Low field irreversibility in twinned and untwinned YBaCuO crystals

Physica A 200 (1993) 314-322 North-Holland SDZ: 037%4371(93)E0215-Z

Low field irreversibility in twinned and untwinned YBaCuO crystals L. Krusin-Elbaum, IBM Research,

Yorktown

L. Civale, Heights,

F. Holtzberg

NY 10598-0218,

and C. Feild

USA

An abrupt collapse of the irreversibility line is observed in both twinned and untwinned YBaCuO crystals within a critical regime. The exponent (Y of the power law describing the irreversibility line H,,, changes from 4/3 at high fields to larger values (between 1.5 and 2) below the collapse. We propose that the observed low field anomaly, which extends down to temperatures well below the irreversibility line, is associated with the thermal softening ds. Below this boundary which increases as TZ and crosses H,,, shifting it to lower crossover, which occurs when the mean-square thermal displacement ? (u’) of the vortices exceeds coherence length 5, the strength of the pinning is strongly reduced.

1. Introduction

Among the many exciting and controversial aspects of high temperature superconductivity are the new features discovered in the magnetic phase diagram. Below the mean-field upper critical field Hc2, the vortex-liquid state exists down to an irreversibility line associated with a transition into a vortexsolid phase [l]. In contrast to the conventional superconductors, the vortexsolid occupies now only a portion of the mixed phase. For a large melted regime to exist an extraordinary combination of high T, small 5 and large anisotropy must be present#’ and it has been argued that in these materials thermal fluctuations are being felt far away from the critical regime (i.e. from H&J PI. The boundary between vortex-liquid and solid phases has been probed early on with dc magnetic measurements on ceramic LaBaCaO by Bednorz and Miiller [3] and later observed in dc and ac susceptibility [4-61, vibrating reed [7] experiments, torque magnetometry [8], and transport measurements [9-111. With the diversity of experimental techniques and theoretical concepts it has been assigned a plethora of names: the depinning line, the melting line, the vortex-glass transition line, and the ‘irreversibility line’. Here we will use the term ‘irreversibility line’ as the most model-neutral. *r For general reviews of the magnetic phase diagram of high-T, superconductors, 037%4371/93/$06.00 @ 1993 - Elsevier Science Publishers B.V. All rights reserved

see ref. [I].

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Empirically, the irreversibility line is an upward curving line in H-T space which essentially delineates the onset of magnetic irreversibility at lower temperatures. It is well described by a power law Hi,, = A(1 - T/T,)”

.

There are differences

between various experiments in the values of amplitude a; values of (Y between 413 and 2 have been reported [3-111. The irreversibility line and its nearly logarithmic frequency dependence was related by Yeshurun and Malozemoff [4] to a very large time relaxation of magnetization, which they argued was due to the thermal activation of vortices over an energy barrier U as described by Anderson and Kim [12]. The simple scaling argument for U goes as follows: if U is proportional to the magnetic condensation energy HZ/&T times a characteristic excitation volume, for sufficiently large fields that volume could be limited laterly by the area which a single flux quantum occupies in the flux line lattice. This area is roughly ai = @$blB,the lattice constant squared. Along the applied field, the smallest extent of the activation volume is 5, hence U m (Hz/87r)&. According to Ginzburg-Landau theory H, m (1 - TIT,) near Hc2 and r scales as (1 T/T,)-? This gives Um(lT/Tc)3’2/B or (Y= 3/2. Indeed, CY= 312 is consistently seen in dc magnetization experiments, but ac measurements at 1 MHz reproducibly give (Yof 4/3, which seems to increase somewhat when the measurement frequency is decreased. In the vortex-glass theory [13] the ‘melting’ line scales essentially as Hc2 0~ 1 /t* in the critical regime [1,2,13]. There ,$ scales as (1 - Tl Tc)-2’3, giving cx = 413. It is not understood in this model why 413 should hold outside of the critical regime as seen experimentally, and none of these theories predict a change in (Ywith measuring frequency. And finally, the melting of a lattice in a pure system is possibly governed by cx = 2, at least in the low field regime [14]. A as well as in the exponent

2. AC susceptibility - determination of the irreversibility line

Some of the observed differences in the irreversibility line are surely due to the differences in the current resolution limits of various techniques. The ac susceptibility, for example, has an order of magnitude better current sensitivity than dc magnetization measurement. The ac technique consists of placing a sample inside a coil supplying a uniform ac field h,, = h, e’“‘, which may be superimposed with the dc field Hdc. In a normal metal or in a superconductor without pinning characterized by a linear resistivity p, the ac field will induce

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eddy currents which will decay within a skin-depth 6, = (c~~/~Tw)“~. The real or in-phase component of the ac susceptibility x’ measures the amount of shielding, and the imaginary or out-of-phase component x” measures the energy loss due to the induced currents. x” exhibits a maximum when the skin-depth 6, equals the thickness [15] of the sample. This resistive absorption is a linear effect and so S, does not depend on the amplitude of the ac field h, [16]. In a superconductor with pinning, E-J (Z-V) curves are nonlinear in some range of fields and temperatures. The condition ‘penetration depth 2: thickness’ may now occur [15,16] #2 in the linear or nonlinear portion of the E-J curves depending on J, w and sample dimensions. In the fully developed critical state [18], Maxwell’s law implies that the magnetic induction B will decay linearly from the surface, not exponentially as in the Ohmic case. The ac field will penetrate to a depth D, = (c/47r)h01J,, beyond which the ac field is totally screened. Thus in the nonlinear regime, the penetration depth D, (and x) will depend on h,. We define the irreversibility line at the onset of nonlinearity, which, of course, is a result of pinning [6]. Irreversibility lines for YBa,Cu,O, crystal measured at 1 MHz with h, = 0.1 Oe and in dc fields up to 6 tesla are shown in fig. 1 for the two extreme alignments of the crystal with respect to the applied dc field. For this 30 km thick crystal, at w = 1 MHz and small excitation amplitude h, of 0.1 Oe, the position of the maximum roughly separates regions of linear and nonlinear amplitude response and corresponds to a current density of =20 A/cm2. For a crystal of different dimensions, the frequency must be adjusted in order to have the transition into a nonlinear response to be at the maximum of x”. At w = 1 MHz, the peak in x” occurs at a resistivity of 3.6 x 10e7 cRcm. Transport measurements on a similar crystal [10,15] confirm

T (K) Fig. 1. Irreversibility lines for a twinned at 1 MHz with h, = 0.1 Oe.

X2 Another ref. [17].

way is to search

YBaCuO

for the onset

crystal

for Hkc and Hi, to the c-axis measured

of the 31d harmonic

in ac response.

See for example

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that under these conditions the maximum in x” will occur very near the temperature where nonlinear behavior is first noted in E-J curves.

3. Irreversibility

collapse at low fields

Now we will describe a remarkable behavior we have recently discovered in low dc fields, namely a sudden collapse of the irreversibility line [6] near T, above the lower critical field H,,. Observed in ac susceptibility measurements, the irreversibility line undergoes an abrupt jump from the usual power-law observed at high fields into a lower field regime near T,, where it follows a different power-law, and where the reversible region is considerably enlarged. We propose that this observation represents experimental evidence for the existence of the thermal softening boundary, below which the pinning force is substantially reduced due to delocalization (on the scale of the coherence length) of vortex cores by thermal fluctuations. Such new crossover in vortex behavior was suggested recently by Feigel’man and Vinokur [19]. They point out that if the pinning involves a highly localized core pinning mechanism on the scale of the coherence length 5, then when the mean-square thermal of the vortices exceeds 5, the strength of the pinning will displacement m be strongly reduced. This is distinct from the Lindemann criterion [1,7], in which melting of the vortex lattice is expected when m becomes larger than some fraction of the distance between vortices (typically -O.la,), and it leads to a qualitatively different prediction, namely of a thermal softening boundary which crosses the usual irreversibility line. Indeed the prediction of the Feigel’man and Vinokur theory [19] is that this new boundary increases in temperature with increasing field. Note that there can be an irreversibility line above and below the thermal softening boundary. And, if the position of the irreversibility line depends on the pinning strength (as it does in the thermal-activation and vortex-glass models but not in the lattice-melting model), then one might expect the irreversibility line to be shifted to lower fields below the thermal softening boundary, i.e. an anomaly where the two lines cross, as shown schematically in fig. 2. In fig. 3 we show in detail the data for a twinned crystal of fig. 1 below 0.6 tesla and near T, for dc field parallel to the c-axis (Hi,). A sharp (and reproducible on cycling) step in H,,,(T) initiates at Hi, 2: 0.1 tesla and completes, within AT - 0.020 K, at Hj, - 200 Oe. The collapse is even more dramatic when displayed in the log-log plot of fig. 3b. The high-field powerlaw is described here by the exponent (Y= 1.33 -f-0.05 (-4/3), while below the

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lc

T

Fig. 2. Schematic drawing of the thermal softening boundary (TSB) crossing the irreversibility line. Below TSB the irreversibility line is shifted to lower temperatures and the pinning is much weaker in the shaded region. The collapse occurs at the crossing of the two lines.

T

Fig. 3. Details orientation, (a) for comparison. edge. The high

(K)

1-t

of the irreversibility line at low fields for the twinned crystal of fig. 1 for the Hj, on linear plot and (b) on log-log plot. The dashed line representing HI, is shown In (b) the lines are fits of the data to the power-laws below and above the collapse

field exponent is a is -4/3 and at low fields (Y=3/2.

step (or edge) the power-law exponent is 1.48 2 0.08 (-3/2). This new transition is not related to twinning and occurs in the same field range in both twinned and fully untwinned crystals as demonstrated in fig. 4. The (Y values are consistently about 4/3 at high fields for both twinned and untwinned crystals, but at lower fields somewhat larger (closer to 2) in the untwinned ones. If the exponent 2 is expected at low fields for the melting in pure systems [14], one can speculate that in the cleaner untwinned crystals the irreversibility line is perhaps related to the melting of a lattice. The idea of Feigel’man and Vinokur [19] is that if the pinning centers are of the atomic origin (i.e. oxygen vacancies), vortex cores become too large (delocalized on the scale of 0 for the pinning wells to be fully effective. The critical current J, is shown to be strongly reduced [19] when the thermal displacement of the vortex core (u”) >, (1.45)‘. In an anisotropic superconductor, the harmonic thermal fluctuation of the vortex line at high temperatures is given (within a logarithmic factor) by [19]

L. Krusin-Elbaum

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1-t

Fig. 4. Same as fig. 3 for the fully untwinned crystal. Here the high field exponent (Yis still = 4/3 but at low fields LY= 1.8.

(2) where r is the anisotropy (e = A,/&,). Equating the rhs of eq. (2) to (1.45)*, a parabolic (-T*) thermal softening boundary is obtained: B _ 167~~~~r 1 96Q3 (W)=~ 0

This boundary crosses the usual upward-curving irreversibility line. We propose that the collapse edge articulates where the irreversibility and thermal softening lines meet. From eq. (3) we estimate that the magnetic field at which the crossing should occur is B = 700 Oe [6], in reasonable agreement with the middle of the observed anomaly.

4. Contour analysis of x” - lines of constant J, As we argued earlier, the position of the maximum in x”, xi,, (T, H) is a reasonable description of the H-,,,(T) line for a 30 Frn thick crystal at 1 MHz. At lower frequencies we are probing into the nonlinear regime, and if our argument holds, the anomaly we observe in H,,,(T) should also appear there. This is clearly evident in fig. 5 where we also show the line obtained from xz,, measured at 0.1 MHz. Another way to examine the nonlinear regime is by projecting the entire peak onto the temperature axis (i.e. the temperature locations of, for example, 90%, 80%, 70%, etc., of the peak height on both sides of the maximum) and tracking it as a function of HdC. The contours in the H-T plane obtained by such a procedure are distinctly different above and

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T (K) Fig. 5.

Fig. 6.

Fig. 5. Lines obtained from the maximum in ,$‘(T,H) at 1 MHz (irreversibility line shown in solid dots) and 0.1 MHz (open squares). The low field anomaly is present in both and is consistent with the thermal softening boundary (TSB), B a T2 (see eq. (3)), indicated as a solid line; TSB crosses the irreversibility line. The contours probing nonlinear regime below H,,,(T) also show the anomaly, suggesting a change in pinning behavior. Fig. 6. Contours

obtained

from

the analysis

of x’ at w = 0.1 MHz.

below the irreversibility line. Above, in the linear regime, they can be interpreted as lines of constant linear resistivity. Our anomaly appears at the irreversibility line and propagates into the nolinear regime towards lower temperatures, convincingly indicating the thermal softening boundary (TSB) which crosses the usual irreversibility line. The 0.1 MHz line, of course, coincides with one of the contours in the nonlinear regime, which all show a reentrant behavior below TSB. Similar analysis of x’ shows an identical contour behavior, which is shown for 0.1 MHz in fig. 6. To understand the contours below the irreversibility line, we need to establish the regime of the appearance of critical current density J,. The complicated E-J behavior causes a rather complex behavior [16] of x”, where the high temperature portion of the peak is a measure of the resistivity in the linear regime, and the lower temperature portion is a measure of the development of nonlinear E-J character, but not necessarily J,. When the frequency of the ac excitation is lowered, the nonlinear E-J behavior is reflected in the ac response. Indeed, for w = 100 kHz, X” exhibits a maximum well into the nonlinear regime [Pi] and we have shown that there is a clear amplitude dependence which is a consequence of the nonlinearity in the electrodynamic response. The observation of the nonlinear behavior is not sufficient to prove that the critical state model [18] applies. In the critical state for a given sample and coil geometry x’ (and x”) is only a function of D,, while J, is only a function of temperature. Since D, = (c/47~)h,lJ,, a simple geometrical scaling procedure can be employed [15] to obtain the shape of J,(T) regardless of the geometry of

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(MHZ)

Fig. 7. Frequency dependence of the peak and onset (defined at 5% of full height) temperatures of x” for the crystal of fig. 1. Below 1 MHz, the temperature, which is a function of resistivity, is varying only weakly with w. The frequency dependences of the onset and the peak can be scaled.

the sample or the coil. Such procedure works for h, greater than 0.1 Oe and the absolute values of J, can be estimated by assuming that for our geometry, D, = d, the sample thickness, at half-screening. For the crystal of fig. 1, for example, J,=25A/cm2 at T=90K. The scaling procedure does not work at all at lower ac amplitudes as the critical state model must fail if h, is small enough. However, the J, construction is consistent with the frequency dependence of x; i.e. the peak position in x” is rather insensitive to the frequency variation below 1 MHz as shown in fig. 7, so we can be reasonably assured that very near the peak for h,, = 0.1 Oe, we are outside of the linear Campbell regime [20] and the low field anomalies we observe are not associated with the nonlinearities within the pinning well. Finally, we note that the applied dc field at which the collapse occurs is one-to-two orders of magnitude above the lower critical field H$. In our crystals, H,, shows a simple linear behavior (with the slope -10 Oe/K [21]) extrapolating to T,, as shown in fig. 3b. At these fields the flux lattice spacing is smaller than magnetic penetration depth A and, hence, it is unlikely that this new effect is due to the change in the nature of the vortex-vortex interaction (i.e. from logarithmic at higher fields to exponential near H,,).

5. Concluding

remarks

In summary, we have discussed a remarkable new pinning behavior apparent from the ac magnetic measurements. We have seen that the effect of large thermal fluctuations combined with the presence of the atomic scale disorder leads to a surprising collapse of the irreversibility line in both twinned and untwinned YBaCuO crystals within a critical regime. We have proposed that the observed low field anomaly, which extends down to temperatures well

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below the irreversibility line Hi,, shifting it to lower fields. Surprisingly, the constant .I, contours turn back and then reenter at low fields. The nature of the ‘back-flow’ and the reentrant regime at high temperatures and low fields is still not understood and the theory of the regime close to I&, where the elastic energy becomes negligible, is not yet available. The role of the entropic effects and the possible presence of the entangled vortex-liquid and the reentrant solid phase near H,, need to be further explored.

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