Ferromagnetic correlations
in bilayered Sr3_xCaxRu207

Shin-ichi Ikeda
Department of Physics,
Faculty of Science,
Hiroshima University
February 1998

Abstract
Wehavesynthesized anew bilayered ruthenate solid solution Sr3-x CaxRu 2 0 7(0$t~2.0),

which is homologous to copper-free layered perovskite

superconductor Sr 2 Ru0 4 (Tc =1.5 K), with the aim of searching for new
superconductors. We have also succeeded in growing single crystals of
Sr3Ru 2 0 7 by a floating zone (FZ) method. A systematic measurement has
been carried out for the x dependence of the lattice parameters, magnetic
susceptibility X( 1), magnetization M(H), and electrical resistivity AT). No
indication of superconductivity has been observed down to 100 mK for x=O(single crystals), 300 mK for x=l, and 2 K for other compositions. The
measured values of lattice parameters and of magnetic quantities for thepresent single crystal samples are in good agreement with those forpolycrystalline samples. Polycrystalline samples for

0.6<x~2.0

showmagnetic ordering below 50 K. It is intriguing that the magnetic correlations
vary with increasing Ca content, from nearly ferromagnetic, to itinerant
weakly ferromagnetic, and finally to localized antiferromagnetic. For
x(Ca)=O, we have concluded that the ground state is the strongly-correlated

Fermi liquid accompanied by enhanced ferromagnetic correlations. The
lowest magnetic ordering temperature in this series is observed at 3.2 K in
the sample with x (Ca) =1.0. This transition is described well as that due to a
weakly ferromagnetic ordering by the self-consistent renormalization (SCR)
theory of spin fluctuations. To the best of our knowledge, this is the firstexample to demonstrate an applicability of the SCR theory to a weakferromagnet with a quasi -two dimensional crystal structure.

Contents
Chapter 1. Introduction --------------------------------------- 1
Chapter 2. Experimental -------------------------------------- 4
2.1 Sample preparation and characterization ----------------- 4
2.2 Measurements ------------------------------------------------ 6

Chapter 3 • Phase diagram of Sr3~Cax Ru20 7---------------- 7
3.1 Lattice parameters and oxygen content ------------------- 7
3.2 Resistivity ----------------------------------------------------- 9
3.3 Magnetic susceptibility-------------------------------------- 9
3.4 AC magnetization -------------------------------------------- 12
3.5 Magnetization curves ---------------------------------------- 13
3.6 Phase diagram ------------------------------------------------ 15

Chapter 4. Sr3Ru 2 0 7 : nearly ferromagnetic metal -------- 16
Chapter 5. Sr2 CaRu 20 7 : weakly ferromagnetic metal---- 22
Chapter 6. Conclusions --------------------------------------- 26
Acknowledgments --------------------------------------------- 27
References ------------------------------------------------------ 28

Chapter 1. Introduction
Since the discovery of high- Tc cuprate (copper oxide) superconductors(HTCS) [1] a decade ago, studies of HTCS have greatly improved ourunderstandings of two-dimensional metallic states, strong electron-electron
correlations, and antiferromagnetic spin fluctuations. Mainly two different
perspectives have been discussed to explain the unusual behavior of HTCS.
One approach starts from a localized electron system of the Mott insulator
described, for example, in terms of the resonating valence bond (RVB) theory[2]. The otherstarts from an itinerant electron model including the self-consistentrenormalization (SCR) theory [3] or Fermi liquid theory [4]. However, theexact mechanism of the high transition temperatures and anomalous metallic
state above Tc have not been fully understood as yet.
The first superconductivity (SC) in non-cuprate layered oxides has beenfound [5] in Sr2RuO 4' which motivated us to search for other SC compound
among ruthenates and other 4d- electron systems [6]. In spite of its low
superconducting transition temperature of Tc =1.5 K, many intriguing aspects
have been recognized in Sr 2RuO4' There are, for example, the theoretical
expectation of p-wave pairing symmetry [7-9] similar to the superfluid stateof 3He and the exotic SC state of heavy fermion compound UPt 3, experimental
evidence for non-s-wave symmetry [10-13], two-dimensional Fermi liquidbehavior [14], anomalous increase in Tc in Sr2RuO 4-Ru hybrid system (3 Kphase) [15], and so on. In addition, we have recently isolated a new ruthenate
Mott insulator Ca 2Ru0 4[16]. They are isostructural to Sr 2Ru04 except for
distortions present in Ca 2RuO 4' It is particularly interesting that Mott insulators
are found in the vicinity of a superconductor not only for cuprates but also forruthenates. In these ruthenates, strong electron-electron correlations appear toplaya key role in determining their diverse properties as well as in cuprates.
A related ruthenate Sr 3Ru207' which has a tetragonal layered perovskite
1

structure (Fig. 1), shows antiferromagnet-like cusp in the temperaturedependence of magnetic susceptibility [6,17] around 15 K and nearly metallic
behavior. We regard Sr 3Ru207 as a next candidate for SC ruthenate because of
its two-dimensional Ru0 2 bilayers, much weaker magnetic correlations thanthat of ferromagnetic SrRu0 3 (the Curie temperature Tc = 160 K) and thesimilarity

in structure

betweenHTCS (La,Sr)2Cu04 (Tc --40

K)

and

(La,Sr)2CaCu206+6 (Tc --60 K) [18].
According to the band structure calculation of Sr3Ru 20 7 by Hase et al.
[19], four Ru-4d electrons in the t 2g orbitals constitute low spin state with spin
S=l and mainly contribute to the density of states near the Fermi energy.

Strong hybridization between Ru-4d in the t 2g orbitals and 0-2p give rise to
antibonding pdn * bands, a similar electronic state to that in Sr 2RuO 4 [20].
The resulting bands have six quasi -two-dimensional Fermi surfaces in Sr 3Ru207.
Together with three quasi-two-dimensional Fermi surfaces in Sr 2Ru0 4, these
multi-bands near Fermi energy show a remarkable contrast with the single
Fermi surface in HTCS. This orbital degeneracy in these ruthenates may play
an important part in magnetism and transport properties.
The observation of zero-resistivity only in the single-crystalline Sr 2Ru0 4[5] obviously indicates that the study on good-quality single crystals is very
important in searching for SC in ruthenates. Furthermore, investigations using
single crystals are of crucial importance especially in extracting both anisotropic
properties and intrinsic transport properties. In spite of some previous attempts[21] to grow large and high-quality single crystals of perovskite ruthenates by
a floating-zone (FZ) method, successful growth had never been reported except
for the superconducting Sr 2Ru0 4 •In the present study, we have finally succeeded in growing single crystalsof Sr 3Ru207 by the FZ method using high oxygen pressure. Physical propertiesof these single crystals are in good agreement with those of pol ycrystals. Justprior to our crystal growth, Cao et al. have investigated remarkable magnetic

2

and transport properties of Ruddelsden-Popper (R-P) type ruthenates(Sr,Ca)n+lRun03n+l with n=1,2,3 and 00 using single crystals grown by a chlorine
flux method [22-27]. They have concluded that the ground state of Sr .,RU 20 7

[22] and Ca 3Ru 20 7 [23] are an itinerant ferromagnet and a nonmetallic
antiferromagnet, respectively. Lattice parameters and magnetic behavior ofthese flux-method crystals, however, are inconsistent with those of bothpolycrystals [28] and our single crystals grown by the FZ method. The
discrepancies are especially serious in Sr3Ru 20 7, as we will describe below.
The origin of the discrepancies has not been understood at present, but thedifference in stoichiometry or inclusions of impurity elements may play a
crucial role. Therefore, we believe that the data obtained from poly crystals
gives important complementary information to those of the single crystals
grown by the flux-method.
In order to modify the magnetic correlations and search for the SC
ground state, we have performed substitution of smaller Ca cation into Srsites in polycrystalline Sr3_xCaxRu20y (SCRO) with x up to 2.0 [28].
In this paper, we will show that a sharp change in the magnetic properties
occurs at x=0.7 and x=1.2, accompanied by the change in the lattice parametersin SCRO. We will also clarify a salient difference in the physical propertiesof single crystals Sr 3Ru 20 7 associated with different crystal-growth methods.
In addition, we suggest that the ground state ofSr 3 Ru 20 7 is a nearly ferromagnetic
and strongly correlated Fermi liquid. We will conclude that the magnetism
around x= 1.0, where the lowest magnetic ordering temperature is observed, iswell described by means of the self-consistent renormalization theory (SCR)
of ferromagnetic spin fluctuations.

3

Chapter 2. Experimental
2.1 Sample preparation and characterization
For the synthesis of polycrystalline SCRO, we used a conventional
solid-state reaction method. Stoichiometric mixtures of powders of SrC03(99.99 %), CaC0 3 (99.99 %) and Ru0 2 (99.9 %) were ground and calcined in
air for 24 hat 1173 K. The calcined samples were reground and pressed into
pellets. They were then reacted and sintered in a flow of a weakly reducing
gas mixture (99 % Ar and 1 %°J

at 1473 K for 24 h and cooled in the

furnace. The procedure was repeated at 1573 K and 1623 K to obtain "asprepared" samples. The reducing atmosphere is necessary to obtain SCRO
phases. For example, firing the sample with x(Ca) = 1.5 in a flow of 0.1 MPa
02 at 1623 K results in decomposition into (Sr, Ca)O and unidentified phases.
Some as-prepared samples were then oxidized by annealing at 773 K underan oxygen atmosphere at relatively high pressure (1 and 5 MPa). For annealing
at 773 K, ambient 02 pressure was not adequate to prepare homogeneously
oxidized samples because it resulted in the broadening of the peaks in the
powder x-ray diffraction patterns, while 1 MPa 02 annealing sustains thehomogeneity of the samples.
The single crystals of Sr 3Ru207 were grown by the floating-zone (FZ)
method. The starting materials were SrC03 with purity of 99.99% (Ba<5ppm)
and Ru0 2 with 99.9%. The mixture in the molar ratio of Sr:Ru=3:2.25 was
fired and sintered in air at 1573 K with an intermediate grinding. The excess
Ru02 was added because of the high vapor pressure of Ru oxides at hightemperature during the crystal growth. After being pressed into a rod with adiameter of 6 mm, it was sintered in air at 1623 K for 2 hours. The rod wasthen set in the FZ furnace (Nichiden Machinery: SC-K15HD-HP). The growthof crystals was performed in 1 MPa oxygen atmosphere at the feed speed of4

40 mm/h. The rod and seed crystal were oppositely rotated each other at 30rpm.
The crystal-growth atmosphere should be kept at high oxygen pressure
because of the instability of Ru0 2 at high temperatures as described below.
The Sr 2Ru0 4 -Ru metal hybrid system, so-called 3 K phase [15] , has been
described by the eutectic solidification at the solidus line in the SrO-Ru phase
diagram in 0.1 MPa air (--20 kPa oxygen partial pressure). This means that
Sr3Ru 20 7 and SrRu0 3 do not exist in 0.1 MPa air at higher temperatures thanthe melting point (solidus line) in the SrO-Ru (not Ru0 2) phase diagram.
As shown in the phase diagram (Fig. 2), Ru0 2 is decomposed into Ru andoxygen at higher temperatures or at lower oxygen partial pressures [29-32]. In
other words, high oxygen pressures stabilize Ru0 2 with tetravalent oxidation
state Ru 4+ at high temperatures. Considering that formal valence number of
Ru ion is also four in the R-P type ruthenates, it is necessary to stabilize Ru0 2
at higher temperatures (--2200 K) than melting point during crystal growth byapplying high oxygen pressures (--1.3 MPa) to obtain single crystals of Sr 3Ru20 7or SrRu0 3 • Therefore, we have tried to grow single crystalline Sr 3Ru 2 0 7 at 1
MPa oxygen pressure, which is the maximum pressure for our FZ furnace.

52.2 Measurements
The crystal structures of the samples at room temperature were characterized
by powder x-ray diffraction. The oxygen content y was determined by thethermogravimetric analysis (TGA). The temperature dependence of magnetic
susceptibility X( 1) from 2 K to 3S0 K mostly under 1 T, the field dependenceof magnetization M(H) up to S T, and the AC magnetization with the frequencyof 1 kHz and the amplitude of 0.1 mT were all measured by a superconducting
quantum interference device (SQUID) magnetometer ( Quantum Design, model
MPMS-SS). We used sintered-bar samples with the weight of 10-S0 mg. For
magnetization measurements of single crystalline Sr3Ru207' we performed
sample rotation around the horizontal axis by the rotator equipped in MPMS-SS.
We can make the crystal axes exactly parallel to a field direction within 0.2
degree by using this horizontal rotator. The electrical resistivity p (T) was
measured by a standard four terminal DC technique from 4.2 K to 300 K. The
specific heat C p of Sr 3Ru207 was measured by the adiabatic heat pul e methodfrom 1.2 to 2S K using the sample pellet with a diameter of 12 mm and theweight of about 2.S g. The AC susceptibility down to 0.1 K and 0.3 K was
measured by a mutual-inductance method using a commercial dilution
refrigerator (Oxford, Kelvinox-2S) and a commercial 3He refrigerator (Oxford,
Heliox), respectively.

6

Chapter 3. Phase diagram of Sr 3_xCaxRu207
3.1 Lattice parameters and oxygen content
Powder x-ray diffraction spectra of as-prepared SCRO are shown in Fig. 3
for different x(Ca). The samples are essentially of single phase in the region 0~ x ~ 2.0, although very weak impurity peaks of Sr 2Ru0 4 are detected in the

spectra of the samples with Osx~0.6. The spectra are well indexed in terms of
the symmetry of tetragonal 14/mmm group up to x=2.0. It is clear that thesolubility range of Ca in Sr 3Ru207 is considerably wide although the ionicradius of divalent Ca is substantially smaller than that of Sr. Lattice parameters
for both as-prepared and oxidized samples determined from the x-ray diffraction
spectra are plotted in Fig. 4. As we shall see below, three regions of distinct
phases are clearly recognized: I( 0 ~ x ~ 0.6 ), II( 0.6 < x ~ 1.2 ) and III ( 1.2< x ~ 2.0 ). Reflecting the smaller size of Ca ions, the unit cell volume

exhibits nearly linear contraction with increasing x for 0 ~ x ~ 2.0. With
increasing x, monotonic decrease in the c parameter is observed except for
samples in the region II around x =1.0. The crystal structure in the region II ischaracterized by abrupt shortening of the a parameter by about 0.5 % andstretching of the c parameter by about 1.0 %. In Fig. 4, we also included thelattice parameters of single crystals and polycrystals reported by several groups
as described in Chapter 4.
For the investigations of crystal structures and electronic configuration, it
is important to determine the oxygen content. We decomposed powders of the
as-prepared sample into SrO, CaO and Ru in an alumina crucible by heating
up to 1473K at 2 Klmin under the atmosphere of flowing Ar with 10 % H2 in
a commercial TGA equipment. Before decomposing the samples, we dried
both samples and alumina crucibles at 473 K in air for half an hour. The
results give the oxygen content y in Sr3_xCaxRu20y to be 6.95±O.06 for x=O,
6.99±0.06 for x=1.0 and 7.01±O.05 for x=2.0, indicating that y is essentially77.0. This implies that the formal valency of Ru ion remains tetravalent withfour 4d electrons. Therefore the observed structural changes by Ca substitution
are not driven by the change in oxygen content. Lattice distortions ofpolycrystalline Sr 3 Ru20 7 has been examined by Inoue et al. [33] usingtransmission electron microscopy. They reported the evidence for rotation of
the Ru0 6 octahedra by about 1 degree around the c-axis, with the direction of
the rotation alternating from one layer to another within the bilayers. The
existence of the rotation of the Ru0 6 octahedra is in contrast with the absenceof any lattice distortion in Sr 2Ru0 4 down to low temperatures [34,35]. Neutron
diffraction measurements on our samples by Morii et al. [36] suggest that
Sr(Ca) atomic ordering does not occur in polycrystalline Sr 2CaRu 20 r
Oxidation effects on the lattice parameters are observed as shown in Fig.
4. For x = 1.5, annealing in 1 MPa 02 results in the increase in the c parameterby 0.63 % and the decrease in the a parameter by 0.54 %. The increase in theoxygen content ~y inferred from the sample weight is 0.25 (y=7.25 ). The
excess oxygen atoms are probably positioned at interstitial sites within the
rock-salt (Sr,Ca)202Iayers. The same tendency is observed for x = 2.0. On theother hand, for x = 1.0, the c parameter decreases by 0.45 %, the a parameter
slightly increases by 0.18 % and ~y=0.10 (y=7.10) upon annealing in 5 MPa
02 atmosphere. This behavior indicates that the oxidation effects in the region
II and III are quite different. It is also remarkable that oxidation of samples in
the region III noticeably reduce the unit cell volume, which is not seen in theregion II.

8

3.2 Ilesistivity
The electrical resistivities p( T) of the as-prepared polycrystalline samples
are shown in Fig. 5. Metallic temperature dependence is observed for x = 0,

anddp /dTsubstantially increases below 20 K. This behavior is nearly consistent
with Pab and Pc of FZ single crystals of Sr3 Ru 20 7 as explained in Chapter 4.
Metallic temperature dependence is also observed for x = 1.0, 1.5 and 2.0,
although it changes to nonmetallic behavior at lower temperatures. Nevertheless,the measured values of p at 300 K are p =8--- 30 mQcm for 0~::;;2.0, at least
three orders of magnitude lower in comparison with the results of thepolycrystalline insulators Ca 2Ru0 4 [16] and Sr 2IrO4 [37,38]. Therefore thenonmetallic behavior may be ascribed to grain-boundary resistance, and the
intrinsic behavior may be metallic to lower temperatures.

3.3 Magnetic susceptibility
For polycrystals, the temperature dependence of the magnetic susceptibility

X (T )=M/H under a field of 1 T, for both field cooling (FC) and zero fieldcooling (ZFC) processes, is shown in Fig. 6. For 0 ::;; x ::;; 2.0, X (T) is fitted
well with the Curie-Weiss behavior above 200 K and shows a cusp below 50
K. A temperature Tmax defined at maximum X( T) varies with x as indicated byarrows in Fig. 6 and shown in the top frame of Fig. 7. In the region I except
for x = 0, T max weakly increases with increasing x. The samples in the region I
contain ferromagnetic impurity phase {Sr, Ca)RuO 3 ( Tc::;; 160 K ) with estimatedamount of about 1.6% from the magnetization measurements for x=O, although
it is not detected in the x-ray spectra. In the region II, T max shows small valuesof 3-5 K and is nearly independent of x. Across the boundary (x = 1.2) fromthe region II to region III, T max shows an abrupt increase. It increases up to 43
K (x = 2.0) with further increasing x. The peak feature around Tmax in the X - T
9curve in the region III is suppressed by a field of 5 T (Fig. 8), indicating that
it is ascribed to weak antiferromagnetic ordering with small ferromagnetic
components such as those induced by canted moments. Magnetization
measurements under a weak magnetic field « 10-3 T) indicated no sign ofsuperconductivity above 2 K in all the as-prepared and oxidized samples.
We fitted the data of x(T) between 200 and 350 K with x(T)=Xo+Xcw(T)(Xo : the temperature independent term, Xcw (T)= C/( T-ew ) : the Curie-Weissterm). Here C is the Curie constant and e w is the Weiss temperature. The
effective Bohr magneton number Peff is deduced from C=NAPeff2f.1,B2/3kB' where
NA is the Avogadro number, /lB is the Bohr magneton and kB is the Boltzmann

constant, are shown in Fig. 7. We do not show Peff and e w in the region I for
polycrystals because the data in the region I clearly contain the contribution
from the ferromagnetic impurity (Sr,Ca)Ru0 3 • Assuming that Ru4+ is in the
low spin state in the tetragonal crystalline electric field t 2/e (S=I) and thatOgthe orbital moment is quenched, we expect Peff to be g[S(S+ 1)f/2= 2.83, if thespins are localized. As shown in the bottom of Fig. 7, the observed P eff
remains almost constant (Peff-2.7). The fair agreement of the Peff values are
somewhat fortuitous since we are dealing with itinerant -electron system here.
Nevertheless the constancy of P eff is consistent with the TGA results that theeffective valence of Ru ion in SCRO changes little by Ca substitution. On theother hand, the inverse susceptibility X-I of samples with x = 1.0 and 2.0 as afunction of T shown in Fig. 9 clearly indicates that the magnetic correlationsof SCRO change with increasing Ca content. Because of the constancy offormal valence of Ru, this drastic change is quite possibly related to thestructural modifications. Since the a parameter is almost constant but the cparameter shrinks rapidly with increasing x except in the region II, the changeof magnetic correlations may have a relation to the change of c parameter.
Similar variation of the magnetic correlation is well known in (Sr,Ca)Ru0 3[39]. With substitution of Ca into SrRu0 3 , magnetic correlation changes from10

ferromagnetic to antiferromagnetic at SrOACaO.6Ru03' despite the con tancy of
the formal Ru valency. In this three-dimensional system, only SrRuO ~ shows
ferromagnetic ordering, while no magnetic ordering occurs in compoundswith antiferromagnetic Weiss temperatures such as CaRu0 3 and LaRu0 3 [40].
Recent study of single crystalline (Sr,Ca)Ru0 3 by Cao et al. [25] sugge ts
that Sro.osCao.9sRu03' containing a very small amount ofSr, shows spin-glass-likeordering. It is noted that corresponding polycrystalline samples do not yield
any magnetic ordering. The origin of such discrepancies between single crystals
grown by the flux method and polycrystalline samples will be discussed in
Chapter 4.
The temperature independent Xo is estimated at about ±10-4 emu/Ru molfor Osxs2.0. Taking into account that core diamagnetic contribution is about-8x10-s emu/f.u. mol, we estimate the Pauli paramagnetic contribution XPauli to
be rather small and at most 2x10-4 emu/Ru mol. This contrasts with a large
Pauli contribution of nearly 1x10-3emu/Ru mol for the superconductor Sr Ru0 •2

4

It is noted that the difference in X( T) between FC and ZFC is substantial
in all the regions, especially strong in the region I. However, there is no suchdifference in x( T) of the FZ crystals for x=O as shown in Fig. 10. Therefore
these indications of weak ferromagnetic ordering above Tmax for polycrystal
are probably not intrinsic. In the region III, a minimum in x(T) below Tmax isrecognized for FC sequence as shown in Fig. 6. We therefore define anothercharacteristic temperature T min. for this minimum, which shows gradual increase
with increasing x up to 2.0.

11

3.4 AC magnetization
In order to detect Tmax and Tmm. clearly, the real part of AC magnetization
M'(T) under almost zero field (HDc :s10-4 T and H Ac=O.l mT) is displayed inFig. 11. There exist two characteristic peaks in M '(T) at temperatures Tl' andT2 ' , in addition to the ones ascribable to the ferromagnetic transition attributable
to the impurity (Sr,Ca)Ru0 3 and unidentified impurity phases. Thesetemperatures are plotted against x (Fig. 12) by open circles and triangles. It isclear that Tl' is identified with T max ' According to the reports by Cao et al.
[22,23], flux-method single crystalline Sr 3 Ru 20 7 (Ca3 Ru 2 0 7) has two
characteristic temperatures T*=66 K and Tc=104 K (TM=48 K and TN=56 K).
We also include these temperatures by open squares in Fig. 12. For Sr-richcompounds, some inconsistency of the characteristic temperatures as well as
the lattice parameters is recognized between poly crystalline samples or FZ
crystals (our work and that of Cava et al. [17]) and flux-method single crystals(Cao et al.). In particular, magnetic features at T max and Tl ' have not beenrecognized for the flux-method single crystals. On the other hand, the data of
single crystalline Ca 3 Ru 20 7 appears consistent with the extrapolation of thedata of poly crystalline SCRO. The T-x diagram suggests that T max and T min in
the region III correspond to TN and T M' respectively, of flux-method single
crystalline Ca 3Ru 20 7' We will also discuss magnetic phases in the T-x diagram
later. We have also measured the AC susceptibility of polycrystals for x=O
and 1.0 down to 0.3 K but proved negative evidence for superconductivity.

12

3.5 Magnetization curves
The nature of magnetism can be clarified from the field dependence ofmagnetization M(H). Figure 13 shows M(H) for the samples with different x
at 2 K, below any magnetic ordering temperatures. It should be noted that thecurvature of M(H) for x = 1.0 is quite different from those for x = 0 and 2.0.
With increasing applied field, M(H) of x = 1.0 reveals saturation behavior. On
the other hand, such saturation is not observed in M(H) of x = 0 and 2.0,
suggestive of metamagnetic transition at higher fields. M(H) data of thesethree samples all show hysteresis. The magnitude of M(5 T) increases withincreasing x(Ca). This implies that localized character of Ru-4d electrons in
the ground state is enhanced in the Ca-rich phase, although its resistivity is
metallic at high temperatures (1)200 K) and its magnetic moment is still only
about one forth of what is expected for the localized Heisenberg spin system.
Now let us consider the relation between structural instability and Ru-4d
electron states. Increasing the content of smaller Ca leads to contraction of
the unit cell volume. By this contraction, stronger mixing between Ru-4d and

0-2p electrons is naively expected. However, the results show the opposite
tendency. The enhanced localized character with increasing x may be due tothe reduction in the overlap of wave functions of Ru-4d and 0-2p which is
caused by the distortion of RuO 6 octahedra. This is analogous to the difference
between metallic Sr 2RuO4 and insulating Ca 2RuO 4 [16]. In addition, by oxidationof the samples in the region III, considered as the most distorted region, the cparameter increases, a parameter decreases, and the temperature of theantiferromagnet-like transition at Tmax is depressed as shown in Fig. 14. This
indicates that the distortions of RuO 6 octahedra are released by interstitialoxygen and are important for antiferromagnet-like transition in the region III.
At low temperatures, spin reorientation is often associated with structuralphase transitions. To investigate whether the tetragonal crystal structure of13

SrCa 2Ru 2 0 7 changes below T min' which corresponds to the metal-nonmetaltransition in Ca 3Ru 20 7 , we have measured powder x-ray spectra at 4 K, which
is well below Tmin • The spectrum at 4 K is shown in Fig. 15 along with theresult at 300 K. No symmetry change is observed from the spectra, although
the a parameter elongates by 0.05% with lowering temperature down to 4 K,

in contrast to the c parameter showing 0.55% shrink. This suggests that theeffective increase of the a parameter, equivalent to Ru-Ru distance within theab-plane, is associated with the metal-nonmetal transition. Recent structural
study by Braden et al. [41] indicates that lattice distortions in orthorhombic
Ca 2Ru0 4 are described as the tiltings (rotations about in-plane axes) androtations (rotations about the c axis) of rigid Ru0 6 octahedra. In this SCRO
system, exact structural refinements by neutron diffraction at low temperatures
are needed to deepen the understanding of the ground state.

14

3.6 Phase diagram
In this section, we summarize the structural and magnetic phase diagramof Sr3-xCaxRu20T Three regions I, II and III are well distinguished by thelattice parameters and magnetic ordering temperatures. For each region, there
exist one or two characteristic temperatures as observed in the magnetization
measurements. We give the interpretation of these temperatures below.
In the region I, Tmax is not a definite magnetic ordering temperature as
described in Chapter 4. In the region II, T max is the Curie temperature
characterized by itinerant weak ferromagnetism as described in Chapter 5. In
the region III, T max is antiferromagnetic transition temperature with canted
ferromagnetism. According to the result of powder x-ray diffraction at 4 K
for SrCa 2 Ru 2 0 7 , T min may correspond to spin reorientation temperature to
greater canting without first order phase transition, which would have changed
the symmetry of crystal structure. Ultimately, we can make the magnetic
phase diagram of SCRO shown in Fig. 12. Structural study below characteristic
temperatures of each phase will help confirming the interpretation given here.
Next, we discuss the distinction between three phases I, II and III. A
analyzed in Chapter 5, the region II is well described by the itinerant weakferromagnetism and is quite different from the others. This difference is al 0
consistent with the singularity of x dependence of lattice parameters. The
expectation of metamagnetic transition above a field of 5 T suggests that themagnetic ground state is rather localized in the region III than in the region II.

As already described, the region III with enhanced lattice distortion should
correspond to a more localized spin system than the region II. As a result, themagnetic ground states of Sr3-x CaxRu 20 7 system are characterized by thechangeover from the itinerant weak ferromagnetism in the region II to the
localized antiferromagnetic spin system in the region III with increasing x.
For the region I, we will discuss the ground state based on the results ofsingle crystalline Sr 3 Ru 2 0 7 in the following Chapter.

15

Chapter 4. Sr3 Ru 20 7 : nearly ferromagnetic metal
In this Chapter, we will describe the experimental results of Sr3Ru 20 7
using FZ single crystals and will present the evidence for a nearly ferromagnetic
metal with the strongly correlated Fermi liquid ground state. We will also
discuss the difference of Sr3Ru 20 7 synthesized by different methods reported
by several groups.
The cleaved single-crystals of Sr 3Ru207 were obtained by crushing abar-shape single crystal (5 mm<t>x25 mm). The 327 structure was confirmed
using crushed crystals by the powder x-ray diffraction spectra, which indicatedno impurity peaks as shown in Fig. 16(a). Details of the crystal structure withatomic coordinates have been described elsewhere [19]. Lattice parameters ato0room temperature were deduced as a= 3.8872(4) A and c=20.732(3) A byassuming tetragonal 14/mmm symmetry. These values are in good agreementwith those of polycrystals within an experimental error but show significant
difference from the reported values for single crystals grown by a flux method[22] as described below. Figure 16(b) shows the (OOf) reflection pectrum
from several pieces of cleaved plate-like crystals. All (OOf) peaks allowed forthe tetragonal symmetry are clearl y observed and the corresponding c parametero(c=20.741 A) is consistent with that obtained from the powder diffraction

spectra. This is strong evidence that the cleaved surface is a two-dimensionalab-plane.
The temperature dependence of magnetic susceptibility Xab(T) and X/T) in
the field of 0.3 T is shown in Fig. 17. Little magnetic anisotropy is observedin contrast to large anisotropy (-10 2) of crystals grown by a flux method [22].
This nearly isotropic susceptibility ofSr 3Ru 20 7 is similar to that of the enhanced
Pauli-paramagnetic behavior in Sr2Ru0 4 [14]. Around Tmax =17 K, Xoo(T) andXc(T) show a cusp without ferromagnetically ordered components. This behavior
is almost the same as that of polycrystals [6,17]. Below 5 K, both Xab (1) and16

Xc(T) are temperature independent and completely isotropic. Furthermore thesusceptibilities below 5 K retain a quite large value (,...,1.5 X 10-2 emu/mol Ru).
Both Xab(T) and Xc(T) exhibit the Curie-Weiss behavior above 200 K. We
have fitted the observed Xab(T) and Xc(T) with X(1)= Xo+Xcw (1), where Xo isthe temperature independent term and Xcw(1) = C/(T-ew ) is the Curie-Weissterm in the temperature range between 200 K and 350 K. The effective Bohrmagneton numbers Peff deduced from C are listed in Table 1 along with Xo and

ewe In Fig. 18, we show the field dependence of magnetization M(H) for
fields along the ab-plane and the c- axis at several temperatures. The magnetic
moment at 5 T is at most 0.25 flB and no spin-flip reorientation is recognized
up to 5 T. This means that simple localized spin system with a small exchange
energy is not a plausible model for Sr 3Ru207. Furthermore, the magnetization
curves show no hysteresis between increasing and decreasing field. Therefore,
explicit ferromagnetically ordered moments never exist in Sr 3 Ru 20 7 •It is interesting to compare the enhanced Pauli-paramagnetic Sr 2Ru0 4 andCurie-Weiss-like Sr 3Ru20r Recent theoretical and experimental results ofPauli-paramagnetic Sr 2 Ru0 4 suggest the possibility of spin-triplet pairing by
ferromagnetic spin fluctuations in the superconducting state. The crystal
structure of Sr 3Ru207 is more three-dimensional than that of Sr 2RuO 4 .
Considering that the formal valence of Ru ion is the same (Ru 4+), the majordifference in the electronic properties between them probably originates fromthe dimensionality. Sr 3Ru 20 7exhibits a cusp at 17 Kin x(T), naively suggestiveof antiferromagnetic correlations. On the other hand, further increase of threedimensionality on Sr3Ru 20 7 leads to ferromagnetic metal SrRu0 3 (Tc=160 K)[42]. Other evidence for ferromagnetic correlations in Sr3 Ru 20 7 is discussed
later. Thus, the q-dependence of x(q, w) must be such that both ferromagnetic(q=O) and antiferromagnetic (q~O) correlations are important.
Such a complicated magnetism has been studied in UPt 3 • Inelastic neutron
diffraction measurements [43] suggested a weak antiferromagnetic ordering

17

below TN=5 K accompanied by a very small moment (-0.02 fJ- B) . However, atpresent, it has not been confirmed whether this anomaly at 5 K in UPt 3
corresponds to a static ordering or not [44]. At the same time, low temperature
specific heat is described by a paramagnon mode i.e. ferromagnetic spin
fluctuations [45]. The similarity between Sr3RU 20 7and UPt 3may help clarifying
the magnetism of each other. Although we had hoped that the FZ crystals of
Sr3Ru 20 7 to exhibit SC below 1 K as UPt 3, AC susceptibility down to 100 mK
resulted in negative evidence.
Temperature dependence of the electrical resistivity peT) is shown in Fig.

19 in the range between 4 and 300 K. Both Pab(I) and Pc(T) are metallic(dpldT >0). The ratio of P/ Pab is about 160 at 4 K and 20 at 300 K. Thisanisotropic resistivity is consistent with the quasi-two-dimensional Fermi
surface sheets obtained from the band structure calculations for Sr 3Ru 20 7[19]. In contrast to the T2-dependence of both Pab(T) and pc(T) for Sr 2Ru0 4 ,characteristic of a Fermi liquid, Sr 3Ru207 yields a complicated temperaturedependence of resistivity. With lowering temperature below 100 K, a remarkabledecrease of Pc is observed. Below 17 K where X(T) shows a maximum, p/T)
appears to be proportional to T. On the other hand, Pab(T) shows a slightincrease of dpldT and a quadratic temperature dependence below 7 K. We
fitted Pab(T) by the formula Pab=po+AabT2below 7 K and obtained p o=5.9 fJ-Q

cm and Aab=0.14fJ-Q cmJK2. Since the susceptibility is quite isotropic andtemperature independent below 5 K as expressed above, the ground state of
Sr3Ru 20 7 is a Fermi liquid. The resistivity measurements below 4 K will be
required in order to define whether Pc(T) shows T2 -dependence or not.
In order to clarify the magnetic anomaly at 17 K in x(T) of Sr3Ru 20 7, thenuclear magnetic relaxation rate liT} has been measured by Mukuda et al.
using our polycrystalline samples (Fig. 20). At around 17 K, we can hardly
observe any divergence in II T 1• The experimental data suggests that the cusp
at 17 K in x(T) does not indicate a definite magnetic ordering. Nevertheless,18

the substantial decrease in the Ru-nuclear relaxation rate below 17 K indicatesthat the amplitude of spin fluctuations is reduced by something or other. From
the analysis of temperature dependence of Knight shift by Mukuda et al., it iconcluded that short range antiferromagnetic ordering develops below 60 K.
Specific heat divided by temperature e/r is shown for polycrystalline
Sr3 Ru 20 7 in Fig. 21. It is noted that no clear peak is observed around T max =17
K. Instead, the T 2 dependence of e piT does not follow the simple relation ofe /T = Y + f3T 2 below 17 K. As observed in Fig. 21, the deviation, i.e.
additional entropy, may be due to the substantial development of short range
antiferromagnetic ordering observed in the Knight shift. Below 4 K, the same
region that Fermi liquid state is suggested, e,iT shows a strong decrease. In
the range of temperature between 400 K2;:5;T 2;:5;800 K2, fitting the data using
the formula above gives the Sommerfeld coefficient of Y = 63 mJ/Ru mol K2
and f3 = 0.273 mJ/Ru mol K4. The Debye temperature is evaluated as e D =350 K from f3 = 12rr4Nk B /5 eD3 where N=6 is half of the number of atoms informula unit. The largest specific heat y value of Sr 3Ru 20 7 among the R-P
type ruthenates (30 mJ/Ru mol K2 for SrRu0 3 [46] and 38 mJ/Ru mol K2 for
Sr2Ru0 4 [14,47]) provides clear evidence that Sr 3Ru20 7 is a strongly correlated
4d-electron

metallicoxide.

A

local-density

electronic-band-structure

calculation has been performed for Sr 3Ru 20 7 by Hase and Nishihara [19].
They deduced the density of states at the Fermi energy D(E F)=10.3 states/eV
cell, corresponding to the electronic specific heat coefficient y band=12.1 mJ/Ru
mol K2. Thus the mass enhancement factor y.exp / y ban d=5.2 surpasses that of
Sr2Ru0 4 at Yexp/Y band=3.6 [14,20].
For estimating the magnetic contributions em from Ru-4d electrons to
specific heat e p' we subtracted the lattice part [Jt3 from the raw data as e m=C P- (Jr. Magnetic entropy Sm is calculated by Sm(T)= KC;dT. Then, we obtain
Sm(T=17 K)=Rln(2Seff +1)=1.4 I/K Ru mol with R=8.31 11K mol. The effective
spin Seff is about 0.09. This entropy is about 7 times smaller than Sm=9.13 11K
19

mol for Seff=l corresponding to well localized Ru 4+(4d 4 ) pins in the low pIn
state. Therefore magnetic anomaly at 17 K in Sr3Ru 20 7 is associated with avery small magnetic moment ( ..... 0.18 f.1rJ, similar to the weak antiferromagnetic
correlations characterized by a small U-5f moment in UPt 3 [43].
It is important to note that even at temperatures much lower than 17 K,

the magnetic susceptibility remains quite large. It appears that the groundstate maintains a highly enhanced magnetic susceptibility of 1.5 X 10-2emu/mol
Ru. Considering that the observed magnetic susceptibility is due to the quasiparticle of Fermi liquid state, we can estimate the Wilson ratio Rw = rt 2k 8 2Xc/3 f.1 8 2 y= 7.291x 108Xc/Y where Xo (in emu/Ru mol) is a magnetic susceptibility and y(in erg/K2 Ru mol) is a Sommerfeld coefficient of specific heat in the groundstate, respectively. If we regard the observed X at 2 K as that at 0 K, we
obtain Rw =17.4. This value of Rw much larger than unity implies thatferromagnetic correlations are strongly enhanced in this compound. Such aground state is known as a nearly ferromagnetic metal. In addition, we canalso estimate Kadowaki-Woods ratio A/y2, whereA is the resistivity coefficientof T2 in Fermi liquid state. For Sr 3Ru207' assuming that electronic pecificheat is mainly due to the ab-plane component, we obtain A/y2=Aa/y 2=3.5 x
10-5 f.1Q cm/(mJ/K 2mol RU)2 similar to that observed in heavy fermion
compounds as shown in Fig. 22. These results indicate that the ground stateof Sr 3Ru207 is a strongly correlated Fermi liquid with the enhanced
ferromagnetic correlations.

At high temperature around 17 K, magnetic

excitations are dominated by the short range antiferromagnetic correlations.
Therefore we conclude that Sr3Ru 20 7 is a nearly ferromagnetic metal basedon the strongly correlated Fermi liquid as the ground state and exhibiting
antiferromagnetic excitations at high temperatures.
Now we discuss the distinction of lattice parameters, susceptibility andresistivity among different synthesis methods of poly crystalline and single
crystalline Sr 3Ru20?, Lattice parameters reported by Mtiller-Buschbaum et al.

20[48], Cao et al. [22,24] and Cava et al. [17] as well as ours are shown in Fig.
23. Systematic difference in the c parameter between the flux-method andothers is recognized. The flux-grown single crystals show a clear ferromagnetictransition at Tc=104 K and its ordered moment below Tc is about 1.3 J-lB/Ru
even under a weak magnetic field J-lcf/=0.3 T along the c-axis [22]. On theother hand, FZ crystals do not exhibit any ferromagnetic ordering and its
moment under J-lcf/=0.3 T is about 0.01 J-lB/Ru along both ab-plane and c-axis
at 10 K. Temperature dependence of resistivity of flux-grown single crystals
is nearly the same as that of FZ crystals. However, the absolute value forflux-grown single crystals is about 8 times larger than that of FZ crystals. The
5% doping of non-magnetic Th into UPt 3 is known to cause an obvious change

in lattice parameters, 0.2% decrease in the unit cell volume [49], and clear
spin density wave ordering at 6.5 K [50], which is never observed in pure
UPt 3 • Considering that the present-FZ method can prevent crystals fromcontaining the impurity above 0.1 % level, possibility of inclusions in fluxmethod crystals of Sr 3Ru 2 0 7 should be worth investigation in future study.

21

Chapter 5. Sr2 CaRu 20 7 : weakly ferromagnetic metal
The SCRO system shows both the Curie-Weiss behavior of magnetic
susceptibility and non-insulating electrical resistivity. Similar properties wereobserved in the mixed metallic phase (Sr,Ca)Ru0 3 and were discussed interms of the self-consistent renormalization theory (SCR theory [3,51]) as anitinerant ferromagnet [52]. The SCR theory based on the antiferromagnetic
spin fluctuations has been applied also to HTCS in order to understand bothsuperconducting symmetry and normal state properties [3]. Spin fluctuations
for a weak ferromagnet should be an appropriate picture for analyzing themagnetism in SCRO, especially in the region II where very low Tmax (3-5 K)
is observed.
The SCR theory is based on the relation between magnetic free energy F m
per one magnetic ion and the dimensionless magnetization p as follows:(1)

where p = M(R, T)/f.i-BNA, r and ~ represent the second and the fourth order
expansion coefficient, respectively. Especially, ~ has an substantial meaning
as the mode-mode coupling constant among spin fluctuations with different
wave vector q. Considering that thermodynamically stable state can be deduced
from the first derivative of Eq. (1), we obtain the following equation.
16,uB H2

2(2)--=--=p -PS 'F;

P

where spontaneous magnetization Ps=p(T=O K, H=O Oe).
The Arrott plot of magnetization curves (P2vs Hlp) for x = 1.0 at different
temperatures is shown in Fig. 24. The appearance of the positive intercept on
the vertical axis indicates that the intrinsic Curie temperature Tc is below 5 K.
22

Therefore we identify T max =3.2 K as the intrinsic Curie temperature Tc. Only
the data in the region II satisfy the relation that p 2 is proportional to Hlp. The
spontaneous magnetization Ps should be somewhat larger than observed p(T=2K, H=O Oe)=O.OS. However it is suggested that Ps is much smaller than Peff =2.S2 evaluated from X (T). These characterize SCRO in the region II as a
weak ferromagnet.
For itinerant electron systems, magnetic anisotropy is not substantial incomparison with localized electron systems, since magnetic correlation lengthof the itinerant spins is considerably longer than that of the localized spins.
For region II, the low Curie temperature of -100 K indicates that magnetic
anisotropy energy is at most 10-2 -10-1 K. Thus the observed magnetizationp(B) up to 5 T (Fig. 24) for the polycrystalline samples should reflect the
intrinsic process, rather than the average of two strongly anisotropic
contributions. Nevertheless, a recent theory by Hatatani and Moriya [53]discusses a subtle difference in the behavior of the isotropic two-dimensional
system of spin fluctuations from that of the isotropic three-dimensional system.

In weakly ferromagnetic metals, the SCR theory gives another relation:(3)

where c=0.33536 is a constant, Tc is the Curie temperature, and To and TA
characterize the energy width of the dynamical spin-fluctuation spectrum andthe width of the distribution of the static susceptibility in the q-space,respectively. To and TA correspond to the exchange energy J in the localized
spin system. The ratio of TAITc much larger than unity means that spin
fluctuations only near q=O contribute to the magnetic ordering.

23

We consider the relation derived by Takahashi [54]:F = _4k......:;:s......:...TA:.--2(4)

lIST,o£1 can be derived from the gradient of the Arrott plot using Eq. (2).
It is not very precise to estimate the spontaneous magnetization Ps (T=O
K, H=O Oe) from the data of p(H) at 2 K because this temperature cannot be
regarded as much below Tc =3.2 K. Therefore, we regard Ps as a fitting parameterand fit the inverse magnetic susceptibility in the limit of zero field, X -l(T,H=O Oe), using the following relations in order to determine the SCR parameters
as in Ref. [55]. Assuming the weakly ferromagnetic limit, i.e. T/To «1, we
can simplify the relations as follows:- 2{ I~ps
1 + ry 3
Y=--2 - l + - - f17 dz·z
8TA'YJc Jo

1},[lnU---lJf(U)]
2u

(5)

with
(6)
(7)
(8)

(9)
where lJI(u) is the digamma function, U is the intra-atomic exchange energy
and t=T/Tc • Using these relations and assuming U=10 4 K, we can predict

X(T,H =0 Oe) above Tc for several values of Ps as shown in Fig. 25. For
experimental X(T,H=O Oe) we employ positive intercepts in the Arrott plot
(Fig. 24) where the line of extrapolation of high field data crosses the horizontal

24

aXls. Adequate reproduction of xJ.T,H=O Oe) is obtained when P s is 0.2.
Furthermore, To and TA are evaluated self-consistently from Eqs. (3), (4) and(5). All the SCR parameters thus evaluated are, Te = 3.2 K, p

= 0.2, FI = 433

K, To = 133 K and TA = 465 K.
The ratios T/To=0.0241 and Peff/P s = 14.1 are important for the classificationof the itinerant/localized ferromagnets. Figure 26 is based on the generalized
Rhodes-Wohlfarth plot (P eff/P s vs T ITo) for weak ferromagnets by Takahashi[54]. In the original Rhodes-Wohlfarth plot ,Pef/P sis plotted against Te' In thisplot, large P eff/P s and small T/To represents the strong itinerant character ofelectrons. The localized Heisenberg system is characterized by Peff/Ps =T/To=l.
Sr2 CaRu 20 7 (x=1.0) is regarded as a weakly ferromagnetic metal withintermediate character as shown.
For polycrystalline SrOACaO.6Ru03' Kiyama et al. [52] obtained Te =25 K
and TA = 5000 K from M(H), thus TA/Te = 200. A similar value of TA/Tc=145
for Sr 2 CaRu2 0 7 indicates that the similar weak ferromagnetism occurs in bothcompounds despite the difference in dimensionality of Ru-O network. Our
study is probably the first example of applying the SCR theory to ferromagnet
with a quasi-two-dimensional layered crystal structure [53]. Theoreticalmodification of Takahashi's relation [Eq. (4)] for a quasi -two-dimensional
system should be required in order to advance the investigation of the twodimensional weak ferromagnet. Nevertheless it is expected that the analysis
presented here remains qualitatively valid also for systems with twodimensional ferromagnetic spin fluctuations [56].
The strong ferromagnetic spin fluctuations in Sr 2CaRu207 implies thatsimilar ferromagnetic correlations are present also in Sr3Ru 20 7. All the results
point toward the presence of ferromagnetic correlations in Sr-Ru-O R-P phases.
Hence further study of Sr-Ru-O R-P phases will provide the dimensionality
dependence of ferromagnetic correlations and will help searching for othertwo-dimensional ferromagnets.
25

Chapter 6. Conclusion
In conclusion, we have characterized the magnetic and structural propertiesof the new bilayered ruthenate series Sr 3_ Ca Ru2 0 y (O~x~2.0). The oxygen
X

X

content y has been determined as essentially 7.0 for all x before annealing in
the oxidizing atmosphere. In addition, we have firstly succeeded in growing
large and high quality single crystals of Sr3Ru 20 7 by the floating-zone method.
The results of magnetization, resistivity and specific heat measurements suggestthat Sr 3Ru207 is a strongly correlated Fermi liquid with nearly ferromagnetic
ground state. The magnetic properties in the region around x=1.0 are associatedwith the appearance of the itinerant weak ferromagnetism. On the basis of the
SCR parameters Sr 2CaRu 20 7 is classified as the first weak ferromagnet withquasi -two-dimensional crystal structure. With increasing Ca, the ground stateof SCRO changes dramatically from nearly ferromagnetic and strongly
correlated Fermi liquid, to weakly ferromagnetic metal, and finally to localized
antiferromagnetic spin system.

26

Acknowledgments
The author wishes to express his sincere thanks to Professor Toshizo
Fujita for stimulating discussion and critical advice. He appreciates Associate
Professor Y oshiteru Maeno for being a great help during his research days at
Kyoto University. He thanks Hiroshi Muranishi, Shuji Nishizaki, Satoru
Nakatsuji, Yasumitsu Mori, Takashi Ando and Zhiqiang Mao for valuable
discussions and greatly acknowledge Professor Takehiko Ishiguro and themembers of Ishiguro' s laboratory for their supports. He is grateful to Associate
Professor Kazuyoshi Yoshimura, Mr. Takashi Kiyama, Professor TOfU Moriya,
and Professor Y oshinori Takahashi for their useful advice in analyzing thedata using the SCR theory. He is grateful also to Professor Yasumasa Koyama,
Dr. Gang Cao, Dr. Markus Braden, Dr. Yukio Morii, Dr. Yasuhide Inoue, Mr.
Masayuki Hara, Professor Kazumasa Miyake and Professor Kosaku Yamada
for their useful advice. He thanks Dr. Izumi Hase for discussing his band
structure calculation results prior to publication. He acknowledges Dr. Andy
Mackenzie for his collaboration with the author. He thanks Dr. Kenji Ishida
and Mr. Hidekazu Mukuda for discussing their NMR results prior to publication.
He thanks Mr. Kou-ichi Izawa, Miss Kimie Senami, Dr. Fumihiko Nakamura,and Associate Professor Takashi Suzuki for their help on everything in
Hiroshima University. Some of the measurements were performed at the
Cryogenic Center of Hiroshima University. He has also been a research
student also for two years in Department of Physics, Graduate School of
Science, Kyoto University. He really appreciates a lot of help during his
school days by his family.

27

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31

Table 1. Effective Bohr magneton number P efb Weiss temperature Bw
and temperature independent term Xo for FZ crystals of Sr3Ru207.

H//ab

H//c

Peff

2.52

2.99

8w(K)

-39.4

-44.7

3.64 X 10-4

-5.21 X 10-5

Xo( emu/Ru mol)aFig. 1 . The crystal structure of Sr3Ru207.
The large circles represent Sr and small circles
Ru. The cubes indicate Ru06 octahedra.

827

1427

2

o
N

ce
(J\

o

(a)
:(b) .

-2

..J

Ru

0.6

0.7

0.8

0.9

Fig. 2. Equilibrium pressure for the reaction RuO 2 ~ Ru+O 2
investigated by several groups. (a) Ref. 29, (b) Ref. 30,(c) Ref. 31, (d) Ref. 32.

x3.0
2.5
. 2.0
~1"'''''_ 1\.~~ 1.8
1.6
1.5.~I- ..... . ~ . 1.4
1.3
1.2
1.0
0.8
0.6
0.4
.J

-0.2

o

O. 000

2Q.00080.00028 (degree)

Fig. 3. X-ray powder diffraction patterns of Sr3_xCaxRu20y withvarying Ca concentration x. All peaks of O$ts2.0 are consistent
with the symmetry of 14/mmm. The asterisks indicate Sr2 Ru0 4 impurity.

3.90...-... 3.88:~

0«
~ 3.86

It 0.5%

~i
6

(\S

,

!J.

3.84
!J.

,
,
,

,
,'~',

20.6
...-...

20.4,:

0« 20.2

:~

,

,.

,'

20.0

t

:
'1.0%

:,,

~

(,)

6

!J.

,,

,

,

19.8
19.6
315
...-...
cry

310

•

0« 305
~

~

300

,
,
• ,

.'

'.

~

.'.... •

295
290
0.0

,
,
,
'

1.0

!J.

:t

2.0

2.0%

3.0

x (Ca)
Fig. 4. The Ca concentration dependence of the a parameter, c parameterand unit cell volume. • :as-prepared sample, 6. :oxidized sample(present work), 0 :flux-method single crystals (Miiller-Buschbaum
et aI., Ref. 1[48]), \l :polycrystals ,(Cava et aI., Ref. [17]), 0 :flux-method
single crystals (Cao et aI., Ref. [22-24]).

0.1

Sr3-x CaX RU 2 0 7

5
4

..-..

3

E
()

X

=0

a
---~

x = 1.00.()1.. . .. ' - "

8
7
6

5

0

x = 2.0
X = 1.5

100

200

300

T (K)

Fig. 5. Electrical resistivity of polycrystalline Sr3-xCaxRu207.

0.12

0.08

0.04
0.00

x=o

T max

L:c

.... :... .

ZFC........................................... .

.

~-~ 0.15 '\FC

0.12 ~"'~'30.10
E

o
E

0.08

::J

0.04

-a:

::J

E
Q)

............

O 00

.~

"-

~

;z: 0.05 f- T max • I
~

0.00

•

t···.....

I.. ..

ZFC •

.....

-

I

o

20

40

60

T(K)

........ ....................................
x=1.0 .

H---4----4--+----4--....:....:....:~

T min

FC I

0.12 \ ,

'-'"

it".

0.08 \ T max' ••0.04

x =1.5ZFC

o. 00 H--~--+--+-----+---+-~
0.12
T min

0.08 F~ +X =2.00.04 ( } \ZFCT max •••••

0.00 0..................................... .
100

200

300

T (K)
Fig. 6. Magnetic susceptibility under the field of IT. Both zero field cooling(ZFC) and field cooling (FC) data are shown. Characteristic temperature
Tmax is defined as the temperature of the susceptibility maximum.
See text for other notations.

(I)

40

(II)

.-.
~

---

~3

20

I--t:

0

•
50

•

•

6.

.1

1

6.

1
1

1

••••· .... • .. •·• .... •...... •.... • .. ·1· .... •· .. · .... ••• .. •.. •.... 1·· ........ ···· ...................... ..

(t)

1
1

H//ab
-50 H//c

3.0 H//c
~:
Q)

a..

2.5

1

•

.1
1

6.

H//ab

1
1

•

•

~

2.0
1'8.0

0.5

1.0

1.5

2.0

x (Ca)

Fig. 7. lfhe Ca concentration dependence of T

max

,Weiss temperature eWand the effective Bohr magneton number Peff' • :as-prepared samples,
6. :oxidized samples, and • :FZ single crystals.

,

0.1 2 r----~--___._--_____r__--____,

l: 0.04

~

0.02
20

40

60

80

T (K)

Fig. 8. Magnetic susceptibility of x(Ca)=2.0 under different fields.
Both zero field cooling (ZFC) and field cooling (FC) data are shown.

:::J

E
Cl)

;300

-o
E

:::J

x=1.0

;200

CC

100

o
o

100

200

300

T (K)

Fig. 9. The reciprocal magnetic susceptibility for x=l.O and 2.0.

I

I

100

I

I

I

I

I

200

300

T (K)

Fig. 10. Magnetic susceptibility of Sr3Ru 2 0 7 for both single
crystals and polycrystals. The difference of susceptibility
below 160 K is due to the ferromagnetic impurity SrRu03'

x =0

x =0.2

• T'1

t:

:\

t

~~
x =0.6x =1.0

• T'1

X

=2.0

/(\

r'"
2

o

._

------.............................

100

200

300

T (K)
Fig. 11. The temperature dependence of AC magnetization M' for different
x from 2 to 300 K. Thick arrows indicate the peaks due to (Sr,Ca)Ru0 3
and thin arrows unidentified impurities.

q
'-"

en
Jo-.

::J

Ct1

Sr3-xCaxRu207

Tc

Q)

(I)

100

(II)

(III)

Jo-.

Q)

P

c..

E
Q)

T*
P

+-'

U
+-'

en
·c

50

p

TN

canted AF

...-

Q)

...-...-...-"'- - - T M

+-'

u

Cd
Jo-.
Cd

AF?

..c
u

00

WF

V-~-AF?
2

1
X

3

(Ca)

Fig. 12 . T-x(Ca) phase diagram inferred from the results of DC and AC
magnetization measurements. WF:weakly ferromagnetic phase, P:paramagnetic phase, AF:antiferromagnetic phase. • :Tmax' ~ :Tmin'
o :TI ', \l :T2', 0 :characteristic temperatures defined for fluxmethod single crystals (Ref. [22,23]).

0.8~--~----~--~----~--~~

Sr3_xCaxRu207.-....

0.6
T=2 K

c:

01

x=1.0

0.2

1

2

3

4

5

floH (T)Fig. 13. The field dependence of magnetization at 2 K
up to 5 T for x=O, 1.0 and 2.0. For x=1.0, quite different
behavior from others are recognized.

01.20,....---,------"T"""---r----,-------r-----r----,
I

•

I

\

I

oxidized sample

-

t..

t..

A

t

.......:1

A/-:. as-prepared sample
I

~

-

t..'
t.. •

~ 0.05r-

0.00

a

100

200

300

T(K)

Fig. 14. Oxidation effects on X(T)=M/H for x=l.S. The
cusp observed in X(T) of as-prepared sample in the Fe
curve is diminished by O2 annealing.

(a) T =300 K(b) T =4 K
~

.~

en

c

CD
......,
C

o

20

60

80

Fig. 15. Powder x-ray diffraction patternsof SrCa2Ru 20 7 at 300 K (a) and 4 K (b).

1

I

I

(a)

.c
CJ)

c

Q)

+-'

C

\~- L J U'II"J...... ... ~ld_ •.J..
I

I

I

I

I

I

~

(b)

~

0
0

~

"'-'"

~

+-'

C\J
0
0

C

Q)

C

~

0
0

0
0
"'-'"

2,

~

0

~

co

0
0

"'-'"

+-'

~

~

"'-'"

~

CJ)

C\J

~

0

"'-'"
~

c..o
~

~

c..o

0
0

0
0

"'-'"

"'-'"
I
I

o

20

~ ~L..-.-.l
I

I

I

60

80

Fig. 16. X-ray diffraction spectrum (a) of powder and (One)reflection spectrum (b) of FZ crystals of Sr 3Ru 20 7•

(a)

C)

E: 25

Sr3 Ru 2 0 7

:J

a: 20
--_

fl oH =0.3 T

:J

~3 15

Ct)
I

--~~ 10......

100

200

300

T (K)
30~--~,----~,----~,~--~,----~

(b) -

I

1

I

I

10

20

30

40

50

T (K)

Fig. 17. Magnetic susceptibility of FZ crystals of Sr3Ru 2 0 7
under 0.3 T field in the range of (a)2-300 K and (b)2-50 K.

1234
floH (T)5

Fig. 18. Field dependence of magnetization M (H)of FZ single crystalline Sr3Ru207'

6

10

(a)

400
,..-,
E
()

a

8
"'b
(')

6~

300

<0I

o
.,.'-' 200

o
I

!

w

4[)
(')
3
'-'

..0
l\S

c:t

2

100 :
B

100

308

200

T (I<)
70~--~'----~'~--~1----~'----~

60 r- (b)

00

2

0

.!

T max
-

I

I

I

I

200

400

600

800

1000

T 2(1<)
Fig. 19. (a) Electrical resistivity of FZ crystals of Sr3 Ru 20 7in the range of 4-300 K. Both pdependence of pabbelow 7 K.

aband p are shown. (b) T 2_
c

1()O
6
4

Tmax

011
0
Q)

---

6
4

(J)

~

"'-'"

~

• •

2

~

1
6
4

~.. . • • •... ..

2

•

•

•

••

•

••

.

•

Sr3 Ru 2 0 7
99Ru-NMR

2

0. 1
1

2

4

6

8

10
T (K)

2

4

6

8

100

Fig. 20. Temperature dependence of liT 1 at Ru sitein polycrystalline Sr3Ru 20 7 by Mukuda et al.

300::=-- 250
0

E

::J

a:

2

200

T max

C\J

~

---E 150
J

'-"

1,00

~ ,50

o~----~------~------~----~

o800

Fig. 21. Specific heat divided by temperature of Sr3Ru207.
Solid line represents the fitting C/T=y +{J P.

Sr3Ru207(Aab)
•

UA1 3

UPt2 0 0UPt
UPd 3
Uln 3
UGa3

!~

{:) Sr2 Ru04(A a b)
CeSn 3
Pd/
<>
Pt~N·
'
1

Co(§>

.' Fe
R e :'<9" Os

10- 6 1----L--L.-I-~__1_---L........L-L~---'--~~~~~
1
2
3
0
10
10
10
10
Y (mJ/K2mol)rFig. 22. The coefficient A of theterm of the resistivity, plotted against
the Sommerfeld coefficient y of the specific heat for heavy fermion compounds
and some transition metals. The solid and broken lines represent the KadowakiWoods ratioA/y2=ao=1.0x10-5.uQcm/(mJ/K2mol)2 and a /25, respectively.

o

Heavy fermion compounds follow the former universality.

I

I

I

I

I

3.905 --...-, 3.900 0«
--".
C1:l

0<1:

-

3.895 3.890~

3.88520.80..-......

0

-

•
I

I

I

I

I

T

I

\l

•

20.70 -

•

I

•

-

I

I

•

-

-

' -......

t)

-

0

1.0%

20.60020.50~

-

,

-

0
I

I

I

I

I

M.Buschbaum Cao Cava Ikeda Ikeda(flux-s)(flux-s) (poly) (poly) (FZ-s)Fig. 23. Comparison of the lattice parameters of Sr3Ru207 reported
for different syntheses. 0 :flux-method single crystals (MtillerBuschbaum et al. Ref.[48]), 0 :flux-method single crystals(Cao et al. Ref.[22,24] ), \l :polycrystals (Cava et al. Ref.[17] ),• :polycrystals (present work), • :FZ crystals (present work).

0.20
0.15
C\J

Q

0.10

30K

0.05

50K
100

200

300

3

Hlp (10 Oe)

Fig. 24., Arrott plot of p(H) data with x=1.0 at different temperatures.

S 50

E

--

p s = 0.4

CD

o 40

E
::J

fS 30

0.2

..-..

o

II

:r:

20

T"""

~ 10
10

20

30
40
T (K)

50

60

Fig. 25. Results of x(T,H =0 Oe)-l calculated for x=1.0 by means of
the SC::R theory. The curves depend on parameters F, T ,T and T1c0

in addition to Ps. Several different values for Ps are assumed and
Ps=0.2 gives the best fit as shown.

A

35
30

itinerant

25
en

Cl..

"""-....

20

:t::
Q)

Cl

15 o •Ni3A1
Sc3 1n
....
o

10
5

Sr2CaRu207

ZrZn 2o ZrZn .
19

MnSi
Au 4V

00

oo

localized
CeF2

0.05 0.10 0.15 0.20 0.25 0.30

Tc IToFig. 26. (ieneralized Rhodes-Wohlfarth plots after Takahashi (Ref. [54 ]).
The data IOf Sr2CaRu 20 7 is shown by a solid circle. Other intermetallic
compounds are weak ferromagnets with three-dimensional crystal structure.
Solid line is the theoretical expectation.

(1)Weak ferromagnetism in two-dimensional bilayered Sr 3_ xCa xRu20 7'
S. Ikeda, Y. Maeno, and T. Fujita.
Physical Review B, 57(2), 978-986 (1998).

(2)

Two Distinct Structural Phases in Sr3_xCa xRu20 y'
S. Ikeda, Y. Maeno, H. Muranishi, and T. Fujita.
Journal of Low Temperature Physics, 105 (5/6), 1599-1604 (1996).

(1)Sr2CaRu 20 y: a new phase of layered perovskite.
S. Ikeda, Y. Maeno, M. Nohara, and T. Fujita.
Physica C, 263, 558-561 (1996).

(2)

Ca 2Ru0 4 : New Matt Insulators of Layered Ruthenate.
Satoru NAKATSUJI, Shin-ichi IKEDA and Yoshiteru MAENO.
Journal of the Physical Society of Japan, 66 (7), 1868-1871(1997).

(3)Interplay between Kondo Effect and RKKY Interaction in UCu3+ xGa 2- x 'S. Ikeda, S. Nishigori, T. Suzuki, T. Fujita,
Y. Maeda, T. Takabatake, and H. Fujii.
Physica B, 194-196,465-466 (1994).