G. Yashwant et al. / Physica C 468 (2008) 944–947
947
field range between zero and Hc, where the superconductor exhib-
its diamagnetism. In bulk materials, m/H is expected to be a con-
stant. The analysis presented in Fig. 6 clearly indicates the
London screening current induced pair breaking and the whole
field range falls under a single regime of field dependent penetra-
tion depth as discussed above, and the type II like description is
perhaps not necessary in the case of nano-scale superconductors.
In conclusion, we presented magnetization measurements on
lead nanoparticles in the size range 35–45 nm with critical tem-
perature same as that in the bulk. It is shown that the critical
fields in these nanoparticles are enhanced significantly above
their bulk values. Further the critical fields are higher for smaller
particles. Moreover, they exhibit magnetic behavior reminiscent
of type II superconductors. The results are interpreted by invoking
the pair breaking effect of the London screening currents which
pervade all over the volume of the particles. This makes the pen-
etration depth increase with field. Further, the enhancement in
the critical field Hc and its temperature dependence in the nano-
particles are shown to be consistent with the Ginzburg–Landau
theory.
Fig. 6. Data in Fig. 3 re-plotted in the form m/H vs. H2.
clearly suggesting that the critical field increases with reducing
particle size. Further Hc0 ꢂ (1 ꢁ t) and k ꢂ (1 ꢁ t)ꢁ1/2 therefore
Hc ꢂ (1 ꢁ t)1/2 where the exponent 0.5 is close to the observed
exponent 0.6–0.7.
To understand the field dependence of the magnetization, let us
consider k2eff to the lowest significant order in R/k by combining
Eqs. (3) and (8) to obtain
References
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"
#
ꢀ
ꢁ
2
HR
2Hc0k
k2eff ¼ k2 1 þ 0:1
:
ð10Þ
[7] P.W. Anderson, J. Phys. Chem. Solids 11 (1959) 26.
[8] C. Kittel, Introduction to Solid State Physics, seventh ed., John Wiley and Sons
Inc., New York, 1995. Chapter 12.
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Peeters, Nature 390 (1997) 259.
[10] A.K. Geim, S.V. Dubonos, J.J. Palacios, I.V. Grigorieva, M. Henini, J.J. Schermer,
Phys. Rev. Lett. 85 (2000) 1528.
[11] V.V. Schmidt, The Physics of Superconductors, in: P. Mller, A.V. Ustinov, (Eds.),
Springer-Verlag, Berlin, Heidelberg, 1997 (Chapter 3).
[12] F. London, Superfluids, vol. I, John Wiley and Sons Inc., New York, 1950
(Chapter B).
We now calculate the magnetization of a sphere of radius R fol-
lowing London [10] in the small particle limit, i.e., R/keff < p to
obtain
"
#
ꢀ ꢁ
ꢀ
ꢁ
2
2
3
8
R
k
HR
2Hc0k
M ꢀ ꢁ
1 ꢁ 0:1
H:
ð11Þ
Following above equation, we re-plot the M–H data in Fig. 6 in
the form M/H vs. H2, which exhibits linear behavior in the entire