PHYSICAL REVIEW B
VOLUME 62, NUMBER 14
1 OCTOBER 2000-II
High-field breakdown of the superconducting critical state in Bi2Sr2CaCu2O single crystals
A. Gerber and A. Milner
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Ramat Aviv,
69978 Tel Aviv, Israel
共Received 7 June 2000兲
The critical state in Bi2Sr2CaCu2O single crystals is found to become unstable at low temperatures and high
magnetic fields. Reproducible and almost periodic flux jumps developed at high fields only are qualitatively
different from those known in conventional superconductors and predicted by existing models. The breakdown
can occur in the regime considered to be stable, which compromises the existing criteria for the potential
high-field applications of high-T c materials.
The critical state in hard type-II superconductors is metastable and, as such, can collapse under certain conditions.
Magnetothermal instability is the only mechanism extensively studied so far 共for reviews see Refs. 1 and 2 and
references therein兲 which can lead to a local or global breakdown of the critical state. The theory predicts a number of
well defined characteristics of the phenomenon, including
the onset of the first runaway event and its dependence on
both intrinsic properties of material and external conditions.
Depending on the parameters, the system is expected to become unstable for thermal or magnetic fluctuations when the
difference between the external B 0 and internal B i fields exceeds a certain critical value ⌬B j . 3 The difference B 0 ⫺B i
reaches its maximum at the so-called full penetration field
B p , when, following the Bean model, the magnetic field has
just penetrated up to the center of a sample. Since the critical
current density is assumed to be a monotonously decreasing
function of applied magnetic field, this difference decreases
at higher fields. Following these arguments the system will
be stable at any applied field if its B p ⬍⌬B j . In other words,
if the critical state is stable in the region 0⬍B 0 ⬍B p then it is
stable for any magnetic field. For a given critical current
density J c ,B p is proportional to the sample’s cross section,
and that is why superconducting wires for high-field applications are manufactured in the form of thin fibers such that
their radius R⬍B j / ␮ 0 J c . This practice has been approved
by numerous applications of conventional low-temperature
superconducting materials and one could safely claim that if
the critical state has not collapsed at fields up to B p it will
remain stable up to the upper critical field B c2 共or the irreversibility field for high-temperature superconductors兲. In
this paper we wish to demonstrate that this rule does not hold
in high-temperature superconductors at low temperatures, at
least not as a general statement.
The magnetic field close to the surface of singlecrystalline Bi2Sr2CaCu2O 共BSCCO兲 samples was measured
by a commercial Hall sensor between 4.2 and 0.3 K in fields
up to 17 T. Magnetization was defined as the difference between the field measured by the sensor and magnetic induction generated by the magnet. Crystals with T c ⫽92 K and
the transition width of about 1 K were grown several years
ago at the University of Amsterdam by using a travelingsolvent floating-zone technique. All three samples studied
had a platelike form with surfaces of few mm2 and thickness
0163-1829/2000/62共14兲/9753共4兲/$15.00
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of few tenths mm. The samples were oriented with the c axis
along the applied field. Two cryostats were used: variable
temperature cryostat 共VT兲 in the range 1.5–4.2 K, in which
samples were immersed directly into liquid helium, and He3
cryostat for the range 0.3–4.2 K. Thermal stabilization in the
latter was provided by a mechanical contact to a copper He3
pot via a thin layer of thermally conducting grease.
The major unusual result is shown in Fig. 1. Magnetization of a BSCCO crystal is measured as a function of applied
magnetic field at 0.3 K. Full field penetration is achieved at
about 1.5 T. The magnetization curve is smooth below and
far beyond this B p . Only at field above 6 T magnetization
drops sharply indicating a breakdown of the critical state.
Additional flux jumps follow the first one up to 17 T, the
highest field reached in this experiment. When field is decreased, similar flux jumps develop in the high-field range
and disappear below 7 T. The pattern reproduces itself when
the field polarity is reversed.
Flux jumps can start also at fields below B p , but even in
this case their characteristics are very unusual. Both onset
and offset of flux jumps for increasing and decreasing field,
respectively, and the entire pattern may depend on the experimental conditions and on magnetic prehistory of the
sample. Conditions of the experiment are the most elusive to
FIG. 1. Magnetization of a BSCCO single crystal 共sample 1兲 as
a function of applied magnetic field measured at 0.3 K. Arrows in
this and following figures indicate the direction of the field sweep.
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©2000 The American Physical Society
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A. GERBER AND A. MILNER
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FIG. 3. Two magnetization measurements 共solid and dashed
lines兲 of sample 2 at 0.33 K after a number of earlier cycles.
FIG. 2. Development of the magnetization curves after a number of successive field cycles. 共a兲 the first measurement; 共b兲 final
stabilized pattern. T⫽1.5 K.
define. Thermal coupling to the environment is evidently important. For example, the pattern of jumps shown by the
same sample measured at the same temperature 共e.g., 1.6 K兲
in different cryostats may be different 共the sample is cooled
by liquid helium in the VT cryostat and is thermally stabilized by a mechanical contact in the He3 one兲. However,
other parameters, like stiffness of mounting, can be important as well.
A noticeable effect of the magnetic prehistory is the
change of the flux jumps pattern with successive field cycling, as shown in Fig. 2. Numerous large and small flux
jumps can take place in the entire field range during the first
ramp, with an onset of jumps clearly below the field of full
penetration. After a number of cycles the pattern changes:
low-field jumps disappear and the sample reaches a certain
reproducibility under the following cycling. Heating of
samples up to room temperature does not seem to affect significantly the process of ‘‘training’’: low-field and random
jumps disappear irreversibly. High-field jumps, however, are
preserved in all our measurements and do not disappear after
numerous cycling.
After ‘‘training’’ the pattern of jumps can become remarkably reproducible. Figure 3 presents the first quarter of
two M (B 0 ) measurements of sample 2 at 0.33 K after a
number of earlier cycles. Notably, the sequence of jumps in
these two measurements is almost identical both in the magnitude and field intervals between the events.
Temperature and magnetic-field dependence of reproducible flux jumps is shown in Fig. 4. Plotted are the field intervals between the successive jumps ⌬B 0 and the magnitude
of flux jumps ⌬M as a function of applied magnetic field
measured at few temperatures. Two regimes can be identified
in the field dependence of the flux jumps: the low-field regime, where the magnitude and intervals between the successive jumps decrease with increasing field, and the high-field
regime, where both characteristics of the jumps saturate and
become almost periodic. The transition between two regimes
is, at least roughly, temperature independent and takes place
at about 7–8 T. The period and magnitude of the jumps
increase with increasing temperature by about a factor of 2
between 0.3 and 1.5 K. No jumps were observed at 4.2 K in
fields up to 17 T.
It should be marked that the ratio between the magnitude
of the jumps ⌬M and the field intervals between the succes-
FIG. 4. Intervals between the successive flux jumps ⌬B 0 共solid
symbols兲 and amplitudes of the jumps ⌬M 共open symbols兲 as a
function of the applied magnetic field at different temperatures.
Curves 1–4 correspond to 0.33, 0.7, 1.1, and 1.5 K, respectively.
⌬M is shown for 0.33 K only.
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HIGH-FIELD BREAKDOWN OF THE SUPERCONDUCTING . . .
sive jumps ⌬B 0 is close to be constant in the entire field
range. Following Bean model for ⌬B 0 ⬍B p 共which is met in
the present case兲, that could mean that: 共i兲 all flux jumps are
terminated at the same well-defined state 共e.g., with M ⫽0兲,
and 共ii兲 that the critical current density is independent of the
applied field in the discussed range. The latter can be partially confirmed by a stable section of the hysteresis loop in
Fig. 2共b兲.
It has been mentioned above that the entire pattern and the
low-field jumps, in particular, can depend on the experimental conditions. However, the high-field jumps seem to be
almost independent of the change of cooling conditions in
different cryostats and of the rate of magnetic field ramping
共between 20 and 53 Oe/sec兲. The same high-field patterns
were found after a zero-field cooling from 300 to 0.3 K and
when the sample has been cooled in the applied field of 10 T.
Moreover, almost the same periodicity was found in all three
samples studied in the high-field limit. On the other hand,
one can usually indicate differences in the patterns of ascending and descending fields and sometimes even between
the fields of the opposite polarity.
The field dependence of the observed jumps is qualitatively abnormal from the point of common knowledge. It has
been mentioned above that both adiabatic and nonadiabatic
criteria3 of the magnetothermal instabilities are valid only if
the jump field B j is lower than the field of full penetration
B p . Also, if flux jumps did take place at low fields, they are
expected to disappear at high fields. The range of instabilities
is therefore expected to be limited from above but not from
below, contrary to the observed.
A simple adiabatic model of magnetothermal instabilities
predicts the interval between the jumps to be given by
⌬B 0 ⫽
␲
2
冑␮
0 CJ c
,
dJ c /dt
where C is specific heat and J c is the critical current density.
The field dependence of the intervals between the successive
jumps ⌬B 0 could be related to the field dependence of the
critical current density J c . However, it has been argued
above that J c seems to be field independent in this range
which does not explain a strong reduction of ⌬B 0 in the
low-field limit 共Fig. 4兲 共that also rules out the possibility of a
significant peak effect and a nonmonotonic field dependence
of the critical current density, that could increase B 0 ⫺B i at
fields above B p 兲. On the other hand, the temperature dependence of the field-independent high-field range 共Fig. 4兲 also
does not meet the predictions of the same adiabatic model.
Assuming that the low-temperature specific heat of BSCCO
is proportional to T 3 共Ref. 4兲 one could expect an increase of
⌬B 0 by about a factor of 11 when temperature is increased
from 0.3 to 1.5 K. This is about five times larger than the
observed 共Fig. 4兲.
In fact, the appearance of flux jumps at fields exceeding
B p has been presented, but not commented on, in a number
of high-temperature superconducting systems: melt-textured
YbaCuO,5,6 single-crystalline LaSrCuO,7 and singlecrystalline Yba2Cu3O7⫺ ␦ . 8 Zieve et al.8 indicated an unconventional character of avalanches they found in very clean,
untwinned Yba2Cu3O7⫺ ␦ single crystal at temperatures below 1 K. Interesting features reported included the existence
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of avalanches only above well-defined threshold fields of
several T in magnitude and an essential independence of the
onset of avalanches of the external field sweep rate. These
properties overlap with our findings.
Reproducibility and periodicity of the high-field flux
jumps in stabilized samples is unprecedented. The origin of
flux jumps in the framework of the classical theory of magnetothermal instabilities1,2 are self-accelerated fluctuations of
either temperature or field. As such one can expect one predominant scale of avalanches but not a single defined value.
Zieve et al.8 found sharply peaked distributions of the jump
sizes. This distribution is different from a power-law distribution found in NbTi tubes9 and associated with the selforganized-criticality model.10 One should note, however, that
in these cases the avalanches were small and magnetization
did not drop to zero. Although sensitivity of our measurements does not allow us to define accurately the absolute
magnetization value, the collapse of the critical state is, probably, not far from being complete.
Partial or total disappearance of flux jumps in a limited
field range after the field cycling has been observed in
single-crystalline LaSrCuO 共Ref. 7兲 and melt-textured
YbaCuO 共Ref. 5兲 samples. For the latter it has been proposed
that the twin boundaries present in YBaCuO samples may
become mobile under the stress generated by the critical state
at fields of few T. The plastic flow of twin boundaries may
generate sufficient heating to trigger the runaway flux jump.
Repeated field cycling can then have the same effect as multiple mechanical loading, which is known to increase the
stability of the critical state in conventional superconductors,
giving rise to the so-called training effect. Although the idea
of the stress generated plastic flow as the trigger mechanism
for the high-field jumps is appealing, it cannot be used in the
straightforward way in our case because of the very absence
of twin boundaries in BSCCO.
An interesting buckling type of instability in the critical
state of thin type-II superconductors has been recently proposed by Mints and Brandt.11 This elastic bending instability
can occur in thin platelike superconducting samples under
longitudinal compression produced in the critical state. The
instability appears in high perpendicular magnetic fields and
may cause almost periodic series of flux jumps. Unfortunately for our case, the model predicts instabilities under
compression only, i.e., under increasing magnetic field. Under descending field superconducting samples are stretched
and application of the model in this mode is not evident.
Finally, we wish to mention a very different approach to
the observed phenomenon. It has been recently
suggested12–15 that the vortex lattice in the high-field limit
can exhibit melting into a quantum fluid with properties of a
quantum Hall phase. At high field, when the concentration of
vortices is large, the uncertainty principle does not allow
them to form a lattice, in the same manner as it prevents
helium from crystallizing down to T⫽0. In this phase the
average internal magnetic field along c axis of the superconductor takes macroscopic discrete values B⫽B * /m, where
B * ⫽n⌽ 0 /2 is a constant of the material and mⰇ1 is an
integer. In conventional superconductors the field required
for the quantum melting would be higher than B c2 . For hightemperature superconductors B⬇15 T has been estimated15
to melt the vortex lattice at T⫽0 with the magnetic field
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A. GERBER AND A. MILNER
inside the superconductor changing by steps of about 0.5 T,
the values close to the observed in our experiments. It is not
known, however, whether the quantum fluid phase can survive pinning and how the steps of internal field will develop
on the background of the critical state.
In summary, we have shown that in BSCCO crystals: 共i兲
flux jumps can appear at fields above the field of full penetration; 共ii兲 there exist an effect of training: total or partial
disappearance of jumps at low fields after successive cycling;
共iii兲 development of jumps in ‘‘trained’’ samples can be remarkably reproducible and almost periodic; 共iv兲 regardless
the experimental conditions, flux jumps were always observed in all our samples at low temperatures at sufficiently
high fields. Reproducibility and weak dependence on external conditions might indicate a robust intrinsic triggering
mechanism. Therefore the superconducting critical state in
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BSCCO crystals can be intrinsically unstable at high fields
and low temperatures. Characteristics of the observed flux
jumps are qualitatively different from those known in conventional superconductors and predicted by existing theories
of instability. Part of the anomalies have been reported before for YBaCuO and LSCCO samples which makes us believe in a general character of our findings. From the practical point of view, the basic rules accepted so far in highcurrent/high-field applications of superconductivity might be
compromised for high-temperature superconductors.
We are grateful to V. H. M. Duijn and A. Menovsky for
BSCCO crystals, and to R. Mints and E. Chudnovsky for
numerous stimulating discussions. A.G. acknowledges support from the Alexander von Humboldt Foundation.
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