Generation and detection of transverse ultrasonic waves via vortex tilting
in superconductive YBa2 Cu3 O7
H. Hanedaa) and T. Ishiguro
Department of Physics, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-01, Japan
M. Murakami
Superconductivity Research Laboratory, International Superconductivity Technology Center, 1-16-25
Shibaura, Minato-ku, Tokyo 105, Japan
~Received 11 March 1996; accepted for publication 1 April 1996!
A rf magnetic field applied to the high-T c superconductor YBa2 Cu3 O7 under a crossed dc magnetic
field generates a transverse ultrasonic wave, associated with the tilt of pinned vortices. The reverse
situation, in which the rf field is generated by the application of the ultrasonic wave, also exists. The
polarization of the transverse ultrasonic wave is parallel to the rf field. Experimental results related
to line and Josephson vortices are presented as functions of temperature and magnetic fields.
© 1996 American Institute of Physics. @S0003-6951~96!04923-6#
The dynamics of vortices in high transition temperature
(T c ) superconductors have been studied intensively in recent
years. We presented a new means to investigate the pinning
and dynamics of vortices in type-II superconductors, the mutual conversion between electromagnetic and ultrasonic
waves.1 The longitudinal ultrasonic waves are generated and
detected by the compressional distortion of the vortex array
via vortex pinning in high-T c superconductor YBa2 Cu3 O7 ,
where the generating and detecting rf magnetic field is set
parallel to a dc magnetic field. It is interesting to consider
whether the tilting distortion2 functions to generate a transverse ultrasonic wave. In this letter, we report on the generation and detection of transverse ultrasonic waves in
YBa2 Cu3 O7 by a rf field and present the results concerning
their characteristics as functions of the dc and rf field amplitudes and temperature.
We used a platelet-shaped melt-powder–melt-growth
YBa2 Cu3 O7 which included 40 mole % Y2 BaCuO5 and had
the aligned c axis.3 The sample was bonded to one end of a
delay line made of a silicon single crystal with a length of
13.5 mm along the crystalline @110# direction, as shown in an
inset of Fig. 1, in order to identify the ultrasonic mode by
measuring its velocity. A Y-cut quartz transducer for the
transverse ultrasonic wave of 16 MHz was attached to the
other end of the delay line. Both the sample and the transducer were bonded to the silicon crystal with a liquid polymer. A dc magnetic field was applied normal to the sample
surface. To either feed or detect a rf wave, a rectangular flat
coil with a cross section 2.230.9 mm2 and length 1.8 mm
was situated near the sample. Measurements were carried out
for two configurations of the vortices with respect to the
crystalline c axis of the sample. In one case, the dc field was
set normal to the superconducting ab-plane, the largest surface of the sample, with dimensions 2.231.630.08 mm3 .
The line ~L! vortices, which are threading through the superconducting planes, are driven to move in the ab-planes causing a tilting deformation. In another case, the dc field was set
parallel to the ab-plane, which is normal to the largest surfaces of the sample, with dimensions 1.531.230.13 mm3 . In
a!
JSPS Research Fellow. Electronic mail: haneda@ss.scphys.kyoto-u.ac.jp
Appl. Phys. Lett. 68 (23), 3 June 1996
this case, Josephson ~J! vortices along the ab-planes appear
due to the dc field, and are driven in the ab-planes, where the
weak pinning of J vortices is concerned. The axis of the coil,
or the direction of the rf field, was set parallel to both the
largest surface and the ab-plane, but perpendicular to the dc
field, in both cases. A superconductivity transition temperature T c of 91.4 K was determined by an ac susceptibility
measurement.
When a rf pulse of 16 MHz with a pulse width of 1.3 ms
is applied to the coil, multiple echoes of the generated ultrasonic wave of the same frequency are detected by a quartz
transducer with a delay time corresponding to the speed of
the ultrasonic propagation. This is evidence of the generation
of ultrasonic waves ~GU!. The detected signal trace at a
transducer is shown in Fig. 1. The first ultrasonic pulse from
the sample and the subsequent echoes with intervals of 5.86
ms can be clearly observed. Based on the transverse sound
velocity of 4594 m/s in the @110# direction of a silicon crystal
with polarization along @11̄0#, the signal is ascribed to transverse ultrasonic wave pulse generated in the sample. The
amplitude of the applied rf field (h 0 ) is estimated to be ;6
mT. On the other hand, when a transverse ultrasonic pulse of
frequency 16 MHz is introduced into the sample from the
FIG. 1. An ultrasonic pulse from the sample ~arrow! and its echoes detected
by a quartz transducer in GU at 4.2 K under a dc field of 3 T. Inset shows
the scheme of measurement; ~a! delay line, ~b! YBCO platelet sample, ~c!
coil, and ~d! Y-cut quartz transducer. The directions of a dc field H 0 and a
rf field h rf5h 0 exp(ivt) are also shown.
0003-6951/96/68(23)/3335/3/$10.00
© 1996 American Institute of Physics
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FIG. 3. dc field dependence for GU at 4.2 K in the L vortex case ~dots! and
in the J vortex case ~open circles!, where each signal is normalized at 5 T.
Inset: H 0 dependence up to 0.3 T in the L vortex case obtained under
zero-field-cooled condition.
FIG. 2. Temperature dependencies for GU ~dots! in the L vortex case ~a!
and in the J vortex case ~b! for several values of a dc field. Arrows indicate
the direction of temperature change in ~a!. Temperature dependence for
GEM in the J vortex case ~open squares! is also shown in ~b!. The vertical
axes represent the amplitude of a generated ultrasonic wave for GU, and the
amplitude of a generated rf field for GEM, normalized with the amplitude
obtained at 4.2 K under 5 T.
transducer, electromagnetic pulses of the same frequency are
detected. These correspond to the arrival of multiple echoes.
This suggests the generation of electromagnetic waves
~GEM! by ultrasonic waves at the sample, where ultrasonic
waves are detected electromagnetically. The polarization of
the transverse ultrasonic wave was determined by using three
values of the angle between the rf field and the polarization
of the Y-cut quartz, 0°, 45°, and 90°.
The signals were observed only below T c and under a dc
field for both GU and GEM. No signal was observed when
the ultrasonic polarization and the rf field were set perpendicular to each other. This indicates that the polarization is in
the direction parallel to the rf field for both GU and GEM.
The temperature ~T! dependencies of GU for several values
of the dc field (H 0 ) are shown in Figs. 2~a! and 2~b!. The
GU signal in the L vortex case is almost constant up to a
certain temperature, which decreases with increasing dc field
strength. Above this temperature the signal drops rapidly.
The irreversible pinning effect is observed as a thermal hysteresis in the temperature region which displays the almost
constant signal. The temperature dependence for GEM in the
L vortex case is similar to that for GU. The GU signals in the
J vortex case decrease gradually with temperature increase.
The temperature dependence for GEM in the J vortex case
also shows gradual decrease with temperature, however, the
behavior above 60 K is different from that for GU in this
case when the signal amplitudes normalized at helium temperature are compared. This difference is due to the nonlinear response of the vortices for GU. In fact, the signal for GU
with a smaller rf amplitude h 0 ;0.6 mT shows a similar
temperature dependence to that for GEM, where the nonlinearity of the vortex response is reduced. The GU and GEM
signals for both the L and J vortex cases increase with H 0 as
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Appl. Phys. Lett., Vol. 68, No. 23, 3 June 1996
shown in Fig. 3. A hysteresis, larger for the L vortex case, is
found at low temperatures. Since no signal was observed for
the zero-field-cooled case in the low field region, as shown in
an inset of Fig. 3, the hysteresis is ascribed to that of the
vortex density ~B! in the sample.
When a rf field is applied to the surface of a type II
superconductor perpendicular to a dc field, the penetrating rf
field, reaching down to the rf penetration depth l rf , induces
a tilt distortion in the vortex array. Then a transverse distortion is generated in the crystalline lattice through the pinning
interaction. Following Domı́nguez et al.,4 the equation of
motion used to describe the crystalline displacement u in a
semi-infinite sample which exists in the half-space x.0 is
r
] 2u
] 2u
2
2
r
c
5 a p ~ v 2u ! ,
s
]t2
]x2
~1!
where v is the vortex displacement, r is the crystalline mass
density, and c s is the transverse sound velocity. Here we
assume that the ultrasonic propagation and the dc field are
directed in the x direction and that the rf field h rf(t)
5h 0 exp(ivt) is applied along the y direction at the sample
surface x50. In this configuration, displacements u and v
are induced along the y direction. The complex parameter
a p 5 a L /(12i/ v t ) ( a L is the Labusch parameter, and t is
the relaxation time for the thermal depinning! gives the pinning force P including the effects of the thermal depinning as
P5 a p v . The vortex displacement induced by the applied rf
field is represented by v (x,t)5(Bh 0 /l rfa p )exp@i(vt
21
2x Im$ l 21
rf % ) # exp(2x Re$ l rf % ), in the linear regime using
the complex rf penetration depth l rf5(l 2 1B 2 / m 0 a p ) 1/2,
where l is the London penetration depth.2 From the expression for v and Eq. ~1! with the boundary condition ] u/ ] x
50 at x50 for a free surface, we obtain the amplitude of an
ultrasonic wave propagating along the x direction as
u 05
1
Bh 0
,
r c s v u 11k 2s l 2rfu
~2!
where k s is the wave number of the ultrasonic wave. Since
the crystalline displacement u is much smaller than the vortex displacement v for the magnetic fields used in this
experiment,4 we replaced the right-hand side of Eq. ~1! by
a p v . The amplitude u 0 is proportional to the vortex density
Haneda, Ishiguro, and Murakami
B ~not the applied dc field H 0 ) and the rf field amplitude
h 0 . When the vortices are thermally depinned, u 0 decreases
due to an increase in l rf through the reduced interaction between the crystal and the vortices. This results in the phase
cancellation of the ultrasonic waves generated at different
points. When u l rfu !l s , an ultrasonic wave is generated at
the surface with magnitude Bh 0 , where the amplitude u 0
does not depend on a p , consistent with the result obtained
by Domı́nguez et al. We remark here that the samples used
had a thickness of ;l s /2, 5 so as to satisfy the mechanical
resonance condition. For u l rfu !l s , the ultrasonic waves
generated on the counter surfaces of the plate interfere so as
to form a standing wave.6
The sharp drop in the signal near T c can be explained by
thermal depinning, characterized by the relaxation time t
5 t 0 exp(U/kBT) ( t 0 [ h / a L is the viscous relaxation time of
the pinned vortices, where h is the viscosity in the vortex
flow!, which decreases rapidly with T near T c , reducing
a p . This results in an increase in l rf . When u 11k 2s l 2rfu 52,
i.e., Re$ l rf% '(B 2 /2m 0 a L v t ) 1/2.0.15l s , u 0 is reduced to a
value approximately half of that in the small l rf limit, while
for Re$ l rf% .0.15l s , u 0 decreases rapidly toward zero. Assuming appropriate temperature and field dependencies of
the pinning potential U(B,T) @ U(B,T)5U 0 (12t) 3/2/B,t
[T/T c ], 7 the nonlinearity with respect to H 0 near T c , as
displayed in Fig. 2~a!, can also be explained. The gradual
decrease of the signal with temperature up to intermediate
temperature region for the J vortex case, which is also observed in the situation where vortex response is in the linear
regime, is ascribed to the small value of the Labusch parameter. However, explaining the temperature dependencies near
T c is an open problem. The rapid drop of the signal near
T c in the L vortex case, and the gradual decrease of the
signal from helium temperature in the J vortex case were also
observed for longitudinal waves.1
A linear dependence on the amplitude of the rf field up
to h 0 ;12 mT was observed at 4.2 K for both the L and J
vortex cases and at temperatures between 80 and 89 K for
the L vortex case under a dc field of 3 T. In the J vortex case,
however, the linearity is violated above 60 K, where the
pinning is thought to be weakened.
On the other hand, when a transverse ultrasonic wave is
introduced into a superconductor, vortices are tilted due to
the pinning interaction. The displacement of vortices v induces a rf field with amplitude B rf5B u ] v / ] x u inside the
sample.4 When the vortices are pinned, v is almost equal to
the ultrasonic wave amplitude u in . However, when they are
depinned, the motion relaxes, and the amplitude of v decreases. The motion for the tilting vortex displacement is
described by4
Appl. Phys. Lett., Vol. 68, No. 23, 3 June 1996
C 44
] 2v
2 a p ~ v 2u ! 50,
]x2
~3!
where u and v are along the y direction, and C 44
5(B 2 / m 0 ) 1/2 is the elastic constant of tilting deformation in
vortices. When a transverse ultrasonic wave u(x,t)
5u in exp@i(vt1ksx)# with k s !2 p /l is introduced, it results
in a vortex displacement v (x,t)5(11k 2s l 2rf) 21 u in exp@i(vt
1ksx)#, where l rf5(B 2 / m 0 a p ) 1/2. The detected rf field is
proportional to B rf5Bu in k s u 11k 2s l 2rfu 21 and therefore to B
and u in . The signal drops when the vortices are depinned, as
in the case for GU. The similarity in temperature dependencies of GU and GEM can be understood by their similar
dependencies on l rf . Since B rf and its associated rf current
are small, the GEM signal reflects the vortex depinning in
the linear regime. In fact, a linear dependence on the ultrasonic amplitude was obtained at helium temperature and near
T c in both the L and J vortex cases, in contrast to the situation for GU.
In conclusion, the generation and detection of transverse
ultrasonic waves in a high-T c superconductor by a rf magnetic field in the vortex state were carried out. The results are
explained in terms of the vortex pinning interaction, with
which a tilt mode of the vortex array is associated. The polarization of the transverse ultrasonic wave is parallel to the
rf field, or the direction of the vortex displacement. The
rather sharp decrease of the signals and the nonlinearity with
respect to H 0 near T c in the line vortex case are ascribed to
thermal depinning. In the Josephson vortex case, a gradual
decrease of the signals with temperature is explained by the
small value of the Labusch parameter, and a nonlinearity of
the ultrasonic generation signal with respect to the rf field is
ascribed to the weak pinning.
This work was supported by a Grant-in-Aid for Scientific Research from Ministry of Education, Science, Sports
and Culture, Japan.
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in Superconductivity VII ~Springer-Verlag, Tokyo, 1995!, pp. 185–187; H.
Haneda, T. Ishiguro, and M. Murakami, Physica B ~to be published!.
2
E. H. Brandt, Physica C 195, 1 ~1992!.
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Eqs. ~1! and ~5! should be read as a minus sign.
5
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~1990!.
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~Benjamin, New York, 1964!, pp. 505–577.
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