PHYSICAL REVIEW LETTERS
Comment on “Peak Effect and the Transition from
Elastic to Plastic Depinning”
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In a recent paper [1] Cha and Fertig (CF) claim to have
made the first numerical observation of “the” peak effect.
They studied a model with strong, dilute pinning centers.
A peak effect indeed has been reported in such systems,
e.g., in twinned YBa2 Cu3 O72d (YBCO). However, much
of the literature addresses instead materials in the weak,
collective pinning regime. Experimentally the biggest
peaks have been observed in the strong-pin-free NbSe2
[2]. We point out that the relevance of CF’s model to the
weak pinning regime is not obvious. Therefore, the peak
effect remains to be observed in the weak pinning regime.
CF tune the bare c66 , the shear modulus, and study their
model for the number of pins, Np ø Ny , the number of
vortices. They find a peak in the depinning current Jc as
a function of c66 . The peak is attributed to a change from
elastic to plastic flow.
The parameters and physics of CF’s peak are different
from the collective pinning regime as follows:
(1) The collective pinning regime is distinguished by
the condition Np ¿ Ny , as the scale of the disordered
pinning potential is of order j ⬃ 15 Å, the superconducting correlation length, whereas the vortex separation
a0 艐 500 Å, for a magnetic field of H ⬃ 1 T. CF emphasize that they observe the peak only for Np ø Ny .
(2) In our view the origin of CF’s peak is that for Np ø
Ny they have two types of vortices: Np directly pinned
vortices and Ny 2 Np vortices between pins that are
indirectly pinned by the repulsion of the directly pinned
vortices. For c66 ! 0 this repulsive interaction decreases,
lowering Jc for the indirectly pinned vortices. For large
and increasing c66 , pinning, and thus Jc , decreases for
the standard reason: all vortices form an elastic manifold,
which becomes less well pinned as it stiffens. Thus Jc
exhibits a peak as it decreases when c66 either decreases
or increases from some intermediate value.
In the collective pinning regime, in contrast, all vortices
feel varying degrees of pinning, and the above two types
of vortices do not exist. To appreciate this note that the
CF approach predicts a peak effect for a perfectly ordered
array of pins. We confirmed this by simulations: see
Fig. 1(a). This clearly establishes that CF’s peak is not
related to the physics of disorder.
(3) The experimental Jc vs H curve has three regions,
where Jc goes down, up, and finally down again with
increasing H. In fact, increasing H generates decreasing
Jc over most of the range of H. Therefore, as c66 ~ H,
for small and increasing c66 , Jc should decrease. The
opposite happens in CF’s model.
(4) Experimentally the peak is observed as a function of
H or T , whereas CF vary the microscopic c66 , essentially
13 SEPTEMBER 1999
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VOLUME 83, NUMBER 11
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FIG. 1. (a) The depinning force Fdep ~ Jc vs the vortex
interaction strength Ay ~ C66 for periodic pins with Ny . Np .
( b) Fdep vs Ay for random pins with Np ¿ Ny .
varying the vortex interaction strength. However, realistic
models of changing H should also involve changing the
vortex density and the BCS renormalization factors. In
such a model, the initial increase of H makes the lattice
stiffer, but on approaching Hm the BCS terms make it
softer again. This results in a nonmonotonic relation
between c66 and H: a peak as a function of c66 does not
necessarily translate to a peak as a function of H.
(5) We carried out molecular dynamics simulations
similar to CF’s, but in the Np ¿ Ny regime. As shown in
Fig. 1(b), Jc decreases with increasing c66 for all values.
Thus in the collective pinning regime, Jc exhibits no peak
in 2D.
(6) CF add an attractive term to the vortex-vortex
interaction, which appears essential to generate the peak
effect. While such a term is useful for tuning model
parameters, it lacks physical justification.
In sum, the parameters and physics of CF’s model
differ from that of collective pinning an several crucial
ways; thus the observation of a peak in their model is
not obviously instructive for understanding the peak effect
in the collective pinning regime. Our simulations, which
address the collective regime more directly, in fact, do not
find a peak effect in 2D: it appears only in 3D [3].
C. Reichhardt,1 K. Moon,2 R. Scalettar,1 and G. Zimányi1
1
University of California at Davis
Davis, California 95616
2
Yonsei University
Seoul 120-749, Korea
Received 12 November 1998
PACS numbers: 74.60.Ge
[1] M. Cha and H. Fertig, Phys. Rev. Lett. 80, 3851 (1998).
[2] S. Bhattacharya and M. J. Higgins, Phys. Rev. Lett. 70,
2620 (1993).
[3] A. van Otterlo, R. Scalettar, G. Zimányi, R. Olson,
A. Petrean, W. Kwok, and V. Vinokur (to be published).
© 1999 The American Physical Society