Abstract: A high-resolution magneto-optical imaging system is de-scribed. In this system magneto-optical Kerr effect is utilized for resolvingindividual flux quanta in a type II superconductor. Using an ultra thin EuSeindicator a spatial resolution of 0.8μm is achieved.
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single vortex observation,” Rev. Sci. Instrum. 74, 141–146 (2003).10. G. Carneiro and E. H. Brandt, ”Vortex lines in films: Fields and interactions,” Phys. Rev. B 61, 6370–6376
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tool for studying optically induced magnetization reversals,” Opt. Lett. 33, 2734–2736 (2008).13. J. Schoenes and P. Wachter, ”Magnetooptic Spectroscopy of EuS, EuSe, and EuTe,” Trans. Magnetic 12, 81–85
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18. T. H. Johansen, M. Baziljevich, D. V. Shantsev, P. E. Goa, Y. M. Gal pe rin, W. N. Kang, H. J. Kim, E. M. Choi,M.-S. Kim and S. I. Lee, ”Dendritic magnetic instability in superconducting MgB2 films,” Europhys. Lett. 59,599–606 (2002)
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1. Introduction
Imaging magnetic fields on surfaces is of great importance both in basic science and technology(e.g. magnetic memories, spintronics). It is of particular interest in type II superconductors,where the magnetic field forms isolated vortices, each carrying a quantum of magnetic fluxΦ0 = 2.07× 10−15Wb confined within an area of radius λ , typically ∼ 100 nm. Magneticimaging methods capable of imaging a single vortex include Electron microscopy [1], Bitterdecoration [2], scanning SQUID microscope [3], Magnetic Force Microscopy [4], and HallProbe Microscopy [5]. Some techniques ([1, 4]) have superior spatial and magnetic resolution,with an ability to investigate the internal structure of the vortex. However, high resolution comesat the expense of speed and the maximal area one could image. Magneto-optical imaging (MOI)on the other hand is typically used for rapid imaging of relatively large areas with a lowerresolution [6]. For a review of the different techniques, see [7, 8]. The field of view variesfrom few millimeters at low magnification down to ∼ 100× 100μm2 at maximal resolution.Relatively short measurement times permit investigation of the dynamics of vortex arrays at lowfields and allow collection of large amounts of data for statistical analysis. However, resolvingindividual vortices with magneto-optics is a challenge met so far only by one group[9]. In thefollowing, we present the design and performance of an MOI system with the best resolutionachieved so far.
2. Experimental system
The signal which we want to detect is a modulation of the magnetic field at the surface ofsuperconductor. Caneiro and Brandt [10] have shown that the magnetic field generated by avortex decays rapidly with the distance from the surface on a submicron scale and so the MOindicator should be as close to the surface as possible. When linearly polarized light is trans-mitted through the magneto-optical (MO) material of thickness d, the polarization rotation iscalled the Faraday effect and is proportional to Bd. Polarization rotation due to reflection fromthe surface of a MO material is known as the magneto-optic Kerr effect. Recent applicationsof the Kerr effect are discussed by [11, 12]. In the case of vortices in superconductor, wherethe magnetic field decays very close to the surface, having a thick MO indicator is of no use.Therefore, we chose a different approach. Our MO system is based on the utilization of the MOKerr effect in Europium Selenide. This material has a huge magneto-optical response in thetemperature range 4-20 Kelvin [13], in a narrow band of wavelengths. In addition EuSe, beingparamagnetic, does not introduce any stray magnetic field into the sample. The limitations ofthis sensor are its limited temperature range and the fact it has a high absorbtion coefficient,which means that the maximum useful thickness is 250nm, which means limited MO signal.Our experiment is designed to get around these problems. To bring the MO indicator as close aspossible to the surface of the sample, we directly evaporate a 40nm film of EuSe on top of thesuperconducting film. In the case of the Kerr effect, the angle of rotation θB is linearly propor-tional to the magnetic field, θB = κB. For 40nm thick EuSe in use κ = 0.02o/mT . The effectproduced by 40nm thick EuSe is of the same magnitude as an effect produced by indicator250nm thick utilized in previous experiments [14, 15]. The superconductor used in this work is200nm thick Nb film, capped by 50 nm of Al. Our Nb films are prepared using DC-Magnetronsputtering [16], and have a critical temperature Tc = 8.9±0.1K. The average roughness at the
#113340 - $15.00 USD Received 26 Jun 2009; revised 10 Aug 2009; accepted 17 Aug 2009; published 26 Aug 2009
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surface of the sample is 2nm.Figure 1 shows a sketch of our setup. The sample stage is focused under the microscope
objective using a XYZ manipulator. To allow this manipulation, the sample stage is connectedby a flexible thermal link to a cold finger cooled by a liquid helium cryostat. In order to reducevibrations, we use a static helium bath instead of a flow cryostat. The pump which evacuatesthe vacuum chamber is disconnected during measurements. The entire system is positioned ona floating optical table. By superimposing images we can detect motion of the sample as smallas 0.1μm. In this way we detect a steady drift of the sample due to the thermal expansion of theliquid helium container. We did not find any rapid vibrations. Evaporation of the liquid heliumchanges the temperature profile along the wall of the container and leads to expansion of thecontainer which is rigidly attached to the cold finger. This drift has an average rate of 1μm/minperpendicularly to the optical axis, and it is slow enough to be corrected using image trackingmethods. The objective of the microscope is mounted inside the vacuum chamber and thereforethe vacuum window is not in a converging part of the beam. The vacuum window itself is tiltedby a small angle to avoid reflections. To illuminate the sample we use a monochromatic lightbeam (548nm) from a Mercury-100W lamp. The light intensity is detected by a HamamatzuPeltier cooled CCD camera. Magnetic fields up to 4mT can be applied using a solenoid wound
#113340 - $15.00 USD Received 26 Jun 2009; revised 10 Aug 2009; accepted 17 Aug 2009; published 26 Aug 2009
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around the objective. The sample region is shielded by multiple layers of μ-metal in order toreduce the magnetic field of the earth. The residual magnetic field on the sample is lower than5μT . In order to increase the signal to noise ratio,we typically average images over one minute.Direct averaging is not possible due to constant drift of the sample mentioned before. In orderto compensate for the drift we record images every 0.3sec. A computer program tracks the driftof the sample using markers on the sample itself. Image averaging is done only after drift com-pensation. The signal produced by asingle vortex is about 1×10−2 of the background intensity.Therefore background subtraction is essential. Background image is taken at same tempera-ture at zero magnetic field. To minimize the drift, the time interval between background andmeasurement images was kept as short as possible. In our case, good background subtractionwas achieved with a time interval of a few minutes. In a superconductor the magnetic field isuniform only if the sample is cooled under an external field. In order to avoid spurious magneticfield resulting from electrical heating we use IR light to heat up our sample and then allow it tocool with the field on.
The light reflected from the sample passes through a second polarizer oriented at an angleπ/2−φ relative to the original polarization. Maximal contrast is achieved when φ =
√e, where
e is extinction ratio, namely the ratio of the residual intensity of light measured with the polar-izers crossed to the maximum intensity. The contrast in this case is C = θB/
√e. The extinction
ratio of the system at room temperature is e = 4×10−3. When the sample is cooled down theobjective is exposed to the low temperature environment and cools by thermal radiation. As aresult, thermal strains of the lens degrade the extinction ratio to e = 1× 10−2. In this case theangle between polarizers should be φ � 5o. Experimentally the contrast doesn’t change signif-icantly in the range φ = 3−10o. The intensity on the other hand is proportional to φ2. In orderto increase the signal to noise ratio as much as possible we used φ = 10o.
In our system, at the maximal magnification (×50 objective), each pixel of the image coversan area of 0.12×0.12μm2 of the sample. The total field of view is 110×160μm2.
3. Results and discussion
An image of a superconductor cooled at two different external magnetic fields shown in Figure2. The brightness is proportional to the local magnetic field. Each spot represents a singlevortex. This figure vividly illustrates the power of the MOI technique where enough individualvortices can be seen to permit the determination of spatial correlations, long and short rangeorder, etc. At Figure 2.b some of the vortices are 1μm apart, approaching our spatial resolutionlimit, but still can be resolved.
Within the small thickness of MO indicator the magnetic field of a single vortex is localizedinside an area much smaller than our optical resolution.
Therefore the image of individual vortex can be approximated by an optical pointspread Airyfunction [17] I ∼ (J1(kx)/kx)2, where J1 is a first order Bessel function of the first kind. Figure3 shows the intensity profile produced by an individual vortex. The intensity is fitted with anAiry function with k = 4.4μm−1. Using the Rayleigh criterion, our MO spatial resolution is0.8μm, which is much better than 1.3μm reported by [9]. Note that the spatial resolution islimited by optical diffraction.
Another example of the power of this technique can be seen in figure 4. Here we show theedge of a dendrite-like formation of a magnetic flux inside the superconductor. Dendrite-likeformations are observed at temperatures well below Tc, where magnetic flux penetrates into thesample via a thermo-magnetic instability [18]. This phenomenon was extensively investigatedusing conventional magneto-optics (see [19]). In this case, we see a magnetic structure with ahigh density of positive flux (bright region) penetrates into a sample having an initially uniformdistributed negative magnetic flux (dark region). With our high resolution, individual vortices
#113340 - $15.00 USD Received 26 Jun 2009; revised 10 Aug 2009; accepted 17 Aug 2009; published 26 Aug 2009
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Fig. 2. MO images of superconducting Nb film under external magnetic fields. The field is:(a) 0.4mT , (b) 1.2mT . The scale bar represents 5μm. Each bright spot represents a singlevortex. At these low fields, the positions of individual vortices are determined by localdisorder rather then by vortex-vortex interaction.
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Fig. 3. Intensity profile across a single vortex. The line is a fit to an Airy function.
#113340 - $15.00 USD Received 26 Jun 2009; revised 10 Aug 2009; accepted 17 Aug 2009; published 26 Aug 2009
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Fig. 4. Edge of a dendrite-like magnetic structure pinned in a superconductor. To producethis structure, the superconductor was first cooled through Tc in the presence of a magneticfield (−4mT ) and then the field was reduced to zero. The inset shows a low resolutionimage of a similar structure. The scale bar in the inset represents 100μm.
can be distinguished at the front edge of this structure. Notice that flux lines of different po-larities (bright and dark spots) are separated by an annihilation zone where the density of thevortices is low. Such images allow us to study annihilation dynamics.
4. Conclusion
In conclusion, we have developed a high resolution MO imaging system which can be usedfor studies of vortex arrays on spatial scales ranging from single flux quanta up to structurescontaining thousands of vortices. Work is already underway to study out of equilibrium vortexformation and spatial correlation of the emerging vortex arrays.
Acknowledgments
We thank E. Buks for sharing with us his Nb film deposition system. We thank S. Hoida, L.Iomin and O. Shtempluk for technical assistance. This work was supported by Israel ScienceFoundation and by the Technion Fund for Research.
#113340 - $15.00 USD Received 26 Jun 2009; revised 10 Aug 2009; accepted 17 Aug 2009; published 26 Aug 2009
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