Direct evidence for a transition from elastic to plastic vortex phases in YBa2Cu3O7-δδ
S. Kokkaliaris, A. A. Zhukov, S. N. Gordeev and P. A. J. de Groot
Department of Physics, University of Southampton, Southampton, SO17 1BJ, UK
R. Gagnon and L. Taillefer
Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada
Abstract— We have performed partial magnetization
loops in order to study history effects in high quality detwinned YBa2Cu3O7−−δ single crystals. The obtained results
have disclosed a transition within the vortex system from
a dislocation-free Bragg glass to a disordered vortex
phase. This boundary has been mapped in the field –
temperature phase diagram and found to lie in the vicinity of the onset of the second magnetization peak. Above
the transition line, metastable topological disorder invades the vortex system leading to a prominent dependence of the critical current density on the thermomagnetic
history of the superconductor.
I. INTRODUCTION
The significantly enhanced role of fluctuations in the high
temperature superconductors (HTSC) due to the high operating temperatures, large anisotropies and penetration depths
results in a phase diagram far more complicated than the
mean field description [1]. Indeed it has been predicted theoretically and observed experimentally that in these systems
the vortex lattice melts well below Hc2 thus defining a transition between a solid and a liquid vortex phases [2, 3]. Moreover recent theoretical investigations have established the existence of a transition within the vortex system (VS) from an
elastic phase (termed the Bragg glass) characterised with
quasi-long-range order to a disordered phase where topological defects such as dislocations are energetically favorable
[4]. Experimentally the existence of such a transition was
recently reported for pure detwinned YBa2Cu3O7-δ single
crystals and its boundary was mapped in the B – T phase diagram [5].
In this work we present a study of history effects in the
irreversible magnetization of pure, detwinned YBa2Cu3O7-δ
single crystals. By employing a partial loop technique we find
clear evidence for the theoretically proposed transition between a dislocation-free Bragg glass and a disordered vortex
phase [4], as indicated by the proliferation of topological defects in the VS.
II. EXPERIMENTAL DETAILS
We have studied several samples. For brevity, however, we
This work is part of a project supported by the EPSRC (U.K.). S.K. ac-
.
knowledges financial support from the University of Southampton R.G. and
L.T. acknowledge funding from NSERC (Canada).
present results for a detwinned YBa2Cu3O7-δ single crystal
(called hereafter D3), grown by a conventional self-flux
method using Y-stabilized zirconia crucibles [5]. The sample
had oxygen content of 7-δ = 6.97 and Tc = 91.7 K with a
width ∆Tc = 0.3 K. Magnetization measurements have been
performed using an Oxford Instruments vibrating sample
magnetometer for fields up to 12 T and various sweep rates.
The partial loop technique is realized in two ways. In method
I the sample is cooled in zero field that is subsequently swept
up to a maximum value Bmax before it is decreased back to
zero. In a series of runs Bmax is increased with a fine step finally reaching values above the irreversibility field. In this
case we obtain a complete loop (CL). In method II the previous procedure is inverted: after cooling the sample in zero
field, the field is increased up to 12 T and then after decreasing it down to a certain value Bmin it is swept again to 12 T.
III. RESULTS AND DISCUSSION
Fig. 1 shows typical magnetization loops for D3 at 66 K.
The solid line represents the complete magnetization loop
whereas with the dashed and dotted lines we show partial
loops (PLs) obtained by methods I and II respectively for Bmax
= Bmin = 4 T. As can be seen, after reversing the field from
Bmax the descending legs of method I PLs do not follow the
CL but rather the magnetization attains lower values. Nevertheless with further decreasing field the PLs finally merge
with the CL; the field reduction ∆Bsup below Bmax required for
this can be as high as 3 T. We note that the deviation of the
PLs from the CL cannot be associated with the influence of
an incomplete reversal of the field profile. Indeed simple calculations following Ref. [6] demonstrate that for the sample
under study at 66 K the field of full penetration is less than 10
mT, a value much smaller than ∆Bsup.. For PLs obtained by
method II the behaviour is opposite: increasing the field
above Bmin results in enhanced hysteresis (see Fig 1). No
merging with the CL is seen and a small increase in the magnetization of the PLs persists up to the irreversibility field.
From these results it becomes clear that the irreversible
magnetization and thus the critical current density (Jc) depends on the measuring procedure i.e. on the magnetic history of the sample. For D3 at 66 K the magnetization on the
decreasing or increasing field branches of PLs obtained by
methods I or II respectively can deviate by up to 50% from
the CL magnetization width, suggesting that the current density on these branches can be varied by as much as 100%.
Since for an elastically distorted lattice Jc is a single valued
function of field and temperature, the memory effects point to
elastically deformed lattice no history effects should be observed. Consequently within this range of Bmax the PLs must
follow the same universal line, which is what we observe for
Bmax below 3 T, that is found to be independent of the sweep
rate, as can be seen in the inset of Fig 1. For Bmax > Bpl and in
a narrow field range the PLs strongly deviate from the universal curve exhibiting prominent history dependence. This
clearly demonstrates the introduction of metastable topological disorder and the onset of plasticity in the VS.
Our results strongly indicate that below Bpl the VS is characterized by elasticity and the absence of topological defects.
These characteristics are identical to the Bragg glass phase
[4]. Therefore Bpl features the transition from the Bragg glass
to a disordered phase where plasticity dominates. The loci of
the Bpl values are shown in the B – T phase diagram of Fig. 2.
In this plot we also show the lines corresponding to the magnetization peak BP and the peak onset Bon. The melting line
obtained from resistivity measurements on a crystal from the
same batch [8] is also given.
M a g n e tiz a tio n ( m T )
100
80
M a g n e tiz a tio n ( m T )
60
40
-4
-6
-8
-1 0
-1 2
2 .5
20
3 .0
3 .5
4 .0
M a g n e ti c F i e l d ( T )
0
-2 0
-4 0
-6 0
66 K
-8 0
-1 0 0
0
1
2
3
4
5
6
7
8
9
10 11 12
M a g n e tic F ie ld ( T )
12
the presence of plastic deformations in the VS, which lead to
a dependence of the lattice structure on the history of the
sample. The path dependent current further implies that description by a simple Bean model, where Jc is determined
only by the value of B and T should not apply in this case.
Recent theoretical predictions have shown that due to the
enhancement of the effective disorder with increasing field,
above a threshold value, Bpl dislocations proliferate resulting
to a plastically deformed VS [4]. The introduction of topological defects leads to an enhancement of Jc [4]. Increasing
the field during an isothermal magnetization loop in the regime where dislocations are present forces the VS into an
increasingly disordered state. When the field is decreased
dislocations remain trapped in local energy minima, thus exhibiting metastability as discussed in detail in Ref. [7]. Hence
the density of dislocations does not change with field in a
reversible way and one should expect a path dependent hysteresis. That is the case shown in Fig. 1: in the descending
branch of the CL, the VS tends to retain dislocations from the
high field state leading to higher critical currents as compared
to the PLs. This effect persists until the field is reduced
enough to expel out residual topological defects thus erasing
any memory on the formation history of the VS, as demonstrated by the coincidence of the PLs with the CL at low Bmax
and Bmin.
The introduction of the partial loop technique is very important as it allows the detection of the point where dislocations invade the vortex system for the first time. Indeed as
long as the maximum field excursion is not high enough to
drive the VS out of the region where elasticity dominates,
then due to the reversibility characterizing the structure of an
Magnetic Field ( T )
Fig. 1. M(B) curves for D3 at 66 K. The solid line is the CL whereas the
dashed and dotted lines represent PLs obtained with methods I and II for Bmax
= Bmin = 4 T respectively. The inset shows in detail several method I PLs in
the range 2.6 T ≤ Bmax ≤ 4.2 T with Bmax increasing with a step of 0.2 T.
Bm
10
Bp
8
B on
B pl
6
4
2
0
55
60
65
70
75
80
85
90
95
Temperature ( K )
Fig. 2. Position of the characteristic fields Bp, Bpl and Bon in the B – T phase
diagram for D3.
IV. CONCLUSIONS
In conclusion, we have studied history effects in the magnetization of pure YBa2Cu3O7-δ single crystals. A partial loop
technique has enabled the detection of a transition from the
Bragg glass to a disordered vortex phase. The location of this
transition was identified in the B-T phase diagram and found
to be in proximity to the onset of the magnetization peak.
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