Physica C 290 Ž1997. 206–214
Temperature pulse induced thermal instability in Y1 Ba 2 Cu 3 O 7yd
superconductors
I. Kirschner
a
a,)
, R. Laiho b, A.C. Bodi
´ c , E. Lahderanta
¨
b
Department for Low Temperature Physics, EotÕos
¨ ¨ UniÕersity, Puskin u. 5–7, H-1088 Budapest, Hungary
b
Wihuri Physical Laboratory, UniÕersity of Turku, FIN-20500 Turku, Finland
c
Institute of Experimental Physics, Kossuth UniÕersity, H-4001 Debrecen, Hungary
Received 19 June 1997; accepted 1 August 1997
Abstract
As a common effect of a large and variable temperature gradient and a temperature pulse, a thermal instability of a new
type has been observed in high-Tc superconductors. The primary effect is the temporal change of local energy density, that
causes a dynamic state of simultaneously coexisting normal and superconducting domains, establishing a spatial and
temporal variation of superconducting and normal states. The fluctuation of the ratio of the superconducting and normal
volume fractions can be detected by the oscillation of DC and AC voltages measured on the samples. Supposing that every
jump of the AC voltage represents the transformation of a single coherent domain, it leads to the average value of the linear
dimension of domains as 2.1 mm, characteristic time of the transformation as 7.5 s and velocity of the propagation of this
effect as 0.3 mmrs in the case of Y1 Ba 2 Cu 3 O 7y d specimens. The macroscopic consequence of the thermal disturbance
introduced into the sample is the appearance of a giant flux creep. Its existence is confirmed by comparison of our
measurements to others, by analytical and numerical calculations of the forces acting on the vortices and by evaluation of the
effect of the huge fluctuation created in the samples by our experiments. q 1997 Elsevier Science B.V.
PACS: 74.70 q k; 74.70.Vy; 74.72.Bk; 75.40.s
Keywords: Thermal and magnetic excitations; Fluctuations; Coherent domains; Instability
1. Introduction
Difficulties of achieving a uniform normal–superconducting ŽN–S. or superconducting–normal ŽS–N.
transition throughout the entire high-Tc superconducting sample led us to investigate the gradual
character and its escorting phenomena of N–S and
S–N transitions. It is experienced w1x that during a
)
Corresponding author. Tel.: q36 1 266 7929; Fax: q36 1
266 0206.
heating process, some small islands of the material
will tend to go into normal state before the bulk due
to local inhomogeneities. The temperature of these
regions may increase very rapidly due to their high
resistivity and they can fuse very quickly causing an
avalanche-like, fast transition. In the case of a cooling stage, local inhomogeneities can result in only
local instabilities, which cause a non-uniform transition into the superconducting state.
Coherent domains, which can develop in the samples have small, but macroscopic sizes. They possess
0921-4534r97r$17.00 q 1997 Elsevier Science B.V. All rights reserved.
PII S 0 9 2 1 - 4 5 3 4 Ž 9 7 . 0 1 6 3 9 - 0
I. Kirschner et al.r Physica C 290 (1997) 206–214
different local superconducting properties and form
together the characteristic parameters of a given
specimen. The study of the effect of local inhomogeneities provides new information from points of
view both of fundamental research and technical
applications. As an example of the first, to find out
possible correlations among preparation, structure
and character of the transition can serve w2x, while
that of the second, the enhancement of the operation
of a superconducting fault current limiter w1x can be
mentioned where its efficiency is determined by the
width of the S–N transition.
2. Thermometric mapping method
In order to examine the fine structure of N–S or
S–N transitions a new procedure of investigation,
namely the thermometric mapping method ŽTMM.
has been elaborated as an appropriate and efficient
tool. According to this, samples are submitted to a
large and variable temperature gradient that broadens
significantly the transition to reveal its gradual nature. This procedure is in a strong contrast with the
conventional electrical and magnetic measuring technique, where generally a homogeneous temperature
distribution is used to avoid the uncertainty of results.
The basic characteristics of TMM can be summarized as follows w3x.
Ž1. The necessary condition of the method is the
application of a wide temperature gradient of the
order of 10–100 K along the sample during the
measurement.
Ž2. It can be realized so that one Že.g. bottom. end
of the specimen is kept at an approximately constant
value T b of liquid nitrogen temperatures, while the
temperature of the other Že.g. top. end Tt is changed
continuously between room temperature and the liquid nitrogen one Žor in the needed temperature interval. with a variable speed. This procedure leads to a
changing temperature gradient across the sample.
Ž3. As a result of this operation, the borderline
between superconducting and normal ranges sweeps
up the whole specimen. The share-rate of the superconducting and normal volumes or masses depends
on the local superconducting and normal properties
at a given moment of time at the actual, local
temperature.
207
Ž4. The velocity of the thermometric mapping is
determined by the speed of change of the value of
Tt , in which certain non-linearity is caused by deviating structural, thermal and magnetic properties Ždistribution and density of imperfections or pinning
centres, heat capacity and conductivity, vortex density and distribution, etc.. of different coherent domains located in the vicinity of each other.
Ž5. The sensitivity of the methods depends on the
sweeping speed, while its resolution is higher at the
beginning of the mapping process and decreases due
to the reduction of the temperature difference during
the measurement.
The procedure is sensitive enough to detect not
only the fine structure of the transition w4x, or to
select slightly unlike properties of different specimens w5x, but to trace a very small change of the
features of a given sample w6x, too.
If this method is complemented with the employment of a thermal pulse w7x, it induces a thermodynamically unstable state of the sample accompanied
by non-linear electrical and magnetic effects.
3. Measurement of x , UL and UR by TMM
Complex AC susceptibility x has been measured
on Y–Ba–Cu–O bulk samples having the shape of
prisms of different sizes Ž1 = 4 = 8 mm3 and 4 = 4
= 8 mm3 . by an inductive four-probe method with
the help of a computer controlled RLC meter Žtype
HP 4284A.. A closely wound exciting coil produces
AC magnetic fields of 0.04–1 Oe on the specimen’s
surface at measuring frequencies of 1 kHz–1 MHz.
The errors of measurements are lower than dT " 0.03
K, d D s "0.01 and d L s "0.05 mH for the temperature T, the dissipation factor D and the inductance L, respectively. During the variation of Tt the
width of the N–S or S–N transition can be controlled by regulation of the sweeping time, assuring
the coexistence of normal and superconducting domains. Depending on the velocity of the cooling or
heating process, the speed of the change of local
temperatures lies generally in the interval 0.5–5
Krmin at different places of the samples.
The measuring procedure can be characterized by
the following features:
Ž1. As the amplitude of the AC magnetic field is
small, it does not separate the intergrain and intra-
208
I. Kirschner et al.r Physica C 290 (1997) 206–214
grain properties and gives information on the whole
specimen.
Ž2. Consequently the change of the temperature in
time reflects local inhomogeneities of the sample.
Ž3. The actual value of the top and bottom temperatures and so the variation of the temperature
gradient along the specimen is continuously measured.
Ž4. The real part x X of the complex AC susceptibility can be obtained directly from the measurement
of the inductance of the measuring coil, L. The
evaluation of data is based on the conditions that
x X s 0, i.e. zero diamagnetism corresponds to the
inductance of the coil Lm0 at temperatures above the
superconducting AC magnetic onset temperature T0m
and x X s y1, i.e. full diamagnetism, refers to the
value of L s 0. This scaling is permitted on the one
hand, because the inductances of the filled and empty
coil are practically the same above T0m and on the
other hand, the normal skin depth is larger, than the
sample’s size, thus the variation of the magnetic field
in normal parts of the specimen can be neglected,
moreover the change of the demagnetization factor
due to the thermal gradient is also negligible.
Ž5. The imaginary part x Y of the susceptibility
can be determined from the measured dissipation
factor Ži.e. loss tangent. D s 1rQ s Rrv L with the
help of the relation x Y s 2D D, where D D is the
Fig. 1. Fine structure of the dispersion and absorption curves
detected by the thermometric mapping method during a cooling
process.
Fig. 2. Fine structure of the dispersion and absorption curves
detected by the thermometric mapping method in the course of a
heating stage.
deviation from the value of D detected at T0m , Q is
the quality factor, R is the resistance and v is the
angular frequency.
Figs. 1 and 2 show the efficiency of TMM representing the fine structure of dispersion and absorption curves. The real x X and the imaginary x Y parts
of x versus Tt were measured on Y–Ba–Cu–O
samples w4x during a cooling and a heating process.
The specimens had the dominant component of
Y1 Ba 2 Cu 3 O 7y d in 90% and other compounds ŽY2 O 3 ,
BaCuO 2 , Y1 Ba 2 Cu 4 O 8y d , Y1 Ba 2 Cu 5 O 9y d and
CuO. in low quantities. Their conventional isothermic onset and critical temperatures were 94 and 91
K, respectively. As is seen, significant jumps aX aY ,
bX bY , cX cY , dX dY , eX eY and f X f Y appear equally during
cooling and heating stages in the dispersion and the
absorption curves, which demonstrate the gradual
nature of N–S and S–N transitions depending on
local inhomogeneities of the samples.
In order to explain the discontinuities of the curves
x X –Tt and x Y –Tt , the change of the state of a
coherent domain can be analyzed. As a consequence
of the cooling, the region in question goes over into
superconducting state and so the magnetic field is
repulsed from its volume into the environment. The
appearing flux jump induces a voltage pulse due to
the sudden change of the properties of this island and
warms up temporarily its surroundings with the help
I. Kirschner et al.r Physica C 290 (1997) 206–214
of the transient current. The local heating w8x results
in an abrupt increase of the normal volume fraction
Ž x X . and a quick jump of the absorption Ž x Y .. Since
the magnetic energy flows out of the new superconducting region into its neighbouring material, this is
the direct cause of the appearance of the local S–N
transition as a consequence of the primary cooling.
The non-linearity of this process is strengthened by
thermodynamic cross-effects, i.e. local energy transformations, local fluctuation of the vortex density
and velocity and of the temperature w9x, which affect
the superconducting properties.
Due to the heating process, a small but macroscopic domain of the specimen loses its superconductivity, creating a new normal subsystem, which
increases the normal volume fraction until a flux
jump appears. The arising transient current conveys
over the magnetic field into the new normal island
from its environment, resulting in cooling of the
material in the vicinity of this new normal region. It
produces a fast increase of the superconducting volume fraction Ž x X ., which is accompanied by sudden
change of the absorption Ž x Y . at the same time. The
direct reason of the appearing N–S transition is the
conduction of the magnetic energy into the new
normal domain, in consequence of which the magnetically depleted normal environment cools down
temporarily into superconducting state. Although the
process is originally non-linear, this character is
amplified further by thermodynamic cross-effects.
Application of a temperature pulse superposed
onto the state of originally non-equilibrium temperature distribution induces primarily a temporal change
of local energy density leading to a thermodynamic
instability in the sample. The effect of this pulse can
be directly detected by the investigation of unusual
behaviour of the DC voltage UR and AC voltage UL
appearing on the specimens due to the thermal instability created.
Measurements were carried out on bulk ceramic
Y1 Ba 2 Cu 3 O 7y d samples of sizes 6 = 6 = 18 mm3
and 6 = 6 = 21 mm3 having onset, critical and AC
magnetic onset temperatures T0 s 97 K, Tc s 92 K
and T0m s 112 K, respectively. The samples have
been prepared from YŽ1,2,3. powder Žwith an average grain diameter of ; 1 mm. by dynamic pressing
of high pressure, employing the so-called mechanochemical effect. This procedure provides highly
209
Fig. 3. Variation of the top and bottom temperatures during a
cooling process, indicating the applied thermal pulse by an arrow.
compact specimens of high density in the interval of
4.82–4.89 grcm3 , having a very smooth surface.
The specimens are very pure w6x, the composition of
which is Y1.01 Ba 1.95 Cu 2.97 O 7y d in 95 mass%, containing impurity compounds Y2 O 3 , BaCuO 2 and CuO
in less than 5 mass% and impurity metals Fe, Si, Al,
Ti, V, Zn, Cr, Ni and Co only in the concentration
below 0.005 mass%. After the thermal cycling they
have a very homogeneous microstructure detected by
electron microscopy. During the experiments low
exciting magnetic fields of 0.1–1 Oe at frequencies
of 1 kHz–1 MHz and DC driving currents of 100–
250 mA were used. The investigation procedure can
be drawn as a simultaneous and continuous measurement w10x of the time dependence of the temperature
gradient Žcaused by different Tt and T b ., and of UR
and UL before and after application of a temperature
pulse. T b was kept at 84–85 K during the process of
measurements, according to this the bottom end of
the samples was continuously in superconducting
state, while Tt had values above T0m at the beginning
of the cooling process and then moved towards Tc
Žsee Fig. 3... This operation results in a non-equilibrium spatial temperature distribution which is the
necessary condition of the thermal instability, as the
middle part of the specimens becomes into an intermediate state, when normal and superconducting islands coexist in it, depending on the local sample’s
properties and actual values of the temperature at the
given place. The middle part of the samples on
210
I. Kirschner et al.r Physica C 290 (1997) 206–214
Fig. 4. Change of the DC voltage and AC voltage having a
damped oscillation superposed onto their continuous decrease.
which the pick-up coil was wound can be taken as its
active zone, which has a volume of V s 6 = 6 = 6
mm3. Employment of a negative temperature pulse
onto the specimen Žmarked with an arrow in Fig. 3..
creates a damped oscillation in UR and UL Žsee Fig.
4., if T b F Tc < Tt F T0m is fulfilled, which represents an intermediate range of the sample large
enough for the development of coexisting normal
and superconducting domains. Similar experiments
lead to the same effect Žsee Figs. 5 and 6., the result
of which together with the earlier mentioned one
concerning UL is demonstrated in Fig. 7.
Fig. 5. Variation of the bottom and top temperatures during a
cooling process slower than the earlier one together with a thermal
pulse, that is marked by an arrow.
Fig. 6. Change of the DC voltage and AC voltage possessing a
damped oscillation on their continuous decrease.
Based on the correspondence, by which decreasing UL and UR characterize an increasing superconducting Žand decreasing normal. volume fraction and
vice versa, UL s max and UR s max represent zero
diamagnetism and maximum resistivity, while UL s 0
and UR s 0 demonstrate total diamagnetism and zero
resistivity. The oscillation of UL and UR can be
attributed to the sudden disturbance of the originally
non-equilibrium thermal state of the specimens in the
presence of coexisting normal and superconducting
Fig. 7. Oscillations of AC voltage during different cooling processes in Y1 Ba 2 Cu 3 O 7y d specimens.
I. Kirschner et al.r Physica C 290 (1997) 206–214
domains. As far as the direct physical reason is
concerned, the fluctuation of N–S and S–N transitions of coherent islands due to the thermal pulse
may be found, determined by the local material’s
structure, temperature and magnetic field.
The up–down oscillation of the curve UL versus t
demonstrates unambiguously the temporal fluctuation of the ratio of superconducting and normal
volume fractions. Seeing that the fluctuation of the
curve UR versus t has the same periodicity and
shape, it hints at the dissipative character of the
process, which is supported by its damped nature.
ŽThis observation seems to contradict the adiabatic
criterion of local S–N or N–S transitions w11,12x,
which precludes the possibility of energy dissipation
during this fluctuation..
4. Interpretation of the phenomenon observed
The evaluation of these experiments provides
some characteristic physical parameters, which can
be directly extracted from the measurements accomplished. The extent of DUL measures the change of
L of the detecting coil and that of x X related to the
increase or the decrease of the normal and superconducting volume fractions during the full time period
2t th of the oscillation. Since the well-measurable 20
peaks of Figs. 4 and 6 give an average ratio of
DVrV s 4.3% for transforming domains, it results in
a direct determination of the mean linear dimensions
of the coherent domains as l s 2.1 mm, if every DUL
is supposed to represent the transformation of a
single island. The average characteristic time of the
full superconducting–normal–superconducting or
normal–superconducting–normal Žflip–flop. transition can be estimated from the phase of the peaks in
Fig. 7, as 2t th s 15 s and so t th s 7.5 s. Based on
these data, the mean velocity of the spread of the
thermal instability inside a given coherent domain is
obtained as Õth s 0.3 mmrs. If Õth is calculated
individually for each domain, it provides very similar
magnitudes. Thus, to extend this value for the whole
sample seems to be reasonable, presuming macroscopic homogeneity in the material Žwhich is plausible in consequence of the observed global superconductivity in the specimens.. This consideration leads
to an average result for the velocity of the propaga-
211
tion of the thermal instability in Y–Ba–Cu–O high-Tc
superconductors in the order of the value got above.
Results of an independent experiment on optically
induced magnetic relaxation in a ceramic Y–Ba–
Cu–O SQUID w13x confirm the values of l and t th
obtained from our measurements. When a visible
light of 10 mWrmm2 was switched on or off onto
the wall of the SQUID having a thickness of d f 2
mm, in a low magnetic field at 77 K, the change of
the magnetic moment M shows an exponential relation
M Ž t . s M0 eyt r t ,
Ž 1.
with the time constant t f 5 s, where M0 is the
starting value of M at the time t s 0. Since this
experiment can be taken as an indirect investigation
of the thermal disturbance, its characteristic parameters d and t correspond to l and t th , respectively,
having values very close to our data.
The phenomenon observed can be explained thermodynamically as a giant macroscopic flux creep
appearing in high-Tc superconductors as a consequence of the thermal disturbance employed.
This statement is directly supported by the results
of other investigations, too. As is shown in a former
paper w14x, the dependence of the ratio of the vortex
creation energy Ev to the condensation energy Ec on
the Ginzburg–Landau parameter k is less, than 10y3
in the range of k G 100 in high-Tc superconductors.
This means, that a great number of vortices can
come into being, when a local domain of the sample
reaches the mixed state due to the varying temperature gradient and applied DC and AC magnetic
fields. The quantity of the far non-equilibrium change
of energy during N–S or S–N transitions characterizes the sizes of the transforming coherent domains
and render possible to develop or cease local vortex
densities in the specimen. Different specific values
of the energy absorbed or emitted by different domains, corresponding to the peaks of Figs. 1 and 2
reflect the change of the local superconducting Žor
normal. share-rate at different places of the samples
via the magnitude of the condensation energy. The
appearing or disappearing flux line densities are
n v s 10 6 –10 7rcm 2 as determined by the experimental conditions detailed above.
In order to characterize the interaction between
ith and the k th straight and parallel vortex lines of
I. Kirschner et al.r Physica C 290 (1997) 206–214
212
an arbitrary arrangement, the local magnetic field
can be introduced, that can exist in the centre of one
vortex originated from the other w15–18x as
h i k s h k i s h i Ž r k . s h k Ž ri . s
s
F0
2 pl
B0
2
r k y ri
ž
l
/
F0
2 pl
2
B0
,
ž
ri y r k
l
/
Ž 2.
where F 0 is the magnetic flux quantum, B0 is the
zeroth order Bessel function of imaginary argument,
r is the space vector and l is the mean penetration
depth l s Ž l2a b l c .1r3. This leads to a potential of
repulsive interaction
F 02
Pi k s Pk i s
s
8p 2l
F 02
2 2
8p l
B0
ž
B
2 0
ž
< ri y r k <
< r k y ri <
l
l
/
/
,
Ž 3.
which varies by ry1 r2 eyr r l, if the vortex density is
low enough, i.e. r s < r < s < r i y r k < s < r k y r i < ) l and
becomes divergent as lnŽ lrr . in the case of high
vortex density, i.e. when r - l. If the vortex lines
are curved, the interaction between 3D vortex pairs
can be described by a vectorial potential w19,20x
Pi k s Pk is
s
F 02
8p r l
F 02
8p r l
)
)
eyr r l w d r i = d r k x
)
)
eyr r l w d r k = d r i x .
Ž 4.
These results are valid at vortex densities up to
HrHc2 f 0.2–0.25, increasing the range of the magnetic repulsion until l) s lrŽ1 y HrHc2 .1r2 and
revealing the existence of a competing attractive
interaction, too in the range of j ) s jrŽ2 y
2 HrHc2 .1r2 , which originates from the accidental
overlapping of vortex cores at low fields.
Numerical calculation in the case of our samples
˚ . shows, that in the vicinity of the
Žwhere l f 1800 A
temperature at which the thermal pulse is applied,
the variation of the strength of the external magnetic
field by one order induces a change of the interaction
potential of repulsive character by two orders. It
provides a suitable starting condition w21x for the flux
creep, activated by a thermal fluctuation. The magnitude of developing creeping effect is only very
weakly limited due to the experimentally produced
huge fluctuation of states and thus it may be very
large as compared to the conventional one.
According to an elastic model of vortex line
lattice w22x, the total force acting on it contains the
elementary pinning force f p , the driving force fd and
the deformation force fdef , too. Supposing that the
pinning centres are randomly distributed in the sample and the distance between vortex lines and pinning centers is in the order of the size of the latter,
the effective pinning force Fpeff can be obtained by
the direct summation of f p , i.e.
Fpeff s Np f p
if
f p ) 12 Cs,
Ž 5.
where Np is the volume density of the pinning
centres, C is the elastic modulus of the vortex lattice
w23x and s is the static flux line spacing. This
relation confirms again the possibility of the appearance of a large flux creep, if the local parameters
have the values of current density, magnetic field,
pinning centres, pinning sizes, pinning forces and
vortex line spacing as J s 0.5–0.7 Arcm2 , H s
H DC q HAC s 1–2 Oe, Np s 10 10 –10 12 cmy3 , f p s
10y1 2 –10y10 N and s s Ž3–5. = 10y4 cm, respectively. In this case the difference of minimum 1–2
orders among the acting forces to the benefit of the
pinning force prevents the continuous flux flow, but
the eleastic vortex lattice is able to creep due to a
suitable fluctuation.
As the early measurements carried out on Y–Ba–
Cu–O materials demonstrate w24x, the N–S transition
in high-Tc superconductors can be broadened by the
application of an external magnetic field H. In the
case of Y-based samples the observed wide tail of
resistivity–temperature curves increases even 5–7
times the width of the transitional range. A similar
result on a LaŽSr. –Cu–O single crystal in the presence of an electric current, I, was observed by
Kitazawa et al. w25x, who showed that the large
magnetic broadening of the transition was determined mainly by the angle between H and the c-axis
and was practically independent from the angle between H and I. According to other experiments
w26–28x, by which the broadening of the resistive
transition can also be attributed to the magnetic field
along the c-axis, this observation corresponds to a
Lorentz-force-free dissipation, in that not the vortex
motion, but the high fluctuation plays the dominant
I. Kirschner et al.r Physica C 290 (1997) 206–214
role. In this case the observed resistivity is ohmic.
This effect can be explained in the frame of the
concept of giant vortex creep w29–31x, supposing a
low pinning potential of the order of thermal energy
kT Žwhere k is the Boltzmann constant..
Looking for the essential reasons of the broadening of the resistive transition D r s D r Ž H,T ., its
main part originates from the thermal fluctuation of
the order parameter w32x at high temperatures near
Tc . This effect manifests itself in developing and
decaying superconducting islands. Thermal nucleation of vortex–antivortex pairs can also appear,
having less importance and leading to the Kosterlitz–Thouless transition w33,34x and non-ohmic power
dissipation. In the lowest tail region, low dissipation
depending on the H–I angle can also be detected
w35x hinting at the very limited thermally assisted
flow type continuous vortex motion.
A significant contribution of the fluctuation was
also emphasized by reversible magnetic susceptibility measurements on Y–Ba–Cu–O w36,37x, where
the observed discontinuities at low magnetic fields
can be caused by the vortex lattice, just only starting
to form.
In contrast with these measurements, our experiments have been designed on the basis of a new and
radically different principle in order to attain a giant
flux creep by a large thermal disturbance introduced
into the specimen. It consists of a slowly time-dependent non-equilibrium thermal gradient along the
sample, to which a relatively fast temperature pulse
is added. As their collective effect, a thermal instability appears primarily in the form of a temporal
oscillation of local energy density. The aim of this
experiment is exactly to create intentionally a huge
fluctuation to bring about a giant vortex creep in the
least restricted way. Since the oscillation DUL of UL
has maximum values of 8–15% and average values
of 4.1–4.5% concerning different measuring series,
they seem to be large enough to exceed the conventional critical fluctuations and to establish a giant
flux creep. This fundamentally new type of fluctuation is produced by using a complex thermal disturbance created from outside and can therefore be
considered as a huge extrinsic thermodynamic fluctuation.
As is well-known, different kinds of vortices come
into being in high-Tc superconductors depending on
213
the microstructure of the specimen and on the temperature and external magnetic field. It means, that
besides the conventional flux lines, other types of
vortices can appear Že.g. point vortices in Cu–O
planes, threading the layers, pancake vortices,
Josephson vortices, vortex kinks composed of point
vortices and Josephson ones, evaporation of single
vortex lines into independent point vortices, dissociation of vortex–antivortex pairs, flux line nucleation,
vortex line cutting and recombination.. Under the
effect of highly non-equilibrium and unstable conditions arising due to the created huge fluctuation, the
actual vortex state can be formed as a mixture of
coexisting unlike vortices having strongly time-dependent behaviour. The vortices interact with pinning centres, each other and currents existing in the
sample, moreover they are expected to be subjected
to different possible Õortex phase transitions producing highly non-linear phenomena. According to these,
the state can be characterized by a temporarily decaying series of vortex transformations after each
amplitude of the fluctuation. To understand the nature and the effect of pinning centres in high-Tc
compounds, the relations and transformations of vortices, their actual reasons, rates and speeds claim
further and detailed investigation. It must be noted,
however, that the flux-creep measurements furnish a
very important way for the research of microscopic
mechanisms of the flux dynamics and pinning in
high-Tc superconductors.
5. Conclusions
The research discussed above leads to some general conclusions as follows.
Ž1. The thermometric mapping method as an effective procedure of investigation is capable to provide new information on non-linear dynamic phenomena taking place in high-Tc superconductors.
Ž2. Combining this method with a temperature
pulse, a thermal instability is induced in the superconducting material resulting in a directly detectable,
huge fluctuation of superconducting and normal
states. The thermal disturbance influences strongly
the vortex state of samples, causing the development
of a giant flux creep. The velocity of the propagation
of the thermal instability within a coherent domain
214
I. Kirschner et al.r Physica C 290 (1997) 206–214
can be determined by the method elaborated and its
value can be extended to the bulk material.
Ž3. This research may be continued in the direction to detect the possibly arising thermal wave,
similar to the second sound in superfluid helium. For
this purpose, the same thermal disturbance, as discussed above, should be created in a given place of
the sample in order to observe and measure its
possible effect at a reasonable distance from this
point.
References
w1x R.F. Giese, M. Runde, Fault Current Limiters, Study of the
International Energy Agency, Argonne, 1991, 63 pp.
w2x I. Kirschner, J. Bankuti,
M. Gal,
´
´ K. Torkos, Phys. Rev. B 36
Ž1987. 2313.
w3x A.C. Bodi,
Phys. Lett. A 158
´ I. Kirschner, S. Leppavuori,
¨
Ž1991. 318.
w4x I. Kirschner, S. Leppavuori,
A.C. Bodi,
¨
´ A. Uusimaki,
¨ I.
Dodony,
Appl. Supercond. 1 Ž1993. 1721.
´
w5x A.C. Bodi,
´ I. Kirschner, Phys. Lett. A 181 Ž1993. 479.
w6x I. Kirschner, A.C. Bodi,
A. Uusimaki,
´ S. Leppavuori,
¨
¨ I.
Dodony,
T. Porjesz, Phys. Lett. A 178 Ž1993. 315.
´
w7x A.C. Bodi,
Z. Physik B 97
´ I. Kirschner, S. Leppavuori,
¨
Ž1995. 481.
w8x M. Frank, A. Sigsaas, L. Stradolsky, S. Cooper, Phys. Rev. B
43 Ž1991. 5321.
w9x I. Kirschner, K. Martinas,
´ J. Low Temp. Phys. 14 Ž1974.
427.
w10x I. Kirschner, A.C. Bodi,
Physica C
´ R. Laiho, E. Lahderanta,
¨
252 Ž1995. 22.
w11x J.L. Tholence, H. Noel, J.C. Levet, M. Potel, P. Gougeon,
Solid State Commun. 65 Ž1988. 1131.
w12x A. Gerber, Z. Tarnawsky, J.M. Franse, J.N. Li, A.A. Menovsky, Appl. Supercond. 1 Ž1993. 961.
w13x R. Laiho, E.V. Il’ichev, V.M. Zakosarenko, Physica C 223
Ž1994. 123.
w14x I. Kirschner, R. Laiho, Z. Physik B 100 Ž1996. 179.
w15x C. Caroli, P.G. de Gennes, J. Matricon, Phys. Lett. 9 Ž1964.
307.
w16x J. Bardeen, M.J. Stephen, Phys. Rev. A 140 Ž1965. 1197.
w17x K. Maki, Physics 1 Ž1964. 21.
w18x K. Maki, Physics 1 Ž1964. 127.
w19x E.H. Brandt, Phys. Rev. B 34 Ž1986. 6514.
w20x E.H. Brandt, J. Low. Temp. Phys. 28 Ž1977. 291.
w21x I. Kirschner, S. Leppavuori,
R. Laiho, I. Altfeder, I. Ddony,
¨
A. Uusimaki,
T. Porjesz, J. Hagberg, Gy. Kovacs,
E.
¨
´
Lahderanta,
A. Volodin, G. Zsolt, Z. Physik B 85 Ž1991.
¨
175.
w22x I. Kirschner, K. Martinas,
´ J. Low. Temp. Phys. 47 Ž1982.
105.
w23x J. Matricon, Phys. Lett. 9 Ž1964. 289.
w24x Y. Yye, T. Tamegai, H. Takeya, H. Takei, Jpn. J. Appl.
Phys. 26 Ž1987. L1057.
w25x K. Kitazawa, S. Kambe, M. Naito, I. Tanaka, H. Kojima,
Jpn. J. Appl. Phys. 28 Ž1989. L555.
w26x T.T.M. Palstra, B. Battlog, R.V. van Dover, L.F.
Schneemeyer, J.V. Vaszczak, Phys. Rev. B 41 Ž1990. 6621.
w27x H. Safar, P.L. Gammel, D.A. Huse, J. Bishop, J.P. Rice,
D.M. Ginsberg, Phys. Rev. Lett. 69 Ž1992. 824.
w28x Ph. Seng, R. Gross, U. Baier, M. Rupp, D. Koelle, R.B.
Huebener, P. Schmitt, G. Saemann-Ischenko, L. Schultz,
Physica C 192 Ž1992. 403.
w29x Y. Yeshrun, A.P. Malozemoff, Phys. Rev. Lett. 60 Ž1988.
2202.
w30x D. Dew-Hughes, Cryogenics 28 Ž1988. 674.
w31x P.H. Kes, J. Aarts, J. van der Berg, C.J. van der Beek, J.A.
Mydosh, Supercond. Sci. Technol. 1 Ž1989. 242.
w32x E.H. Brandt, Act. Pass. Electr. Comp. 15 Ž1993. 193.
w33x J.R. Clem, Phys. Rev. B 43 Ž1991. 7837.
w34x P.H. Kes, J. Aarts, V.M. Vinokur, C.J. van der Beek, Phys.
Rev. Lett. 64 Ž1990. 1063.
w35x W.K. Kwok, U. Welpand, G.W. Crabtree, Phys. Rev. Lett.
64 Ž1990. 966.
w36x W.C. Lee, R.A. Clemm, D.C. Johnston, Phys. Rev. Lett. 63
Ž1989. 1032.
w37x W.K. Kwok, J. Fendrich, S. Fleshler, U. Welp, J. Downey,
G.W. Crabtree, Phys. Rev. Lett. 72 Ž1994. 1092.