JOURNAL OF APPLIED PHYSICS
VOLUME 87, NUMBER 10
15 MAY 2000
Terahertz radiation imaging of supercurrent distribution
in vortex-penetrated YBa2Cu3O7À ␦ thin film strips
Masayoshi Tonouchi,a) Masatsugu Yamashita, and Masanori Hangyo
Research Center for Superconducting Materials and Electronics, Osaka University, 2-1 Yamadaoka, Suita,
Osaka 565-0871, Japan
共Received 18 June 1999; accepted for publication 7 February 2000兲
We have developed a supercurrent distribution imaging system for high T c superconductive thin
films and demonstrated the visualization of the supercurrent distribution in the vortex-penetrated
YBa2Cu3O7⫺ ␦ thin film strips. The terahertz 共THz兲 radiation and detection system with a scanning
femtosecond laser was employed to visualize the distribution. The imaging system utilizes the
principle that the femtosecond optical pulses excite THz radiation into the free space by optical
supercurrent modulation, and the radiation amplitude is proportional to the local supercurrent
density at the optically excited area. Prior to the observation of the supercurrent distribution, we
studied optical excitation effects on the vortices trapped in the strips, calibration of the current
density from the THz radiation amplitude, temperature dependence of the THz radiation properties,
etc. The laser power dependence of the THz radiation in the remanent state revealed that the
excitation with powers larger than the relatively weak finite value 共about 10 mW in the present case兲
strongly affects the vortices trapped in the films. We attributed this behavior to the optically excited
depinning effect. We derived a calibration function from the THz radiation images into the
supercurrent density distributions by observing the bias-current dependence of the THz radiation,
and applied it for the diagnosis of the distributions in the vortex-penetrated strips. The THz radiation
images were successfully transferred into the supercurrent density distributions with quantitative
agreement. The minimum magnetic flux resolution at the optically excited area was roughly
estimated to be 3 ␾ 0 where ␾ 0 is a single flux quantum. The measurement of the laser beam profile
indicated that the spatial resolution of the THz radiation images is limited by the laser beam
diameter: 25 ␮m in our case. The observed distributions revealed that the vortices easily penetrate
into the strip under an external magnetic field B EX of 0.9 mT, and the persistent supercurrent exists
only near the strip edges in the remanent state after removal of the field. The calculations of the
convolution between the observed laser pattern and the trial functions suggested that the
supercurrent distribution width in the remanent state after removal of the field of 0.9 mT is estimated
to be less than 1 ␮m. The temperature dependence of the supercurrent distributions revealed that,
below 60 K, the thermal activation produces no significant effects on the penetrated vortices at
B EX⫽0.9 mT, whereas, the vortices in the remanent state after removal of the field of 15 mT were
strongly affected by the thermal activation. The decreasing rate of the supercurrent density at the
edge with increasing temperature was larger than that inside the strip. This suggested that the
vortices trapped near the edges exhibit rather different behavior from the ones that penetrated into
the inner part of the strip. © 2000 American Institute of Physics. 关S0021-8979共00兲00410-2兴
I. INTRODUCTION
magnetic field. Since voltage detection implies that the phase
transition from the superconductive to normal state occurs in
an excited area, techniques such as the LT-SEM and the laser
imaging would affect the magnetic flux penetrating into the
HTSs, which results in destructive evaluation. On the other
hand, magnetic field detection techniques such as MO sampling and scanning SQUID microscope can detect the magnetic flux distribution nondestructively. Although the scanning SQUID can detect a single vortex that penetrated the
film, the system is too sensitive to evaluate the supercurrent
distribution in the films biased with a large amount of current. Thus, the MO sampling method has been widely used
as a powerful technique to study the supercurrent distribution
in the HTS thin films.8–15 The macroscopic pictures in the
observed images are generally understandable with theoretical works.16–19 However, the MO sampling technique has
There have been a number of experimental and theoretical studies of magnetic flux and supercurrent distribution in
high T c superconductors 共HTSs兲. This led to the development of a variety of experimental techniques such as scanning Hall probe,1 scanning superconducting quantum interference device 共SQUID兲 microscope,2 magneto-optical 共MO兲
imaging method,3 low-temperature secondary-electronmicroscopy 共LT-SEM兲,4,5 and scanning laser microscopy.6,7
These techniques are categorized mainly into two groups;
one is to measure induced voltage and the other is to measure
Also at: PRESTO, Japan Science and Technology 共JST兲, 2-1
Yamadaoka,
Suita,
Osaka 565-0871,
Japan;
electronic
mail:
tonouchi@rcsuper.osaka-u.ac.jp
a兲
0021-8979/2000/87(10)/7366/10/$17.00
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© 2000 American Institute of Physics
J. Appl. Phys., Vol. 87, No. 10, 15 May 2000
some disadvantages. Since the technique utilizes the MO indicator such as an ion garnet film prepared on a gallium
gadolinium substrate, the spatial resolution is larger than a
few microns. The spatial resolution can be improved to about
1 ␮m by evaporating EuSe film directly onto the
materials,8,14 which results in the destructive evaluation. Recently, we developed a technique to visualize supercurrent
distribution in HTSs thin films by means of terahertz 共THz兲
radiation imaging.20–22 The technique can provide a noncontact, nondestructive, and free space evaluation for the supercurrent distribution.
In a series of our recent works,20–30 we have discovered
and studied a type of THz radiation from HTSs. The pulsed
electromagnetic 共EM兲 radiation with a THz spectral bandwidth 共THz radiation兲 is generated from the current-biased
films excited with femtosecond 共fs兲 laser pulses. The THz
radiation from semiconductive photoswitches has been intensively studied in the last decade and can be explained by
classical EM dynamics.31–33 The electric field E observed in
the far field is proportional to dJ/dt, where J is the photocurrent. The radiation from semiconductors is explained by a
transient photocurrent, whereas in superconductors the radiation is explained by the partial supercurrent modulation without phase transition due to optical pair breaking and subsequent quasiparticle recombination.23–25 It has been
theoretically and experimentally indicated that the detected
radiation amplitude is proportional to the local supercurrent
density at the optically excited area.27 We then demonstrated
a direct observation of the supercurrent distribution in HTS
thin films by means of THz radiation imaging.20–22 The images were obtained by scanning the laser beam on the
samples and detecting the two-dimensional map of the THz
radiation.
In the present work, we apply this technique to observe
the supercurrent distribution in vortex-penetrated
YBa2Cu3O7⫺ ␦ 共YBCO兲 thin films and discuss its performance as the supercurrent visualization system. This article
is organized as follows. Section II describes experimental
details. Section III A demonstrates the visualization of the
supercurrent distribution while Sec III B explains the calibration procedures from the THz radiation images to the supercurrent density distributions in the thin film strips. The discussion of the optical and thermal effects on the imaging is
in Sec. III C. Sections III D and III E describe experimental
results and discussion of the observed supercurrent distribution in the vortex-penetrated thin film strips.
II. EXPERIMENTAL PROCEDURE
Figure 1共a兲 shows a schematic configuration of the femtosecond time-resolved EM pulse generation and detection
system. A mode-locked Ti:sapphire laser operating at a repetition rate of 82 MHz was used to produce 50 fs pulses with
a center wavelength of about 800 nm. The fs light pulses
were focused by an objective lens onto the sample mounted
on a cold finger of a closed-cycle helium cryostat. THz radiation emitted from the opposite side was collimated and
focused by a pair of off-axis paraboloidal mirrors onto the
detector through a Si hemispherical lens. An Au/Ge/Ni alloy
Tonouchi, Yamashita, and Hangyo
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FIG. 1. 共a兲 Schematic view of the experimental setup. 共b兲 Schematic structure of the bow-tie antenna detector fabricated on LT-GaAs.
bow-tie antenna fabricated on a low-temperature grown
GaAs 共LT-GaAs兲, as shown in Fig. 1共b兲, was used as a photoconductive detector. The detector was triggered by fs
pulses separated from the main beam by a beam splitter. The
integrated photocurrent was lock-in detected after being amplified. The EM pulse wave forms in time domain were
monitored by changing a delay time between the main and
trigger pulses. After fixing the delay time at the maximum
amplitude position, the laser beam was scanned to visualize
the THz radiation images by translating the sample. The
movable sample holder was connected to a cold base of the
refrigerator using a metal mesh and also to an exterior X-Z
stage controlled by LabView using a thermally insulating
polyethylene rod. The spatial resolution is limited by the
laser spot size. Using the beam profiler, the minimum full
width at half maximum of the beam diameter was measured
to be 25 ␮m. The large beam size is one of the disadvantages
of the present system. However, this can be improved by
employing the expanded fs laser beam or a lens with a
shorter focal length.
Commercially available YBCO films grown on 0.5-mmthick MgO substrates with a thickness of 100 nm were pat-
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Tonouchi, Yamashita, and Hangyo
FIG. 3. A typical waveform of the THz radiation emitted with a bias current
of 30 mA and a laser power of 30 mW.
FIG. 2. 共a兲 Schematic structure of the fabricated YBCO antenna and orientation of the coordinates. 共b兲 Schematic configuration of the sample mount.
terned into a bow-tie antenna structure as illustrated in Fig.
2共a兲 using conventional photolithographic techniques and Ar
ion milling. A hemispherical MgO lens with a diameter of 3
mm was attached to the back side of the substrate with
vacuum grease as illustrated in Fig. 2共b兲 to increase the collection efficiency of the THz radiation. Although the MgO
lens enhances the collection efficiency about ten time larger
than that without the lens,29 the observable area is limited to
about 200 ␮m in diameter. Thus, we examined the supercurrent distributions only at the center strip line of the antennas.
The orientation of the coordinates is shown in Fig. 2共a兲.
The visualized images contain 40⫻20 pixels with a pixel
size of 5 ␮ m⫻5 ␮ m. External magnetic field B EX of 0.9 or
15 mT was applied perpendicular to the sample surface by
placing the permanent magnet outside the cryostat after the
sample being cooled without an intentional external field,
which corresponds to a zero-field-cool 共ZFC兲 state. The transition temperature T c of the sample was 79 K. Since we
measured the temperature at the cold finger, the observed
temperatures differ from the center of the bridge, which is
the other disadvantage for our system at present. The difference between the monitored temperature and the actual
sample temperature was roughly estimated to be about 5 K.
This was done by comparing T c measured using the mapping
system and that of the four point probe method.
III. RESULTS AND DISCUSSION
radiation peak amplitude distribution near the center of the
device at 16.5 K when a current of 30 mA is biased. The
image indicates that the supercurrent flows along the antenna
edge, which is qualitatively explained by the Bean’s critical
state model.20 Since the LT-GaAs bowtie antenna mainly
detects the radiation polarized in the x direction as expected
from the antenna structure in Fig. 2共b兲, the radiation from the
center strip is larger than that from the inclined antenna
edges. However, the difference in the radiation amplitude
was much larger than expected, which is presumably attributed to the difference in the collection efficiency. We will
report details of the supercurrent observation elsewhere.22,34
The results suggest that the observable region is limited
within an area of 200 ␮m in diameter. Thus we characterize
the supercurrent distribution only at the center strips.
Figure 5 shows the three-dimensional plots of the radiation amplitude emitted from the strip under B EX of 0.9 mT,
and after removal of the field. The images indicate that the
supercurrent under the magnetic field flows in opposite directions along each edge, which corresponds to the conventional shielding current. The supercurrent direction is reversed after the removal of the field. This reveals that the
vortices are trapped near the strip edges. The results indicate
that the THz radiation imaging technique can be used for
observation of the supercurrent in the vortex-penetrated strip.
In order to discuss the supercurrent distributions quantitatively, we examine calibration procedures from the detected
THz radiation amplitude to the supercurrent density.
A. THz radiation images
Figure 3 shows an example of the THz radiation wave
form emitted from YBCO thin films observed with a laser
power P probe of 10 mW and a bias current I B of 100 mA. The
wave form shows that the radiation has the maximum amplitude at around 6.3 ps. The THz radiation wave form measured by a dipole antenna detector, which is explained by the
time derivative of the supercurrent,24 is equal to the time
derivative of the signal measured by the bow-tie antenna
detector.33 Thus, the observed wave form corresponds to the
transient response in the supercurrent: at the maximum position, the supercurrent density becomes minimum at the excited area. After fixing the time delay at 6.3 ps as indicated
by the dashed line in Fig. 3, the sample is scanned along the
x and z directions. Figure 4 shows an example of the THz
FIG. 4. Two-dimensional plot of the THz radiation amplitude near the
center of the device.
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Tonouchi, Yamashita, and Hangyo
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FIG. 7. THz radiation amplitude distribution along the z direction for various temperatures. The profiles are measured with I B of 10 mA and P probe of
2 mW.
FIG. 5. Three-dimensional plots of the THz radiation amplitude emitted
near the center strip 共a兲 under B EX⫽0.9 mT, and 共b兲 in the remanent state.
The distributions are visualized in the area of 100 ␮m in the x direction and
200 ␮m in the z direction. The images are observed with P probe of 2 mW.
B. Calibration procedures
We estimate the local current density from the detected
THz radiation amplitude in the following manner. We first
estimate the conversion function to change the amplitude
distribution mirror symmetric at the center of the bridge to
avoid a slight distortion in the images due to the misalignment of the system. We then estimate the current density by
calibrating the distribution so that the integrated amplitude
becomes identical to the bias current. Figure 6 shows the
estimated supercurrent density distribution along the z direction for various bias currents. The origin z⫽0 is set at the
center of the strip hereafter, and the bridge is located between z⫽⫺50 ␮ m and z⫽⫹50 ␮ m. We thus determine the
calibration function from the observed THz radiation amplitude images to the current density distribution. The supercurrent density distribution in the vortex-penetrated films is then
estimated using the calibration function.
FIG. 6. Distributions along the z direction of the calibrated supercurrent
density for various bias current. The profiles are measured at 16.5 K with
P probe of 2 mW.
Previously we reported that THz radiation efficiency depends on temperature.26 The effect is mainly attributed to the
temperature dependence of the EM wave transmittance in the
THz region. Figure 7 shows the radiation distribution along
the z direction for various temperatures observed in the strip
at I B ⫽10 mA and P probe⫽5 mW. The radiation amplitude
increases with increasing temperature without significant deformation in the distributions below 60 K. Therefore one has
to take the temperature dependence of the radiation efficiency into account to evaluate the temperature dependence
of the current distribution. We derive the calibration function
from the temperature dependence of the maximum amplitude
of the distribution as indicated by the solid line in Fig. 8.
Here we normalize the radiation amplitude by the value at
16.5 K to define the radiation efficiency. Above 60 K, the
bias current of 10 mA induced dc voltages at the bridge due
to flux flow and we observed the anomaly of the radiation.
This implies that the flux creep affects the THz radiation and
the detected signals would be also affected. The anomaly
strongly depends on the measurement conditions such as the
bias current and the laser power. The details will be discussed elsewhere.34
FIG. 8. Temperature dependence of the maximum THz radiation amplitude.
The solid line is a fit by the function c 0 ⫹c 1 T⫹c 2 T 2 ⫹c 3 T 3 , which gives
c 0 ⫽0.91, c 1 ⫽0.014, c 2 ⫽⫺7.8⫻10⫺4 , and c 3 ⫽2.0⫻10⫺5 when the radiation amplitude at 16.5 K is set unit.
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FIG. 9. The probe power dependence of the maximum THz radiation amplitude emitted from the strip in the remanent state. The circles and the
triangles represent the data for B EX⫽15 and 0.9 mT, respectively. The
closed and open symbols represent the data for the initial scan and the
second scan, respectively. The closed diamonds represent the data for the
radiation from the 20-␮m-wide strip with a bias current of 100 mA. The
solid and dashed lines are drawn to indicate the trend, both of which have
the same slope.
C. Laser exposure influence
The fs laser exposure strongly affects the THz radiation
wave forms and the vortices trapped in the YBCO thin films.
This indicates that there exists a heating effect on the
radiation.25,35,36 Thus, one has to study the optical excitation
effects prior to the evaluation of the vortex penetration. Figure 9 shows the probe power dependence of the radiation
peak amplitude at around the strip edge. The magnetic flux is
trapped with B EX of 0.9 or 15 mT in the ZFC state. The peak
amplitude is expected to increase proportionally with increasing probe power.26 This is confirmed in the currentbiased dipole antenna regardless of P probe , and in the vortextrapped strip below P probe of about 2 mW as indicated by the
dashed and solid lines, respectively. Above this value, however, deviation from the linear dependence is observed in the
remanent state. This suggests that probing with higher laser
power induces the photoassisted flux creep in the strip. The
closed and open symbols represent the data obtained by the
initial scan and the second scan, respectively, indicating that
the amount of the trapped flux decays by the laser scanning
using large probe power. The attenuation ratio is defined as
the value of the maximum amplitude for the second scan
divided by the one for the first scan and is summarized in
Fig. 10. A slight decay is observed below P probe of 10 mW,
whereas probing above this value remarkably decreases the
amount of the trapped magnetic flux. The fact that THz radiation can be excited with P probe larger than 150 mW,29,36
and the YBCO thin film loops can keep the magnetic flux
after irradiation with P probe of 100 mW,37 suggests that the
temperature rise ⌬T(K) due to the laser exposure is expected
to be smaller than 0.4⫻ P probe(mW). Therefore, the laser exposure effect with a power greater than 10 mW cannot be
explained by the simple heating, and the detrapping effect of
the flux would originate in the optical excitation with the
laser energy of about 1.6 eV. To avoid the optical effect in
the imaging procedure, one has to reduce P probe below the
critical power. In the present work, we examine the distribution with P probe smaller than 5 mW.
Tonouchi, Yamashita, and Hangyo
FIG. 10. The probe power dependence of the attenuation ratio. The open
and closed symbols represent the data for B EX⫽15 mT and 0.9 mT, respectively. The solid line is drawn as a guide to the eye.
D. Supercurrent distribution at 16.5 K
Supercurrent density distributions along the z direction,
averaged in the x direction J x (z), corresponding to the current distributions in Figs. 5共a兲 and 5共b兲, are summarized in
Fig. 11共a兲. The maximum supercurrent density and distribution, respectively, under B EX of 0.9 mT are about three times
larger and slightly wider than those observed after removal
of the field. Furthermore, the maximum current density under this field is observed at the slightly inner portion of the
strip, whereas the one with the flux-trapped strip is observed
just at the edges. These results suggest that the vortices under
this field penetrate into the inner part of the strip compared to
the ones after removal of the field. It is also found that al-
FIG. 11. 共a兲 Supercurrent density distributions along the z direction. Closed
and open circles represent the distribution measured under B EX⫽0.9 mT and
after removal of the field, respectively. 共b兲 Calculated magnetic field distributions corresponding to the supercurrent density distributions. The solid
and dashed lines are drawn as a guide to the eye.
J. Appl. Phys., Vol. 87, No. 10, 15 May 2000
Tonouchi, Yamashita, and Hangyo
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though the maximum current density in the flux-trapped state
coincides roughly with the one in the current biased strip at
I B ⫽80 mA, the supercurrent distributions are quite different
from each other. The supercurrent in the current biased strip
at I B ⫽30 mA is observed to flow even at the center of the
strip as shown in Fig. 6, whereas no supercurrent flows at the
center in the remanent state.
The magnetic field distribution for a thin strip can be
calculated by solving Biot-Savart’s law. The y component of
the magnetic flux density B y (z) is expressed by the following formula:
B y共 z 兲⫽
␮0
2␲
冕
J x共 z ⬘ 兲 d
dz ⬘ ⫹B EX ,
⫺⬁ z⫺z ⬘
⬁
共1兲
where d is a film thickness. Figure 11共b兲 shows the calculated flux density profiles across the strip corresponding to
the distributions in Fig. 11共a兲. The distribution under the
magnetic field indicates that the field is compressed near the
strip edge, and no flux penetrates into the center of the strip
as shown in the closed symbol. This profile agrees with the
distribution observed by other techniques.12,38 The results indicate that the calibration from the detected THz radiation
amplitude of the supercurrent density is quantitatively correct within our experimental resolution. Due to the poor spatial resolution at present, we cannot distinguish whether or
not the vortices with the reversed polarity are trapped inside
the strip.
We were able to observe a minimum supercurrent density of less than 0.02 MA/cm2, which implies that the present
technique with a laser power of 5 mW can detect a magnetic
field less than 0.01 mT. By assuming a laser beam spot area
of 4.8⫻10⫺6 cm2, the minimum resolution of the flux quanta
in the excited region is estimated to be 3 ␾ 0 , where ␾ 0 is a
single flux quantum. Since it is possible to improve the sensitivity by employing a spiral antenna detector and a thinner
optical window, the value could be reduced less than ␾ 0 .
Since the obtained distributions are visualized by the
convolution between the laser beam pattern and the supercurrent distribution, we here examine the laser beam profiles,
and discuss the actual distribution speculatively. A solid line
in Fig. 12 represents the measured laser beam profile along
the z direction. We see that the laser beam profile coincides
almost exactly with the supercurrent distribution in the strip
in the remanent state. This indicates that the minimum spatial resolution of 25 ␮m is determined by the laser beam
pattern. We then examined the supercurrent distribution by
calculating the convolution between the observed profile and
the trial function J T (z). We assume that J T (z) is given by18
冦
⫾1,
J T共 z 兲 ⫽ ⫿
⫺w⭐z⬍⫺a
冉冑
2
z
arctan
␲
w
⫿1,
冊
w 2 ⫺a 2
,
a 2 ⫺z 2
FIG. 12. Measured laser beam profile along the z direction. The closed
circles represent the observed distributions measured after removal of the
field of 0.9 mT. The intensity is normalized with respect to the maximum
value.
the field and in the remanent state, respectively, as a fitting
parameter. Although the expression 关Eq. 共2兲兴 is not available
in the present case, which has a very narrow vortex penetration depth compared to the London penetration depth,18 the
functions at least indicate that the supercurrent distribution in
the remanent state is simply explained by the edge current
with a width less than 1 ␮m, whereas the strip in the presence of the magnetic field had a slightly wider supercurrent
distribution. These results indicates that the present method
can potentially be a noncontact, nondestructive, and free
space evaluation technique for the supercurrent distribution
in the HTS thin films.
⫺a⭐z⭐a , 共2兲
a⬍z⭐w
where w is a half of the strip width and a is a critical position. We obtained the fits as given by the solid lines in Fig.
13共a兲 to the data using the distribution function as given in
Fig. 13共b兲. In the calculation, we used the vortex penetration
depth l(⫽w⫺a), of 100 and 1 nm for the distribution under
FIG. 13. 共a兲 The fits to the data given in Fig. 11共a兲, calculated by the
convolution between the solid line given in Fig. 12, and the trial functions.
共b兲 The supercurrent distribution functions used in the calculation. The solid
and dashed lines represent the functions for the fits with the data under
B EX⫽0.9 mT and in the remanent state, respectively.
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Tonouchi, Yamashita, and Hangyo
E. Temperature dependence of the distribution
Although it is obvious that the temperature dependence
of the vortex behavior is an important subject, and much
research has been done,39–47 to our knowledge, there is no
systematic study on the temperature dependence of the supercurrent distribution in the vortex-penetrated strips. One of
the advantages of the present observation technique is that
once the calibration from the THz amplitude to the current
density is made in the well-aligned system, one can diagnose
the temperature dependence of the supercurrent distribution
easily. Here we demonstrate the observation of the temperature dependence of the supercurrent distribution in the fluxpenetrated strip.
Figure 14共a兲 shows the current density distributions in
the strip near the edge for various temperatures measured at
B EX⫽0.9 mT with P probe of 2 mW. The maximum current
density decreases, the width of the distribution increases, and
the peak position at the maximum current density shifts to
the inner part of the strip with increasing temperature. The
results indicate that the amount of the vortex decreases and
the distribution spreads at high temperature. The deviation
from the symmetric distribution is also observed above 60 K.
The supercurrent in the minus region flows more than that in
the plus region, which suggests that the vortex penetration
depth in the minus region is deeper than that in the plus one.
The laser beam scanned from the minus region to the plus
region might assist the vortex penetration in the minus region
more than that in the plus region. We then examine the temperature dependence of the distributions in the strip in the
remanent state after removal of the external magnetic field of
0.9 mT. Figure 14共b兲 shows the distributions for various temperatures measured with P probe of 5 mW. Since the excitation
brought about by the laser power is expected to affect the
distributions due to the optical excitation, we monitored the
distribution after the sample temperature was elevated to a
finite value, kept for 5 min at that temperature, and then
cooled down to 16.5 K. Although the maximum current density decreases with increasing temperature similar to that of
Fig. 14共a兲, the broadening and center shift of the distribution
are not observed within our experimental resolution. This
suggests that some of the vortices escape from the strip due
to thermal activation and the rest remain near the edge regardless of the temperature.
Figure 14共c兲 shows the distributions for various temperatures in the strip measured with P probe of 0.75 mW after the
vortices were trapped with B EX of 15 mT. The maximum
current density is approximately ten times larger than that
measured in the remanent state after removal of the magnetic
field of 0.9 mT. The maximum current density decreases, the
width of the distribution increases, and the peak position at
the maximum current density shifts inner to the strip with
increasing temperature. Although this behavior is similar to
the results in Fig. 14共a兲, the depinning rate for the temperature increase is much larger than the other.
The temperature dependence of the maximum current
density for the various conditions is summarized in Fig. 15.
Both the strips, that with applied B EX of 0.9 mT and that
with trapped vortices after removal of B EX , show weak tem-
FIG. 14. Supercurrent density distributions in the half of the strip for various temperatures. The measurements were carried out under the conditions:
共a兲 applied with B EX⫽0.9 mT, 共b兲 in the remanent state after removal of
B EX⫽0.9 mT, and 共c兲 in the remanent state after removal of B EX⫽15 mT,
with P probe’s of 2, 5, and 0.75 mW, respectively. The distributions in 共b兲
were measured at 16.5 K after the temperature was elevated to a finite value,
and kept for 5 min, and cooled down without optical excitation.
perature dependence of the maximum supercurrent density
below 60 K. However, above this value the supercurrent density rapidly decreases with increasing temperature. The rate
of decrease of the supercurrent density in the strip under the
field above 60 K is larger than that in the vortex-trapped
strip. This would be attributed to the optical excitation effects. By neglecting those effects, one can expect similar
behavior in both cases. Namely, the supercurrent distribution
and the trapped-vortex distribution are not affected by the
thermal activation below around 60 K. On the other hand,
the temperature dependence in the strip with trapped vortices
under B EX of 15 mT remarkably differs from the above dependencies. The rate of decrease of the maximum supercurrent density below 60 K is observed to be much larger than
J. Appl. Phys., Vol. 87, No. 10, 15 May 2000
Tonouchi, Yamashita, and Hangyo
J C ⫽J 0 exp共 ⫺A 冑T/T C 兲 ,
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共4兲
where A is a constant. However, this relationship also failed
to explain the dependence. We then tried to explain it by a
power-law dependence. The dashed line in Fig. 15 is a fit to
the data below 65 K with a power law of the form
共5兲
J⫽J 0 共 1⫺T/T C 兲 n ,
which yields n⫽1.5 and J 0 ⫽15 MA/cm . The nonlinear behavior with n⫽1.5 is explained by the Ginzburg–Landau
theory.45 In the HTS thin films, however, this dependence is
usually observed only near T c . Therefore, the observed temperature dependence of the maximum current density in the
remanent state cannot be simply explained by the temperature dependence of the critical current density. Cukauskus
et al. reported that the composite thin films of Au and YBCO
prepared on various substrates have large n, which strongly
depends on the substrates and the deposition conditions.
They suggested that the grain boundary plays an important
role in determining the temperature dependence.46 In Sec.
III D, we suggested that the vortex behavior near the film
edges differs from that inside the film. As shown in Fig.
14共c兲, the rate of decrease of the maximum current density
with increasing temperature at the edges is larger than that at
the inner part of the strip. This suggests that the edge has
weaker pinning force than the inner part of the strip, and may
be originated in the process damage, which would affect the
coupling properties between the grains. The coexistence of
this edge effect and the intrinsic one in the strip would account for the observed temperature dependence.
Above around 60 K, we observed abrupt deviation from
the power law dependence in the maximum current density.
Cao et al. found the logarithmic decrease of the critical current density with increasing temperature near T c , and explained it by the pinned vortex liquid.47 The weak trapped
magnetic field in the remanent state might be responsible for
the pinned vortex-liquid regime formation. More work such
as the extraction of the optical excitation effect from the
observed data remains to be undertaken to discuss the vortex
behavior near T c .
2
FIG. 15. Temperature dependence of the maximum supercurrent density.
Open circles, closed triangles, and closed circles represent the data measured under the conditions 共a兲 applied with B EX⫽0.9 mT, 共b兲 in the remanent state after removal of B EX⫽0.9 mT, and 共c兲 in the remanent state after
removal of B EX⫽15 mT, respectively. The other conditions are the same in
Fig. 14. The three open triangles represent the data measured at temperatures of 16.5, 35, and 16.5 K, in that order. The two closed diamonds
represent the data measured at 16.5 K before and after the sample temperature is elevated to 35 K from the initial-flux-trapped state, and then cooled
down to 16.5 K without imaging. The closed diamonds and the open triangles are also shown in the inset. The solid lines are drawn as a guide to the
eye; the dashed line represents the fit to the data with a power law.
that in the former cases. This thermal effect was confirmed
by measuring the maximum current density at temperatures
of 16.5, 35, and 16.5 K, in that order, as indicated by the
open triangles in Fig. 15. We were able to obtain almost
same current density in the last two cases. It is also confirmed that the maximum current densities in the strip before
and after the sample temperature is elevated to 35 K from the
initial-flux-trapped state, and then cooled down to 16.5 K
without imaging at 35 K, are identical to the first and the last,
respectively, as indicated by the closed diamonds. The results indicate that the decrease in the maximum current density with increasing temperature below 60 K originates in the
thermal activation effect.
One may expect that the thermal effect can be attributed
to the temperature dependence of the critical current density
J C (T) in the YBCO thin film. Here, we discuss the temperature dependence of the maximum current density in the strip
in the remanent state trapped with B EX of 15 mT. At temperatures below the near-temperature regime, J C (T) has
been explained by the nearly linear (1⫺T/T C )
dependence,41,42 or by a flux-creep-controlled transport current with the form39,40
冋
J C 共 T 兲 ⫽J 0 1⫺ ␣
冉 冊册
T
T
⫺␤
TC
Tc
2
,
共3兲
where ␣ and ␤ are coefficients, and J 0 is the critical current
density at 0 K. The linear dependence cannot explain the
observed temperature dependence. The curve fitting to the
relationship given by Eq. 共3兲 gives ␣ ⫽1.5 and ␤ ⫽⫺0.45.
Since ␣ and ␤ are usually selected to be close to 1, and
positive, respectively, the flux-creep-controlled model also
cannot explain such dependence. Baziljevich et al. explained
the temperature dependence under a weak magnetic field of
60 mT, with an exponential term of the form10
IV. CONCLUSION
We have developed a novel supercurrent distribution imaging system for HTS thin films and demonstrated the visualization of the supercurrent density distribution in the
vortex-penetrated YBCO thin film strips. The THz radiation
and detection system with a scanning femtosecond laser was
employed to visualize the distribution. The imaging system
utilizes the principle that the femtosecond optical pulses excite THz radiation into the free space by optical supercurrent
modulation, and that the radiation amplitude is proportional
to the local supercurrent density at the optically excited area.
The calibration function was determined by the THz radiation images obtained from the current-biased strips to investigate the supercurrent density distribution. The magnetic
field profile calculated using Biot–Savart’s law suggested
that the THz radiation images obtained from the vortexpenetrated strip can be transferred into the supercurrent density distribution with quantitative agreement. The minimum
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J. Appl. Phys., Vol. 87, No. 10, 15 May 2000
magnetic flux resolution at the optically excited area was
roughly estimated to be 3 ␾ 0 . The measurement of the laser
beam profile indicated that the spatial resolution of the THz
radiation images is limited by the laser beam diameter: 25
␮m in our case.
The temperature dependence of the THz radiation amplitude emitted from the current-biased strip confirmed that the
radiation coefficient increases with increasing temperature.
The calibration function to study the temperature dependence
of the supercurrent distribution in the vortex-penetrated
strips was determined from this dependency.
Since the radiation amplitude due to the optical supercurrent modulation increases linearly with increasing laser
power, the system became more sensitive with higher laser
power. However, the laser power dependence of the THz
radiation from the strips in the remanent state revealed that
the excitation with powers larger than the relatively weak
finite value 共about 10 mW in the present case兲 strongly affects the vortices trapped in the films. We pointed out that
this behavior is attributed to the optically excited depinning
effect.
The observed distributions revealed that the vortices easily penetrate into the strip under an external magnetic field of
0.9 mT, and the persistent supercurrent exists only near the
strip edges in the remanent state after removal of the field.
The calculations of the convolution between the observed
laser pattern and the trial functions suggested that the supercurrent distribution width in the remanent state after removal
of the field of 0.9 mT was estimated to be less than 1 ␮m.
The temperature dependence of the supercurrent distributions revealed that, below 60 K, the thermal activation
produces no significant effects on the penetrated vortices at
B EX⫽0.9 mT, whereas, the vortices in the remanent state
after removal of the field of 15 mT were strongly affected by
the thermal activation.
In conclusion, the proposed imaging technique for the
visualization of the supercurrent distribution can provide a
powerful tool for the nondestructive, noncontact, and freespace evaluation of the current transport properties in HTS’s
thin films. Further improvement is now underway for spatial
resolution, enhancing the sensitivity, and visualizing the supercurrent distribution at higher frequencies.
ACKNOWLEDGMENTS
The authors are grateful to Dr. M. Tani and Dr. K. Sakai
共Communications Research Laboratory, M.P.T., Japan兲 for
their helpful discussions, and to H. Saijo 共Osaka University兲
for his help in fabricating the devices. The authors thank H.
Wald 共Friedrich-Schiller-University兲 and A. Quema 共Osaka
University兲 for their comments on the manuscript. M.
Tonouchi acknowledges support in part by a Grant-in-Aid
for Scientific Research on Priority Area 共A兲, Grant No.
10142101, from the Ministry of Education, Science, Sports,
and Culture, Japan.
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