Physlca C 209 (1993) 147-150 North-Holland

Magnetic Instabilities in High Temperature Superconductors

A.Gerber, Z.Tarnawski and J.J.M.Franse

Van der Waals - Zeeman Laboratonum, UmversiteR van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.

Magnetic instabilities in single-crystaUme samples of l~gh temperature superconductors have been studied by magnetocaloric and magnetization measurements under varying magnetic fields. Sharp repetitive jumps are observed and are interpreted as been caused by the avalanche-like flux flow and the transition from isothermal to adiabatic limit of the flux propagation. Periodicity, size and ttme duration of the instabilities are discussed.

One of the main shortcomings of the usually discussed critical state models is the assumption of strictly isothermal conditions during the process of current and flux penetration rote the bulk of hard type II superconductors and in particular, of high temperature superconductors. The isothermal assumption is, however, invalid m many situations and departure from isothermal conditions can be the source of numerous peculiarities. For the early superconducting 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 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 multifilament high-field magnets is a direct result of these efforts. Inspite of this technical success, the detaded understanding of the underlying mechanism is far from bemg reached. The investigation of flux mstabdlties in high temperature superconductors is challenging m relation to their potential applications as well as m view of a fundamental understanding of the p h e n o n l ~ n o n .

As was pointed out by Ktm et al.~ 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 htgh temperature

superconductors, the magnetic diffusivity D,~ can be much larger than the thermal diffusivity Dth. 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. When we change the external field, further flux penetrates into the material. There is dissipation, 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. Thts, m turn, is accompanied by a further dissipation and a further temperature rise. Under favourable eondmons 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 LaSr2CuO 4 and Bi2Sr2CaCu20 which have been prepared by using a travelling-solvent-floating-zone techmque 2.

The mare part of the measurements has been performed m the 40 Tesla semi-continuous field facdtty at the University of Amsterdam. This installation can produce any pulse shape that is compatible with the thermal and ,mechanical constraints 3. The field sweep rate can be regulated within the interval from 0.1 T/see up to 60 T/sec

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148 A Gerber et al /Magnettc mstabthttes m htgh temperature superconductors

after an initial rapid field increase to 1 T. The magnetization is measured by integration of the output voltage of a carefully compensated coil system. Complementary magnetization measurements have been performed at constant fields up to 7 Tesla by a two-coil extraction technique. Magnetocalonc 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 m Fig. 1. In this experiment a LaSrCuO single crystal was kept in quasi-adiahatlc 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.

12 ' , ' ' '

10

\ 6 °

o o o o o

4 •

2;

0

Q • o o

• ~ o • e

I I i I I

2oo ,4oo soo coo Iooo 12oo

t (s)

Fig. 1. Temperature variation of the LaSrCuO single- crystalline sample under quasi-adiabatic conditions during a constant field sweep.

In presumably isothermal conditions, i.e. the sample is immersed in a liquid helium bath, flux jumps manifest themselves in the magnetization curves when the applied field is vaned quickly. The irreversible magnetization loops of the single- crystalline sample of LaSrCuO are shown in Fig.2 as measured under different conditions of the field variation at 4.2 K: a) dH/dt -- O, 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/sec respectively.

8

-6 0 2 4 6 fl i0

B {T}

Fig.2. Irreversible magnetization loops measured in the single-crystalline sample of LaSrCuO at 4.2 K at different applied field sweep rates: ( I ) - dB/dt -- 0; (o) - dB/dt -- 5 T/sec; (v) - dB/dt -- 42 T/sec.

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 magnetization loop in (c).

The repetition of the magnetization jumps (Fig.2b) can be described as semi-periodic. Although one also finds a number of randomly distributed partial jumps, the periodiczty of the main jumps is found to be well defined by the field sweeping rate dB/dt. We show m Fig.3 the repetition period of the jumps as a function of the sweep rate.

Two.regimes are found: 1) a "low" sweep-rate regime with dB/dt < 5 T/sec in which the oscillation period decreases with increasing sweep rate and can be approximated by AB = ct - 131ogdB/dt; 2) a "high" sweep rate regime with 5 T/sec < dB/dt < 20 T/see 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/sec, no jumps are observed (see Fig. lc). The situation described here Is very s~rmlar to that previously reported for the conventional superconducting alloys. The flux jump field is fbund to decrease as logdB/dt in Nb3Sn,

A Gerber et al /Magnetw instabtlEttes tn high temperature superconductors 149

NbZr and saturate assymptotically at high sweep rates 4 in the same way as we find in l~SrCuO.

t o

E ~ o s

0 - 0 6

0 4

D

t 2

I

O 2

o o . . . .

0 0 ill

t o 1

On /d r ( ' r / see)

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.

In the adiabatic description s of a semi-infinite sample, the critical field at whtch the mstabihty occurs, H~ (flux jump field), is given by:

a.,rTaT] a (1)

where Cv is the specific heat per unit of volume, J¢ is the critical current density and ot a coefficient of the order of unity.

Assuming that C~ --- BT 3 and Jc -- J~(0)(1 - T/T¢), I~ passes a maximum for T = 0.75% and falls to zero both at T ffi 0 and T -- %. For the LaSrCuO sample with T~ ffi 34 K and Cv = 17T 3 (erg/cm3K) e, this equation gives a maximum value for Ho of about 8.6 kO¢ at 25 K and a value of 1.1 kOe at 4.2 K.

The fulfillment of the adiabatic condition is usually estimated by comparing the thermal ¢~ and magnetic ¢~s diffusion time, both are inversely proportional to the corresponding diffusion coefficients Do and D~, s. Dth can be calculated as D~

K/C.~, where K is the thermal conductivity. Taking for LaSrCuO the value K -- 0.002 W/cmK e we get D,h = 10 cm2/sec at 4.2 K. On the other hand, the magnetic diffusivity related to the viscous motion of vortices Dm~ can be expressed in terms of

the flux-flow resistivity as D ~ ffi o.B/Ba, where p. Is the normal state resistivity, which gives Dins of the order of 10 4 cm:/sec under the field of I Tesla, A simple comparison between Do 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 denvative, and not on the external conditions like the field sweep rate, which is found to influence strongly the jumps periodicity (Fig.3).

5

&--

~ 4

x 3 Z

- ' 2

. . . . . i

0

1

0 " . . . . " 10 0

. , . . . . . . . ] . . . . . . . . . . . . . . i

@

@

o

!

101 t0 2 ~ R / d t I T / s e c )

Fig.4. The maximum (o) and minimum (x) magnetization values (the starting and final jump pomts) 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 magnetization values (the starting and final jump points) as a function of the sweeping rate for single- crystalline LaSrCuO in fields m the vicinity of 3 Tesla.

When the sweep rate is increased the maximum magnetization level reached between the jumps (the external magnetizataon envelope) is found to decrease. On the contrary, the internal magnetization envelope (nunimum magnetization at which the jump is stabilized) shows an opposite tendene]~: its value increases for higher sweeping rates. As a result, the

150 A Gerber et al / Magnetic mstablhtzes m high temperature superconductors

size of the jumps monotonically decreases and, what seems surprising, the jumps are totally suppressed for the sweeping rates exceeding 20 T/sec. This result is interesting both technically and fundamentally. Technically, it imphes that the material becomes thermally and magnetically stable when energized quickly (the magmtude of the irreversible magnetizaUon is, however, strongly reduced). Fundamentally, it strongly suggests a development of a new dynamical dmtribution of the magnetic field inside the superconductor, its profile depending not only on the mtrmsic bulk parameter Jc(T,B), but also on the rate of the flux variation when the vortices enter or leave the body of the superconductor.

At ascribing the modifications of the magnetization to an intrinsic mstabihty 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. Ftrstly, the typical bebaviour is not modified when the helium bath temperature is lowered below the superflmdity point and the heat transfer to the bath is strongly improved. Secondly, in an admbatic model of magnetic instabilities the flux-jump field Ho is expected to increase with temperature as follows from (Eqs.l,2). Indeed, an increase of the jumps repetition period with temperature has been observed in LaSrCuO s. 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 T/sec (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 T/sec for the studied single-

crystalhne samples of LaSrCuO and BISrCaCuO. For htgher sweepmg rates no periodic instabdities are observed and the magnetization is stabilized on the lower level. This strongly suggests the development of a new dynamical equilibrium dmtnbutlon of the magnetic field w_side 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 flus regime, magnetization 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 m the hard superconductors under rapidly varying field.

The mechanism of the magnetic instabilities and the dynanucs of a non-eqmlibrium 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 stabd~zation etc.

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