We have performed a high-resolution study of the temperature dependence of vortex dynamics for 5×10^(−4)<T/Tc<10^(−2) in untwinned single crystals of the high-T_c superconductor, YBa_2Cu_3O_(7-δ). Through the introduction of a “bithermal” magnetization relaxation technique, we have uncovered a previously unresolved, linear temperature contribution to the semiclassical action for vortex tunneling. Finally, we have compared the weak and strong pinning regimes through heavy ion irradiation of a series of crystals

Beauchamp, K. M.

Crabtree, G. W.

Jaeger, H. M.

Rosenbaum, T. F.

Seidler, G. T.

Vinokur, V. M.

Welp, U.

Caltech Authors - Main

VOLUME 74, NUMBER 8 PH YS ICAL REVIEW LETTERS 20 FEBRUARY 1995
Low Temperature Action in YBa2Cu307 —J
G. T. Seidler
NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540
T. F. Rosenbaum, K. M. Beauchamp, and H. M. Jaeger
The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637
G. W. Crabtree, U. Welp, and V. M. Vinokur
Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439
(Received 1 September 1994)
We have performed a high-resolution study of the temperature dependence of vortex dynamics for
5 X 10 4 ( T/T, ( 10 '- in untwinned single crystals of the high-T, . superconductor, YBa&Cu&07 —(c.
Through the introduction of a "bithermal" magnetization relaxation technique, we have uncovered a
previously unresolved, linear temperature contribution to the semiclassical action for vortex tunneling.
Finally, we have compared the weak and strong pinning regimes through heavy ion irradiation of a
series of crystals.
PACS numbers: 74.60.Ge, 74.SO.+r, 74.72.—h
Even at the very lowest temperatures, it is possible
to measure significant relaxation of the magnetization
in type II superconductors. In high-T, . superconductors
[1—6], v(here ]]ux flow is formidable, as well as in more
traditional superconducting alloys [7,8], a sizable mag-
netization relaxation rate appears to extrapolate to a fi-
nite value at zero temperature. Furthermore, within the
10% scatter typical of these measurements, the relaxation
rate is found to be essentially temperature independent.
Taken together, these results imply that quantum pro-
cesses need to be included in any low-temperature de-
scription of vortex motion.
We report here the first high-resolution study of
temperature dependence in vortex dynamics at very low
temperatures. By applying a modified magnetization
relaxation technique to untwinned single crystals of
YBa2Cu307 q at millikelvin temperatures, we reveal a
linear temperature dependence in the Euclidean action
for tunneling of vortices.
Theoretical discussions of vortex tunneling [9—13] rely
on the instanton approximation. The vortex is envisioned
as a semiclassical entity, and its tunneling rate is taken to
be proportional to exp( —Ss/h), where S~ is the action of
the classical (extremal) trajectory. Assuming a Bean-like
state with near spatially constant bulk shielding currents,
the time t derivative of the magnetization M is given by
dM(t)
dt
= a exp[ —S,(M(t, ), T)/h]
t aS, (M(t), T)& expl (3M
30
20
0
R ~R
BSCCO 2212
YBCO 123
If the magnetization experiment is performed isother-
mally, then integration of Eq. (2) provides dM/d[ln(t)] =
—Il/(BSE/RM). If SE has only a weak power-law de-
pendence on M, then S~ —hM(t = 0)/[dM/d(ln(t))]—
10 h. Hence, isothermal relaxation measurements with a
characteristic scatter of 10% can only bound !RSc/dT! (
106/K [subject again to the above assumption about
SE(M)]. As shown in Fig. 1 for a variety of high-T, .
superconductors, the normalized magnetization relaxation
rate deviates little below T = l K from its finite zero-
temperature intercept. It is difficult to ascertain whether
dM(t)
= A exp[ —SE(M(t), T)/h],dt
10 YBCO 123
~ &&&&&8 && ~
—
~ ~
0 0
YBCO 124
providing a connection between theory and experiment.
Hence, a sufficiently sensitive determination of flux flow
characteristics in the quantum limit permits experimental
characterization of the semiclassical action, a fundamen-
tal, but usually inaccessible, theoretical quantity.
As magnetization relaxation at low T typically shows
little deviation from ln(t) behavior, Eq. (1) can be ex-
panded about some time t] giving
0
0 0.5 1.5 2.5
FIG. 1. Normalized magnetization relaxation rate in the low-
temperature limit for a number of high-r, . superconduc-
tors. Squares (Ref. [5], H = 5 kOe, single crystal); triangles
(Our work, H = 20 kOe, untwinned single crystal); diamonds
(Ref. [3], H = 2 kOe, single crystal); circles (Ref. [1], H = 0,
granular bulk).
0031-9007/95/74(S)/1442(4)$06. 00 0«1995 The American Physical Society
VOLUME 74, NUMBER 8 PHYSICAL REVIEW LETTERS 20 FEBRUARY 1995
dM/dt
n' i
dM/dr
t tn iT Ti
= exp(S (M(t ), T;) —S (M(t ), Tf)).
The magnitude of the discontinuity in dM/dt will be mea-
surably dependent on t only if BSz/BM is sufficiently
different at the initial and final temperatures; this can be
seen by the increasing vertical displacement between the
curves in Fig. 2 as the absolute value of magnetization
decreases.
The bismuth Hall-probe gaussmeter used in this experi-
ment was photolithographically prepared on a 0.3 mm
thick sapphire substrate. The contact pads consisted of
100 nm of Au on top of 10 nm of Cr. The thermally
evaporated 500 nm thick bismuth films were granular
with a grain size of 0.5 p, m and a Hall coefficient approxi-
or not the relaxation rate truly is temperature indepen-
dent in the T 0 limit.
We now present an analysis of the relaxation rate's re-
sponse to a single rapid change of the sample tempera-
ture during a magnetization relaxation measurement. We
show that this "bithermal" relaxation measurement per-
mits a direct and far more sensitive determination of the
temperature dependence of the semiclassical action. We
illustrate schematically in Fig. 2 the behavior of Eq. (2)
for two temperatures, with the hypotheses of a nonzero
temperature dependence of S~(M, T) and a temperature-
independent prefactor A. The prefactor A depends mainly
on the quantum attempt frequency and, therefore, should
have little temperature dependence in the quantum regime.
Consider a typical experiment starting at temperature T;
just after magnet ramping has been completed. The sys-
tem then evolves with time toward equilibrium, as shown.
After a time t, has elapsed, the sample temperature is
rapidly changed to Tf. The continuing time evolution of
the magnetization is then determined by the middle curve
in Fig. 2. Clearly, dM/dt will show a discontinuity at the
change in temperature. Quantitatively,
mately 10% of the bulk Bi value. A thin layer of
Apiezon N grease separated the 2 p, m X 2 p, m active
region of the gaussmeter from a large a-b face of the
YBa2Cu307 p crystal, placed at least 0.3 mm away from
any edge. Details of gaussmeter calibration have been
discussed elsewhere [4]. The Hall probe and sample
were top loaded into a helium dilution refrigerator and
measured by an ac lock-in technique at 16 Hz with a 3
sec time constant and an rms current limited to 0.1 p, A to
avoid heating. Under typical experimental conditions at
H = 30 kOe, the device resolution was 2 Oe.
We report complete results on a 1.05 X 0.50 X
0.05 mm YBa2Cu307 —$ single crystal grown by a con-
ventional Aux method in a gold crucible and detwinned
by applying uniaxial stress at elevated temperature [14].
Relaxation measurements were prepared by ramping the
superconducting solenoid from zero field to the target
field at 10 Oe/sec, with 0 parallel to the crystallographic
c axis. The magnet was quickly switched to persistent
mode after initial current stabilization, and the resulting
magnetization relaxation measured to times as long as
5 X 104 sec.
We plot in Figs. 3(a) and 3(b) isothermal relaxation
at H = 30 kOe for T = 0.3 and 0.1 K. The relaxation
rates are dM/d[ln(t)] = 44.2 ~ 0.8 and 43.9 ~ 0.6 Oe
respectively. By contrast, we obtain curve 3(c) by apply-
ing the bithermal relaxation technique with T; = 0.3 K,
Tf = 0.1 K, and t = 4 X 10 sec. The data have a clear
kink at t, and they are fitted with a single free parameter,
ASg = SF(M(t ), Tf) Sp(M(t ), T;) via integration of
Eq. (2) with t~ = t We obta. in AS~ = (0.97 ~ 0.25)6.
102 104-
I
M(t )
I
M(t=0)
FIG. 2. Schematic of bithermal magnetization M relaxation,
changing temperature from T; to Tf at time t„. See text for
details.
t (sec)
FIG. 3. Magnetization M vs logarithm of time t after ramping
to magnetic field H = 30 koe for (a) temperature T = 0.3 K,
(b) T = 0.1 K, and (c) isothermal relaxation at T = 0.3 K until
4 X 10 sec, followed by cooling to T = 0.1 K and subsequent
isothermal relaxation. The curves have been offset for clarity.
1443
VOLUME 74, NUMBER 8 PH YS ICAL REVIEW LETTERS 20 FEBRUARY 1995
0 — g YBagCu307
H=30 koe
O
—2
V)
I
1 GISE
= —5.2 K
(f) hdT
4
0
I
0.2 0.4
T (K)
1
0.6
&0' &0'
t (sec)
I'IG. 5. Temperature T dependence of the Euclidean action SF
determined by the bithermal relaxation method. Line is a linear
least squares fit.
FIG. 4. Bithermal relaxation with heating from initial temper-
ature T; = 0.1 K to three different final temperatures T&. Solid
lines are best fits obtained by the integration of Eq. (2) with
one free parameter.
We show in Fig. 4 bithermal relaxation data with T; =
0.1 K, but with three different values of T~. In all three
cases, kinks are observed at t, and the data are again
fitted well by integration of Eq. (2). Note that the sign
change in ASE refIects the self-consistency of the data in
Figs. 3 and 4; the former were obtained by cooling at t
and the latter by heating at t„, . These results provide con-
clusive evidence for a significant, measurable temperature
dependence in Se(M, T) for YBa2cuqOq s well below
T = 1 K. The existence of such a temperature depen-
dence in the semiclassical action is the central result of
this Letter.
We performed bithermal relaxation measurements for a
variety of initial and final temperatures at H = 30 kOe.
We plot in Fig. 5 the fitted temperature dependence
of 5~ for 0,05 ~ T ~ 0.75 K. At lower temperatures
inductive heating of the refrigerator and sample becomes
important, while significant temperature dependence in
the magnetization relaxation rate becomes apparent for
T ~ 0.8 K (see Fig. 1). The errors are dominated by the
error in defining t„„because of the finite time necessary
to execute the temperature step and uncertainties in
dM/d[ln(t)] (and thus in dS~/dM) at T = Tt. The linear
least squares fit has a slope dS+/dt = (—5.2 ~ 0.2)R/K.
Theoretical studies of the quantum behavior of vor-
tices agree that vortex tunneling is expected to be
strongly dependent on dissipation and pinning. Ao
and Thouless [12] have included the role of the vor-
tex velocity dependent part of the Magnus force in
a recent treatment of vortex tunneling, and in the
limit of low dissipation and weak pinning predict a
linear decrease in Se(T) with increasing temperature.
Their finding is in qualitative agreement with the
data shown in Fig. 5 and, together, support arguments
that high-T, , superconductors are in the "superclean"
limit at low temperatures [11]. Quantitative comparison
of experiment of theory, however, is inhibited by the
difficulty in defining an appropriate "vortex mass. "
The contribution to the tunneling rate from the pres-
ence of the Magnus force is expected to decrease as the
effects of dissipation and pinning grow [12]. Although
it is unclear how to estimate if our samples are suffi-
ciently clean for the theory to apply, we can move to
the strongly pinned limit by introducing columnar de-
fects along the c axis through heavy ion irradiation [15].
For this test, we used thin (12 to 20 p, m), untwinned as-
grown YBa2Cu307 z single crystals. Before the intro-
duction of columnar defects, these samples exhibited a
ASF(T) identical (within error bars) to that of the thicker
YBa2Cu307 —$ single crystal discussed above. After ir-
radiation, a different story emerged. We found no kink
at t in the bithermal relaxation and, hence, no rneasur-
able temperature dependence in the semic/assical action
for samples with columnar defect densities B~ of either 10
or 20 kOe (defined relative to an equivalent vortex density
at internal magnetic field B), subject to the constraint that
B/B~ & 1. When B && B~, so that each vortex was no
longer pinned by a column, then we moved back to the
clean (point defect pinning) limit and recovered the tem-
perature dependence in S~.
In conclusion, we have developed a modified magne-
tization relaxation technique which reveals definitively a
temperature dependence in the semiclassical action asso-
ciated with the tunneling of vortices in untwinned single-
crystal YBa2Cu307 q at millikelvin temperatures. We
find a linear decrease in 5& with increasing temperature
on the scale of 5h/K which has not been reported in pre-
vious magnetization relaxation experiments on type II su-
perconductors in the T 0 limit. The introduction of
VOLUME 74, NUMBER 8 PH YSICAL REVIEW LETTERS 20 FEBRUARY 1995
strong pinning through columnar defects suppresses the
temperature dependence of the action. Hence, high-T, . su-
perconductors can be used for unique explorations of the
interplay of vortex tunneling, pinning, and dissipation be-
cause of this sensitivity of the temperature dependence of
the action to defect morphology.
The work at the University of Chicago and at Argonne
National Laboratory was supported by the National Sci-
ence Foundation (Grant No. DMR91-20000) through the
Science and Technology Center for Superconductivity.
G. W. C. acknowledges support from the U.S. Department
of Energy, Basic Energy Sciences-Materials Science un-
der Contract No. %'-31-109-ENG-38.
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1445


Low Temperature Action in YBa_2Cu_3O_(7-δ)

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Low Temperature Action in YBa_2Cu_3O_(7-δ)

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