CHINESE
JOII;R.NAL
OF PHYSICS
VOL. 35,
30.
4
AUGUST
1997
The Science and Technology of Condensed Matter Physics
-
From Atomic Imaging to Space Research
N.-C.
Yeh
’
Department
of Physics,
Calafornia
Institute of Technology,
Pasadena, CA 91125, U.S.A.
(Received May
19, 1997)
Various areas of our ongoing condensed matter physics research which involve both
fundamental physics and advanced technology are described. The research topics in-
clude studies of the vortex dynamics and pairing symmetry of high-temperature super-
conductors; development of precision clocks using high-Q superconducting microwave
cavities; state-of-the-art measurements of the density and critical phenomena of liquid
helium near phase transitions and under microgravity; as well as the physics and device
applications of various magnetoresistive perovskites. The experimental scope encom-
passes techniques from atomic imaging to space research, and the important interplay
of fundamental science and frontier technology in our research is also addressed.
PACS.
74.60.-w
-
Type-II superconductivity.
PACS.
74.50.+r
-
Proximity effects, weak links, tunneling phenomena, and Josephson
effects.
PACS.
75,50.-y
-
Studies of specific magnetic materials.
I. Introduction
The rapid advances and diversification in condensed matter physics have prompted
new development in technology to achieve higher-precision and better-resolution measure-
ments. Conversely, the advances at the technological front have also provided unprecedented
opportunities for investigating various fundamental science-related issues in condensed mat-
ter physics. In this paper we describe several areas of our ongoing experimental research
in condensed matter physics which involve both basic science and advanced technology.
The research topics include studies of the vortex dynamics and pairing symmetry
high-
temperature superconductors; development of precision clocks using high-Q superconduct-
ing cavities for both basic research and device applications; state-of-the-art measurements
of the density and critical phenomena of quantum fluids near phase transitions; and the
physical properties and device applications of magnetoresistive perovskites that exhibit
either colossal magnetoresistance or giant ferromagnetic Hall effect. The experimental
approach encompasses techniques from atomically-resolved imaging and spectroscopy to
microgravity-related space research. The anticipated scientific and technological impact of
these studies is also discussed.
373
@
1997
THE PHYSICAL SOCIETY
OF THE REPUBLIC OF CHINA
374
THESCIENCEANDTECHNOLOGYOFCONDENSED...
VOL.35
II.
Superconductivity-vortex dynamics, pairing symmetry, and precision clocks
II-~.
Vortex dynamics of high-temperature superconductors
The combined effects of large thermal fluctuations, short coherence lengths, long
penetration depths and large mass anisotropies are known to result in novel vortex dynamics
in the mixed state of high-temperature superconducting
cuprates
[I]. A new thermodynamic
phase,
the
vortex-liquid, occurs between a low-temperature vortex-solid phase and the
normal state. Despite the rich and novel physics associated with this vortex-liquid state and
the phase transitions between the vortex-solid and vortex-liquid
[2-81,
the thermally-induced
vortex motion in the vortex-liquid state results in dissipation which imposes limitation
on the usefulness of high-temperature superconductors to lower temperatures. Hence, for
practical purposes such as device applications, it is essential to understand how to minimize
vortex motion in high-temperature superconductors through the introduction of different
types of pinning defects.
We have systematically investigated the effects of static disorder on the vortex dy-
namics of high-temperature superconductors
[6-81.
In the clean limit and for a constant
magnetic field, the vortex-solid to liquid transition of
YBazCusOr
single crystals is con-
sistent with a first-order melting transition
[4,7].
On the other hand, in the presence of
significant static disorder, the vortex-solid phase becomes glass-like, and the phase transi-
tion between the solid and liquid phases becomes second-order
[2,3,5].
Depending on the
type of static disorder in the superconductors, these second-order vortex phase transitions
may be categorized into different universality classes
[6-81,
as illustrated in Fig. 1. In
addition to the variations in the universality classes of phase transitions, correlated static
disorder also induces anisotropic vortex dynamics
[6-81,
as manifested by the changes in
the angular dependent vortex phase transition temperatures shown in Fig. 2 for a given
magnetic field (H).
In addition to the important effects of symmetry-breaking and anisotropic vortex
dynamics induced by static disorder, there are two important consequences associated with
the introduction of pinning defects, as illustrated in Fig. 3 and Fig. 4, where the
vortex-
solid to liquid phase transition temperatures and the critical current densities are shown
to be enhanced with the introduction of columnar defects. The physics knowledge derived
from these investigations are being applied to improving microwave device performance
and manufacturing high-temperature superconducting wires in research laboratories and
industry worldwide.
11-2. Studies of the superconducting pairing symmetry using a low temperature
scanning tunneling microscope
With the modern invention of low-temperature scanning tunneling microscopy (STM),
atomically-resolved images and spectroscopy of materials can be obtained. As exemplified in
Fig. 5, our low-temperature scanning tunneling microscope can resolve the atomic structure
of a superconducting
NbSez
single crystal to fine details
(-
0.25
8,
resolution), including an
atomic vacancy on the surface layer. Using this spatially-resolved tool, we have investigated
the anisotropic tunneling spectroscopy of a high-temperature superconducting single crystal
of
YBa2Cus07
along different
k
vectors.
As illustrated in Figs. 6(a)-(d), the anisotropic
superconducting energy gap on a
YBa$us07
single crystal along the
{loo},
(001) and
--
VOL.
35
N.-C. YEH
375
(b)
FIG. 1.
Effects of static disorder on the vor-
tex phases of high-temperature
SU-
perconductors
[6-81:
(a)
vortex-glass
(VG), (b) Bose-glass (BG), and (c)
splayed-glass (SG). Here
v
represents
the isotropic static exponent of the
vortex correlation length in the vor-
tex-glass;
~11
and
VJ_
are the parrallel
and perpendicular static exponents of
the Bose-glass; and
~1)
vk
and
~11
are the anisotropic static exponents
of the splayed-glass.
91.2
G
;:
90.7
91.55
H=jkOe
i
z
91.30
h
Sin (8)
FIG.
2.
Representative anisotropic vortex
phase diagrams of
YBazCus07
sin-
gle crystals:
(a)
as-grown with di-
lute twin planes; (b) irradiated with
c-axis columnar defects; (c) irradi-
ated with two sets of canted colum-
nar defects at
f7.5
”
relative to the
crystalline c-axis. Here
0
is the angle
between the applied magnetic field
H
and the crystalline c-axis.
-
.~
.,-..
__L_
376
THE SCIENCE AND TECHNOLOGY OF CONDENSED
VOL. 35
10
0
0.92
0.94
0.96
0.98
1.00
T/Tc
FIG. 3.
The magnetic field (H) vs. temper-
ature (T) vortex phase diagram of
YBazCusOr
single crystals, showing
the enhancement of vortex-solid to
vortex-liquid transition temperatures
with the introduction of columnar de-
fects.
-
106
ìF
:
t;
’
105
s
i
+Y
104
1
m
(T = 15 K)
$
1031
’
’
’
”
I
III
104
H
(oe)
FIG. 4. Enhancement of the critical current
densities
(Jc)
in
BizSrzCaCuzOz
due
to the presence of columnar defects.
FIG.
5.
Surface image of superconducting
NbSez,
taken at T = 4.2 K with our low-temperature
scanning tunneling microscope. The distance between two consecutive atoms is
3.5
A.
VOL.
35
N:C.YEH
2
I.I.l.,.,.,I,
2
I.,.,.,.,.,.,
(a)
(
100) tunnel junction
(b) (00 1) tunnel junction
l-
-
1-
377
l-
&ii
3f!ii3El:
(c)
{
100)
pt.
contact junction
(d)
(
110)
tunnel junction
o
I~,~,.,~,~,11
O.Z.,.,.,.,.,.,?
-150 -100 -50 0 50
100
150
-150
-100 -50 0 50 100 150
v(mV)
FIG. 6. Differential conductance
(dl/dV)
b
e
t
ween
a Pt-tip and a
YBazCu307
single crystal at 4.2
K. (See text for detailed descriptions of the spectroscopy.)
{
llO}
directions are obtained by tunneling into these high-symmetry crystalline axes. We
find
that along the (100)
d
irection
the superconducting gap (33
f
5
meV)
is larger than
that along the (001)
d
irection
(23
f
5
meV),
the latter represents the average gap value
in the
k,k,
plane.
On the other hand, along the (110)
d
irection,
we observe a zero-bias
conducting peak
[9,10]
(Fig. 6(d))
consistent with the prediction of d-wave nodal junction
along the (110) d
irection.
We have also observed Andreev reflection spectra along various
crystalline axes, as exemplified in Fig. 6(c) for the (100) d
irection
[9].
In the inset of Fig.
6(c), we show the comparison of the theoretical calculations based on the BTK theory
[ll]:
lz-:
K
s,
_a
fwf(E
-
ev>
-
fW1P
+
Iww
-
lw>121~
A =
A
î,
/[E2
+
(A:
-
E2)(1
t
22
î)ì]
,
B=l-A,
(E
<
A,),
A
=
+Qy2,
B
=
(ui
-
?$)?P(l
t
Z
î)
/y
î,
(E
>
Ak),
(1)
378
THE SCIENCE AND TECHNOLOGY OF CONDENSED
VOL.
35
YZ
=
[
ëu
.i
+
Z
î(
?L;
-
vi)]
2
(
21;
=
1
-
v;
=
f
[1+
(E2
-
A;)/E2]1
í2
,
(1)
&
=
+3s
k,
-
cos
I$].
Here
V
denotes the biased voltage, and f(E) is th
e
F
ermi-Dirac function. As shown in Fig.
6(c) and its inset, our Andreev reflection data are consistent with the d-wave BTK theory
[II]
with a barrier strength parameter
2
=
0.4. Similarly, we use the d-wave nodal junction
model
[lo]
to analyze the (110) conduction peak spectra
[9]:
1
ZI
2
Jm
dE[_f(E
-
ev)
-
f(E)1
[l
+
b(-WI
”
-
lb(E)12]
)
a =
ii-)(&).
D=l+(&)($),
(2)
As shown in Fig. 6(d) and its inset, the d-wave nodal junction model appears to fit our tun-
neling data (with
2
=
1) along the (110)
d
irection
well. These tunneling spectra unambigu-
ously identify the superconducting pairing symmetry in
YBa2CusOT
as d-wave symmetry.
We plan to extend the STM studies to samples with different intrinsic anisotropies, such
as the Hg-based HTS compounds of
HgBa2Can-rCun02n+z+6,
(n
=
1,2,3),
in order to
unravel one of the most fundamental issues associated with the pairing mechanism of
high-
temperature superconductors:
the effect of interplanar coupling on the superconducting
energy gap and its anisotropy.
11-3.
High-Q superconducting microwave cavities for precision clocks
Very low-loss superconducting niobium cavities, with the quality factor
(Q) as
high
as Q
N
1Oro
at
T
5
2
K, can be achieved by annealing niobium under ultra-high vacuum
(-
10-r
’
Torr) and at high temperatures (up to
N
18OO
íC
).
The high-Q superconduct-
ing cavities are very stable oscillators which can be used in precision clocks, frequency
standards, and various microwave device components. The frequency stability of a super-
conducting oscillator may be estimated by considering the following equation
[12]:
__
_
_coPo40)
A(O)
1
dw
A@>
wdT
N
[
1
--
2l?
kBT2
exp
kBT
’
(3)
where
w
denotes the angular frequency of a resonant mode in a superconducting cavity with
a geometric factor
I,
CO
is a constant of the order of unity, X(0) is the zero temperature
penetration depth,
~0
is the vacuum permeability,
kB
is the Boltzmann constant, and A(0)
is the zero-temperature superconducting energy gap. Using the material parameters for Nb,
and assuming that w
=
27r
x
101osec-l,
we find that
(h
íw
/dT)/w
sz
-10-8K-1.
Incorporat-
ing modern high-resolution thermometry (HRT)
b
ased
on the SQUID (Superconducting
Quantum Interference Device) technology, the temperature of the superconducting cavity
can be controlled to a stability of AT
<N
1O-1o
K. Hence, the corresponding frequency
VOL. 35
N.-C. YEH
379
NIST
Low Noise
High Frequency
f,-f2
-
I Hz
Interval Counter
FIG.
7. Block diagram of the phase-locked loop for our precision density measurements of liquid
helium using a superconducting (SC)
niobium microwave cavity. The principle of operation
is to compare the resonant frequency of the superconducting cavity,
fo,
with that gener-
ated by the low-noise high-frequency synthesizer,
fc,
so that the feedback voltage
(V,,,)
is
proportional to the frequency difference
(fc
-
fo),
and the resonant frequency
f0
can be
read to high precisions by the comparison of
(fc
-
fo)
with a quartz frequency standard.
stability
(AU/W)
of a high-Q superconducting niobium cavity can be as good as one part
in
lOIs.
This capability may
be achieved by using the state-of-the-art frequency control
and readout system, the phase-locked loop, as schematically illustrated in Fig. 7. With the
phase-locked loop and a niobium microwave cavity of Q =
10
’
N
lOlo,
we expect to achieve
superconducting oscillators with a frequency stability of one part in
1017
N
lOIs.
The high-resolution oscillators based on superconducting cavities can further achieve
high accuracy in the frequency when compared with accurate atomic clocks. We are in
the process of constructing and optimizing the superconducting cavity-based oscillators, in
order to achieve state-of-the-art precision clocks for applications ranging from gravitational
wave detection to space navigation.
III. Critical phenomena of superfluidity under gravity and microgravity
As mentioned in the previous section, modern microwave technology combined with
high-Q resonators can achieve frequency readout and control with a resolution up to one
part in
1017
N
1Or8
Such high-resolution measurements are better than most experimental
.
techniques, and therefore may be applied to research areas that require state-of-the-art
precisions.
We have recently initiated a research project which aims at unravelling the
fundamental nature of continuous phase transitions by studying the static and dynamic
critical properties of condensed phases of helium near phase transitions with the use of
various state-of-the-art technologies that can provide unprecedented precisions. The basic
380
VOL.35
Z
Z
___.................
;\
.
.
.
.
_.........
I,____
0
1
IE?
.
.
.
.
.
.
.
.
.
.
.
\
.
.
.
.
.
.
.
.
.
.
i
Gl
&
FIG.
8.
A
schematic showing how the gravity-induced density profile of helium in the supercon-
ducting microwave cavity can be deconvolved by the electric field of the
TEoll
mode. Here
to
denotes the superfluid (S)
-
normal
(N)
fluid interface position, and
d
is the height, of
the cavity. The lambda transition temperatures are
TX(O)
for the bottom of the cavity and
TX(~)
for the top of the cavity.
concept is to utilize the unique capability of resolving the resonant frequencies of a
helium-
filled superconducting microwave cavity to extremely high precision (better than one part
in
1017),
in conjunction with the high-resolution thermometry (HRT) and high-resolution
pressure control, to obtain precise measurements of the density and the phase transition
temperatures of helium. The principle of using microwave techniques to perform precision
density measurements of the helium in condensed phases is based on the Clausius-Masotti
relation which relates the density (p) of liquid
4He
to its dielectric constant
E:
E-1
47rPP
-=-
Et2
3M
’
where
oP
is the polarizability and
M
the molecular weight of helium. If we contain helium in
a high-Q superconducting microwave cavity, the temperature-dependent dielectric constant
of helium will couple to the electric field of the resonant modes in the cavity, yielding
temperature-dependent frequency shifts
(Af)
1 t
re a ive
to the resonant frequency
(fu)
at
T =
TX
according to the following relation:
where
A&
is the temperature-dependent change in dielectric constant relative
tric
constant at
TX,
E.
is the electric field of the resonant mode in the cavity,
to the
dielec-
and
Vo
is the
volume of the microwave cavity. Thus, the density
p
can be obtained from Eqs. (4) and
(5). As illustrated in Fig. 8 and in Ref.
[13],
even under the influence of gravity which
gives rise to a gradient in the superfluid Lambda transition
TX(Z),
with
z
being the position
measured from the bottom of the microwave cavity, our numerical simulations have demon-
strated that our microwave techniques together with the fine resolution in detecting the
(5)
VOL.
35
N.-C.
YEH
381
temperature-dependent frequency shifts
(A_f/f
)
0
can be transformed into high resolutions
in the dielectric constant
(A&/E)
as well as the density, thereby identifying the Lambda
transition temperature for a given pressure to a very high precision. The resolution can be
further improved by at least two orders of magnitude under the microgravity environment.
Our current capability can resolve frequencies to better than one part in
1017,
which
transforms into resolving the density to one part in
1Or4
under microgravity if not limited by
the current HRT capability. (Current HRT capability for temperature control at
N
lo-l1
K would yield a density resolution to one part in
1012,
about more than four orders of mag-
nitude better than other measurement techniques achievable to date). Hence, in principle
both the phase transition temperatures and density-related critical properties of helium,
such as the static and dynamic critical exponents and the amplitude coefficients associ-
ated with the thermal expansion coefficient
pp
[14]
can be determined to unprecedented
precisions
using the high-Q microwave techniques.
IV. Physics and applications of magnetoresistive perovskites
IV-l. The physical origin of colossal magnetoresistance in
Lnr_XMXMnOs
and
potential device applications
Recent discovery of the colossal negative magnetoresistance (CMR) in the perovskite
manganites
[15-171,
Lnr_,M,MnOs
(Ln: trivalent rare earth ions, M:
divalent
alkaline
earth ions) has spurred intense research in understanding the origin and providing further
improvement of the magnetoresistive effects.
Our recent experimental studies
[18-221
have
unambiguously identified two important criteria for the occurrence of CMR in the
man-
ganites. One is the double-exchange interaction
[23,24],
the other is the lattice distortion
associated with both the Jahn-Teller effect
[16]
and the ionic size mismatch between the
Mn ions and La (Ca) ions
[25].
Th
ese
two criteria result in half-metallic ferromagnetism
below the Curie temperature
(Tc)
[25].
As illustrated in Fig. 9, the large exchange en-
ergy split between the majority and minority bands results in complete spin polarization
in the ferromagnetic state, in contrast to typical ferromagnetic metals (such as Ni) where
the energy splitting between the majority and minority carriers below
Tc
is much smaller
than the conduction bandwidth, yielding a small fraction of spin polarization
[17].
The
half-metallicity has an important consequence on the electrical conduction
[17,20,22,25].
In the presence of magnetic domains below
Tc,
any misalignment of the spins between
two adjacent domains will result in a large energy barrier for the conducting carriers and
therefore a large resistivity in the absence of an external magnetic field. The application of
a magnetic field aligns the spins in different magnetic domains, thereby lowering the energy
barrier for carriers and yielding colossal negative magnetoresistance.
The complete spin polarization due to the half-metallic ferromagnetism in the
man-
ganites has a great promise for device applications.
For instance, we may consider injecting
spins from the manganites into a high-temperature superconductor via epitaxial thin film
growth of
Lnr_,M,MnOs
on top of a high-temperature superconductor (e.g.,
YBa2Cus07)
film. By injecting a current through the manganites, polarized carriers will diffuse into the
superconductor underneath, resulting in Cooper-pair breaking and the suppression of super-
conductivity. Therefore the superconducting critical current may be varied by controlling
the magnitude of the magnetic current. This concept can be used to develop three-terminal
382
THESCIENCEANDTECHNOLOGYOFCONDENSED...
VOL.35
FIG. 9
1
I
I
I
I
I
Lao.7Cao.3Mn03
at
T =
77
K
Ni
STM
spectroscopy data for an
Lao,7Cao,sMn03
epitaxial film on
LaAlOs
taken in the
ferromagnetic state at
77 K
(<
Tc
M
260
K), plotted as the normalized conductance vs.
the sample bias voltage (V). The pronounced peaks at
~t1.75
eV
and a gap structure with
edges at
*0.5
eV.
The spectroscopy is in excellent agreement with the density of states
calculated by
Pickett
and Sighn
[25]
for
th
e
exchange energy splitting of the majority and
minority bands. The inset is a schematic comparison between a half-metallic ferromagnet
such as
Lao.7Cao.3MnOs
and a typical metallic ferromagnet Ni. Note that the latter yields
a small fraction of spin polarization, in contrast to the complete spin polarization in the
manganites.
devices for a wide range of applications, and
is another example of advancing technology
from new understanding of fundamental physics.
IV-Z.
Giant ferromagnetic Hall resistivity in
Lnl_,M,CoOa
and potential device
applications
The cobaltites
Lnl__,M,CoOs
are interesting magnetic
materials particularly because
of the coexistence of multiple spin configurations in the Co ions
[26].
For
z
= 0.15
N
0.6,
these cobaltites are ferromagnetic at low temperatures.
It
is known that clusters of
high-
spin Co ions form better conducting regions which are imbedded in the less conducting
matrix consisting of low-spin Co ions
[26].
W
e ave recently discovered giant ferromagnetic
h
Hall effects in
Lal_,Ca,Co03
epitaxial films with
z
= 0.2, 0.3, 0.5 and at
T <
TC
[al].
VOL.35
N.-C. YEH
383
FIG. 10.
-0
100
200
3;o
-I-
WI
The ferromagnetic Hall coefficient
R,
VS
.
temperature T data of an
Lao,5Cao,sCoOs
epitaxial film on
LaAlO
s,
compared with the corresponding data of Gd. The maximum
in
R,
occurs near
Tc
in both samples, and the magnitude of
R,
in
Lao,5Cao,sCoOs
is
significantly larger than that in Gd.
For all Ca-doping levels,
the.ferromagnetic
Hall resistivity
(pzy)
is found to be larger than
any known single-phase ferromagnets, as exemplified in Fig. 10 where the ferromagnetic
Hall coefficients
R,
as a
fucntion of the temperature for
Lae.sCau.sCoOs
and Gd are com-
pared. Here
R,
is related to the Hall resistivity by the following expression:
pzy
=
~~Bt&-df,
(6)
where
RH
is the normal Hall coefficient due to the
Lorentz
force on carriers,
B
is the
magnetic induction, and
M
is the magnetization.
Another interesting finding is that the
Hall resistivity increases significantly as the Ca doping level decreases, and the cobaltites
approaches the magnetic percolation threshold
[21].
Although to date there is lack of
quantitative theoretical understanding of the giant ferromagnetic Hall effect
[al],
our studies
have revealed two important criteria that are closely associated with the enhancement of
the ferromagnetic Hall effect. One is the large spin fluctuations amongst the multiple spin
configurations near
Z
íc
,
the other is the presence of magnetic percolating process.
The giant ferromagnetic Hall effect in the cobaltites may be used as sensitive mag-
netometers which operate at temperatures significantly higher than liquid helium temper-
atures. As shown in Fig. 11, the
pry-
vs.-H data for a thin film of
Lae.7Cao.sCoOs
shows
an extremely steep slope near
Tc(=:
180K).
This sensitive change with magnetic fields
near
H
=
0
may be considered for making low-field magnetometers. The device specifica-
tions based on these cobaltites may be particularly useful for lower-cost magnetometers in
unmanned space missions, such as for magnetic field detections on the surface of Mars.
384
THE SCIENCE AND TECHNOLOGY OF CONDENSED
VOL. 35
16
4
&+@o.&
ëì
,
6
4
2
162K
177K
188K
203K
22OK
234K
267K
0
20
40
60
60
100
H
(kOe)
FIG. 11.
The Hall resistivity
(pzY)
vs. magnetic field (H) isotherms of a
Lao,Cao,aCoOs
epitaxial
film on
LaAlOs
substrate. The Curie temperature
TC
is approximately 180 K.
V. Summary
We have described some of our current research efforts in condensed matter physics.
The research topics include vortex dynamics and pairing symmetry of high-temperature su-
perconductors; development of precision clocks for gravitational physics studies and space
navigation; state-of-the-art measurements of the density and critical phenomena of he-
lium near phase transitions under microgravity, using high-Q superconducting microwave
cavities; and the physics and device concepts of magnetic perovskites with either
cobossal
magnetoresistance or giant ferromagnetic Hall resistivity.
These examples clearly under-
score the mutual enhancement of fundamental science and frontier technology in modern
condensed matter physics research.
Acknowledgment
The research at
Caltech
is supported by the National Aeronautics and Space Admin-
istration (NASA), National Science Foundation (NSF), Office of Naval Research (ONR),
and the Packard Foundation. Part of the research was performed by the Center for Space
Microelectronics Technology, Jet Propulsion Laboratory,
Caltech,
under a contract with
NASA. The heavy-ion irradiation was performed at GRANIL in Cean, France.