Abstract
A basic inversion problem for the magnetic force microscopy (MFM) of a semiinfinite superconductor in the Meissner state is formulated, ac Detection is assumed, with the MFM tip oscillating at angular frequency Ω. The coupling of all electrodynamic fields is treated, including a normal-current density in the superconductor. Under certain assumptions on the tip and superconductor geometry, a unique penetration depth λ(z) can be recovered from onedimensional force gradient measurements. This development opens new possibilities for the nondestructive evaluation of superconducting crystals and films.
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References
P. Grütter, inForces in Scanning Probe Methods, H.-J. Güntherodtet al eds., p. 447 (1995); D. Rugaret al, J. Appl. Phys. 68, 1169 (1990); C. Schönenbergeret al, J. Appl. Phys. 67, 7278 (1990); H. J. Maminet al, Appl. Phys. Lett. 55, 318 (1989); H. J. Maminet al, Appl. Phvs. Lett. 53, 1563 (1988).
A. Wadas and H.-J. Güntherodt,Phys. Lett. A 146, 277(1990); T. Göddenhenrichet ai, Appl. Phys. Lett. 57, 2612 (1990); C. Schönenberger and S. F. Alvarado,Z. Phys. B 80, 373 (1990).
H. J Reittu and R. Laiho,Supercond. Sci. Technol. 5, 448 (1992); A. Wadaset al., Z. Phys. B 88, 317 (1992); H. J. Huget al, Physica C 175, 357 (1991).
H. J. Huget al, Phvsica B 194–196, 377 (1994); A. Moseret al J. Vac. Sci. Technol. B 12, 1586 (1994); H. J. Huget al., Phvsica C 235-240, 2695 (1994); A. Moseret al, Phvs. Rev. Lett. 74, 1847 (1995).
D. N. Ghosh Roy,Methods of Inverse Problems in Physics (CRC Press, BocaRaton, Florida, 1991); D. W. McLaughlin, ed.Inverse Problems (AMS, Providence, Rhode Island, 1984);Electromagnetic Inverse Profiling: Theory and Numerical Implementation (VNU Science Press, Amsterdam, 1987).
W. A. Essah and L. M. Delves,Inv. Problems 4, 705 (1988).
R. Ono,Mater. Res. Soc. Bull., Aug. 1992, p. 34.
J. Annett, N. Goldenfeld, and S. R. Renn,Phys. Rev. B 43, 2778 (1991).
M. W. Coffey,Phvs. Rev. B 52, R9851 (1995); M. W. Coffey and E. T. Phipps.Rev. B 53, 389 (1996).
M. W. Coffey,J. Phvs. A 28, 4201 (1995).
M. W. Coffey,Phys. Rev. B 52, 1187 (1995).
M. W. Coffey, to appear inInv. Probs. (1997).
The notation here follows a conventional abuse in condensed matter physics, wherein a function and its Fourier transform are distinguished by their argument.
E. Hille,Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, Massachusetts, 1969).
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products (Academic Press, New York, 1980).
M. W. Coffey, unpublished, 1996.
B. Davies and B. Martin,J. Comp. Phvs. 33, 1 (1979).
R. Piessens,J. Inst. Math. Appl. 10, 185 (1972).
D. P. Gaver,Operations Res. 14, 444 (1966); H. Stehtest,Commun. ACM 13, 47, 624 (1970).
S. Zhang and J. Jin,Computation of Special Functions (Wiley, New York, 1996); L. Baker, CMathematical Function Book (McGraw-Hill, New York, 1992).
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Coffey, M.W. An Inverse Problem for the ac Magnetic Force Microscopy of Superconductors. J Supercond 10, 567–575 (1997). https://doi.org/10.1007/BF02767697
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DOI: https://doi.org/10.1007/BF02767697