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Distance between vortices in a thin YBa2Cu3O7 film in parallel magnetic field
ARTICLE IN PRESS
Physica B 350 (2004) e331–e334
Distance between vortices in a thin YBa2Cu3O7 film in parallel magnetic field H. Lautera, V. Lauter-Pasyuka,b,c, M. Jernenkova,c,*, M. Meschked, A. Petrenkoc, M. Lorenze, V. Aksenovc a
Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France b Physik Department, TU Munchen, D-85747 Garching, Germany . c Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia d CRTBT/CNRS, F-38042 Grenoble, France e Universitat . Leipzig, D-04103 Leipzig, Germany
Abstract A direct measurement of the distance between the vortices was performed by neutron surface diffraction. The vortices were created by an external magnetic field Hext parallel to the surface of a thin YBa2Cu3O7 film. The behavior of the equilibrium vortex configurations in increasing Hext beyond the first critical field was studied. The distances between vortices within the vortex rows parallel to the sample surface were deduced from the positions of the Bragg-peaks measured in grazing incidence configuration GID for Hext ¼ 1:0 and 1.5 T. The obtained values of the distance of 445 ( respectively, belong to the equilibrium configurations with four and five vortex rows perpendicular to the and 480 A, film surface. r 2004 Elsevier B.V. All rights reserved. PACS: 61.12.Ha; 74.25.Qt; 74.78.Bz Keywords: HTc thin films; Vortex row transition; Grazing incidence diffraction
In superconducting films, the vortex row transition in increasing external magnetic field oriented parallel to the film surface is a new feature with respect to the behavior in bulk [1]. In our earlier measurements, the location of the vortex rows inside the HTc film was determined and the event of the penetration of new vortex rows was *Corresponding author. Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France. Fax: +33-4-76-20-71-20. E-mail addresses: [email protected], [email protected] (M. Jernenkov).
observed using polarized neutron reflectometry [2]. In the present work, we report on the first direct experimental determination of the distance between the vortices within vortex rows inside a thin HTc film and parallel to its surface. A special scattering technique is required in order to get enough scattered intensity from the vortex lines, which are parallel to the film surface and within the penetration depth of the magnetic field. In a normal diffraction experiment, the intensity is determined by the volume of the sample, which is in the case of our HTc film
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.081
ARTICLE IN PRESS e332
H. Lauter et al. / Physica B 350 (2004) e331–e334
the product of film surface and film thickness=20 20 2 104 mm3=8 102 mm3. It is not possible to get a measurable signal from such a small sample. However, the footprint of the sample replaces the film thickness in scattering under grazing incidence. This is due to the evanescent wave traveling along the surface under total reflection. The effect is biggest at the critical angle ac : ac is 19.2 mrad for the YBa2Cu3O7 film at ( yielding a footprint of a wavelength of 10 A 0.38 mm. Thus, the effective thickness increases by a factor B2000 and the effective volume of the sample increases to 160 mm3 being still a small volume, but a signal from the vortices can be obtained as will be shown. This study has been carried out on the small angle instrument D11 at ILL, Grenoble. ( thick YBa2Cu3O7 film The sample, a 2500 A (c-oriented), was cooled to a temperature of 4 K in zero-field. The scheme of the experiment is
Fig. 1. A schematic presentation of the experiment. Dashed lines—vortices inside the sample. a and a0 —the incoming and outgoing angle of the neutron beam, f—the angle to turn the sample around the normal to its surface. 1—specular reflected beam, 2—beam diffracted from the vortex lattice under specular reflection at the critical angle ac ; H—external magnetic field. The inset shows the evolution of the number and configuration of the vortex rows with nv the number vortices rows and av the distance between the vortices [1].
presented in Fig. 1. The sample was slightly turned (f ¼ 1:1 ) around its surface normal to maximize the scattered intensity from the vortex line array. The exact scattering angle giving the distance between the points 1 and 2 in Fig. 1 is determined as described in the following. The two-dimensional (2D) detector images for Hext ¼ 0 G and 10 kG are presented in Fig. 2. The direct beam is found in the center of the detector being blocked by a beam stop. The spot to the left in z-direction is the reflected beam for a ¼ ac : The continued intensity in z-direction is Yoneda
Fig. 2. 2D map of the intensity for Hext ¼ 10 kG (top) and for Hext ¼ 0 kG (bottom). The coordinates are pixel numbers. The pixel size is 1 cm in y- as well as in z-direction. The white-dashed lines denote the positions between which the intensity has been summed up for the presentation in Fig. 3. The log-gray scale in both figures is the same, but the statistics is lower in the bottom one.
ARTICLE IN PRESS H. Lauter et al. / Physica B 350 (2004) e331–e334
scattering from roughness of the interfaces visible at 0 field as well as at 10 kG. It is of no direct interest for this study. The weak intensity in y-direction above the intensity at ac (marked by the dotted lines in Fig. 2 or the spot 2 in Fig. 1) is the wanted diffraction from the vortex lines. However, this intensity is also detected at zerofield but with lower intensity. In order to explain this feature, one has to first look to the intensity
e333
found above the direct beam in y-direction. This bright spot moves in y-direction as a function of f (see Fig. 1) and coincides with the direct beam at f ¼ 0: So, it is the diffraction from a Bragg-rod of the YBa2Cu3O7 film through the ð0; 0; 0Þ Braggpeak. Also this scattering is of no direct interest in this study; however, it appears being scattered with ac at the same position between the dotted lines in Fig. 2 as the diffracted intensity from the vortex array. So, this extra intensity found directly at zero-field has to be subtracted from the scattered intensity obtained at higher external fields in order to get the diffracted intensity from the vortex array alone. In order to obtain the peak diffracted from the vortex lattice, the collected intensities between the dotted lines in Fig. 2 along y-direction were taken and smoothened by an FFT filter. After that procedure the spectrum obtained at zero-field was subtracted from the spectra obtained with external field. The results for two values of the external magnetic field of 10 and 15 kG are presented in Table 1 Distances between vortices within a vortex row
Fig. 3. Results of the subtraction procedure. Black dots—the intensity of the spectra as a function of the Y-detector pixel number added between the dotted lines in Fig. 2 in the presence of a magnetic field, curve through the black dots—FFT smoothing, curve underneath—FFT smoothing of the added intensity of the spectra but without magnetic field. Lowest curve is the result of subtraction of the two top curves. (a) Hext ¼ 10 kG and (b) Hext ¼ 15 kG. The detector counts (i.e. the intensity) are presented in a normalized scale within (a) and (b).
Hext (kG)
( av (A)
( Dav (A)
10 15
445 480
35 40
Fig. 4. Distances between vortices within a vortex row [1] for ( l ¼ 1400 A, ( Hc1 ¼ 1:2 kG. the film of thickness of D ¼ 2500 A, Squares—obtained distances av with error bars for Hext ¼ 10 and 15 kG.
ARTICLE IN PRESS e334
H. Lauter et al. / Physica B 350 (2004) e331–e334
Fig. 3. For the other two values of Hext at which spectra were taken, namely 5 and 7 kG, the resulting peaks lie within the error bars and could not be evaluated. The distance between vortices within a vortex row was calculated from the positions of the obtained diffraction peaks (first- and second-order Bragg-peaks) using Bragg’s equation. The calculated distances between vortices and the error bars are presented in Table 1. In agreement with theoretical calculations [1], the obtained distances between vortices correspond to the equilibrium configurations, which contain nv ¼ 4 and 5 vortex rows for Hext ¼ 10 and 15 kG,
respectively (see inset in Fig. 1). This result is visualized in Fig. 4. It is evident that the relaxed distance between the vortices at a higher field, a fact, which seems to be a contradiction, finds its origin in the appearance of an extra flux line row and thus a relaxed vortex density within a vortex row.
References [1] G. Carneiro, Phys. Rev. B 57 (1998) 6077. [2] V. Lauter-Pasyuk, H. Lauter, M. Lorenz, V.L. Aksenov, P. Leiderer, Physica B 267–243 (1999) 149.
Physica B 350 (2004) e331–e334
Distance between vortices in a thin YBa2Cu3O7 film in parallel magnetic field H. Lautera, V. Lauter-Pasyuka,b,c, M. Jernenkova,c,*, M. Meschked, A. Petrenkoc, M. Lorenze, V. Aksenovc a
Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France b Physik Department, TU Munchen, D-85747 Garching, Germany . c Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia d CRTBT/CNRS, F-38042 Grenoble, France e Universitat . Leipzig, D-04103 Leipzig, Germany
Abstract A direct measurement of the distance between the vortices was performed by neutron surface diffraction. The vortices were created by an external magnetic field Hext parallel to the surface of a thin YBa2Cu3O7 film. The behavior of the equilibrium vortex configurations in increasing Hext beyond the first critical field was studied. The distances between vortices within the vortex rows parallel to the sample surface were deduced from the positions of the Bragg-peaks measured in grazing incidence configuration GID for Hext ¼ 1:0 and 1.5 T. The obtained values of the distance of 445 ( respectively, belong to the equilibrium configurations with four and five vortex rows perpendicular to the and 480 A, film surface. r 2004 Elsevier B.V. All rights reserved. PACS: 61.12.Ha; 74.25.Qt; 74.78.Bz Keywords: HTc thin films; Vortex row transition; Grazing incidence diffraction
In superconducting films, the vortex row transition in increasing external magnetic field oriented parallel to the film surface is a new feature with respect to the behavior in bulk [1]. In our earlier measurements, the location of the vortex rows inside the HTc film was determined and the event of the penetration of new vortex rows was *Corresponding author. Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France. Fax: +33-4-76-20-71-20. E-mail addresses: [email protected], [email protected] (M. Jernenkov).
observed using polarized neutron reflectometry [2]. In the present work, we report on the first direct experimental determination of the distance between the vortices within vortex rows inside a thin HTc film and parallel to its surface. A special scattering technique is required in order to get enough scattered intensity from the vortex lines, which are parallel to the film surface and within the penetration depth of the magnetic field. In a normal diffraction experiment, the intensity is determined by the volume of the sample, which is in the case of our HTc film
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.081
ARTICLE IN PRESS e332
H. Lauter et al. / Physica B 350 (2004) e331–e334
the product of film surface and film thickness=20 20 2 104 mm3=8 102 mm3. It is not possible to get a measurable signal from such a small sample. However, the footprint of the sample replaces the film thickness in scattering under grazing incidence. This is due to the evanescent wave traveling along the surface under total reflection. The effect is biggest at the critical angle ac : ac is 19.2 mrad for the YBa2Cu3O7 film at ( yielding a footprint of a wavelength of 10 A 0.38 mm. Thus, the effective thickness increases by a factor B2000 and the effective volume of the sample increases to 160 mm3 being still a small volume, but a signal from the vortices can be obtained as will be shown. This study has been carried out on the small angle instrument D11 at ILL, Grenoble. ( thick YBa2Cu3O7 film The sample, a 2500 A (c-oriented), was cooled to a temperature of 4 K in zero-field. The scheme of the experiment is
Fig. 1. A schematic presentation of the experiment. Dashed lines—vortices inside the sample. a and a0 —the incoming and outgoing angle of the neutron beam, f—the angle to turn the sample around the normal to its surface. 1—specular reflected beam, 2—beam diffracted from the vortex lattice under specular reflection at the critical angle ac ; H—external magnetic field. The inset shows the evolution of the number and configuration of the vortex rows with nv the number vortices rows and av the distance between the vortices [1].
presented in Fig. 1. The sample was slightly turned (f ¼ 1:1 ) around its surface normal to maximize the scattered intensity from the vortex line array. The exact scattering angle giving the distance between the points 1 and 2 in Fig. 1 is determined as described in the following. The two-dimensional (2D) detector images for Hext ¼ 0 G and 10 kG are presented in Fig. 2. The direct beam is found in the center of the detector being blocked by a beam stop. The spot to the left in z-direction is the reflected beam for a ¼ ac : The continued intensity in z-direction is Yoneda
Fig. 2. 2D map of the intensity for Hext ¼ 10 kG (top) and for Hext ¼ 0 kG (bottom). The coordinates are pixel numbers. The pixel size is 1 cm in y- as well as in z-direction. The white-dashed lines denote the positions between which the intensity has been summed up for the presentation in Fig. 3. The log-gray scale in both figures is the same, but the statistics is lower in the bottom one.
ARTICLE IN PRESS H. Lauter et al. / Physica B 350 (2004) e331–e334
scattering from roughness of the interfaces visible at 0 field as well as at 10 kG. It is of no direct interest for this study. The weak intensity in y-direction above the intensity at ac (marked by the dotted lines in Fig. 2 or the spot 2 in Fig. 1) is the wanted diffraction from the vortex lines. However, this intensity is also detected at zerofield but with lower intensity. In order to explain this feature, one has to first look to the intensity
e333
found above the direct beam in y-direction. This bright spot moves in y-direction as a function of f (see Fig. 1) and coincides with the direct beam at f ¼ 0: So, it is the diffraction from a Bragg-rod of the YBa2Cu3O7 film through the ð0; 0; 0Þ Braggpeak. Also this scattering is of no direct interest in this study; however, it appears being scattered with ac at the same position between the dotted lines in Fig. 2 as the diffracted intensity from the vortex array. So, this extra intensity found directly at zero-field has to be subtracted from the scattered intensity obtained at higher external fields in order to get the diffracted intensity from the vortex array alone. In order to obtain the peak diffracted from the vortex lattice, the collected intensities between the dotted lines in Fig. 2 along y-direction were taken and smoothened by an FFT filter. After that procedure the spectrum obtained at zero-field was subtracted from the spectra obtained with external field. The results for two values of the external magnetic field of 10 and 15 kG are presented in Table 1 Distances between vortices within a vortex row
Fig. 3. Results of the subtraction procedure. Black dots—the intensity of the spectra as a function of the Y-detector pixel number added between the dotted lines in Fig. 2 in the presence of a magnetic field, curve through the black dots—FFT smoothing, curve underneath—FFT smoothing of the added intensity of the spectra but without magnetic field. Lowest curve is the result of subtraction of the two top curves. (a) Hext ¼ 10 kG and (b) Hext ¼ 15 kG. The detector counts (i.e. the intensity) are presented in a normalized scale within (a) and (b).
Hext (kG)
( av (A)
( Dav (A)
10 15
445 480
35 40
Fig. 4. Distances between vortices within a vortex row [1] for ( l ¼ 1400 A, ( Hc1 ¼ 1:2 kG. the film of thickness of D ¼ 2500 A, Squares—obtained distances av with error bars for Hext ¼ 10 and 15 kG.
ARTICLE IN PRESS e334
H. Lauter et al. / Physica B 350 (2004) e331–e334
Fig. 3. For the other two values of Hext at which spectra were taken, namely 5 and 7 kG, the resulting peaks lie within the error bars and could not be evaluated. The distance between vortices within a vortex row was calculated from the positions of the obtained diffraction peaks (first- and second-order Bragg-peaks) using Bragg’s equation. The calculated distances between vortices and the error bars are presented in Table 1. In agreement with theoretical calculations [1], the obtained distances between vortices correspond to the equilibrium configurations, which contain nv ¼ 4 and 5 vortex rows for Hext ¼ 10 and 15 kG,
respectively (see inset in Fig. 1). This result is visualized in Fig. 4. It is evident that the relaxed distance between the vortices at a higher field, a fact, which seems to be a contradiction, finds its origin in the appearance of an extra flux line row and thus a relaxed vortex density within a vortex row.
References [1] G. Carneiro, Phys. Rev. B 57 (1998) 6077. [2] V. Lauter-Pasyuk, H. Lauter, M. Lorenz, V.L. Aksenov, P. Leiderer, Physica B 267–243 (1999) 149.