Abstract

A high-resolution magneto-optical imaging system is described. In this system magneto-optical Kerr effect is utilized for resolving individual flux quanta in a type II superconductor. Using an ultra thin EuSe indicator a spatial resolution of 0.8µm is achieved.

© 2009 Optical Society of America

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 flux Φ0=2.07×10-15 Wb confined within an area of radius λ, typically ~100 nm. Magnetic imaging methods capable of imaging a single vortex include Electron microscopy [1], Bitter decoration [2], scanning SQUID microscope [3], Magnetic Force Microscopy [4], and Hall Probe 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 comes at 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 lower resolution [6]. For a review of the different techniques, see [7, 8]. The field of view varies from few millimeters at low magnification down to ~100×100µm 2 at maximal resolution. Relatively short measurement times permit investigation of the dynamics of vortex arrays at low fields and allow collection of large amounts of data for statistical analysis. However, resolving individual vortices with magneto-optics is a challenge met so far only by one group[9]. In the following, we present the design and performance of an MOI system with the best resolution achieved so far.

2. Experimental system

The signal which we want to detect is a modulation of the magnetic field at the surface of superconductor. Caneiro and Brandt [10] have shown that the magnetic field generated by a vortex decays rapidly with the distance from the surface on a submicron scale and so the MO indicator should be as close to the surface as possible. When linearly polarized light is transmitted through the magneto-optical (MO) material of thickness d, the polarization rotation is called the Faraday effect and is proportional to Bd. Polarization rotation due to reflection from the surface of a MO material is known as the magneto-optic Kerr effect. Recent applications of the Kerr effect are discussed by [11, 12]. In the case of vortices in superconductor, where the 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 MO Kerr effect in Europium Selenide. This material has a huge magneto-optical response in the temperature range 4–20 Kelvin [13], in a narrow band of wavelengths. In addition EuSe, being paramagnetic, does not introduce any stray magnetic field into the sample. The limitations of this 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 as possible to the surface of the sample, we directly evaporate a 40nm film of EuSe on top of the superconducting film. In the case of the Kerr effect, the angle of rotation θB is linearly proportional to the magnetic field, θB=κB. For 40nm thick EuSe in use κ=0.02°/mT. The effect produced by 40nm thick EuSe is of the same magnitude as an effect produced by indicator 250nm thick utilized in previous experiments [14, 15]. The superconductor used in this work is 200nm thick Nb film, capped by 50 nm of Al. Our Nb films are prepared using DC-Magnetron sputtering [16], and have a critical temperature Tc=8.9±0.1K. The average roughness at the surface of the sample is 2nm.

 

Fig. 1. Schematic sketch of the experimental system: (1) Hg 100W light source, (2) Interference filters, (3) Polarizer (extinction ratio 1:10000), (4)Analyzer (extinction ratio 1:10000), (5) Non polarizing beam splitter, (6) Objective, (7)Vacuum windows, (8) Sample holder, (9) Flexible thermal connection, (10) CCD camera, (11) Cold finger, (12) Liquid Helium bath, (13) Vacuum chamber, (14) XYZ manipulator, (15) Manipulator to sample holder coupling, (16) Optical fiber.

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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 connected by a flexible thermal link to a cold finger cooled by a liquid helium cryostat. In order to reduce vibrations, we use a static helium bath instead of a flow cryostat. The pump which evacuates the vacuum chamber is disconnected during measurements. The entire system is positioned on a floating optical table. By superimposing images we can detect motion of the sample as small as 0.1µm. In this way we detect a steady drift of the sample due to the thermal expansion of the liquid helium container. We did not find any rapid vibrations. Evaporation of the liquid helium changes the temperature profile along the wall of the container and leads to expansion of the container which is rigidly attached to the cold finger. This drift has an average rate of 1µm/min perpendicularly to the optical axis, and it is slow enough to be corrected using image tracking methods. The objective of the microscope is mounted inside the vacuum chamber and therefore the vacuum window is not in a converging part of the beam. The vacuum window itself is tilted by a small angle to avoid reflections. To illuminate the sample we use a monochromatic light beam (548nm) from a Mercury-100W lamp. The light intensity is detected by a Hamamatzu Peltier cooled CCD camera. Magnetic fields up to 4mT can be applied using a solenoid wound around the objective. The sample region is shielded by multiple layers of µ-metal in order to reduce the magnetic field of the earth. The residual magnetic field on the sample is lower than 5µT. 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 order to compensate for the drift we record images every 0.3sec. A computer program tracks the drift of the sample using markers on the sample itself. Image averaging is done only after drift compensation. 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 temperature at zero magnetic field. To minimize the drift, the time interval between background and measurement images was kept as short as possible. In our case, good background subtraction was achieved with a time interval of a few minutes. In a superconductor the magnetic field is uniform only if the sample is cooled under an external field. In order to avoid spurious magnetic field resulting from electrical heating we use IR light to heat up our sample and then allow it to cool with the field on.

The light reflected from the sample passes through a second polarizer oriented at an angle π/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 polarizers 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 the objective is exposed to the low temperature environment and cools by thermal radiation. As a result, thermal strains of the lens degrade the extinction ratio to e=1×10-2. In this case the angle between polarizers should be ϕ⋍5°. Experimentally the contrast doesn’t change significantly in the range ϕ=3-10°. The intensity on the other hand is proportional to ϕ 2. In order to increase the signal to noise ratio as much as possible we used ϕ=10°.

In our system, at the maximal magnification (×50 objective), each pixel of the image covers an area of 0.12×0.12µm 2 of the sample. The total field of view is 110×160µm 2.

3. Results and discussion

An image of a superconductor cooled at two different external magnetic fields shown in Figure 2. The brightness is proportional to the local magnetic field. Each spot represents a single vortex. This figure vividly illustrates the power of the MOI technique where enough individual vortices can be seen to permit the determination of spatial correlations, long and short range order, etc. At Figure 2.b some of the vortices are 1µm apart, approaching our spatial resolution limit, but still can be resolved.

Within the small thickness of MO indicator the magnetic field of a single vortex is localized inside an area much smaller than our optical resolution.

Therefore the image of individual vortex can be approximated by an optical pointspread Airy function [17] I ~ (J 1(kx)/kx)2, where J 1 is a first order Bessel function of the first kind. Figure 3 shows the intensity profile produced by an individual vortex. The intensity is fitted with an Airy function with k=4.4µm -1. Using the Rayleigh criterion, our MO spatial resolution is 0.8µm, which is much better than 1.3µm reported by [9]. Note that the spatial resolution is limited by optical diffraction.

Another example of the power of this technique can be seen in figure 4. Here we show the edge of a dendrite-like formation of a magnetic flux inside the superconductor. Dendrite-like formations are observed at temperatures well below Tc, where magnetic flux penetrates into the sample via a thermo-magnetic instability [18]. This phenomenon was extensively investigated using conventional magneto-optics (see [19]). In this case, we see a magnetic structure with a high density of positive flux (bright region) penetrates into a sample having an initially uniform distributed negative magnetic flux (dark region). With our high resolution, individual vortices can be distinguished at the front edge of this structure. Notice that flux lines of different polarities (bright and dark spots) are separated by an annihilation zone where the density of the vortices is low. Such images allow us to study annihilation dynamics.

 

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 single vortex. At these low fields, the positions of individual vortices are determined by local disorder 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.

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Fig. 4. Edge of a dendrite-like magnetic structure pinned in a superconductor. To produce this structure, the superconductor was first cooled through Tc in the presence of a magnetic field (-4mT) and then the field was reduced to zero. The inset shows a low resolution image of a similar structure. The scale bar in the inset represents 100µm.

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4. Conclusion

In conclusion, we have developed a high resolution MO imaging system which can be used for studies of vortex arrays on spatial scales ranging from single flux quanta up to structures containing thousands of vortices. Work is already underway to study out of equilibrium vortex formation 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 Science Foundation and by the Technion Fund for Research.

References and links

1. K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, “Real-time observation of vortex lattices in a superconductor by electron microscopy,” Nature (London) 360, 51–53 (1992). [CrossRef]  

2. I. V. Grigorieva, “Magnetic flux decoration of type-II superconductors,” Superconductor Science and Technology , 7, 161–177 (1994). [CrossRef]  

3. Lock See J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Yu- Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, “Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- δ,” Nature (London) 373, 225–228 (1995). [CrossRef]  

4. Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, “Metal-coated carbon nanotube tips for magnetic force microscopy,” Appl. Phys. Lett. 85, 6263–6265 (2004). [CrossRef]  

5. C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, “Noise characteristics of 100 nm scale GaAs/AlxGa1-xAs scanning Hall probes,” Appl. Phys. Lett. 90, 133512 (2007). [CrossRef]  

6. M. R. Koblischka and R. J. Wijngaarden, “Magneto-optical investigations of superconductors,” Supercond. Sci. Technol. 8, 199–214 (1995). [CrossRef]  

7. S. J. Bending, “Local magnetic probes of superconductors,” Adv. Phys. 48, 449–535 (1999). [CrossRef]  

8. R. P. Hübener, Magnetic Flux Structures in Superconductors2nd edition (Springer, Berlin, 2001).

9. P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, “Magneto-optical imaging setup for single vortex observation,” Rev. Sci. Instrum. 74, 141–146 (2003). [CrossRef]  

10. G. Carneiro and E. H. Brandt, “Vortex lines in films: Fields and interactions,” Phys. Rev. B 61, 6370–6376 (2000). [CrossRef]  

11. A. Laraoui, M. Albrecht, and J. Y. Bigot,“Femtosecond magneto-optical Kerr microscopy,” Opt. Lett. 32, 936–938 (2007). [CrossRef]   [PubMed]  

12. M. Elazar, M. Sahaf, L. Szapiro, D. Cheskis, and S. Bar-Ad, “Single-pulse magneto-optic microscopy: a new tool for studying optically induced magnetization reversals,” Opt. Lett. 33, 2734–2736 (2008). [CrossRef]   [PubMed]  

13. J. Schoenes and P. Wachter, “Magnetooptic Spectroscopy of EuS, EuSe, and EuTe,” Trans. Magnetic 12, 81–85 (1976). [CrossRef]  

14. Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991). [CrossRef]  

15. C. R. Reisin and S. G. Lipson, “Intermediate-state structures of type-I superconductors,” Phys. Rev. B , 61, 4251–4258 (2000). [CrossRef]  

16. B. Abdo, E. Segev, O. Shtempluck, and E. Buks, “Nonlinear Coupling in Nb/NbN Superconducting Microwave Resonators,” arXiv:cond-mat/0501236 v1, (2005).

17. S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical physics3rd ed, (Cambridge University Press, 1995).

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) [CrossRef]  

19. T.H. Johansen, M. Baziljevich, D.V. Shantsev, P.E. Goa, Y.M. Galperin, W.N. Kang, H.J. Kim, E.M. Choi, M. S. Kim, and S.I. Lee, “Dendritic flux patterns in MgB2 films,” Supercond. Sci. Technol. 14, 726–729 (2001). [CrossRef]  

References

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  1. K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
    [CrossRef]
  2. I. V. Grigorieva, "Magnetic flux decoration of type-II superconductors," Supercond. Sci. Technol. 7, 161-177 (1994).
    [CrossRef]
  3. J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
    [CrossRef]
  4. Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
    [CrossRef]
  5. C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
    [CrossRef]
  6. M. R. Koblischka and R. J. Wijngaarden, "Magneto-optical investigations of superconductors," Supercond. Sci. Technol. 8,199-214 (1995).
    [CrossRef]
  7. S. J. Bending, "Local magnetic probes of superconductors," Adv. Phys. 48, 449-535 (1999).
    [CrossRef]
  8. R. P. Hubener, Magnetic Flux Structures in Superconductors 2nd edition (Springer, Berlin, 2001).
  9. P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
    [CrossRef]
  10. G. Carneiro and E. H. Brandt, "Vortex lines in films: Fields and interactions," Phys. Rev. B 61, 6370-6376 (2000).
    [CrossRef]
  11. A. Laraoui, M. Albrecht, and J. Y. Bigot,"Femtosecond magneto-optical Kerr microscopy," Opt. Lett. 32, 936-938 (2007).
    [CrossRef] [PubMed]
  12. M. Elazar, M. Sahaf, L. Szapiro, D. Cheskis, and S. Bar-Ad, "Single-pulse magneto-optic microscopy: a new tool for studying optically induced magnetization reversals," Opt. Lett. 33, 2734-2736 (2008).
    [CrossRef] [PubMed]
  13. J. Schoenes and P. Wachter, "Magnetooptic Spectroscopy of EuS, EuSe, and EuTe," Trans. Magnetic 12, 81-85 (1976).
    [CrossRef]
  14. Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
    [CrossRef]
  15. C. R. Reisin and S. G. Lipson, "Intermediate-state structures of type-I superconductors," Phys. Rev. B 61, 4251-4258 (2000).
    [CrossRef]
  16. B. Abdo, E. Segev, O. Shtempluck, and E. Buks, "Nonlinear Coupling in Nb/NbN Superconducting Microwave Resonators," arXiv:cond-mat/0501236 v1, (2005).
  17. S. G. Lipson, H. Lipson and D. S. Tannhauser, Optical physics 3rd ed, (Cambridge University Press, 1995).
  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)
    [CrossRef]
  19. T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
    [CrossRef]

2008 (1)

2007 (2)

A. Laraoui, M. Albrecht, and J. Y. Bigot,"Femtosecond magneto-optical Kerr microscopy," Opt. Lett. 32, 936-938 (2007).
[CrossRef] [PubMed]

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

2004 (1)

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

2003 (1)

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

2002 (1)

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)
[CrossRef]

2001 (1)

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

2000 (2)

C. R. Reisin and S. G. Lipson, "Intermediate-state structures of type-I superconductors," Phys. Rev. B 61, 4251-4258 (2000).
[CrossRef]

G. Carneiro and E. H. Brandt, "Vortex lines in films: Fields and interactions," Phys. Rev. B 61, 6370-6376 (2000).
[CrossRef]

1999 (1)

S. J. Bending, "Local magnetic probes of superconductors," Adv. Phys. 48, 449-535 (1999).
[CrossRef]

1995 (2)

M. R. Koblischka and R. J. Wijngaarden, "Magneto-optical investigations of superconductors," Supercond. Sci. Technol. 8,199-214 (1995).
[CrossRef]

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

1994 (1)

I. V. Grigorieva, "Magnetic flux decoration of type-II superconductors," Supercond. Sci. Technol. 7, 161-177 (1994).
[CrossRef]

1992 (1)

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

1991 (1)

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

1976 (1)

J. Schoenes and P. Wachter, "Magnetooptic Spectroscopy of EuS, EuSe, and EuTe," Trans. Magnetic 12, 81-85 (1976).
[CrossRef]

Albrecht, M.

Bar-Ad, S.

Baziljevich, M.

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

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)
[CrossRef]

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Bending, S. J.

S. J. Bending, "Local magnetic probes of superconductors," Adv. Phys. 48, 449-535 (1999).
[CrossRef]

Bigot, J. Y.

Bonevich, J.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Brandt, E. H.

G. Carneiro and E. H. Brandt, "Vortex lines in films: Fields and interactions," Phys. Rev. B 61, 6370-6376 (2000).
[CrossRef]

Carneiro, G.

G. Carneiro and E. H. Brandt, "Vortex lines in films: Fields and interactions," Phys. Rev. B 61, 6370-6376 (2000).
[CrossRef]

Cheskis, D.

Chi, C. C.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Choi, E. M.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Dai, H.

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Deng, Z.

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Elazar, M.

Galperin, Y. M.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Goa, P. E.

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

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)
[CrossRef]

Goa, P.E.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Grigorieva, I. V.

I. V. Grigorieva, "Magnetic flux decoration of type-II superconductors," Supercond. Sci. Technol. 7, 161-177 (1994).
[CrossRef]

Gupta, A.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Harada, K.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Hauglin, H.

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

Hicks, C. W.

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

Hoffman, J. E.

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Igarashi, M.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Johansen, T. H.

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

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)
[CrossRef]

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Kang, W. N.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Kawabe, U.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Ketchen, M. B.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Kim, H. J.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Kim, M. S.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Kirtley, J. R.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Koblischka, M. R.

M. R. Koblischka and R. J. Wijngaarden, "Magneto-optical investigations of superconductors," Supercond. Sci. Technol. 8,199-214 (1995).
[CrossRef]

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

Kondo, S.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Kronmuller, H.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

Laraoui, A.

Lee, S. I.

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Leu, J.

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Lipson, S. G.

C. R. Reisin and S. G. Lipson, "Intermediate-state structures of type-I superconductors," Phys. Rev. B 61, 4251-4258 (2000).
[CrossRef]

Lock See Yu-Jahnes, C. C.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Luan, L.

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

Ludescher, B.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

Matsuda, T.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Moler, K. A.

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Moser, N.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

Olsen, A. F.

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

Reisin, C. R.

C. R. Reisin and S. G. Lipson, "Intermediate-state structures of type-I superconductors," Phys. Rev. B 61, 4251-4258 (2000).
[CrossRef]

Rozzi, G.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Rupp, M.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Sahaf, M.

Schoenes, J.

J. Schoenes and P. Wachter, "Magnetooptic Spectroscopy of EuS, EuSe, and EuTe," Trans. Magnetic 12, 81-85 (1976).
[CrossRef]

Schuster, Th.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

Shantsev, D. V.

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)
[CrossRef]

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Shtrikman, H.

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

Straver, E. W. J.

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Sun, J. Z.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Szapiro, L.

Tonomuko, A.

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

Tsuei, C. C.

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Wachter, P.

J. Schoenes and P. Wachter, "Magnetooptic Spectroscopy of EuS, EuSe, and EuTe," Trans. Magnetic 12, 81-85 (1976).
[CrossRef]

Wijngaarden, R. J.

M. R. Koblischka and R. J. Wijngaarden, "Magneto-optical investigations of superconductors," Supercond. Sci. Technol. 8,199-214 (1995).
[CrossRef]

Yenilmez, E.

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

Zeldov, E.

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

Adv. Phys. (1)

S. J. Bending, "Local magnetic probes of superconductors," Adv. Phys. 48, 449-535 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Deng, E. Yenilmez, J. Leu, J. E. Hoffman, E. W. J. Straver, H. Dai, and K. A. Moler, "Metal-coated carbon nanotube tips for magnetic force microscopy," Appl. Phys. Lett. 85, 6263-6265 (2004).
[CrossRef]

C. W. Hicks, L. Luan, K. A. Moler, E. Zeldov, and H. Shtrikman, "Noise characteristics of 100 nm scale GaAs/AlxGa1?xAs scanning Hall probes," Appl. Phys. Lett. 90, 133512 (2007).
[CrossRef]

Cryogenics (1)

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, and H. Kronmuller, "EuSe as magneto-optical active coating for use with the high resolution Faraday effect," Cryogenics 31, 811-816 (1991).
[CrossRef]

Europhys. Lett. (1)

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)
[CrossRef]

Nature (London) (2)

K. Harada, T. Matsuda, J. Bonevich, M. Igarashi, S. Kondo, G. Rozzi, U. Kawabe, and A. Tonomuko, "Real-time observation of vortex lattices in a superconductor by electron microscopy," Nature (London) 360, 51-53 (1992).
[CrossRef]

J. R. Kirtley, C. C. Tsuei, J. Z. Sun, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, M. Rupp, and M. B. Ketchen, "Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- ™," Nature (London) 373, 225-228 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

G. Carneiro and E. H. Brandt, "Vortex lines in films: Fields and interactions," Phys. Rev. B 61, 6370-6376 (2000).
[CrossRef]

C. R. Reisin and S. G. Lipson, "Intermediate-state structures of type-I superconductors," Phys. Rev. B 61, 4251-4258 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

P. E. Goa, H. Hauglin, A. F. Olsen, M. Baziljevich, and T. H. Johansen, "Magneto-optical imaging setup for single vortex observation," Rev. Sci. Instrum. 74, 141-146 (2003).
[CrossRef]

Supercond. Sci. Technol. (3)

I. V. Grigorieva, "Magnetic flux decoration of type-II superconductors," Supercond. Sci. Technol. 7, 161-177 (1994).
[CrossRef]

M. R. Koblischka and R. J. Wijngaarden, "Magneto-optical investigations of superconductors," Supercond. Sci. Technol. 8,199-214 (1995).
[CrossRef]

T. H. Johansen, M. Baziljevich, D. V. Shantsev, P.E. Goa, Y. M. Galperin, W. N. Kang, H. J. Kim, E. M. Choi, M. S. Kim, and S. I. Lee, "Dendritic flux patterns in MgB2 films," Supercond. Sci. Technol. 14, 726-729 (2001).
[CrossRef]

Trans. Magnetic (1)

J. Schoenes and P. Wachter, "Magnetooptic Spectroscopy of EuS, EuSe, and EuTe," Trans. Magnetic 12, 81-85 (1976).
[CrossRef]

Other (3)

B. Abdo, E. Segev, O. Shtempluck, and E. Buks, "Nonlinear Coupling in Nb/NbN Superconducting Microwave Resonators," arXiv:cond-mat/0501236 v1, (2005).

S. G. Lipson, H. Lipson and D. S. Tannhauser, Optical physics 3rd ed, (Cambridge University Press, 1995).

R. P. Hubener, Magnetic Flux Structures in Superconductors 2nd edition (Springer, Berlin, 2001).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic sketch of the experimental system: (1) Hg 100W light source, (2) Interference filters, (3) Polarizer (extinction ratio 1:10000), (4)Analyzer (extinction ratio 1:10000), (5) Non polarizing beam splitter, (6) Objective, (7)Vacuum windows, (8) Sample holder, (9) Flexible thermal connection, (10) CCD camera, (11) Cold finger, (12) Liquid Helium bath, (13) Vacuum chamber, (14) XYZ manipulator, (15) Manipulator to sample holder coupling, (16) Optical fiber.

Fig. 2.
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 single vortex. At these low fields, the positions of individual vortices are determined by local disorder rather then by vortex-vortex interaction.

Fig. 3.
Fig. 3.

Intensity profile across a single vortex. The line is a fit to an Airy function.

Fig. 4.
Fig. 4.

Edge of a dendrite-like magnetic structure pinned in a superconductor. To produce this structure, the superconductor was first cooled through Tc in the presence of a magnetic field (-4mT) and then the field was reduced to zero. The inset shows a low resolution image of a similar structure. The scale bar in the inset represents 100µm.

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