang, D.H. Kim, S.C. Shin, Appl. Phys. Lett. 88 (2006) 092504. [6] J. Fassbender, J. McCord, Appl. Phys. Lett. 88 (2006) 252501. [7] J. McCord, I. Monch, J. Fassbender, A. Gerber, E. Quandt, J. Phys. D: Appl. Phys. 42 (2009) 055006. [8] G.G. Gumarov, V.Yu. Petukhov, V.A. Zhikharev, V.F. Valeev, R.I. Khaibullin, Nucl. Instr. Meth. Phys. Res. B 267 (2009) 1600. [9] W.A. Hines, A.H. Menotti, J.I. Budnick, T.J. Burch, T. Litrenta, V. Niculescu, K. Raj, Phys. Rev. B 13 (1976) 4060. [10] L.K. Varga, F. Mazaleyrat, J. Kovac, J.M. Greneche, J. Phys.: Condens. Matter 14 (2002) 1985.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
MOKE investigation of silicide films ion-beam synthesized in single-crystal silicon G.G. Gumarov a,b,⇑, V.Yu. Petukhov a,b, A.I. Gumarov b, R.A. Khalikov a, D.A. Konovalov a, V.F. Valeev a, R.I. Khaibullin a,b a b
Zavoisky Physical-Technical Institute of RAS, Sibirsky tract 10/7, 420029 Kazan, Russia Kazan (Volga Region) Federal University, Kremlyovskaya St. 18, 420008 Kazan, Russia
a r t i c l e
i n f o
Article history: Available online 2 February 2011 Keywords: Ion implantation Magnetic nanoparticles MOKE
a b s t r a c t Magnetic-field-assisted ion-beam synthesis was used to produce thin magnetic films. Si wafers were implanted with 40 keV Fe+ ions with a fluence of 3 1017 cm2 in the external magnetic field of 9.6 104 A/m. The samples were investigated by scanning magneto-optical Kerr effect magnetometry, inductive magnetometry and reflection high-energy electron diffraction. The main synthesized phase was ferromagnetic Fe3Si. In some regions of the samples the deviations of the easy magnetic axis near the applied magnetic field were revealed. These local changes can be caused by various reasons: the presence of mechanical stresses in a silicon substrate during the ion bombardment, the appearance of temperature gradients, inhomogeneous sputtering and the appearance of small magnetic fields in the chamber of the accelerator. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The study of the induced magnetic anisotropy in ferromagnetic thin films is of significant importance both for fundamental science and for practical applications. Usually the uniaxial anisotropy in ferromagnetic alloys is induced by applying magnetic saturation fields during film deposition or by subsequent thermomagnetic treatment. Recently, the alteration of magnetic properties in magnetic thin films by ion irradiation in external magnetic field has gained increased attention [1–7]. This technique is especially useful as it also can be used to locally alter magnetic properties like saturation magnetization, magnetic anisotropy and etc. [7]. Earlier we used magnetic-field-assisted ion-beam synthesis to produce thin films of ferromagnetic silicide Fe3Si in single-crystal silicon substrates [8]. The samples were investigated by Mössbauer spectroscopy, X-ray diffraction and autodyne method. The obtained thin films consisted of ferromagnetic Fe3Si and a small amount of nonmagnetic FeSi phases. Other phases were not detected. It was shown that application of the magnetic field during the high-dose Fe ion implantation led to the pronounced in-plane magnetic anisotropy in the synthesized films. The observed anisotropy was a superposition of the magnetocrystalline anisotropy of cubic Fe3Si and induced uniaxial anisotropy. The observed angular ⇑ Corresponding author at: Zavoisky Physical-Technical Institute of RAS, Sibirsky tract 10/7, 420029 Kazan, Russia. Tel.: +7 843 272 12 41; fax: +7 843 272 50 75. E-mail addresses: [email protected] (G.G. Gumarov), [email protected] (V.Yu. Petukhov), [email protected] (A.I. Gumarov), [email protected] (R.A. Khalikov), [email protected] (D.A. Konovalov), [email protected] (V.F. Valeev), [email protected] (R.I. Khaibullin). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.01.043
dependence of in-plane magnetic susceptibility measured by autodyne method was described on the basis of the Stoner–Wohlfarth model. The general features of the calculated curves are in good agreement with the experiment but the obtained results should be averaged over the sizes and the orientations of different clusters in the films. The goal of the present work is to closely investigate the magnetic properties of thin silicide films ion-beam synthesized in single-crystal silicon in external magnetic field using the magneto-optical Kerr effect (MOKE). In addition, this method allows studying local magnetic in-plane characteristics.
2. Experimental 40 keV Fe ions were implanted into (1 1 1) single-crystal silicon wafers at room temperature. The implantation fluence was 3 1017 cm2, the ion current density being about 4 lA/cm2. The external magnetic field Hi of 9.6 104 A/m was applied parallel to the sample surface during implantation. Reflection high-energy electron diffraction (RHEED) was used for investigation of the phase composition and the texture of the synthesized films. The RHEED gun was operated at 75 kV primary voltage, the pattern was recorded at room temperature. The integral magnetic properties of the films were investigated using an induction magnetometer. A dependence of the magnitude of the induced magnetic moment on the value of the magnetic field applied in the sample plane was registered at the magnetic field sweep up to 500 mT. While processing the results of magnetic
G.G. Gumarov et al. / Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
109
measurements, a diamagnetic contribution from the silicon substrate was subtracted. The local magnetic properties of samples were investigated by scanning Kerr polarimeter in the longitudinal mode. The measuring part of the polarimeter is constructed on the basis of an optical PCSA-ellipsometer LEF-3M-1 and has a computer-controlled goniometer for obtaining the azimuthal dependences. For investigation of local magnetic characteristics the polarimeter was equipped with an automated system for the sample movement relative to the probing laser beam and with a focusing system. Within the frames of the present research, a laser spot on the sample surface with a diameter of about 200 lm at the beam incidence angle of 45° was used.
3. Results and discussion Fig. 1 show the RHEED pattern obtained for Si implanted with Fe+ ions with a fluence of 3 1017 cm2. The pattern consists of diffraction rings which are typical for polycrystalline films. Small thickenings (brighter areas) are observed on the diffraction rings pointing to a weak texture. Identification of the diffraction rings represented in Fig. 1 has shown that the reflexes correspond to polycrystalline silicide a0 -Fe3Si. It agrees with the results of the phase analysis obtained earlier by methods of grazing angle Xray diffraction and Mossbauer spectroscopy of conversion electrons [8]. From magnetic measurements it has been revealed that all samples synthesized at specified regimes of implantation are ferromagnetic at room temperature. The control samples implanted in the absence of the magnetic field are isotropic (Figs. 3 and 4). Azimuthal dependences of the remanence measured both with inductive magnetometer (Fig. 2 and MOKE (Fig. 5) showed that all samples implanted in the applied magnetic field possess uniaxial anisotropy. However, directions of the easy magnetization axis (EMA) in various sections of the sample surface differ. For some regions the EMA direction does not coincide with that of the magnetic field applied during implantation. More detailed information about EMA directions on the surface was obtained by a scanning MOKE method. The greatest deviation of the EMA direction is observed in the regions closest to the sample clips (Fig. 6). The rectangular hysteresis loop and anhysteretic magnetization curve are observed in the easy and the hard magnetization axes, respectively (Fig. 7). Since the thickness of the synthesized layer does not exceed 50 nm we consider that particles in the synthesized layer are one-domain.
Fig. 2. Polar plot of the Jr/Ji ratio measured by a inductive magnetometer for 2.5 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m. Jr – remanent magnetic moment, Ji – induced magnetic moment.
Fig. 3. Polar plot of the Mr/Ms ratio measured by MOKE for Si implanted with 3 1017Jr Fe+/cm2 without magnetic field.
Fig. 4. Normalized hysteresis loop of Si implanted with 3 1017 Fe+/cm2 without applied magnetic field (MOKE). The loop shape remains unchanged for various azimuthal directions.
Fig. 1. RHEED pattern of Si implanted with 2.5 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m.
Azimuthal dependence of the normalized remanence in all regions of the surface is typical for uniaxial anisotropy – it has
110
G.G. Gumarov et al. / Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
Fig. 5. Polar plot of the Mr/Ms ratio for Si implanted with 3 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m measured by MOKE).
well-expressed dependence of the sin2 u type. Magnetic measurements on the inductive magnetometer allowed us to estimate the saturation magnetization of 4.7 105 A/m for the ferromagnetic layer synthesized with an implantation fluence of 3 1017 cm2. From Mossbauer spectroscopy data the filling factor was assumed to be equal g = 0.85 [8]. The volume saturation magnetization for stoichiometric compound Fe3Si is 9.7 105 A/m [9]. The difference can be explained by the deviation from stoichiometry towards the less iron concentration. Considering the anisotropy field Hk = 1100 A/m (see Fig. 7), the constant of the induced anisotropy equals to 330 J/m3. This value significantly exceeds those calculated earlier from autodyne curves. However, it is necessary to consider that the method of autodyne generator gives integral characteristics averaged over the sample. In the case of EMA deviations over the sample surface the method gives decreased values of anisotropy constants. In the samples the deviation of the EMA direction from that of the magnetic field Hi applied during implantation can be caused by several reasons. It can be due to the presence of mechanical stresses in a silicon substrate during the ion bombardment (Fe1xSix alloys have negative magnetostriction k 6 106 at x = 0.25 [10]), the appearance of temperature gradients, inhomogeneous sputtering and the appearance of small magnetic fields in the
Fig. 7. Normalized magnetization curves for Si implanted with 3 1017 Fe+/cm2 in applied magnetic field Hi = 9.6 104 A/m (MOKE). During measurements magnetic field was directed along the easy magnetization axis (blue) and the hard magnetization axis (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
chamber of the accelerator. It should be noted that mechanical stresses can be induced by clipping of samples and/or due to ionbeam irradiation. 4. Conclusion In summary, we carried out the detailed investigations of local magnetic characteristics of samples obtained by high-dose Fe+ implantation into single-crystal silicon at applied magnetic field. In some regions of the samples the deviations of EMA near the applied magnetic field were revealed by using a scanning magnetooptical Kerr polarimeter. These local changes can be caused by the presence of mechanical stresses in a silicon substrate during the ion bombardment, the appearance of temperature gradients, inhomogeneous sputtering and the appearance of small magnetic fields in the chamber of the accelerator. Acknowledgment The work was supported by the Grant of Presidium of RAS No. B60.
Fig. 6. Scanning Kerr polarimetry image of Fe-implanted Si. For each point of the surface the anisotropy direction is specified by the azimuthal dependence of the normalized remanence measured with an angle step of 9° and with a coordinate step of 1 mm. During the ion-beam synthesis the magnetic field Hi has been directed vertically. The gray rectangle in the left lower corner specifies the layout of the sample fixing to the holder.
G.G. Gumarov et al. / Nuclear Instruments and Methods in Physics Research B 272 (2012) 108–111
References [1] K. Zhang, K.P. Lieb, P. Schaaf, M. Uhrmacher, W. Felsch, M. Munzenberg, Nucl. Instr. Meth. Phys. Res., Sec. B 161–163 (2000) 1016. [2] G.S. Chang, Y.P. Lee, J.Y. Rhee, J. Lee, K. Jeong, C.N. Whang, Phys. Rev. Lett. 87 (2001) 067208. [3] G.G. Gumarov, V.Yu. Petukhov, I.B. Khaibullin, E.P. Zheglov, E.N. Dulov, N.G. Ivoilov, Abstract Book of International Conf. on ‘‘Modern Development of Magnetic Resonance’’, August 15–20th, 2004, Kazan, Russia, p. 247. [4] R. Gupta, K.P. Lieb, G.A. Muller, P. Schaaf, K. Zhang, Hyperfine Interact. 160 (2005) 107–121.
111
[5] G.S. Chang, A. Moewes, S.H. Kim, J. Lee, K. Jeong, C.N. Whang, D.H. Kim, S.C. Shin, Appl. Phys. Lett. 88 (2006) 092504. [6] J. Fassbender, J. McCord, Appl. Phys. Lett. 88 (2006) 252501. [7] J. McCord, I. Monch, J. Fassbender, A. Gerber, E. Quandt, J. Phys. D: Appl. Phys. 42 (2009) 055006. [8] G.G. Gumarov, V.Yu. Petukhov, V.A. Zhikharev, V.F. Valeev, R.I. Khaibullin, Nucl. Instr. Meth. Phys. Res. B 267 (2009) 1600. [9] W.A. Hines, A.H. Menotti, J.I. Budnick, T.J. Burch, T. Litrenta, V. Niculescu, K. Raj, Phys. Rev. B 13 (1976) 4060. [10] L.K. Varga, F. Mazaleyrat, J. Kovac, J.M. Greneche, J. Phys.: Condens. Matter 14 (2002) 1985.