Highly anisotropic superconducting and normal-state properties of Sr2Ru04
Koji YoshidaL)epartment of Physics, Faculty of Science, Hiroshima University
1-3-1 Kagamiyama, Higashi-Hiroshima 739, Japan
Abstract
We have recently discovered superconductivity of Sr2Ru04 with Tc ~ 1 K . This compoundis the only layered perovskite superconductor without copper that is known so far : the same
crystal structure as a high- Tc superconducting copper oxide . In this study, we have investigated
the superconducting and normal-state properties of Sr2Ru04 by measuring the electrical resistivity,
magnetic susceptibility and specific heat using single crystals .
In the noml1al state we found the T2 dependence of the resistivity below 25 K, the enhanced
paramagnetic spin susceptibility, and the enhanced Sommerfeld coefficient of the specific heat.
These three results can consistently be described as a highly-anisotropic Fermi-liquid behavior of
the nonnal state of Sr2Ru04. In addition, concerning the peculiar temperature dependence of theresistivity along the c axis, we present a systematic interpretation based on competition between
the life time of the quasiparticles governed by a number of scattering processes and the time forthe quasiparticles to travel the interlayer distance d.
From the upper critical fields H c2, we will show that the superconducting state of Sr2Ru04
is also highly anisotropic with the ratio of the coherence lengths F.-; = (ob(O) / (c(O) = 26 evaluatedfor zero temperature. Furthennore, we found peculiar anisotropic flux-pinning behavior: a second
dissipation peak in the ac susceptibility prominently appears only when the direction of the flux
lines, as well as of their induced motions, is parallel to the ab planes. The peak effect in Sr2Ru04
is attributed to the synchronization of the flux lines to the pinning centers as the flux-line latticesoftens with increasing magnetic field and temperature.

In this study we clarify that Sr2Ru04 serves as an ideal reference material for investigationof the limits of applicability of the Fermi liquid theory to other highly correlated layered
compounds, including high- Tc cuprates. In addition., the comparison with these physical properties
of Sr2Ru04 and those of high- Tc superconductors are very important to clarify the mechanism of
the high Tc , which still remains unclear at present.

Contents
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)'"'

2. Experimental .. . ... ... . . .. .. . . ........ . ........ . . . ..................... 6
2 .1 Samp ~ e preparation
2. 2 Measurements
3. Normal-State Properties...... . .. . .................................. 6. .... .. . .. ......... . ...... . ..................... 6. .. . .. .. .... ... ... .. .. .. ... . . . .................. 7

3. 1 Experimental results............................................ 7

3.1.1 Resistivity .. . . . ... . ..... . . ... . .. . ..... . ........... . ....... 7
3. 1.2 Susceptibility.. ... . ... .. . . ... ... ..... . ............... . ... 8

3.1.3 Specific heat... .... . . . . . ... . . .. . . . .. ......... . .......... 8

3.2 Highly anisotropic F errru liquid state . .. .. . . . . .. . ... . . . . . .......... . ... 9
3. 3 Anomalous temperature dependence of resistivity along the c axis
4. Superconducting Properties. ......... 10. . .. . . .... .... . . . .... .. . ...... . ...... .. . . ... 15

4 .1 Anisotropic superconducting state. .. ...... ... . .... . . .. .. ... .. . . .. . . 15

4 .1.1 Anisotropic upper critical fields H c2.. . .. . . . . . . . . . . . . . . . . . . . 15

4.1 .2 Anisotropic superconducting parameters
4 .2 Peculiar flux pinning in the mixed state
4 .2 .1 Detailed experimental procedure. .. .. . .. ....... .. . .. 16. .. . .... ... . ... .. . ..... . ... ... 17..... .. ... . .. . .. . . ......... . . . 17

4.2 .2 Peak effect with dc field along the ab planes
4 .2 .3 Field and temperature dependence of Hp
4 .2 .4 Frequency independence of Hp. ..... . .. . . . . . ..... · 17...... . .. . .. . .. . . . ... . .. ] 8.. .. . ..... ........ . .. .. .. . ... · 19

4 .2 .5 Peculiar anisotropic flu x pinning ' .. . . ..... .. .... . ... . .. . ... .. . . ·20
5. Conclusions
Acknowledgments
References.. . ..... . . ........... . ... .. . . ... .. . .. ........ .. . .. ..... .. · 23... . ..... . ... .. ... .. . . . . .. . .... . . . .. .. . . ... . . . . . ..... · 25.... . ..... ........ . ........ . . . . .. . . . . .. ... .............. . .. .. . 26

2

1. Introduction
Since the discovery ofrugh- Te superconductors (HTSC) [1], active investigations continue
to clarify the mechanism of the high- Te superconductivity. However, the origin of the high- Tesuperconductivity still remains unclear. The formation of the Cooper pairs cannot be explained
at least by a simple s-wave coupling originating from conventional electron-phonon interactions .
One of the key characteristics of HTSC is the quasi-two dimensionality attributed to the
conductive planes of CU02, the key elements of the layered perovskite structure .

Thesuperconductivity appears by carrier doping into the CU02 planes of the parent compounds, which
are Mott-Hubbard insulators owing to the strong Coulomb interactions among the electrons . An
example of the parent compound is

La2CU04, for which La2-xSrxCU04 exhibits thesuperconductivity with Te ~ 40 K. In addition, the fact that no superconductor exists in a varietyof layered perovskite compounds without copper had suggested that the special electronic stateof the CU02 planes is responsible not only for the high Te, but also for the appearance of thesuperconductivity itself.
We discovered, however, a year and a half ago that Sr2Ru04 is the first layered perovskite
superconductor(Te:::: 1 K) without copper [2].

The variations of the resistivity and ac

susceptibility with temperature are shown in Fig. 1. The crystal structure is of the same K2NiF 4 type as a typical HTSC, La2-xSrxCU04, containing quasi-two-dimensional conductive planes of
RU02, as depicted in Fig. 2. This indicates that the two-dimensional electronic state of the CU02
planes is not always required for the appearance of superconductivity in the layered perovskite
oxides . Therefore, it is very important to investigate the differences, as well as the similarities,
between the physical properties of Sr2Ru04 and those of HTSC in order to help clarifying themechanism of the high Te .
Let us compare the basic electronic states of Sr2Ru04 and La2-xSrxCU04 . The ionic stateofRu in Sr2Ru04 is Ru 4+ in the 4~ (12g4) electron configuration in the low spin state [3] with spinquantum number S = 1.

This is compared with Cu 2- in 3cP (12g6e/' ) configuration with S = 1/2

in La2Cu04 . It should be noted that the electronic states at the Fermi level in Sr2Ru04 consist of
hybridized orbitals of Ru 4d and 0 2p electrons (pd;r* anti-bonding orbitals) [4] , analogous tothose of Cu 3d and 0 2p in HTSC (pd 0* anti-bonding orbitals) . Experiments on quantum
oscillations in the normal state of Sr2Ru04 indicated three nearly cylindrical sheets of Fermi
surfaces with slight dispersion along the c axis [5]. Similarly the band calculations [4] predicted
three Fermi surfaces, two of which are electron-like and the other is hole-like . These electronic3

states of the RU02 planes must be important as the stage for the superconductivity in Sr2Ru04.

It should be noted that Sr2Ru04 is intrinsically metallic without acquired carrier doping, in contrast
to La2Cu04 . Although the band calculations [6] predict that La2Cu04 is a metal with a single
cylindrical Fermi surface, it is actually an insulator because of the strong electronic correlations
which are not properly taken into account in the band structure calculations. Despite the similar
Fermi surfaces of the experimental results and the band calculations for Sr2Ru04, this ruthenate
is possibly in the vicinity of the Mott-Hubbard insulators, because the photoemission spectra [7]clearly indicate the formation of the lower Hubbard band owing to the electron correlations .
Therefore, Sr2Ru04 has key components in its basic electronic structure, which are consideredessential for the understanding of the high-Te superconductivity.
Not only the high Te but also the peculiar metallic behavior in the normal state [8] and theunique vortex phases in the mixed state [9] distinguish HTSC from conventional superconductors .
The resistivity along the ab planes shows the linear dependence on temperature over a quite wide
temperature range from just above Te to a temperature higher than the Debye temperature [] 0,] 1]. This behavior can not simply be explained in terms of the electron-phonon scattering. The
peculiar scattering mechanisms, for example that based on the scattering of charge carriers due
to spin fluctuation [11] has been discussed . It is believed that this unusual resistivitive properties
reflect the peculiar electronic states generating the high- Te superconductivity.
A recent controversy is whether the ground state of HTSC after suppressing the high- Tesuperconductivity is a Fermi liquid . The Fermi liquid theory has been helpful to explain thenormal-state properties ofHTSC in the heavily over-doped region, where the superconductivity
does not appear. :However, for TbBa2Cu06-r o (Te < 15 K), which is the material near the overdoped regime, the strong temperature-linear term in the resistivity along the ab planes survives
even down to millikelvin temperatures under a magnetic field of 16 T (II c) [] 2] , in contrast to
the T2 dependence predicted for a Fermi liquid.
Another controversy is whether a non-metallic conduction appears along all crystalline
direction at low temperatures in HTSC in the underdoped regime when the high-7~
superconductivity is suppressed.

The resistivity along both the ab plane and the c axis of

La2-xSrxCU04 with x = 0.08 and 0.13 under high magnetic fields JioH of 6] T, by which Te issuppressed to less than 1 K, shows the non-metallic behavior over a wide range of temperatures
below TeCH = 0 T)~ it seems to diverge as In (l/T) as T approaches the absolute zero [13]. On theother hand , in YBa2Cu3-J.Znx 07 although the resistivity along the c axis is non-metallic at low

4temperatures, that along the ab planes remains metallic [14] . The localization in the c direction
alone is inconsistent with the general scaling theory of disordered systems . This behavior isprobably attributable to the confinement of the carriers within the ab planes [14, 15].
It is also quite important to clarify the mechanism of the anomalous flux pinning of high- Tc
cuprate superconductors (HTSC), because the complex magnetic phase diagram of the mixed state
may be intimately related to the basic nature of high Tc itself . Among a variety of peculiarities ofthe mixed state are the peak effect and the loss of irreversibility of flux lattice in a particular H- T
region. The fonner refers to the presence of a peak in the critical current as a function of magnetic
field or temperature, or to the associated peak in the energy dissipation . The peak effect often
reflects a changeover in the pinning mechanism within the mixed state. The corresponding H-Tlines in the magnetic phase diagram depend onJy on the component of the dc magnetic field parallelto the c axis which is normal to the CU02 planes. This anisotropic behavior has been frequently
interpreted as an evidence for unusual two-dimensional vortices, namely pancake vortices [16] ,originating from the highly anisotropic superconducting state which reflects the layered structures
ofHTSC.
Given the structural and electronic analogy with the cuprate superconductors, and the factthat Sr2Ru04 is the only layered-perovskite superconductor without copper that is known so far,the understanding of the superconducting, normal-state and vortex-state properties of high quality
single crystals is of great interest in clarifying the connections to the cuprates . In the present
work, we investigated the dc-susceptibility and specific heat above Tc, as well as the resistivity andthe ac-susceptibility under magnetic fields below 2 K, using single crystalline Sr2Ru04. We
observed the quadratic temperature dependence of resistiyjty, the enhanced magnetic susceptibility
which is nearly temperature independent , and linear temperature dependence of the specific heatwith the enhanced Sommerfeld constant (Sec. 3.1) . Based on these results, we will show in Sec.
3.2 that the normal state of Sr2RU04 is described very well as an anisotropic Fermi liquid with anearly two-dimensional electronic character of the RU02 planes . The resistivity along the c axisof Sr2Ru04 exhibits a crossover at TM = 130 K from the metallic to non-metallic temperaturedependence with decreasing temperature . In Sec. 3.3, we will quantitatively explain this peculiar
phenomenon in terms of relaxation times of the quasiparticles for a number of scattering processes.
The investigation of the upper critical fields H c2 shows that the superconducting state ofSr2Ru04 is also highly anisotropic with the ratio of the coherence lengths F." = (ob(O) / (c(O) = 26
evaluated for zero temperature (Sec 4.1 .1)

We present the superconducting parameters5evaluated from l-le2 and Te (Sec. 4.1.2) . We also report peculiar anisotropic properties of flux
pinning (Sec. 4.2) . We will extensively discuss a second dissipation peak which was found at low
fields only when Hde is applied parallel to the ab planes in Sec. 4 .2 .5.

2. Experimentall
2.1 Sampl1e preparation
The crystals used were grown by a floating-zone method similar to that reported previously[17]. The starting materials were SrC03 with a purity of 99 .99 % and RU02 with that of 99 .9 0/ 0 .
They were weighed in the molar ratio of Sr : Ru = 2 : 1.1 . The excess Ru is added because of thehigh vapor pressure of Ru at high temperature during the crystal growth. The powders wereground in a dry nitrogen atmosphere and the mixture was prereacted in air at 900 °C and 11 50 °C
for a total of 48 hr with intermediate grindings . After being pressed into a rod with a diameter of
6 mm, it was sintered in air at 1350 °C for 4 hr. The rod was then set in a floating-zone furnace(Nichiden Machinery: SC-15HS-M). The growth of the crystals was performed in air at the feed
speed of 20 mmlhr. The rod and crystal seed were oppositely rotated each other at 30 rpm .
The grown crystals were easily cleaved, so we obtained plate-like crystals . From X-ray Lauediffraction, it was found that the planar surface is the (001) plane. A typical size of the crystals
used in ac susceptibility measurements is (2 x 2 x 0 .5) mm 3 , with the shortest dimension along thec axis . Powder X-ray diffraction of crashed crystals at room temperature did not detect any
impurity peaks and is consistent with the tetragonal K2NiF4-type structure with a = b = 3 .87 A andc = 12.74 A. The samples e'xhibit a Te of :::: 1 K with a transition width of - 0 .1 K . The crystals
used in this study are taken from the same crystal rod used for quantum oscillation measurements[5].
2.2 Measurements
The resistivity was measured using a standard four probe method. A silver paste (Dupont,
6838) is used for attaching electrocodes and is cured in air at 500 cC for 5 min [18]. This process
does not affect the oxygen stoichiometry [19] and results in a strong reduction in the contact
resistance: we attained the contact resistance of < 0.5 Q . This low contact resistance is importantto achieve the hornogeneous current paths within the sample. Measurements of the magnetic
susceptibility of the normal state were performed between 5 and 700 K with a constant field of 1

6

T by using a SQUID magnetometer.

The magnitude of the magnetic fields was precisely

calibrated using the standard sample of Pd . The specific heat measurements were performed bya conventional adiabatic method using a 4He cryostat with a mechanical switch .

The acsusceptibility (x', X") was measured by a mutual-inductance method under dc fields }loHdc up to
8 T, using a commercial dilution and 3He refrigerators .

3. Normal-Stat'e Properties
In this chapter, we will first show the Fermi-liquid behavior in the resistivity, magnetic
susceptibility and specific heat. We will then discuss how these results are interrelated to describe
coherently the anisotropic Fermi-liquid behavior of Sr2Ru04 [20]. In addition, we discuss theobserved peculiar temperature dependence of the resistivity along the c axis .

3.1 Experimental results
3.1.1 Resistivity
The variations of the resistivity of Sr2Ru04 with temperature between Te and 300 K isshown in Fig . 3 .

The resistivity along the ab planes is metallic (dpab/dT > 0) and shows

superlinear dependence on T over the measured temperatures with a large residual resistivity ratio

Pab(300 K)/ Pab(l K) ~ 150 and with a very small residual resistivity of pab ~ ] /1 Q cm just above
Te. In contrast, the resistivity along the c axis is non-metallic with negative dpc/dT at temperatures
above TM ~ 130 K , but becomes metallic at temperatures below TM
crossover at TM from the two dimensional

Therefore, there is ato the three dimensional metal with decreasing

temperature . The square of the anisotropy ratio estimated from the resistivities just above Tc isr; = m*jm*ab = pj Pab ::: 400, where m*ab and m*c are the effective masses of the quasiparticles
for the motion in the ab planes and along the c axis, respectively [2]]. This large anisotropy,
reflecting its layered structure, agrees well with the ratio of the Fermi velocities estimated fromthe Fermi-surface parameters obtained from the quantum oscillations [5]. It should be noted thatthe resistivities along both the ab planes and the c axis below about 25 K follow the T-squared
dependence quite precisely: P = po + AT 2 , as shown in Fig . 4. By fitting the p-T curves, we
obtained Aab = 7.3 nQcm/K? and Ac = 4 .0 /1 QcmJK 2. This I-squared dependence implies theimportance of the Umklapp process of the electron-electron scattering at low temperatures,consistent with the formation of the Fermi liquid state.

7

3.1.2 Susceptibility
The variation of the magnetic susceptibility with temperature under a field H of 1 T is shownin Fig . 5 . In contrast with the large anisotropy of the resistivity, the magnetic susceptibility
depends only weakly on the direction of the external field : Xab = 0 .88 x 10-3 emu/mol (H II ab)
and Xc = 0.98 x 10-3 emu/mol (H II c) at 300 K , respectively, after correction for the isotropic core
diamagnetism of Xcore = - 0.96 x 10-4 emu/mol [22]. These values of Xab and Xc are enhanced bya factor of ~ 4 from that observed in the ordinary d-band metal RU02, for which the susceptibility
is 0.2 x 10-3 emu/mol at 300 K after the diamagnetic correction of - 0.42 x 10-4 emu/mol [22].
The gradual increase of Xab and Xc below about 200 K might be attributable to small inclusions(~ 0.04 %) offerromagnetic SrRu03 (TCurie - 160 K) . Both Xab and Xc exhibit weak temperaturedependence up to 700 K with a weak and broad maximum at about 500 K . This maximum is often
observed in the weakly anisotropic quadratic-layer antiferromagnet [21] . The large magnitudes
and the small temperature dependence of Xab and Xc, however, cannot be solely fitted with those
expected for the two-dimensional Heisenberg model with S = 1 [23] .
From the argument above, we deduce that the large and weakly T-dependent Xab and Xc
consist of the temperature-independent paramagnetic contributions: Xi = XI) + X V\'. i (i = ab or c) .
Here, Xi is the susceptibility after correction for the core diamagnetism, XCJ is the isotropic Paulispin paramagnetic susceptibility and X vv. i is the anisotropic Van Vleck susceptibility.

It isgenerally difficult to estimate the magnitude of the Van Vleck susceptibility . We note that for thecorresponding cuprate La2-xSrxCU04, a band-structure prediction of X vv = 0 . 15 x 10-4 emu/mol(H I I ab) and 0.4 x 10-4 emu/mol (H II c) for SC2CU04 [24] is often used . Considering thedifference in the symmetry of the relevant d orbitals of the ruthenates and the cuprates, theanisotropy of Xvv, i would be sufficient to explain the difference between Xab and Xc of Sr2Ru04 .
In other words, the anisotropy in Sr2Ru04 is probably attributed to the small and anisotropic
contribution of X vv to X. From the above consideration, Xah and Xc are most likely dominatedby an enhanced Pauli spin susceptibility Xo, and in the remainder of the paper we conveniently
make the approxin1ation that XCJ :::: Xab or Xc.

3.1.3 Specific heat
Figure 6 shov/s the specific heat divided by temperature CplT above 2 K for zero field andunder a magnetic field of 14 T applied parallel to the c axis [25]. Fitting with Cpl T = y + J3T2
gives the Sommerfeld constant of y = 37.5 mJIK2mol and J3 = 0.191 mJIK4mol for zero field . The

8

Debye temperature

eo is estimated as - 410 K using the relati on en = (12n4NkB/5jJ)J /3, where

N is the number of atoms per mol and kB is the Boltzmann constant. T he density of states at theF ermi level estimated from y is enhanced from the theoretical expectation based o n the bandstructure calculation by a factor of 3 .6. A similar enhanced y has also been observed in recent
investigations using polycrystalline samples [26] . This enhancement is too large t o be account forsolely by the electron-phonon interaction. It should be noted that even with the field of 14 T, ydoes not change within our experimental accuracy of ± 1. 5 mJIK 2mol. This indicates that theenhancement does not originate from weak spin fluctuations . In fact , recent phot oemission
measurements [7] suggest the presence of the coherence peak at the Fermi level, expected in astrongly correlated system in the vicinity of a Mott-Hubbard insulator. The band w idth of thecoherent states is estimated as - 0 .3 eV, corresponding the magnetic energy of 5000 T .
Therefore, we conclude that the enhanced y is attributed to the increased density of states by thestrong electronic correlation.

3.2 Highly anisotropic Fermi liquid state
Let us discuss w hether the strong electronic correlations in the normal state of Sr2Ru04 is
related to the appearance of the Fermi liquid state. One of the parameters to characterize theFermi-liquid state, frequently used for heavy-Fermion materials, is the Wilson ratio , R w ==(n 2kB2/3JiB2)(Xo/ y) , where fiB is Bohr magneton, xois the Pauli spin susceptibility expressed in
emu/mol, and y is expressed in ergIK2mol (= 10-4 mJ/K 2mol) . Rw is unity for a free electron gas,
and is expected to increase up to two if the enhancements of both xoand y are attributable to thesame origin of the strong correlations among electrons [27] . On the other hand, R w » 1 if xois
mainly enhanced by ferromagnetic spin correlations, and Rw < 1 if y is mainly enhanced by strong
electron-phonon correlations .
In Fig. 7 we plot xo against y for Sr2Ru04 along with many highl y correlated electron
systems including heavy-Fermion compounds . Rw = 1.7 - 1.9 for Sr2Ru04 is comparable to thatof compounds with the Fermi-liquid state and suggests the strong electronic correlation as acommon origin of the enhancements in the susceptibility and the electronic specific heat.
Secondly, we examine the Kadowaki-Woods ratio [28] which is defined as the ratio A I y2,
where A is the coefficient of the T 2 term of the resistivity. Phenomenologically it is expected totake the universal value Go = 1.0 x 10- 5 IlQcm/(mJ/K.mol)2 as long as the conduction and theenhanced yare governed by the same quasiparticles with a self-energy that depends strongl y on

9

frequency [29] . It is also known that for systems without such mass renormalization, AI ? isconsistently smaller than ao by a factor of about 25 .
In Fig . 8 'Ne plot A against r for Sr2Ru04 along with many highly correlated electron
systems including heavy-Fennion compounds, as well as some transition metals. The ratio for thein-plane conduction Aabl y2 = 0 .52ao is in fair agreement with the universal trend . This confirmsthat the same quasiparticle states probed by the enhanced electronic specific heat predominate theconduction within the RU02 planes . This consideration is strongly supported by the fact that theobtained r is well comparable to r = 32 mJIK2mol estimated from the cyclotron masses of thequasiparticles for the motion in the ab planes determined by the quantum oscillations [5] using thefollowing relation :(3 .1)r = (l/3)n 2kB2D(£F)NA = 1.47J.:m*ab1m e mJlK 2mol,where D(EF) = (a 2/n t?)m*ab is the electronic density of states ofa two dimensional system, NA
is the Avogadro's number, me is the bare electron mass, and the summation is taken over all the
Fermi-surface cornponents . In contrast, Acl r2 = 280ao severely deviates from the universality .
This ratio originates from the interlayer conduction which is characterized by a small velocity
component Vc of the same quasiparticles; Vc is associated with the slight dispersion along the c axisof the nearly cylindrical Fermi surface. In this sense, the observed Ac reflects the renormalized
effective mass of the quasiparticles for the motion along the c axis given by m *c = m *ab(Vablvc)2/2.
This ratio (vablvc)2/2 is expected to be greater than 550, if it is estimated from the Fermi surface
parameters inferred from the quantum· oscillations [5]:(Vab /Vc)2/2 = (4/c 2){J.:(kF2/m*ab)/ J.:(kF2 iJkF2/m*ab)d ,(3 .2)

as described in the next section. This value is in good agreement with the observed Ac/Aab :::: 550 .
From the above considerations, we conclude that the normal state of Sr2Ru04 is described as ahighly anisotropic Fermi-liquid state.

3.3 Anomafious temperature dependence of resistivity along the c axis
As mentioned in Sec. 3.1.1, the resistivity along the c axis of Sr2Ru04 exhibits curious
temperature dependence: the crossover from the metallic to non-metallic behavior at TM - 130 K
with increasing temperature. It is well known that pc of La2-xSrxCU04 is profoundly affected by
the structural transition from the high-temperature tetragonal phase to the mid-temperatureorthorhombic phase [11). Our investigation of powder X-ray diffraction at low temperatures [2,30] shows that Sr2Ru04 does not exhibit any structural transition down to 5 K or any change in10the temperature dependence of the lattice parameters across TM. This result is consistent withrecent electron diffraction [31], Raman-scattering [32] and neutron-scattering [33] measurements .
Therefore, the origin of the sign change in dpc/dTwith temperature in the present system appears
to be purely electronic.

Since the mechanism of the dimensional crossover in the metallic

conduction is ant important issue in HTSC, it is of great interest to understand the crossovermechanism in Sr2Ru04 .
Let us discuss what criteria determine the boundary between the metallic and nonmetallic
conduction at T = TM, as well as that between the Fermi-liquid behavior and non-Fermi-liquidbehavior at T : : 25 K . We will analyze the temperature dependence of Pc from the viewpoint of
the relaxation time, or the life time, for scattering of the quasiparticles . (The derivation in thissection is motivated by the argument in Ref. 5, which adopted the approximation of a common
mean-free-path .)First, we consider the criterion for the Fermi-liquid description. The resistivity along the caXIS Pe of Sr2Ru04 is associated with a small velocity component of the quasi particles, as
discussed in Sec. 3.2. Let us define the characteristic time for the quasiparticles to move between
adjacent Ru02 planes as Tc (= dive) , where d = c/2 is the interlayer spacing and Vc is the rms groupvelocity along the c direction of the Fermi surface. When the life time T of the quasiparticles isshorter than T e , the coherent metallic conduction in that direction is not expected to occur.
We consider an energy dispersion for each band near the Fermi level of the elementary form

oCk = t?kFokFlm*ab - 2tecos(kce),(3.3)

where te and ke represent a hopping matrix element and the wavevector, respectively, and n= hl2rr
as h is the Plank constant. This results in the relationsVc =ntcc/nand te = n2kF~kF/(4m*ab) ,(3.4)

where ~kF is the dispersion along the c axis for each Fermi surface. Using these relations weobtain the rate at which the quasiparticles travel to the adjacent planes aslire = 2I2t/ n = nkF~kF/(nm*ab) .

(3 .5)

From the Fermi-surface parameters determined from the quantum oscillations [5], we can estimate
the characteristic transfer rate 11 Te for each Fermi surface as summarized in Table] :II re = 4.5 x lOll S-1 for the a-Fermi surface,= 6.3 x 10 12 S-I for the ~-Fermi surface,= 3.4 x 10 12 S-I for the y-Fermi surface .

We note that the transfer rate is greatest for the ~-Fermi surface, and is larger by an order of11magnitude than that for the a-Fermi surface.
Let us estimate the life time T at low temperatures, which is governed by the relaxation timeof the impurity scattering Timp and that of the electron-electron scattering Tee. We use the Drude
relationship 0 = 1: (ne 2 rim *)i, where 0 is the conductivity, n is the carrier number, e is theelementary electronic charge, m * is the effective mass of the quasipartic1es and 1: i represents thesummation over the Fermi-surface branches designated by i (parallel resistivity for different bands) .
Using the relation ni = kF. ?/nc (for the two-dimensional system) and m*c. i = m*ab. i(V ab)VC.i)2/2,
Oab = 1: (ne 2 r1m*ab)i=(e 2/nc)1:(kF2r1m*ab)i.
(3 .6a)Oc= 1: (ne 2 T'lm*C)i= (e 2C/4n)1:(k-(21JkF2 T'lm*ab)i .

(3 .6b)In these equations, we omit the index; for the quantities within the summation for brevity . We
can set T' = T for each band because the conductivities are governed by the life time of common
quasipartic1es . In fact , the expected anisotropy ratio of the resistivity Pel pab = Oabl oc =(4/c 2){ 1: (k-(2lm *ab)/ 1: (k-(21JkF2Im *ab)i) : : 550 is consistent with our observation .
At high temperatures, it is a good approximation that the life time is limited by the thermal
process and is therefore independent of the location on the Fermi surfaces (the common- T
approximation) . On the other hand, at lowest temperatures, it is a good approximation that themean free path along the ab planes lab is independent of the Fermi surfaces because it is in the
impurity scattering limit ;lab = Vab , i Ti = nkF. i T/m *aboi = constant and common to a , 0 and y.

(3 .7)

Since kF, /m *abo i estimated from the Fermi surface parameters of Sr2Ru04 (Table. 1) fortunately
does not depend much on the band, the common-lab approximation is crudely equivalent to thecommon- T approximation according to eg . (3 .7) .

Therefore, we adopt the common- T

approximation for all temperature range, which would retain semi-quantitative validity.
In this comrnon- T approximation, we will express pab in order to evaluate the transfer rate
for the electron-electron scattering 1I Tee and for the impurity scattering 1/ Tilllp . We consider theseries resistivity for different scattering: 11OJ = 1:;{ 11 oij), where 1:j represents the summation overscattering processes of the guasiparticles designated by} (j = ee for the quasiparticle scattering andj = imp for the impurity scattering). Along with eq. (3.6a), we obtain

Il 0 ab, i = 1:;{11 Oab, ij) = (nc/e 2 )(m*ab, /kF. ?)1:;{117j).

(3 .8)

Moreover, from the parallel resistivity for different bands: Pab = {L: i( Oah. i)} -I , we obtain12

(3.9)

Pab

Note that the first summation In eq . (3 .9) can be fully evaluated using the Fermi-surface
parameters given in Table 1.
From Pab = pab. 0 + AabT2, we evaluate the transfer rate for the electron-electron scattering

I I Tee and for impurity scattering I I Timp as
II T imp = (e 2Pab.o/ nc )"E. i(kr.?lm*ab. i)(3 .lOa)= 8.2 x lOll S-l = constant and common to (X ,0 and y.
IITee

=

(e2AabT2/nc)"E.i(kr.?lm*ab, i).

(3. lOb)

Figure 9 shows the variations of II T e, 11 Tee and II Timp with temperature . For the band (x ,liT (=IITee + lIT'imp) is larger than liTe even at T= 0 K. On the other hand , for 0, liT is lessthan 11 Te below about 25 K . Therefore, the coherent metallic conductivity along the c axis should
be maintained below 25 K. This explains why the T-squared dependence of Pe is observed below
25 K despite the large magnitude of pe of a few mQcm and the nearly two-dimensional characterof the Ferrrll surfaces,
Second, we discuss the criterion for the metal-non-metal crossover of Pe by comparing therelaxation time Tep of the quasiparticles scattered by phonons and Te. The transfer rate for theelectron-phonon scattering II Tep is proportional to kBT;
(3 .11)
where C is the dimensionless proportional coefficient. Between 25 K and 130 K , where thecoherent metallic description breaks down, the resistivity along the c axis is nevertheless metallic
with dpeldT> O. This is probably attributed to finite probability that the quasiparticles travel
without scattering by phonons, which predicts Pe ex pab [34].
On the other hand, when the thermal energy is larger than the effective band width W, thevelocity distribution of the quasiparticles is too heavily disturbed to maintain the Drude description
for metallic conduction. In the tight-binding model, W is 2zt, where z is the numbers of the nearest
neighbor atomic sites and t is the hopping matrix. We use W = 4te (z = 2) for the conduction along
the c axis in Sr2Ru 04 . Using this relation and equations (3.4) and (3.5) , we can express the rate
at which the quasiparticles travel to the adjacent planes as(3 .12)13

When 1/ Tep is larger than II Te, it is expected that the metallic conduction in the Drude
description changes to the non-metallic conduction by the thermally assisted hopping . We believethat this is the crossover that occurs at TM . From the fact that I I Te for the ~-Fermi surface is thelargest among the three bands, we determine the coefficient C in (3 .12) by assuming that thecrossover for the ~-Fermi surface gives TM for the boundary of the metal-non metal, as shownin Fig. 9:

C = W*lkBTM ,(3. 13 a)with W* = W 1/2,

(3.13b)where W* is defined as the effective band width . This analysis gives W* = 2-l2tc. Therefore, weestimate C = 0.37 using tc = 17 K for the ~-Fermi surface. In addition, when we use the obtained
II Tep for the other band based on the comrnon- T approximation, the transfer rate for the electron-

phonon scattering predicts similar crossover of pc at - 70 K for y -Fermi surface, as shown in Fig.
9. This coincides with the temperature of 65 K above which pc deviates downward from therelation P c ex Pab , as shown in Fig. 10.
Next we discuss the temperature dependence of Pab . With increasing temperature, it starts
to deviate from the P-dependence at 25 K, as well as Pc . The time Ta for the quasiparticles tomove between the nearest Ru atoms is represented by(3 .14 )Here, a is the lattice parameter along the a axis . The estimated II To using the Fermi-surface
parameters is larger by two orders of magnitude than the relaxation time liT (=I I Tee + IITimp) at
25 K. Therefore, the coherent conduction along the ab planes should not be disturbed at thistemperature . In this sense, it is of great interest why the Fermi-liquid description breaks down
for pab above 25 K . In addition, at 65 K and 130 K, the temperature dependence of pab
qualitatively changes : Pab' - pab.O ex T1.55 (25 K ~ T ~ 65 K) , TI .37 (65 K ~ T ~ 130 K) and T1.50(130 K ~ 7), as shown in Fig. 11. Clarification of the relationship between pab and Pc is quite

important for the understanding of the electronic states in Sr2Ru04.
In order to confirm the above considerations, it is very useful to study the Fermi-liquidbehavior by means of impurity doping in the RU02 planes . Such impurities can control the life
time of the quasiparticles, and as a consequence the effective dimensionality of the conduction.
In addition, it is also desirable to study the crossover between the metallic and non-metallic
conduction by measurements under pressures, which controls the hopping matrix element te.

14

4. Superconducting Properties

In this chapter, we first show that Sr2RU04 is a highly anisotropic 3D superconductor basedon the superconducting parameters determined from Tc and the upper critical fields He2 [35].
Secondly, we will show that the peculiar flux dynamics found is originated from the anisotropyof the superconductivity [36].

4.1 Anisotropic superconducting state
4.1.1 Anisotropic upper critical fields Be2
Figure 12 shows the variations of the real part of ac susceptibility X' with Hdc at selected
temperatures for an ac field Hae = 0.58 Oe, parallel to Hde, at a frequency of1= 1000 Hz. With
increasing temperature, the onset of diamagnetic susceptibility shifts to lower field and is notobserved above 1 1(. In this study H e2(l) is defined as the intersection of the linear extrapolationof the most rapidly changing part of X' with that of normal-state X', as indicated in Fig . 12 .
Although this definition will somewhat underestimate the true H e2, we adopted this definition here
for convenience. It should be noted that H e21Iab(l) is an order of magnitude larger than He21Ic(l) .
It is interesting that a peak structure in X' appears below He2 only when Hde(//Hae) is parallel tothe ab planes. We will discuss this peak structure in detail in the next section. In this section, weconcentrate on the anisotropic H e2 .
Shown in Fig. 13 is the H-T phase diagram obtained from the X'_H curves, which isconsistent with that derived from X '-T curves . Te defined as T(H e2) in the limit of JLoH de = 0 T is
0.90 K. Extrapolation of H e2-Tcurves to 0 K gives 'tlOHe21Iab(0) = 0.78 T and JLOHe21/c(0) = 0 .030
T . These values are smaller than the Pauli limiting field
JioHPauli = 1.24kBTJJLB =1.66 T(4.1)

simply expected from the BCS theoretical calculation [37] ; the small He2 values mean that the pairbreaking effects due to the Zeeman energy are negligible. Here, kB is the Boltzmann constant and
J.lB is the Bohr magneton.

These H e2(0) are in good agreement with those derived from theWerthamer-Helfand-Hohenberg formula [38],H e2(0) = 0.693(dHe2/d1)TeTe,(4 .2)

obtained for the weak-coupling BCS theory . The electron-phonon coupling constant Ae-p = 0.37,
estimated on trial from the McMillan formula [39] using Tc = 0.90 K, the Debye temperature 80= 410 K and the Coulomb repulsion parameter J.l* = 0.10, implies that Sr2Ru04 is not in the strong
coupling regime; both Te and 80 are similar to those of aluminum.

The anisotropy in thecoherence lengths, Is= (ab(O)/ (c(O) = 26, agrees well with the square root of the effective mass

15

ratio rN in the normal state of this anisotropic Fermi liquid . Therefore, the superconductivity in
Sr:zRu04 originates from Cooper pairs formed by the highly correlated electrons . In this respect,
although we do not have any information yet to specify the symmetry of the Cooper pairs, thepossibility of unconventional superconductivity cannot be excluded .

4.1.2 Anisotropic superconducting parameters
Using the Ginzburg-Landau (G-L) formula for an anisotropic 3D superconductor,
lie2//e = ¢o/(21t (GLab 2) and He2//ab = cAJ/(21t (GLab(GLe),(4 .3)
where ¢J is the flux quantum, we estimated the coherence lengths of (GLob(O) = 1.05 x l 0 3 A and(GLe(O) = 40 A. 1v1oreover, using(4.4)
where ex = 0.18 for the BCS theory, n = h/21t as h is the Plank constant and VF is the Fermi
velocity, we obtained Vab = 6.9 x 104 m1s and Ve = 2 .6 x 10 3 m1s for VF estimated from (GLab(O)and (GLe(O), respectively. These values are consistent with those obtained from the quantum
oscillation experiment in the normal state [5], but substantially smaller than those from a bandcalculation [4].

A large value for the superconducting anisotropy (GLab(O)/ (GLe(O) = 26 iscompared with - 10 ofLa1.86Sro.14Cu04 [40].
There is an iInportant difference between Sr2Ru04 and HTSC as (GLe is compared with theinterlayer distance d. For Sr2Ru04, (GLe is larger than the interlayer spacing d = c/2 = 6.37 A bya factor of 6, in contrast to (GLe ~ 3 A < d for Lal.86Sro.14Cu04 [40]. In this sense, Sr2Ru04 is
an extremely anisotropic, but 3D superconductor.
Now various superconducting parameters can be estimated usmg relevant theoretical
relations. The BCS relation(4 .5)
where r = 6.53 x 103 ergIK2 cm 3 (= 37.5 mJIK2 mol), gives the thermodynamic critical field J.loHco= 0.018 T. The anisotropic G-L parameters are evaluated from(4 .6)
to be Kab(O) = 31 and Ke(O) = 1.2. Therefore, Sr2Ru04 is a type II superconductor with nearly atype- I character for the length scales within the ab planes . From

Ke = Aab/(GLab and Kab = (AabAe/(GLab(GLe)1 /2,(4.7)
estimations for the penetration depths are Aob(O) = 1.3 x ] 03 A and Ae(O) = 3.3 x ] 04 A. Using

HcJ(0)Hc2(0) = Hc(0)2(lnK{0) + 0.08) valid for K» 1

16

(4.8a)

Hcl (0)Hc2(0) ~ Hc(0)2 valid for K ~ 1,

(4.8b)

the lower critical fields are J1olicl(O) = 1.4 mT (llab) and 0 .011 T (lIe). The mean-free-paths fromref [5], lab - 1.0 x 103 A and Ie - 30 A (see also section 3-3), are almost the same as the coherence
lengths ~ this indicates that Sr2Ru04 is not in the clean limit, in contrast with HTSC .

All theparameters of anisotropic superconductivity thus evaluated are summarized in Table 2.

4.2 Peculiar flux pinning in the mixed state
4.2.1 Detailed experimental procedure

In order to investigate the mechanism of the peculiar anisotropic peak structure of Sr2Ru04,
as described above, we measured ac susceptibility (x', X'') under magnetic fields J10fid c up to 8 Twith a variety of configurations between Hdc and Hac . Here, Hdc and Hac are applied either along
the ab planes or along the e axis ~ there are five distinct configurations of the directions of Hdc and

Hac with respect to the crystalline axes, as shown in Fig . 14 . Figure 14 (a) and (b) depict thelongitudinal configurations with Hdc II Hac, which provide compressional motions of flux lines .
These are the same configurations used for the investigation of the anisotropic H c2 . The others,
Fig . 14 (c )-( e) show the transverse configurations with Hdc -.L Hac , which provide the tilting
motions of flux lines. It is difficult in our present experimental setup to exactly align Hdc, Hac andcrystalline axes . Because of large anisotropy in H c2(0) , 0 .78 T for Hdc II ab and 0 .030 T for Hd c

II e, Hc2 is quite sensitive to the orientation of Hdc with the ab planes . Assuming that Hc2 varies
with the angle ebetween Hdc and the ab planes as

I-Ic2(fJ) = Hc2//ab{cos 28+(Hc2//abIHc2 //c)2sin 2e}-J /2 [41] ,(4 .9)

we can estimate the misalignment angle in this study to be less than 1.5 o. In order to minimize
the influence of the magnetization relaxation during the field sweep, we employed a very slow
sweep rate of Hdc, 0 .5 Tlhr (Hdc II ab) and 0 .05 T/hr (Hdc II e) . The results with the slow fieldsweep agree with those with a field held constant for each measurement . Moreover, the fieldsweep results gave the consistent phase boundary as T-sweep results . These confirm that the
influence of the magnetization relaxation is not important in describing the present results .

4.2.2 Peak effect with dc field along the ah planes
The results for the longitudinal configurations are represented in Fig . ] 5, showing thevariations of the real and imaginary components of ac susceptibility (X', X") with Hdc at T « Tc.
It is interesting to note that a peak structure in X' appears below Hc2 only when Hdc(/IHac) is

17parallel to the ab planes, as described above. The corresponding second dissipation peak is also
observed in the X"_·H curve below the ordinary pronounced peak near H e2( 7), as shown in theupper part of Fig. 15 (a) . With increasing Hde, X" first increases linearly, which implies that X"
is proportional to the number of vortices, and then takes a maximum, the field of which we defineas H p( 7) . This maximum indicates that the number of the flux lines trapped in pinning centers
increases rapidly just above Hp(7) . The crystals used in this study have a single sharp peak in theX"-T curve with Hde = 0 T, indicating high homogeneity of the transition temperature throughout

the crystal. Moreover, essentially the same second peak is observed also in the crystals withdifferent Ll Te. Therefore, the second peak is not attributable to the coexistence of the phases withdifferent Te, but must be intrinsic to the superconductivity of Sr2Ru04 . The field-sweep resultspresented here are taken with increasing fields after zero-field cooling (ZFC)

Actually wemeasured susceptibility with both increasing and decreasing H de and observed a minor quantitative
but no qualitative difference between the two procedures. The difference can be ascribed almost
entirely to a technical artifact due to the time constant, r -20 s, of the magnet used . In addition,
the difference between the results under ZFC and field cooling is negligible.
The variations of X' and X" with Hde in the transverse configurations (Hde -L Hac) at about
0.4 K are shown in Fig. 16. The second peak similar to the one in the longitudinal configuration(Fig . 15 (a)) is also observed for (Hde II ab) -L (Hac II ab) (Fig. 16 (a)). However, X" tends tosaturate before reaching the pe~ in contrast with the linear increase up to the peak for (Hdc II ab)
II (Hac II ab) . This is possibly due to the misalignment. In fact, the obtained H c2(7) is a little

smaller than the H c2(T) for (Hdc II ab) II (Hac II ab). This difference can be explained by amisalignment of Ll e - 1.50,estimated by the angle-dependent H c2 ( fJ) given by the equation (4 .9).

These observations indicate also that the second-peak phenomenon reported here is not too
sensitive to the exact alignment of Hdc with the ab planes .
When the flux lines within the ab planes (Hoc II ab) are tilted towards the c axis (Hac II c),
the dissipation at low :fields is substantially reduced and the second peak is barely visible (Fig. 16(b)) . For (Hdc II c) -L. (Hac II ab) (Fig. 16 (c)), we observed only the peak corresponding to He2
at all temperatures below Tc, similar to the longitudinal observation with Hac II c and Hdc II c .
4.2.3 Field and temperature dependence of Hp
In order to further characterize the peak effect, we will concentrate on the longitudinal
configuration with (Hdc II ab) II (Hac II ab), for which the effect was most clearly observed. The
18

variations of X' with Hdc at selected temperatures are previously plotted in Fig. 12 (a) . The second
peak structure is not observed abov e 0 .77 K . The corresponding vari ations of X" with Hdc are
shown in Fig. 17 (a). With increasing Hde, the dissipation at all temperatures first increases along
a common line up to the second peak. As a result, the second peak heig ht, X " at H p(1), varies
linearly with Hp(T). This is in sharp contrast with the relation between the first peak height andHe2: the height of this peak decreases with increasing H c2( 1) as shown in Fig. 17 (b).
The obtained Hp(1) is plotted in Fig . 18 along with the upper critical fields He2//ab(1) andHe2//c(1) . With increasing temperature, Hp(1) decreases from H p(O ) ~ 0.45 T, estimated by the
extrapolation of the Hp-T curve to 0 K, and vanishes continuously at about 0.8Te . The H p(1)clearly does not merge into H c2(1) even at Te.
Figure 19 shows the variations of longitudinal X' and X" with temperature at selected Hdeparallel to the ab planes .

For Hde < Hp(O), X" irutially remains constant w ith increasing

temperature (Fig. 19 (a)) . This behavior strongly supports the above interpretation that thedissipation below Hp (1) depends linearly on the number of vortices, because the number remains
essentially constant during this T- sweep . Further increasing T results in a small dip in X", whichis accompanied by the decrease in X' indicating the recovery of pinning force . On the other hand,
the T-sweep measurements with constant fields at 0 .5 T ~ ~oHdc ~ 0.7 T show that X' and X "decrease from the lowest temperatures (Fig. 19 (b)) . This behavior is understandable because for
Hdc > Hp a T-sweep process never crosses the Hp(1) line . While there is no obvious second peakin the X"-Tcurves even for Hdc < H p, the onset temperature of the decreasing X " at each Hdc wellcorresponds to T(J-.l p ) , as plotted by open squares in Fig. 18 .

4.2.4 Freqwency independence of Hp
We investigat ed the effect of the frequency f of Hac on the X '-T and X "-T curves at J.l oHdc

= 0.50 T . Because T(Hp) is not defined in this region of Hdc > Hp(O) , the temperature at which
X'-Tcurve takes the minimum is denoted as T(Hp') , in which Hp' is defined as the corresponding
minimum field in the X'_H curve, as indicated in Fig . 19 (b).

This Hp' corresponds to thechangeover field from the increasing flux-pinning near Hp to flux-depinning near H c2.

The

temperature dependence of Hp' corresponds qualitatively well to that of H p, as shown in Fig . 20.
Therefore, T(Hp) is also the characteristic temperature of the peak effect. We show the variationof T(Hp') with the frequency in Fig . 21 . T(Hp') is nearly independent of the frequency of Hac

19between 102 and 104 Hz. In contrast, T(H c21lab ) varies as(4 .10)J =Joexp(- VolkBT) ,where Vo = 0 .7 me V is the estimated pinning potential and kB is the Boltzmann const ant .
Therefore the first dissipation peak near H c2 can be explained in terms of thermally activated flu x
motions, whereas a different process is required to explain the second dissipation peak.

4.2.5 Peculialr anisotropic flux pinning
The second dissipation peak in the X"-H curve indicates a recovery of the flu x pinning for ce.
As we have shown, the second peak is observed only with Hd c II abo Moreover, it is mostprominent for Hac II ab, while it is much suppressed and barely visible for H ac II C . As long as both
Hd c and Hac are within the ab planes, the second peak is clearly observed

regardless of theconfiguration between Hdc and Hac . In HTSC , in contrast, the peak effects have often beenreported for Hdc II C. They are attributable to the melting transition from the vortex solid to thevortex liquid with mainly increasing temperature [42] , or in other cases to the crossover from the
3D to 2D pancake vortices with increasing field [43]. A conventional 3D superconductor witha layered structure, 21-I-NbSe2 with Tc = 7.6 K and the anisotropy parameterr,; 3.3, exhibits a=peak effect for both Hdc II ab [44] and Hdc II c [45] , interpreted as a crossover of the vortex
dynamics from the coherent motion to a plastic flow with increasing field.

In K-(BEDT-

TTF)2Cu[N(CNh]Br with the highest Tc of 10.9 K known among the organic superconductors
and with IS = 4 [46] , the peak effect is absent at least in the ac susceptibility for H d c II c [47] . A
crucial difference in the superconductivity of Sr2Ru04 in comparison with that ofHTSC is thatthe coherence length ( c(O) = 40 A, which is larger than the interlayer spacing d = c/2 = 6 .37 A,
leads Sr2Ru04 to a 3D superconductor. It is this two-dimensional character of superconductivity
ofHTSC that makes its mixed state distinct from that in other layered superconductors .
Before discussing the origin of the second peak, let us concentrate on the observed
anisotropy of the flux pinning. The linearity of initial increase in X" in the X"-H curves (Fig . ] 5(a) and Fig. 17 (a)) and the constancy of X" in the X"-T curves (Fig . ] 9 (a)) with both Hdc II ab
and Hac II ab indicate that the dissipation is proportional to the number of flux lines along the abplanes and that the flux lines easily move along the ab planes without much magnetic impedance.
On the other hand, even with Hdc II ab , the dissipation for Hac II c is much less than that for H ac
II ab o20

We first consider the shielding effect for Hac in highly anisotropic superconductors as theorigin of the anisotropic dissipation. Only when Hac is along the c axis, the shielding current does
not have the component along the c axi s. Sr2Ru04 exhibits a large anisotropy in the criticalcurrents: lc. c is at least two orders of magnitude smaller than J c. ab [2J. Therefore, the screening
current against Hac will much more easily exceed J c for Hac II ab, and results in dissipation . This
interpretation semi-quantitatively agrees with the large dissipation for Hac II ab and small
dissipation Hac II c . In addition, in this mechanism a dissipation in X" is expected to appear alsofor Hdc II c and Hac II ab o In fact , some dissipation below H e21Ic(l) is observed as show n in Fig .
16 (c), in contrast to much less dissipation below H e21Ic(l) for Hd c II c and Hac II c (F ig . 15 (b)) .

In order to confirm the shielding effect the measurements of the field dependence of the criticalcurrents along both the ab planes and c axis may prove very useful.
Secondly, we w ill consider whether the 2D pinning mechanism reflecting its layered
structure, the intrinsic pinning mechanism [48, 49] , operates in Sr2Ru04. A theoretical criterion
for the strictly working intrinsic pinning is that the coupling between the adjacent superconductive
layers is negligible because of intermediating non-conducting layers, i.e. (cld < 1 [48]. Thismechanism works \Nell for HTSC, since this condition is satisfied except in the vicinity of Te [50 ,51]. On the other hand, (c exceeds d by a factor of - 6 even at 0 K in Sr2Ru04, suggesting thatthe intrinsic pinning is probably very weak even if it exists . On the other hand, ( GLc exceeds d byfactor of - 6 even at 0 K in Sr2Ru04. This means that the intrinsic pinning is probably very w eakeven if it exists. In fact, the modulation of the superconducting order parameter along the c axis
between the conductive RU02 planes and the non-conductive SrO layers should be only by few
percent. This is crudely estimated byLl (dI2)= Ll (O)exp[ -(dI2 )2/2 (GL/J,(411 )

where, Ll (z) is the superconducting order parameter as a function of the distance z from RU02
planes . K wok et al. [50]. demonstrated, however, that the effectiveness of the intrinsic pinningpersists in YBa2Cu307-o even near Tc where ( c is larger than d by a factor of 3. Therefore, it is
not surprising that the intrinsic pinning is operating in Sr2Ru04 to some extent , in addition to theanisotropic shielding discussed in the previous paragraph.
Let us now discuss the origin of the peak effect in Sr2Ru04. We will argue below that thesynchronization mechanism consistently explains the observed behavior in Sr2Ru04. But we firstexamine if other mechanisms apply to Sr2Ru04. The peak effect is observed only for Hde II ab ,so that the pancake vortices would not form in this field orientation . In addition, Sr2Ru04 is a 3D21

superconductor, as mentioned above . Therefore, the 2D-3D crossover in the vortex structure is
not relevant. In HTSC the flux melting is often responsible for the peak effects . When thermal
fluctuations become sufficiently large, such that the mean-square displacement of a single vortex
line is comparable to the lattice parameter of the vortex lattice, the system is expected to melt intoa vortex liquid . Such a condition is often satisfied in HTSC because of the high Tc and short (,but is not likely to be satisfied in Sr2Ru04 with the low Tc and long (. For the melting transition,
the characteristic field should vary as (1- TITc)m in the high temperature regime near Tc, valid for

Hdc II c [52] , and vanishes just at Tc. Assuming that the relation is also valid for Hp in Hdc II ab,
the H- T phase diagram of Sr2Ru04, as shown in Fig. 18, is not compatible with the flux melting .
Because of frequency independence of T(H pI) it is neither likely due to the depinning of vortices
driven by the thennal activations, which is discussed also as the origin of the peak effects in HTSC

[53 ].
A dissipation peak attributable to the skin effect appears when the superconducting
penetration depth becomes comparable to the size of the sample. For this geometrical effect, thepeak temperature depends logarithmically on frequencies of Hac [54] , as opposed to the observed

T(Hp') which is frequency independent. From the BCS formula for the penetration depth
A(J)=A(0)/[2(1-TITc)] 1I2 valid for T;:: Tc,(4 .12)the temperature at w'hich A(J) is equal to the size of sample should be very close to Tc : 1- TITe 4 x 10- 5 by using A,c(O) = 3.3 x 104 A. Therefore, this mechanism cannot explain the second
dissipation in Sr2Ru04 . Here, we can also neglect the effect of a potential barrier of geometricalorigin [55] because Hdc II ab is along the planar surfaces of the plate-like sample.
Next we will consider two other possibilities for the origin of the peak effect, which is
discussed for conventional superconductors [56] , the matching and synchronization mechanism;
the fonner is also discussed for HTSC [57]. Firstly, for a material with a periodic distribution of
pinning centers, peak effects may occur when the vortex-lattice spacing matches the pinning-center
spacing. This matching mechanism is immediately identifiable since the peaks should occur at acommon value of the field regardl ess of the temperature. The large temperature dependence of

Hp in Sr2Ru04 naturally eliminates this from the origin of the peak effect .
Now we will consider the synchronization mechanism [56] , which is consistent with the peakeffect of Sr2Ru04 . If the flux-line lattice is nearly perfect, not all of the pinning centers canoperate simultaneously . Therefore at low Hdc and low T, large dissipation can occur. The
softening of the vortex lattice with increasing magnetic field and temperature will enable vortices

22to synchronize with much more pinning centers and hence increase the bulk pinning force. The
field characterizing this synchronization mechanism should be a function of both H de and T, as seenin Fig. 18, although it is difficult to evaluate Hp(1) quantitatively. In addition, since the dissipation
peak in this mechanism is not due to the hopping motions of the vortices between different
metastable states, T(Hp) is not the thermal activation type; consistent with the observed frequency
independence shown in Fig. 21 .
The collective pinning mechanism accompanied by the first order transition t o the FuldeFerrell and Larkin-Ovchinnikov (FFLO) state has recently been discussed as the origin of the peakeffect in CeRu2 [58] and UPd2Al3 [59]. In these materials, the spin susceptibility XOis so high tosatisfy the paramagnetic limiting condition : XJ!ei/2 >He2/2JlO [60], where He is thethermodynamic critical field . In Sr2Ru04 with JloHe = 0.018 T, Xo - 2 x 10-4 m-3 is smaller by afactor of about three than that to satisfy this inequality. In addition, no hysteresis suggesting thefirst order transition is observed across H p . Therefore, the FFLO state is not relevant to theobservation in Sr2Ru04 .
Quite recently, Rice and Sigrist [61] have suggested the possibility of the p-wave pairing
state for the superconductivity of Sr2Ru04 , which is the two-dimensional analog of the BalianWerthamer (BW) state of 3 He. One might be tempted to associate the state below Hp(T) in Fig.

18 with the presence of a different pairing state of the triplet pairing. However, even ifp-wave
pairing is indeed realized, a changeover between different representations of the triplet pairing asa function temperature at Hde = 0 would not occur without a coexisting magnetic order. In fact
the magnetic ordering has never reported in Sr2Ru04. Therefore, Hp does not represent the phaseboundary between t he different representations of the triplet pairing state, but represents thechangeover in the vortex states.

5. Conclusion
We have investigated the superconducting and normal-state properties of Sr2Ru04, w hichis the only layered-perovskite superconductor without copper that is known so far, by measuring
the dc-susceptibility and specific heat above Te, the resistivity, and the ac-susceptibility undermagnetic fields belo'N 2 K using single crystalline Sr2Ru04.

In the normal state we found the T2 dependence of the resistivity below 25 K , the enhanced
paramagnetic spin susceptibility, and the enhanced Sommerfeld coefficient of the specific heat.

23

From the analyses in terms of the Willson ratio and Kadowaki-Woods ratio , these results are
consistently described by the model of a strongly correlated system; the normal state of Sr2Ru04
is well characterized as a highly anisotropic Femliliquid. The anisotropy is attributed to the highJy
anisotropic motion of the quasiparticles, reflecting the nearly two-dimensional electronic states .
The coefficient of the T2 tenn in the resistivity gives m*Jm*ab : : 550, which agrees well with that
calculated from the Fermi-surface parameters obtained from the quantum oscillations .
Concerning the peculiar temperature dependence of the resistivity along the c axis, we
presented a systematic analysis based on a competition between the relaxation time of thequasiparticles for a number of scattering processes and the time required for the quasiparticles tomove the interlayer distance d; in other words, the competition between the mean-free path along
the c axis and d. Hovvever, it still remains unclear why the resistivity along the ab planes exhibitschangeover in the te.m perature dependence at the same temperatures with that along the c axis .
Further study is needed to clarify this mechanism by controlling the relaxation time, for example,
by impurity substitution and by applied pressure .
From investigation of the upper critical fields He2 , we showed that the superconducting
state of Sr2Ru04 is also highly anisotropic with the ratio of the coherence lengths IS =Cab(O)1 Cc(O) = 26. The ratio agrees well with the square root of the effective mass ratio in thenonnal state. Therefore, the superconductivity in Sr2Ru04 originates from Cooper pairs formedby the highly correlated electrons. In the sense that the coherence length along the c axis is muchgreater than the spacing between the adjacent RU02 planes, the superconductivity of Sr2Ru04 has
three-dimensional character, rather than quasi-two dimensional character as in the high- Te cuprate .

In addition, the Ginzburg-Landau (G-L) parameters K(O) = 31 (H II ab) and 1.2 (H II c) indicatethat Sr2Ru04 is a type-II superconductor. The small K(O) value for H II c, however, indicates asoft type-II character.
We have discussed a peculiar anisotropic peak effect found in the layered perovskite
superconductor without copper, Sr2Ru04. The peak effects are observed only when both the dc
and ac magnetic fields are parallel to the ab planes, in contrast with those reported for the high- Te
cuprate superconductors .

We argued that the anisotropic dissipation in X" of Sr2Ru04 is

attributable to the highly anisotropic nature of superconductivity, reflecting the layered structure;in particular, the anisotropic critical current and possibly a minor contribution from the intrinsic
flux-pinning .

We also argued that the peak effects are ascribable to the synchronization

mechanism .

24

Sr2Ru04 and HTSC share the layered perovskite structure and the highly anisotropic
properties in the normal and superconducting states . On the other hand, a crucial difference
between the two systems originates from the difference in dimensionality. The criterion for thedimensionality in the superconducting state is the ratio between the coherence length along the caxis (e and the interlayer spacing d; the criterion in the nonnal state is the ratio between the meanfree path along the c axis Ie and d. The difference in the dimensionality of superconductivity
results in the distinctive vortex dynamics of Sr2Ru04 from those ofHTSC . In this respect, thehighly anisotropic but 3D superconductivity of Sr2Ru04 serves as an ideal and important reference
bridge between the anisotropic 2D superconductivity of HTSC and the less anisotropic
conventional superconductivity in the study of flux dynamics. In addition, the three dimensionality
in the nonnal state at low temperatures leads Sr2Ru04 to a highly anisotropic Fermi liquid .
Therefore, Sr2Ru04 serves as an ideal reference material for investigation of the limits ofapplicability of the Fermi liquid theory to other highly correlated layered compounds, including
high- Tc cuprates.

Acknowledgement
The author wishes to express his sincere thanks to Professor Toshizo Fujita for his
stimulating discussion and encouragement through the course of this work. He is also grateful to
Associate Professor Yoshiteru Maeno for fruitful discussion and advise . He wishes to express his
appreciation to Dr. Tsutomu Nojima, Dr. Fumihiko Nakamura and Dr. Takasi Suzuki for helpful
discussion and Dr. Frank Lichitenberg and Dr. 1. Georg Bednortz for providing crystals. He isgrateful to Dr. Andy P . Mackenzie for the beneficial collaboration. He acknowledges Mr. Shuji
Nishizaki, growing high quality crystals, without which this study would not have been completed,
Mr. Hiroaki Hashimoto for the greatest contribution to the discovery of superconductivity in
Sr2Ru04. without which this work would not have been started, and Mr . Shin-ichi Ikeda for the
excellent specific heat data. He acknowledges Professor Hironobu Fujii for allowing us to use afloating-zone furnace for the crystal growth. He thanks Dr. Masatune Kato for teaching in his
early research days and his colleagues for help in his school life. Some of the measurements were
performed at the Cryogenic Center of Hiroshima University . Last he very much appreciates his
parents.

25

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26

[19] S. Nishizaki, Y . Maeno and T . Fujita, unpublished result .
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We defi ne m*c as(vablvcpm *abl2, which is useful to describe various physical quantities .
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27

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[60] This inequality is obtained based on the equation (4 .1), X (J = 2j.l Bf/( £F) and the BCS
rerations iJ. /kBTc = 1.76 and iJ. 2N(£F)/2 = Hc2/2j.l O, where iJ. is the superconducting gap
parameter.
[61J T. M . Rice and M . Sigrist, preprint (1995) .

28

cx(hole-like)~ (electron-like)y ( electron-}ike)

frequency F (kT)

3.05

12.7

18 .5

Fermi wave number kF (A-1)

0.302

0.621

0.750

dispersion ~kF/kF (0/0)

0.21

1.3

< 0.9

cyclotron mass m * (me)

3.4

6.6

12 .0

carrier number n (per Ru)

0.26

0.91

1.33

hopping matrix element Ie (K)

1.2

17

<9

Fermi velocity Vab (m/s)

1.0 x 10 5

1.1 x 10 5

7.2 x lo"~(m/s)

2.9 x 102

4.0 x 10 3

2.1 x 10 3transfer rate liTe (S-l)

4.5 x l011

6.3 x 10 12

3.4 x 10 12-------------------------------- --------------------------------------------------------------

Vc

Table 1. The Fermi-surface parameters of Sr2Ru04 determined from the quantum oscillations andsome derived quantities. The three nearly cylindrical Fermi surfaces are labeled as cx , ~ and y.

alon abalon ccritical temperature

Te

(K)

upper critical field

fJoHe2(0)

(T)

0.78

0.030

coherence length(GL(O)(A)

1. 05 x l 03

40

Fermi velocity

Vab , Vc(m/s)

6.9x 1042.6x 10 3

thermodynamic criticalfJoHco(O)(T)

lower critical field

fJoHcl (0)(T)

l.4 x 10- 3

penetration depth

A(O)

(A)

1.3 x 103

G-L parameter1<"(0)

0.9

0.018

field

31

2.8x10- 3

1.2

Table 2 Anisotropic superconducting parameters of Sr2Ru04 . The underlined quantities weredirectly measured, and the others were estimated using theoretical relations .

IIX " ..: ~..

-

-

°

-

-"/
004

I

0.8
T(K)

Q

E

I

1.2

G 2 'I

...

~
J

L

I

I

I

..... .. . .

~,

u

-

o

-

L

.r-

cry

Q

:

-

1c

~

(b)

o

. : :

r

.!
. to'·

o

u

:

I

I

-

-

1

i/o':'· • ': :- ..

2 f-

c.o

o

-

x'

f-

-

)\..

I

I

I

1\

:.
I

I

o

.

•

...

0

~
j

2

-

,tc -

4

T (K)

(a) The ac susceptibility of a single crystal of Sr2Ru04 measured by a mutualinductance method at a magnetic field of Hac = 0 .67 Oe parallel to the c axis, and ata frequency of 1000 Hz. Top, X" (imaginary part)~ bottom, X' (real part) .
(b) The anisotropic resistivity of Sr2Ru04 below 4 K . Insets, attachment of theelectrodes.

La (Sr)Fig. 2

eu

c

o

k:a

Schematic crystal structure of superconductors Sr2Ru04 and La2-xSrxCu04. Also
shown are the directions of the tetragonal principal axes . (b = a in a tetragonal
structure.)2~--~--~--~--~--~--~2

..---

a
c

..---

s
c

N

<.)

.

<.)

I

1

0
~

.
..."

,••

~
I

0

1 "-'"

./

~

••

"-'"

c:t

....

."..

",

o

-.c

~

Pab

300

200

100

T (K)
Fig. 3

The anisotropic resistivity of Sr2Ru04 up to 300 K.

Sr2 Ru0 4
,4

12

--E

u

u
G

c;
co

C"')

I

(

I

0

-

.,...-

0

6

')
,-

.,...-

.Q

()

:>

Q

o
Fig. 4--E500
T2 (K 2)

C'U

Q

1000

The resistivities along the ab planes (Pab) and the c axis (Pc) plotted against
solid lines represent the fits below 25 K: P = PO + Ar 2.

r2. The1 . 5 ,.-----r------r--~-___r--,___-_r__-___,-E 1.0

:J
E
ill
'7

Hllc

~iiiii==ooooooOOOOOOClClOO-- _ _ _ •••••••••••••••~

SrRu0 3 0.04%: ; 0.5(TFM =160K)

o

200

•

H II ab

400

600

T (K)
Fig. 5Magnetic susceptibility of Sr2Ru04 in a magnetic field of 1 T, showing very weaktemperature dependence up to 700 K. Data have been corrected for a diamagnetic
contribution from the core electrons of - 0.91 x 10-4 emu/mol.
100~--~----~----~--~

o
E

-J

E

50

o f1 H = OT
+ f1 oH=14T0oFig. 6100
T2 (K)

200

The specific heat divided by temperature, CplT, against T2 for a single crystal in zero
field and under a magnetic field of 14 T along the c axis.

10- 1

I

CeAl2

(!)

YbCuAl 00.Use l3
~ CeCu 2Si 2

Nplr2 0..--...

10-2

U2Zn 17

0 .:

0

~

UPt)

~

E
c:)

~

0

><

10-3
a -Ce 0a-Np 0 o }J6 Fe
a-U

10-4
10°
Fig . 7

0

10

YbAl 2

1

2

3

10
10
Y CmJ/K?mol)10

4

T-independent paramagnetic spin susceptibility, plotted on a logarithmic scale against
the coefficient y of the T-linear term of the specific heat for a variety of compounds .
Values for uranium compounds are expressed per mol-U. The solid and broken lines
represent the Wilson ratio Rw = 2 and 1, respectively.

CeB 6
USn 3
UAl 3
UPt .:

DIn3...UGa3'

10
Fig . 8

1

2

' 10
103
y CmJIK?mol)

The coefficient A of the T 2 term of the resistivity, plotted on a logarithmic scale
against the coefficient y of the T-linear term of the specific heat for a variety ofcompounds . The solid and broken lines represent the Kadowaki-Woods ratio AI y2= ao = 1. 0 x 10- 5 ~ Qcm/(mJlKmol)2 and ao/25 , respectively.

10~~~~~~-------------

8
't.)
Q)

,
,,,
I

1/ rc (S)E3 :-------- -------------------------------------

CJ)

N

o

42
1/ rc (a)o50

1/ Timp

100

150

T (K)
Fig. 9

Schematic. temperature dependence of the inverse relaxation time of quasiparticle fora number of scattering processes and the inverse characteristic time 1ITc for thequasiparticle to move interlayer distance for each band at low temperature. (a) for exFermi surface, (b)~-Fermi surface and (c) y-Fermi surface. Here, Tee, Tep and Timp
are the relaxation times of quasiparticle for the scattering by quasiparticles, byphonons and by impurities, respectively.

10-1r~~~~--~--~~~~--~~

Pc

o
o •

a

"
10

.

Fig. 10

100
T(K)

.

The companson of the temperature dependence of the resistivities Pab and Pc, plottedon a logarithmic scale. Pab is multiplied by 550 (= AclAab) to simplify thecompanson.

Pab.........

oc T
••• •

20

.

. •..

:...
1#.

OC

T1. 55•••

10
Fig. 11•••

The anisotropic resistivity plotted on a logarithmic scale .

0
0

:J

0

H II ab000

T = 1.09 K...
0.97 Ko0.77 K•
0.67 K ...o~o0.46 K•
0.15 K (b)

.....

0

6.

><

(a)

o

0.5
~ol--Ide (T)Fig. 12

100

50
T (K)

......--..

cu
"'--'

T1. 37

OC

1.0

0

•
•

•
•
•
•
•

0

0

•

H II c•... T = 0.92 K

0
0

o

•

•
o

•

0.03

0.73 K
0.50 K
0.30 K
0.10 K

0.06~OHde (T)

Variations of X' (real part) of ac susceptibility of Sr2Ru04 with the dc field Hdc along
the ab planes at selected temperatures .

1.0

Sr2 Ru0 4

.."
.""

-

...-.....

r-'--'"
u

"'0

:r:

."" •

0.5 -

Hc2//ab

\•

\

0

::t

•

\•

Hc2//c

0·.0

\

0.5
T (K)

Fig. 13

1.0

Variations of the upper critical fields Hc2 with temperature.

Ru02 PlaneAM~
~.

(a)

I

(c)

(d)

Flux:Compression(b)Fig. 14

Tilting(e)Five basic configurations of the directions of Hdc and Hac with respect to the
crystalline axes . (a) and (b) depict the longitudinal configurations with Hdc II Hac,
which provide the compressional motion of flux lines . The others are the transverse
configurations with H dc J. Hac, which provide the tilting motion of flux lines. The
stacking of RU02 planes, flux lines and the directions of Hac are sketched by theplanes, lines and arrows, respectively.

Sr2 Ru0 4
T=0.15K

T=O.10K

~
o

o

X

0

"

o

o

o

o

o
00

.,. ..... ::0 i- i-~

·

X'

X'

.........
(a)

o

0.5

0.03

0.06
J10Hdc (T)1 0

floHdc (T)Fig. 15

Variations of the longitudinal ac susceptibilities of Sr2Ru04 with the dc field . (a)(Hdc II ab) II (Hac II ab) and (b) (Hdc II c) II (Hac II c). X' and X" are the real andimaginary components of the ac susceptibility. The ac fields of I-'OHac = 7 I1T (llab)
and 3 11 T (II c) at'a frequency of 1000 Hz were used .

Sr2 Ru0 4-r= 0.38 K

T= 0.43 K

T = 0.42 K

£

tP

X"
%

0'0
0

.,o

--...
:::J

o

~

0

~

o

X"

0
0

0

0

m

0
0

'---'".....

.,
c:eP'tPOoO

~
.....

,

X'

~

o

0.4

X

0.8 0

floHdc (T)Fig. 16

0 .4

0.8 0
J-loHdc (T)

0

a.,

~

........,

0000~0~00

. X

0.02

0.04

)1{)Hdc (T)Variations of the transverse ac susceptibilities of Sr2Ru04 with the dc field . (a) (Hdc
II ab).l (Hac II ab), (b) (Hdc II ab).l (Hac II c) and (c) (Hdc II c).l (Hac II ab) . Theac field used is floHac = 15 11 T.

T=0 .77 K~"
0.57 KH II ab

...

b

...

~

••

~

cu

2

0.36 K
~

... ~

...

••

~

4

0.15 K~. , • •

.- ,
').

&

.t.

•

...

4 •

~

..

.~

\,

....
. ...

•

Sr RuO

_

,

•

•

.....

~~~~

H II ab

(b)

o

0 .4
J10Hdc (T)Fig. 17

o

0.6

0.2

0.2

0 .4

0.6 0.8
J-LOHdc (T)1.0

Variations of X" (imaginary part) of ac susceptibility of Sr2Ru04 with the dc field Hdc
along the ab planes at selected temperatures; (a) the variation of the second
dissipat ion with Hdc and (b) the variation of the first dissipation with Hdc . The ac
field used is Jl.oHac = 7 ~ T. All the curves are scaled with each other and valid forquantitative comparison.

1 .()

'

.

....

~

r-

'-""

u

-0

:r:a

o. r:

"")

Sr2 Ru0 4

",

.",

.~

-J!p....

•

\•

~

::t

"-.&

' ... 0Hc2//c0.0
Fig. 18

Hc2//ab

""

\•

0.5
T (K)

\

-\
1.0

The characteristic fields of Sr2Ru04 in the H-T phase diagram. Hc2 //ab and Hc2//c are
the upper critical fields; Hp is defined by the second peak in X" with Hdc II Hac II ab o

J10Hdc= 0.50
~ X"

o C)

8 lb

I\

o

~
,
•

:

Fig. 19

X

···f
··

····
·····
·

I

J

I

.,.-(a)

J

o

0.5
1.0 0
T (K)

--..J

(b) "T(H p ')

1.0
0.5
T (K)

Variations of the longitudinal ac susceptibility of Sr2Ru04 with temperature.

Hdc II ab.g 0.5:c:o.......

"4..

0.0
Fig. 20

0.5
T (K)

1.0

Variations of Hp and Hp' with temperature . Hp' is defined by the field at which X' H curve takes a minimum.

JioHdc = 0.50 T••

T(Hp ')J

\

•
\
•\

\

••

I

•I

••
I

••

•
•
(Hdc II ab) II (Hac II ab)
2
Fig. 21

3

The fl-equency dependence of T(H c2) and T(Hp') at f.10Hdc = 0.50 T. Here T(Hp') isdefined as the temperature at which X'- T curve takes the minimum (Fig. 7 (b» , which
is well corresponding to T(Hp) .

Anisotropic superconductivity of Sr2Ru04
K. Yoshida, Y. Maeno , S. Nishizaki and T. Fujita
to be published in Physica C.

1~ifflx1S:

Superconductivity in layered perovskaite without copper~;g-1S:

Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz
and F. Lichtenberg
Nature 372 (1994) 532-534.

2

~~x1S

Ion-Size Effects on the Structure and Superconductivity of La-214 compounds
at 1/8 doping~;g-1SK. Yoshida, F. Nakamura, Y. Tanaka, Y.Maeno and T. Fujita*~=±1S

Physica C 230 (1994) 371-377.

~ifflx1S

Effects of Ionic Size on the x = 1/8 Anomaly in La2-xBax _y My Cu04 (M =pJ!:.'

3

Ca, Sr)~;g-1SK. Yoshida, F. Nakamura, Y. Tanaka, Y. Maeno, T. Kagayama, G. Oomi andT. Fujita
Physica B 194-196 (1994) 2051-2052.

4

Stability of Low-Temperature Tetragonal Phase in La2_xBax Cu04 and Related
Compounds
F. Nakamura, K. Yoshida, Y. Tanaka, X. Z. Bao, Y. Maeno and T. Fujita
Journal of Superconductivity 7 (1994) 33-35.

5

~~x1S

Superconductivity and Structural Phase Transition in La2-xBaxCu04 with La
Partially Replaced by Th~;g-1SX. Z. Bao, Y. Maeno, Y. Tanaka, K. Yoshida and T. Fujita*~=±1S

Advances in Superconductivity VI (1993) 375-378.

~~x1S

Magnetic and Transport properties of La2-xSrxCu04 near x = 1~;g-1S

F. Nakamura, K. Yoshida, K. Sugiyama, Y. ~v1aeno and T. Fujita*~=±1S

Physica C 185-189 (1991) 1103-1104.

PJL.'

6

PJL.'

7

Simple and Reliable Method for Determination of Oxygen Content In
High- Tc Copper Oxides
Y. Maeno, H. Teraoka, K. Matsukuma, K. Yoshida, K. Sugiyama,
F. Nakamura and T. Fujita
Physica C 185-189 (1991) 587 -588.