flux jumps in high tc single crystals

Applied Suprrcondwctivity Vol.1, Nos 7-9, pp. 961 - 970, 1993 Printed in Great Britain. All rights reserved

0964-1807/93 $6.00 + 0.00 Copyright @ 1993 Pergamon Press Ltd

FLUX JUMPS in HIGH T, SINGLE CRYSTALS

A.Gerber, ZTarnawski, J.J.M,Franse, J.N.Li and A.A,Menovsky

Van der Waals - Zeeman Laboratorium,

Universiteit van Amsterdam,

Valckenierst~t 65, 1018 XE Amsterdam, The Netherl~ds

The magnetic responce of LaSrCuO and BiSrCaCuO single crystals has been investigated

under quickly varying applied magnetic field. Sharp repetitive jumps in the magnetization vs.

field curve were observed and studied as a function of the magnetic field sweep rate. The

effect is interpreted as an avalanche - like flux flow, caused by a run-away break of the

superconductor stability and the transition from isothermal to adiabatic limit of the flux

propagation.

One of the main shortcomings of the usually discussed critical state models is the

assumption of strictly isotherms conditions during the process of current and flux

penetration into the bulk of hard type II superconductors and in particular, of high

temperature superconductors. The isothermal assumption is, however, invalid in many

situations and departure from isothermal conditions can be the source of numerous

p~uli~ties. For the early su~rconducting coils, the field produced in the bore

generally rose in a series of small abrupt steps which became known as “flux jumps”,

even when the current was increased extremely smoothly. These jumps could be

detected either by monitoring the field in the bore or by careful measurements of the

voltage appearing across the coil or part of it. These flux jumps could have a wide

range of magnitudes, and the large ones could initiate the appearance of a normal zone

and thus cause a premature quenching of the coil. This effect is therefore of paramount

importance for technical applications and has attracted much attention in the late sixties.

The successful construction of multi~lament high-field magnets is a direct result of

these efforts. Inspite of this technical success, the detailed unders~nding of the

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962 World Congress on Superconductivity

underlying mechanism is far from being reached. The investigation of flux instabilities

in high temperature superconductors is challenging in relation to their potential

applications as well as in view of a fundamental understanding of the phenomenon.

As was pointed out by Kim et al.’ and by London* the penetration of flux into a hard

type II superconductor is a dissipative process. In a purely isothermal case the

dissipated energy is immediately absorbed by the bath. However, in large size type II

superconductors, including the high temperature superconductors, the magnetic

diffusivity D, can be much larger than the thermal diffusivity Da. Under conditions

of appreciable flux flow, flux will be free to move and generate heat much more

rapidly than the heat can be conducted away. Let us consider a situation in which the

material is carrying current to a depth x from the surface. We now let the external field

to change or the current to increase so that further flux penetrates into the material.

There is dissipation at all points to the depth x, and a consequent temperature rise

which is determined by the quantity and rate of movement of flux at each point, by the

distance of the specific point to the sample surface and by the thermal diffusivity of the

material. However small this rise is, it results everywhere in a decrease in the value

of the critical current J, and, therefore, in a deeper penetration of flux. This, in turn,

is accompanied by a further dissipation and a further temperature rise. Under

favourable conditions the material remains superconducting, although the field

distribution can hardly be expected to confirm the predictions of an isothermal theory.

Under unfavourable conditions the process can lead to thermal, and therefore magnetic,

run-away.

All experiments reported here have been performed on single-crystalline samples of

LaSr,CuO, and Bi,Sr,CaCu,O which have been prepared by using a travelling-solvent-

floating-zone technique3. The LaSrCuO sample has a disk shape form with a radius of

about lmm and a thickness of 1 mm. The BiSrCaCuO sample is an as-grown piece of

material containing a pile of c-oriented single crystalline slabs. For both samples the

field is oriented along the c-axis.

The main part of the measurements has been performed in the 40 Tesla semi-

continuous field facility at the University of Amsterdam. This installation can produce

World Congress on Superconductivity 963

any pulse shape that is compatible with the thermal and mechanical constraints4. The

field sweep rate can be regulated within the interval from 0.1 T/XX up to 60 Tlsec

after an initial rapid field increase to 1 T. The magnetization is measured by integration

of the output voltage of a carefully compensate coil system. Complement

magnetization measurements have been performed at constant fields up to 7 Tesla by

a two-coil extraction technique, Magnetocaloric measurements have been performed

using a 3He specific heat insert in a cryostat provided with a superconducting magnet.

An explicit illustration of the energy dissipation during the field sweep and by flux

jumps is given in Fig. I. In this experiment a LaSrCuO single crystal was kept in quasi-

adiabatic conditions and its temperature was monitored during a slow variation of the

applied field. A stable heating of the sample due to the continuous penetration of the

flux is interrupted by sharp temperature spikes caused by the run-away flux jumps’.

10

0

6

4

2

?5 0

0 0 0 0 0 0

6 0 0 0 0 0 0 0

B DO

0 0 0 0

0

0 200 400 600 800 1000 1200

t (sl

Fig.1. Temperature variation of the LaSrCuO single-crystalline sample under quasi-adiabatic

conditions during a constant field sweep (the values above 6K are distorted due to improper

thermometer calibration in the high temperatures range).


In presumably isothermal conditions, i.e. the sample is immerse in a liquid helium

bath, flux jumps manifest themselves in the magnetization curves when the applied field

is varied quickly. The irreversible magneti~tion loops of the single-Vaseline sampie

of LaSrCuO are shown in Fig.2 as measured under different conditions of the field

variation at 4.2 K: a) dH/dt = 0, i.e. the field is stabilized and the measurement is

performed 30 seconds later; curves b) and c) have been observed when the field has

been swept with constant rates of 5 and 42 T/XX respectively.

-6 1 I I t I I 0 2 4 6 0 10

B (T1

Fig.2. Irreversible magnetization loops measured in the single-crystalline sample of LaSrCuO

at 4.2 K at different applied field sweep rates: (ml - dB/dt = 0; (0) - dB/dt = 5 T/set;

(~1 - dB/dt = 42 Tlsec.

The difference between the various results is dramatic and demonstrates a

magnetization modulation that depends on the rate of the field change. The smooth

curve in case (a), that is usually observed, is replaced by a sharp saw - tooth structure

(b) which in turn is replaced by a stable but strongly suppressed magneti~tion loop in

(c). Different aspects of the flux instabilities should be discussed, but we shall


concentrate here only on two of them: the dependence of periodicity and magnitude of

the jumps on the applied field sweep rate.

The repetition of the magnetization jumps (Fig2b) can be described as semi-

periodic. Although one also finds a number of randomly distributed partial jumps, the

periodicity of the main jumps is found to be well defined by the field sweeping rate

dB/dt. We show in Fig.3 the repetition period of the jumps as a function of the sweep

rate.

1.4

1.2

1.0 i=

‘5: 0.8

r-

’ 0.6

is 3

-) 0.4

0.2

0.0

I I

0

I

IO0

I

101

dB/dt (T/set)

Fig.3. Magnetization jumps period of the LaSrCuO sample as a function of the field sweep

rate at 4.2 K in the vicinity of 3 Tesla.

Two regimes are found: 1) a “low” sweep-rate regime with dB/dt < 5 Tlsec in

which the oscillation period decreases with increasing sweep rate and can be

approximated by AB = ar - @logdBldt; 2) a “high” sweep rate regime with 5 T/set <

dB/dt < 20 T/set in which the period becomes independent of the sweep rate and

saturates to the limit of about 0.4 Tesla. For still higher sweep rates, i.e. dB/dt > 20

T/set, no jumps are observed (see Fig. lc). The situation described here is very similar

966 World Congress on Superconduclivity

to that previously reported for the conventional superconducting alloys. The flux jump

field is found to decrease as logdB/dt in Nb3Sn6, NbZr7 and saturate assymptotically

at high sweep rates* in the same way as we find in LaSrCuO.

A description of the magneti~tion jumps can be given’ by an extension of the critical

state model” by including the effects of heating when magnetic flux enters or leaves

the bulk of the superconductor. In the adiabatic limit of a semi-infinite sample, the

problem can be solved analytically. The critical field at which the instability occurs,

H, (flux jump field), is given by:

Jc H&CNC3Cv--]'~

iII&.pT (1)

where C, is the specific heat per unit of volume, J, is the critical current density and

(Y a coefficient of the order of unity8.

Assuming that C, = flT3 and J, = J,(O){1 .. TIT,), (Eq. 1) gives the temperature

dependence of the flux jump field as:

H~-[a~3~TcT3(1-TfTc)]1~ (2)

This equation passes a maximum for T = 0.75T, and falls to zero both at T = 0 and

T = T,. For the LaSrCuO sample with T, = 34 K and C, = 17T3 (erg/cm31Q1*, this

equation gives a maximum value for H, of about 8.6 kOe at 25 K and a value of 1.1

kOe at 4.2 IL

The condition that an excess or shielding field H, is larger than H, is expected to be

a necessary and sufficient condition for a flux jump when an additional small field

increment is applied adiabatically to the sample. It is important to note that H,

represents the shielding field, rather than the absolute magnitude of the field. There is

no difference, therefore, between the value of the first flux jump field H, and the

period between the subsequent full jumps AB. The adiabatical concept requires that no

heat leaves the volume of the flux front during the instability. The fulfillment of this

condition is usually estimated by comparing the thermal rti and magnetic r_ diffusion

time, both are inversely proportional to the corresponding diffusion coefficients I& and


D _. D, can be calculated as D,,, = K/C,, where K is the thermal conductivity. Taking

for LaSrCuO the value K = 0.002 W/cmK” we get D, = 10 cm*/sec at 4.2 K. On the

other hand, the magnetic diffusivity related to the viscous motion of vortices D,, can

be expressed in terms of the flux-flow resistivity’* as D, = p,BIB,,, where pa is the

normal state resistivity, which gives D,, of the order of 104 cm*/sec under the field

of 1 Tesla. A simple comparison between Dm and D,, implies that the adiabatic

conditions are automatically met in this material and the model is valid. However, the

flux jump field H, given by (Eq. 1) depends only on the intrinsic material parameters:

specific heat, critical current density and its temperature derivative, and not on the

external conditions like the field sweep rate, which is found to influence strongly the

jumps periodicity (Fig.3).

5

0

I I I

0

0

x .

1 I

.

x I I I

100 IO1 IO2

dB/dt (T/set)

Fig.4. The maximum (0) and minimum lx) magnetization values (the starting and final jump

points) as a function of the sweep rate for single-crystalline LaSrCuO in fields in the vicinity

of 3 Tesla.


Not only the jumps periodicity but also their magnitude is found to depend on the

field sweeping rate. We show in Fig.4. the maximum and minimum magneti~tion

values (the starting and final jump points) as a function of the sweeping rate for single-

crystalline LaSrCuO in fields in the vicinity of 3 Tesla.

When the sweep rate is increased the maximum magnetization level reached between

the jumps (the external magneti~tion envelope) is found to decrease. On the contrary,

the internal magnetization envelope (minimum magnetization at which the jump is

stabilized) shows an opposite tendency: its value increases for higher sweeping rates.

As a result, the size of the jumps monotonically decreases and, what seems surprising,

the jumps are totally suppressed for the sweeping rates exceeding 20 Tlsec. This result

is interesting both technically and fundamentally. Technically, it implies that the

material becomes thermally and magnetic~ly stable when energized quickly (the

magnitude of the effective critical currents is, however, strongly reduced).

Fundamentally, it strongly suggests a development of a new equilibrium distribution

of the magnetic field inside the superconductor, its profile depending not only on the

intrinsic bulk parameter J,(T,B), but also on the rate of the flux variation when the

vortices enter or leave the body of the superconductor. In fact, the loss of the critical

state magnetization in high temperature superconductors is generally explained by a

giant flux creep. Intuitively, one expects that by increasing the field sweeping rate one

assymptotically approaches the maximum magnetization of the critical state. Indeed,

this effect has been recently calculated and observed*3. We find, however, that in the

limit of very high sweeping rates, the tendency is just the opposite and the desc~ption

of superconductors in the framework of standard models is misleading. The

development of this surprising result seems to be intimately connected to the intrinsic

magnetic ins~bility of a su~rconductor under varying magnetic field.

At ascribing the modifications of the magnetization to an intrinsic instability under

varying field, one has to take into account that at least part of the effects observed can

be caused by the overall heating of the sample. Several arguments convince us that this

assumption is not sufficient. Firstly, the typical behaviour is not modified when the

helium bath temperature is lowered below the superfluidity point and the heat transfer


to the bath is strongly improved. Secondly, in an adiabatic model of magnetic

ins~bilities the flux-jump field H, is expected to increase with tem~~ture as follows

from (Eqs. 1,2). Indeed, an increase of the jumps repetition period with temperature has

been observed in LaSrCuOn, as well as in YBaCu0i4 samples. Inspite of the increased

power dissipation we find a strong decrease of the jumps period when the sweeping

rate was increased from 0.5 to 5 Tlsec (Fig.3).

High-temperature as well as conventional low-temperature superconductors are

intrinsically unstable under varying magnetic fields. After its break-down, the critical

or quasi-critical state can be periodically recovered when the applied field-sweeping

rate does not exceed a certain limit, which is of the order of 1 - 10 Tfsec for the

studied single-crystalline samples of LaSrCuO and BiSrCaCuO. For higher sweeping

rates no periodic ins~bilities are observed and the magneti~tion is stabilized on the

lower level. This strongly suggests the development of a new equilibrium distribution

of the magnetic field inside the su~rconductor, its profile de~nding not only on the

intrinsic bulk parameter J,(T,B), but also on the rate of the flux variation when the

vortices enter or leave the body of the superconductor. In this regime, magneti~tion

curves are totally modified and their interpretation based on the standard models is

doubtful. We are not aware of theoretical attempts to describe the field distribution in

the hard superconductors under rapidly varying field.

The mechanism of the magnetic instabilities and the dynamics of a non-equilibrium

flux penetration into a superconductor wait for detailed studies. A number of basic

questions has to be clarified, among them the role of the field-sweeping rate, the role

of the surface layer, the dynamics of the flux run-away, its stabilization etc.


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flux jumps in high tc single crystals

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