ISSP
Activity Report A
2001
Contents

Pages

Preface1

Research Highlights

2 - 26

ISSP Activity Report A 2001

PREFACE- Activity Report A -ISSP was established in 1957 based on the recommendation of the National Council of Japan topromote the cooperative research throughout the country in condensed matter physics in close contact with other related fields of science such as chemistry and earth science on one hand and to pursue its own scientific research on the other hand. This foreseeing philosophy of the founders together
with the constant efforts afterwards had made ISSP very active in both ways in recent years, especially after the introduction of the large group system in 1980 and the moving to the new campus of
Kashiwa. So far there were various forms of the publications to make the status of the research activity of ISSP public. New forms are now introduced; the Activity Reports A and B, which show the upto-date status of these scientific activities in separate ways depending on the styles of the pursuing
the research. This Activity Report A is based on the research activity of the staffs of the ISSP in thefiscal year of 2001. In the first half about 30 topics are reported as the highlights, whereas in its second half a brief summary of scientific activities and all publications of each research groups of ISSP
are listed.
We are happy to receive any comments on the Report for the possible improvement of the overall
research activity of ISSP.

August 19, 2002

Hidetoshi Fukuyama
Director
Institute for Solid State Physics
The University of Tokyo

ISSP Activity Report A 2001

1

Research Highlights
Observation of Quantized Plateaux andMagnetic Superstructures in a 2D Spin
System SrCu2(BO3)2 under High Fields
M. Takigawa, Y. Ueda and T. Goto
The discovery of a spin-gap and magnetization plateauxin SrCu2(BO3)2 [1] stimulated tremendous amount of experimental and theoretical activities. The crystal structure realizes a stack of the two-dimensional Shastry-Sutherland spinmodel [2] (Fig. 1), for which a direct product of dimer singlets is known to be the exact ground state. A remarkableproperty of this material is the magnetization under highfields, which exhibits plateaux at fractional values (1/8, 1/4
and 1/3) of the fully saturated Cu moment.
However, the previous magnetization curve up to 58 T
was far from saturation and thus one could not answer thequestion of, e.g., the existence of the 1/2 plateau under theoretical debates. In 2001, we developed magnets at High
Magnetic Field Laboratory, KYOKUGEN in Osaka
University and performed the magnetization experiment to
69 T, where a single crystal grown by a traveling solvent
floating zone technique was used. The result for H // c at 1.3
K in Fig. 1 has revealed that, although magnetic field is still
not enough to get full magnetization, the 1/3 plateau survives in a range at least as wide as 25 T, meaning that thisplateau is much more stable than the 1/4 and 1/8 plateaux.
Within the experimental accuracy, no hysteretic behavior isobserved between field increasing and decreasing scans.
Another challenging issue is the observation of magnetic
superstructures at the plateaux. Theories based on the hardcore boson model have predicted simple commensurate
superstructures of triplets. Whereas some superstructures at
1/8, for example, are proposed as shown in Fig. 2, there has
been no experimental evidence so far. NMR is best suited todetect magnetic superstructure at high magnetic field. In
June 2000, we have first performed NMR experiments for
11B nuclei up to 28 T using a 20MW resistive magnet at
Grenoble High Magnetic Field Laboratory in the temperature range above 1.5 K. The field range covers the 1/8 magnetization plateau that occurs above 27 T. Although weobserved non-trivial spin dynamics at high field, no indication of static spin structure associated with the 1/8-plateau
was obtained. We then continued NMR experiments in May
and November 2001 for both 11B and 63,65Cu nuclei at aFig. 2. NMR spectrum of 11B nuclei in SrCu2(BO3)2 at 27.9 T and
35 mK. Inset shows the superstructures at the 1/8 plateau proposed
based on the hard core boson approximation, where dumbbells inblue represent singlets and those in red triplets.

much lower temperature of 35 mK. We observed a drasticchange of the 11B NMR spectrum as shown in Fig. 2. A single peak for each of the quadrupole-split three resonancelines observed at 26 T is transformed to multiple-peak structure at 27.9 T. The former is consistent with the uniformly
magnetized state, while the latter provides firm microscopic
evidence for a spatially modulated magnetic superstructure
at the 1/8-plateau. The spectrum at 27.9 T contains peaks
with both positive and negative magnetic hyperfine shifts,
suggesting that while most Cu spins point along the magnetic field, some spins are polarized opposite to the field. This
contradicts the superstructures in Fig. 2 and indicates anartifact of the hard core boson approximation. Triggered byour experiment, Miyaraha et al. proposed a new approachstarting from the original Heisenberg spin Hamiltonian withadiabatic spin-phonon coupling and succeeded to reproduce
quantitatively the magnetization superstructure with a rhomboid unit cell and Friedel-like oscillation. This result will bereported elsewhere soon.
References[1] H. Kageyama et al., Phys. Rev. Lett. 82, 3168 (1999).
[2] S. Miyahara and K. Ueda, Phys. Rev. Lett. 82, 3701 (1999).
Authors
M. Takigawa, K. Kodama, H. Kageyama, Y. Ueda, T. Goto, M.
Horvatica, C. Berthieraa, Y. Narumib, K. Kindob
aCNRS and MPI-FKF, Grenoble, France.
bOsaka University.

Superconductivity at 1 K in Frustrated
Pyrochlore Oxide Cd2Re2O7
Z. Hiroi, T. Sakakibara and M. Takigawa

Fig. 1. Magnetization curve of SrCu2(BO3)2 up to 69 T at 1.3 K. The
1/8, 1/4 and 1/3 plateaux are observed. The Shastry-Sutherland modelis shown in the inset.

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ISSP Activity Report A 2001

Frustration is one of the most interesting topics in thefield of solid state physics. Generally, it suppresses longrange order of spins or charges on lattice points and tends tostabilize a novel quantum-disordered state. The playgroundis triangle-based lattices like a two-dimensional Kagome lattice or a three-dimensional pyrochlore lattice (Fig. 1).
Pyrochlore oxides are typical transition-metal oxides comprising the latter lattice. Although many metallic pyrochlore
oxides are known, no superconductivity has been observed

so far. We report here the first pyrochlore oxide superconductor Cd2Re2O7.
We have prepared single crystals of Cd2Re2O7 (inset to Fig.
2) and measured resistivity, magnetic susceptibility, andspecific heat down to T = 0.4 K. Surprisingly observed at 1
K is a sharp drop in resistivity (Fig. 2), a large diamagnetic
signal in magnetization, and a well-defined λ-type anomaly
in specific heat. These experimental facts give a strong evidence for the occurrence of superconductivity. In addition,
we observed two successive phase transitions at 200 K and
120 K where resistivity shows anomalies (Fig. 2). They arevery intriguing, probably related to charge, spin, and orbital
degrees of freedom for Re ions with two 5d electrons. We
expect a novel physics involved in this compound on thebasis of frustration on the pyrochlore structure.
Principal Publication and Authors
M. Hanawa, Y. Muraoka, T. Tayama, T. Sakakibara, J. Yamaura and
Z. Hiroi; Phys. Rev. Lett. 87, 187001 (2001).

Superconductivity and magnetic
fluctuations in Cd2Re2O7
via Cd NMR and Re NQR
M. Takigawa and Z. Hiroi

Fig. 1. Crystal structure of Cd2Re2O7 (top). Pink octahedra representing the ReO6 unit are linked to each other by their corners. When
only Re or Cd atoms are extracted from the structure, the pyrochlore
lattice made of corner-sharing tetrahedra appears (bottom). Red balls
represent Re or Cd atoms.

Fig. 2. Resistivity showing a superconducting transition at Tc = 1.0 K.
The anomalies at 200 K and 120 K are due to structural phase transitions where the pyrochlore structure are deformed slightly in two
steps. The inset shows the photo of grown single crystals used forvarious measrements.

The pyrochlore oxides has the chemical formula
A2B2O7, where both A and B sites form a network of corner-sharing tetrahedra, known as the pyrochlore lattice.
Localized magnetic moments on a pyrochlore lattice has
attracted enormous recent interest since strong geometricalfrustration inhibits conventional Neel order, resulting in
exotic ground states. In itinerant electron systems, geometrical effects are not as well understood as the case of insulating magnets. However, recent discovery of superconductivity with Tc ~ 1 K and successive structural phase transitionsat Ts1 = 200 K and Ts2 = 120 K in Cd2Re2O7 by Hiroi group
at ISSP have opened new opportunities to investigate therole of lattice geometry in various electronic phases. (Seethe previous article.)
We have performed nuclear magnetic resonance (NMR)

Fig. 1. The spin-lattice relaxation rate (1/T1) of 187Re nuclei near andbelow the superconducting transition temperature (1 K) measured by
NQR at zero magnetic field is plotted against inverse temperature(1/T ). The lines show the results of weak coupling BCS theory
assuming a uniform distribution of the energy gap between Δ-δ andΔ+δ where Δ is the average gap. The red, blue and green lines
indicates the results for δ/Δ= 0.22, 0.27, and 0.17, respectively.

ISSP Activity Report A 2001

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Observation of Coherent Magnon
Oscillation in Sodium Vanadate
T. Suemoto and Y. Ueda

Fig 2. a) The isotropic part of the Knight shift for 111Cd nuclei isplotted against temperature (red, lower scale) or magnetic susceptibility (blue, upper scale). b) The temperature dependence of (T1T)-1 for
111Cd nuclei, indicating steep decrease of the density of states below
the structural transition at 200 K.

and nuclear quadrupole resonance (NQR) experiments on
Cd2Re2O7 to obtain microscopic insight on the superconducting, structural and magnetic properties [1, 2]. The pronounced coherent peak and the activated temperature dependence of the spin-lattice relaxation rate at the Re sites in the
superconducting state shown in Fig. 1 provide strong evidence for weak coupling BSC behavior with a nearly
isotropic energy gap.
A sharp single set of NQR lines at the Re sites rules out
any magnetic or charge order down to 0.4 K. The electricfield gradient (EFG) at the Re sites as revealed from NQR
spectra does not possess axial symmetry, imposing that the
crystal structure is not cubic below Ts1 = 200 K. This has
been confirmed by subsequent various diffraction experiments. The NQR spectrum also shows discontinuous change
near Ts2 = 120 K confirming the first order structural transition in addition to the second order transition at Ts1.
The static and dynamic magnetic properties were investigated by NMR measurements for the Cd sites using a single
crystal as shown in Fig. 2. The steep reduction of the Knight
shift (spin susceptibility) and (T1T)-1 below 200 K indicatethat the structural distortion at Ts1 causes significant loss ofthe density of states (DOS). Thus the transition at Ts1 ischaracteristic of a Peierls transition or band Jahn-Teller
effects. This appears to have common physics with insulating magnets in which lattice distortion occurs to gain magnetic energy by eliminating frustration of exchange interactions and reducing the ground state degeneracy. On the other
hand, little anomalies were observed at Ts2 for thermodynamic properties, where local structure as revealed NQR
spectrum shows pronounced discontinuity. What drives thetransition at Ts2 still remains a puzzle.

Sodium Vanadate : The sodium vanadate α’-NaV2O5
shows a spin-Peierls-like phase transition at Tc = 34 K [1].
Below Tc, this compound exhibits charge ordering withalternating V4+ and V5+ ions accompanied by a lattice distortion[2]. The spins attached to V4+ ions are believed to be
dimerized with anti-parallel orientations in a zig-zag configuration[3]. The dimerized spin system reveals unique magnetic excitation spectra consisting of a triplet branch at the
gap energy Δ, a corresponding two-particle continuum of
spin excitations starting from 2Δ, and well defined magnetic bound states between Δ and 2Δ.
Coherent excitation method : Owing to the recent development of the femtosecond lasers, time domain spectroscopy has become to be a versatile tool for investigating
low energy excitations in solids. By probing the small modulation of the reflectivity after impulsive excitation by using
ultra-short pulses, we can observe the oscillation of lattice or
any other elementary excitations on femtosecond (10-15 sec)time scale, just like electric signals we can watch on an
oscilloscope. Observation of phonons or plasmons has beenreported for many typical semiconductors and some oxides.
However, this method has not been applied for probing
magnons.
We carefully chosen a small flat area on a cleaved
α’-NaV2O5 sample and irradiated it by 25 fs pump pulses
in a 40μm spot as shown in Fig. 1. A probe pulse with anappropriate delay time hits the same area from a slightly different direction and the modulation in the reflected lightintensity (actually the difference in two perpendicular polarizations) was analyzed by a lock-in amplifier.
Two magnon oscillation at 127 cm-1 : The inset of Fig. 2
shows the raw data which is an oscillation signal as a function of delay time. In the Fourier transformed spectrum
shown in the same figure, we found a new excitation peak at
127 cm-1 [2] in addition to well known phonon lines at higher frequencies. In spite of extensive Raman work, this peakhas never been reported before. This peak has been observed
only with circularly polarized light and shows a temperaturedependence characteristic to magnetic excitation. Based onthese facts, we assigned this peak to one of the triplet two

References[1] O. Vyaselev et al. phys. Rev. Left. 89, 017001 (2002).
[2] K. Arai et al. J. Phys. Condens. Matter 14, L461 (2002).
Authors
O. Vyaselev, K. Arai, K. Kobayashi, J. Yamazaki, K. Kodama, M.
Takigawa, M. Hanawa and Z. Hiroi

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ISSP Activity Report A 2001

Fig. 1. Microscope image of the sample surface. The red shaded area
is excited by the pump pulse (Thick green arrow) and the reflectanceis probed by the other pulse (red arrows)

Fig. 2. The time response of the reflection signal (inset) and its
Fourier transform. The peak indicated by an asterisk corresponds to a
newly found two magnon bound state.

magnon bound states, which have been theoretically expected to appear below the two magnon continuum [3].
This demonstrates the generation of coherent magnetic
excitation and the usefulness of “femtosecond spectroscopy”
for investigating the "strongly correlated electron systems".
References[1] M. Isobe and Y. Ueda, J. Phys. Soc. Jpn. 65, 1178 (1996).
[2] T. Ohama, H. Yasuoka, M. Isobe and Y. Ueda, Phys. Rev. B59,
3299 (1999).
[3] H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 67, 2602 (1998).
[4] H. Kamioka, S. Saito, M. Isobe, Y.Ueda and T. Suemoto, Phys.
Rev. Lett. 88 127201 (2002).
[5] S. Trebst et al, Phys. Rev. Lett. 85 4373 (2000).
Authors
H. Kamioka, S. Saito, T. Suemoto, M. Isobe and Y. Ueda

"Devil's Flower" Blooming in NaV2O5
Y. Fujii and Y. Ueda
The most exciting phase diagram in statistical physics Devil's flower [1] - has been reproduced experimentally in
Temperature-Pressure (T-P) phase diagram of NaV2O5[2].
A quarter-filled spin-ladder system NaV2O5 undergoes a

Fig. 1. Schematic charge order pattern determined in ab-plane, consisting two kinds of patterns A and A'. One charge localizes in theblue pyramid of V4+O5. The charge and corresponding lattice modulation along the c-axis are determined by the combination of A and
A'. For example, AAA'A' for 2a × ~ 2b × ~ 4c superstructure below

Fig. 2. Temperature dependence of high-resolution x-ray diffraction
profiles observed along the [13/2, 3/2, qc] direction at 0.92 GPa. One
can clearly see a series of superlattice reflections with qc = 1/4, 1/5,
1/6 and 3/17 which systematically appear and disappear as a functionof temperature.

novel cooperative phase transition at Tc = 34K associatedwith its charge ordering, lattice dimerization (2a × ~2b ×~4c superstructure) and spin-gap formation. By the complementary use of synchrotron x-ray structural analysis and resonant x-ray scattering (RXS) techniques at Photon Factory,
the 2a × ~2b × ~4c superstructure below Tc was solved
unambiguously[3,4]. A oblique charge stripe pattern formedin each V2O5-layer (ab-plane) is shown in Fig. 1 as A andA'. Atomic shifts coupled with such a charge ordering are
not shown in this figure. The charge ordering patterns called
A and A' are related by a phase shift by π along the b-axis,
where a dark blue colored pyramid represents V4+O5 and alight blue V5+O5. The stacking sequence of the patterns A
and A' along the c-axis was unambiguously determined by
the RXS as AAA'A' [4].
By application of high pressure, the stacking sequence
along the c-axis drastically changes. Figure 2 displays temperature dependence of high-resolution diffraction profiles
observed along the [13/2, 3/2, qc] direction at 0.92 GPa. In
this figure a few more reflections are newly observed andone can clearly see a series of superlattice reflections with
qc = 1/4, 1/5, 1/6 and 3/17 which systematically appear anddisappear as a function of temperature. What we observe isFIg. 3. "Devil's Flower" obtained from the ANNNI model. The blue
arrow represents the tracing path corresponding to the temperature
variation of the experiment shown in Fig. 2.

ISSP Activity Report A 2001

5

peak intensities coming from the atomic shifts; however, thecharge also modulates with the same modulation wave number qc[5]. This qc sequence means that the stacking sequence
along the c-axis drastically changes as AAA'A'A' for 1/5,
AAAA'A'A' for 1/6, AAA'A'A'AAAA'A'A'AAAA'A'A' for
3/17 and so on.
The observed qc sequence is well understood by the"Devil's Staircase" type sequence theoretically obtained
from the Axial Next Nearest Neighbor Ising (ANNNI)
model proposed by Bak & von Boehm[1]. Fig. 3 shows the
T versus -J2/J1 phase diagram very well known as "Devil's
Flower". The green arrow corresponds to the scanning pathof Fig. 2, i.e. temperature variation at a fixed pressure 0.92
GPa. We observed the other types of qc sequences in a wide
temperature and pressure range and finally confirmed thatthe "Devil's Flower" is perfectly reproduced in NaV2O5 [2]under high pressure. A microscopic mechanism of the competitive inter-layer interaction resulting in such a phase diagram is a keen subject to further study.
References[1] P. Bak et al. Phys. Rev. B 21, 5297 (1980)[2] K. Ohwada et al. Phys. Rev. Lett. 87, 086402 (2001).
[3] H. Sawa et al. J. Phys. Soc. Jpn. 71, 385 (2001).
[4] Y. Katsuki, Master Thesis (Graduate School of Science, The
University of Tokyo, Mar. 2002); Y. Fujii et al. in preparation.
[5] K. Ohwada et al. private communication.

Authors

K. Ohwada*, Y. Katsuki**, Y. Fujii, M. Isobe, Y. Ueda, H. Nakaoa, Y.
Murakamia, E. Ninomiyab, and H. Sawac*Present address: JAERI/SPring-8. **Present address: Accenture Co.
Ltd. aTohoku University, bChiba University, cKEK-PF

Vanadium element has also carried many metallic oxides;
nevertheless superconductivity has never been found in
vanadium oxides. Many metallic vanadium oxides show
metal-insulator (M-I) transitions as a function of temperature and the ground states of them are magnetic insulators.
The quasi-one-dimensional conductor β-Na0.33V2O5
with a mixed-valence of V4+/V5+ = 1/5 exhibits a M-I transition of a charge ordering type at TCO = 135K and thecharge-ordered structure undergoes an antiferromagnetictransition at TN = 25 K. This M-I transition (charge ordertransition) is suppressed by hydrostatic pressure and thesuperconducting phase with TSC = 9 K appears around
P=8GPa where the charge ordered phase collapses. This is
the first observation of superconductivity in vanadiumoxides and also the first observation of a phase transition
from charge ordered phase to superconducting phase.
Competition of ground states in many-body electron system is a central problem in condensed matter physics. It is
described as a phase diagram in the thermodynamic parameters space such as temperature vs. pressure or magnetic
field. Several exotic phase diagrams including superconducting phases have been observed in various compounds
such as inter 4f/5f metallic alloys, organic conductors andhigh-Tc superconducting cuprates. The obtained phase diagram (Figure 1) is independent of those phase diagrams.
The superconducting phase is adjacent to the charge orderedphase in β-Na0.33V2O5, while it is adjoined the magnetic
ordered phases in the inter 4f/5f metallic alloys and organic
conductors. This suggests an important role of charge fluctuation for the superconductivity in β-Na0.33V2O5.
Principal publication and authors

Discovery of Missing Link:
I. A Superconducting Vanadate
β -Na0.33V2O5
Y. UedaSince the discovery of high-TC superconducting
cuprates, the superconductivity has drawn much interest as
the ground state of strongly correlated electron systems.

T. Yamauchi, Y. Ueda and N. Môri, PRL 89 057003 (2002).

First-order Transition at the Upper
Critical Field in the Heavy Electron
Superconductor CeCoIn5
T. Sakakibara
The tetragonal heavy electron compound CeCoIn5
becomes superconducting at Tc = 2.3 K. Various experimen-

Fig.1. Pressure-temperature (P-T) phase diagram of β-Na0.33V2O5.
With increasing pressure the charge ordering temperature (TCO)
decreases and the Néel temperature (TN) increases, and beyond P = 7
GPa the superconducting phase (SC) appears. This is the first observation of superconductivity in vanadium oxides. The superconducting
transition temperature (TSC) decreases with further increase of pressure and finally the superconducting phase disappears above P = 9
GPa. In β-Na0.33V2O5 the superconducting phase competes with the
charge ordered phase, which suggests an important role of charge
fluctuation for the superconductivity.

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ISSP Activity Report A 2001

Fig.1. Magnetization curves of CeCoIn5 measured at T = 50 mK, withmagnetic field applied parallel to the tetragonal a and c axes. The
sharp jump of the magnetization shows the Hc2 transition is of firstorder. The inset shows the magnetization behavior near Hc2 (H//a) inan expanded scale, revealing a small hysteresis in the transition field.

References[1] K. Izawa et al., Phys. Rev. Lett. 87 057002 (2001) .
[2] T. Tayama et al., Phys. Rev. B 65 180504(R) (2002) .
[3] G. Sarma, J. Phys. Chem. Solids 24 1029 (1963) .

Authors

T. Tayama, A. Harita, T. Sakakibara, Y. Hagaa, H. Shishidob, R.
Settaib, and Y. OnukibaAdvanced Science Research Center, Japan Atomic Energy ResearchInstitute,Tokai, Ibaraki 319-1195.
bGraduate School of Science, Osaka University, Toyonaka, Osaka,
560-0043.

Giant Negative Magnetoresistanceπ Interaction
Originating from the d-π
in a Molecule
H. TajimaFig. 2. Phase diagrams of CeCoIn5 under magnetic field parallel tothe a and c axes. Open circles are the first-order Hc2 transition points
where the magnetization shows a discontinuous jump, whereas thesolid squares are the second-order one.

tal studies indicate that the electron pairing is even parity(spin singlet) with kx2-ky2 gap symmetry[1]. Due to its large
Pauli paramagnetic susceptibility in the normal state,
CeCoIn5 provides an interesting situation where the paramagnetic energy becomes a substantial fraction of the superconducting condensation energy at high fields and may
affect the upper critical field Hc2 at low temperatures. We
have examined the superconducting phase diagram of a single crystal of CeCoIn5 (6.9 mg weight) by means of a lowtemperature DC magnetization measurement using a dilution refrigerator [2].
Figure 1 shows the magnetization curves obtained at thebase temperature of 50 mK with slowly varying magnetic
field applied parallel to the tetragonal a and c axes. The
arrows indicate the direction of the field sweep. Very interestingly, the magnetization exhibits a discontinuous jump at
Hc2 for both field directions. This behavior is in striking
contrast to the case of ordinary type-II superconductors inwhich the magnetization continuously recovers the normal
state value at Hc2. Our results suggest that the Hc2 transitionin CeCoIn5 is of first-order at low temperature. In fact, asmall but distinct hysteresis is observed in the transition
field (the inset of Fig.1).
We carried out the measurements at various temperatures. When the temperature was raised, the magnetization
jump at Hc2 became smaller and eventually vanished ataround 0.7 K for both field directions. Figure 2 shows theresulting Hc2(T) phase diagrams of CeCoIn5. Open circles
indicate the transition points which are considered to be offirst order, whereas the solid squares denote the second
order ones where the magnetization change is continuous.
Thus, a critical point separating the first-order and the second-order transition lines seems to exist at T ~ 0.3 Tc forboth field directions.
Although the origin of the first-order Hc2 transition in
CeCoIn5 is not very clear at present, a promising mechanism
will be the Pauli paramagnetic effect which comes from thedifference in spin susceptibility between superconducting
and normal states. The transition field to the normal state issuppressed at low temperature and may become of firstorder, provided that the spin paramagnetism is strong
enough [3]. CeCoIn5 might be the first system that exhibits astrong Pauli paramagnetic limiting of the upper critical field.

A search for a new function based on the interplay
between local magnetic moments and conduction electrons
is a current topic in the field of molecular conductors. Mostof research works concern charge-transfer complexes composed of inorganic anions having local magnetic moments
and molecular donors affording π- conduction electrons.
The key to synthesize such compounds is the strength of thed-π interaction (the interaction between local magnetic
moments and π- conduction electrons). In the case of thecharge-transfer complexes above mentioned, however, thisstrength is determined by the crystal structure whose design
is still beyond control. One of the ways to solve this problem is to synthesize charge transfer complexes by using themolecules, where the strong d-π interaction is self-contained. In this context, we have studied a new series ofcharge-transfer salts composed of the axial-substituted
phthalocyanine (Pc), [FeIII(Pc)(CN)2]-, in which the strongd-π interaction is self-contained. (See Fig. 1).
Figure 2 shows the temperature dependence of the resistivity for TPP[FeIII(Pc)(CN)2]2 under the magnetic fields of
18 T and 0T [1, 2]. As can be seen from the figure, the resistivity drastically decreases under the applied magnetic field.
The negative magnetoresistance in this salt is highly
anisotropic for the magnetic-field orientation. This field-orientation dependence is consistent with that in the magnetic
susceptibility. The Curie constant for B//a is more than 5-10

Fig. 1. Molecular structure of [FeIII (Pc)(CN)2]-. In this molecule, delectrons in FeIII are the source of the local magnetic moment(S=1/2), and the π-electrons in the phthalocyanine (Pc) ring form theconduction band. The close contact between d- and π-orbitals gives
rise to the strong d-π interaction inside the molecule.

ISSP Activity Report A 2001

7

Fig. 2. Temperature dependence of the electrical resistivity under themagnetic field applied parallel to the c-and a-axis. The field-orientation dependence of the negative magnetoresistance is qualitatively
consistent with the g-factor anisotropy in [FeIII(Pc)(CN)2]- unit.

times larger than that for B//c. Recently we determined theg-tensor of [FeIII(Pc)(CN)2]- using a model compound{(C6H5)3P}2N[FeIII(Pc)(CN)2]. (No ESR signal wasobserved for TPP[FeIII(Pc)(CN)2]2.) The g-factors are g1 =3.6, g2 = 1.1 and g3 = 0.5, where g1 denotes the g-factor forthe static magnetic field approximately perpendicular to the
Pc-ring, and g2 and g3 denote the two g-factors for the fieldapproximately parallel to the Pc-ring [3]. Such large
anisotropy in the g-factors is consistent with the field-orientation dependence of the giant negative magnetoresistance(and magnetic susceptibility) [4]. This strongly supports that
the
giant
negativemagnetoresistancein
TPP[FeIII(Pc)(CN)2]2 essentially originates from the d-πinteraction in the [FeIII(Pc)(CN)2] unit. In addition to
TPP[FeIII(Pc)(CN)2]2, we found the anisotropic giant negative magnetoresistance in PTMAx[FeIII(Pc)(CN)2]·y(MeCN)[5] and PXX[FeIII(Pc)(CN)2]. Both compounds contain[FeIII(Pc)(CN)2] unit.
References[1] M. Matsuda, T. Naito, T. Inabe, N. Hanasaki, H. Tajima, T.
Otsuka, K. Awaga, B. Narymbetov, and H. Kobayashi, J. Mater.
Chem. 10, 631 - 636 (2000).
[2] N. Hanasaki, H. Tajima, M. Matsuda, T. Naito, T. Inabe, Phys.
Rev. B 62, 5839 - 5842 (2000).
[3] N. Hanasaki, M. Matsuda, H. Tajima, T. Naito, T. Inabe, Synth.
Met., in press.
[4] H. Tajima, N. Hanasaki, M. Matsuda, F. Sakai, T. Naito, T. Inabe,
J. Solid State Chem., in press.
[5] M. Matsuda, T. Naito, T. Inabe, N. Hanasaki, H. Tajima, J. Mater.
Chem. 11, 2493 - 2497 (2001)

Fig. 1. Crystal structure of β'-ET3(ZnCl42-)2-x(GaCl41-)x [x=0.66].
The donor layer (ET1-0.5x) and the anion hybrid layer [ET2+ and(GaCl41-, ZnCl42-)] stack alternately along the b-axis. The crystal
structure analysis suggests that the carrier doping is performed mainly in the donor layer.

[x = 0.0, 0.05, 0.06] have been obtained. The resistivity atroom temperature decreases from 3 ohm cm (x = 0.0) to 0.1(x = 0.06) by doping to the antiferromagnet with an effective half-filled band (x = 0.0). (b) Another 2:1 (donor :anion) salt, δ'-ET2(GaCl4-) which is a spin gap material, hasbeen doped like δ'-ET2(GaCl4-)1-x(MCl42-)x [x = 0.05,
0.14]. The resistivity is lowered from 10 ohm cm (x = 0.0)
to 0.3 (x = 0.14). For both 2:1 salts, the semiconducting
behaviors have transferred to relatively conductive semiconducting ones by doping. (c) As for a-type 3:1 salts, the parent material is in the charge ordering state like α (ET+ET+ET0)(CoCl42-)(TCE), where the charge-ordereddonors are dispersed in the two-dimensional conducting
layer. Although the calculation of α-ET3(CoCl42-)(TCE)shows a band insulating nature, and the crystal structure
analysis indicates that this material is in a charge-ordering
state, the metallic behavior down to 165 K has been
observed. With doping (GaCl4-) to the a-system, isostructural α-ET3(CoCl42-)1-x(GaCl4-)x(TCE) [x = 0.54, 0.57, 0.62]
have been afforded, where the pattern of the horizontal
stripe-type charge ordering changes with an increase of x.

Authors

H. Tajima, N. Hanasaki, M. Matsuda, T. Naitoa, T. Inabea
of Chemistry, Graduate School of Science, Hokkaido
University

aDivision

First Systematic Band Filling Control
in Organic Conductors
H. Mori
The systematic study of band filling control for fourkinds of organic conductors with various kinds of groundstates has been succeeded. (a) By partial substitution of(GaCl4-) by (MCl42-) [M = Co, Zn] in the anion blocking
layer of λ-ET2(GaCl4-) [ET = bis(ethylenedithio)tetrathiafulvalene] [1], single crystals of λ-ET2(GaCl4-)1-x(MCl42-)x

8

ISSP Activity Report A 2001

Fig. 2. Doping and pressure effect of β'-ET3(ZnCl4)2. The carrier
doping makes the resistivity at room temperature decrease rapidly,
whereas the physical pressure reduces the resistivity increase at low
temperatures. As a result, the doping system (x = 0.58) transforms
from the semiconducting to the metallic one down to 90 K, and theresistivity for β'-ET3(ZnCl4)2 under 12.6 kbar is almost constantdown to low temperature.

(d) By doping (GaCl4-) to β'-ET3(ZnCl42-)2 with 1/2- filledband [2], the obtained β'-ET3(ZnCl42-)2-x(GaCl4-)x [x =0.58] shows the metallic behavior down to 90 K. These systematic studies of band filling control suggest that the doping to 1/2-filled band is most effective.
References[1] H. Mori, T. Okano, M. Kamiya, M. Haemori, H. Suzuki,
S. Tanaka, Y. Nishio, K. Kajita, and H. Moriyama, Physica C, 357360, 103(2001).
[2] R. P. Shibaeva, R. M. Lobkovskaya, V. E. Korotkov, N. D.
Kuahxh, E. B. Yagubskii, M. K. Makova, Synth. Metals, 27,
A457(1988).

Principal Publication and Authors

H.Mori, M. Kamiyaa,b, M. Haemoria,b, H.Suzukia,b, S. Tanakaa,
Y.Nishiob, K.Kajitab, and H. Moriyamab
J. Am. Chem. Soc., 124, 1251-1260(2002).
aISTEC, bUniversity of Toho

Theory of the Verwey Transition in
Magnetite Fe3O4
H . Fukuyama
The transition metal oxide Fe3O4, called the magnetite,
is a magnet that the human being has known from the earlydays. A modern scientific interest of this compound lies in
the metal-insulator transition called the Verwey transition.
Verwey has discovered this transition in 1939 [1], as a sudden jump in the resistivity at 120 K. In spite of numerous
experimental as well as theoretical studies after the discov-ery, its origin remains to be clarified. The scenario of thecharge ordering among the Fe ions at the B-sites, from astate with an average valence of +2.5 in the metallic state toan ordered state of +2 and +3 in the insulating state, hasbeen believed as a most probable candidate, but its spatial
pattern has not been uniquely identified up to now. Such acharge ordering phenomena attract interest in general, since
they appear in many other systems, not only in the transition
metal oxides, but also in organic conductors, rare earth compounds, and even in quantum hall systems.
Recently, several experimental groups [2] have claimed
that the charge ordering does not actually exist in the insulating state of magnetite. Motivated by these studies, wehave proposed a mechanism of the Verwey transition inmagnetite other than charge ordering based on the studies on
the effects of the orbital degrees of freedom in the d-electrons of Fe ions, which has been recognized to play animportant role in the presence of the strong Coulomb interaction, i.e., in the strongly correlated electron systems.
The Verwey transition is associated with the Fe ions at
the so-called B sites of the spinel structure, shown in Fig. 1(a). Their average valence of +2.5 at room temperature corresponds to half electron per site. We have investigated a 3band spinless fermion model, which is known as a valid
effective model for the Verwey transition in magnetite, since
the spins are fully polarized ferromagnetically in the B sites
due to the ferrimagnetic Neel order below 800 K. There, theelectrons enter in the t2g orbital which is triply degenerate
due to the octahedral surrounding of the oxygen ions. In thiscase a charge ordereng can be realized due to the strong
inter-orbital Coulomb interaction. It is important to note that
this orbital order results in an effectively one-dimensional
electronic structure as shown in Fig. 1 (b), characteristic of
the spinel structure.
Such one-dimensionality of the electronic state is known
to possibly result in the Peierls transition triggered by theelectron-phonon interaction. The detailed studies show that
it is actually possible, even in the three-dimensional structure of magnetite, if one considers the orbital degree of freedom. The lattice distortion accompanying this Peierls transition is schematically shown in Fig. 1 (c), where one can seethat pairs of B sites are formed, which we call “bond dimerization”. Then the system becomes insulating without any
charge ordering. This scenario is consistent with the existing
experimental results and may give the solution to the “mystery” of the Verwey transition in magnetite.
References[1] E. J. W. Verwey, Nature (London) 144, 327 (1939).
[2] P. Novak, H. Stepankova, J. Englich, J. Kohout, and V. A. M.
Brabers, Phys. Rev. B 61, 1256 (2000); J. Garcia, G. Subias, M. G.
Proietti, J. Blasco, H. Renevier, J. L. Hodeau, and Y. Joly, Phys. Rev.
B 63, 054110 (2000); S. Todo, N. Takeshita, T. Kanehara, T. Mori and
N. Môri, J. Appl. Phys. 89, 7347 (2001).

Principle Publication and Authors

H. Seoa, M. Ogatab, and H. Fukuyama: Aspects of the Verwey transition in magnetite: Phys. Rev. B 65, 085107 (2002).
aCERC, AIST Tsukuba, bDepartment of Physics, University of Tokyo

Fig. 1. Orbital order and lattice distortion proposed to be realized inmagnetite Fe3O4. The spinel structure is shown in (a), where the Asite Fe ions, the B site Fe ions, and the oxygen ions are represented
by red, blue and white spheres, respectively. The ferro-type orbital
order (b) and the bond dimerization (c), which we propose to be theorigin of the insulating behavior in magnetite, is shown schematicallyin sectional views of the planes 1 ~ 4 shown in (a).

Interference Effect in Magnetic
Circular Dichroism of Resonant X-Ray
Emission Spectroscopy
A. Kotani
Resonant X-ray emission spectroscopy (RXES) has

ISSP Activity Report A 2001

9

Fig. 1. Geometrical alignment of MCD in RXES is shown in the scattering plane. The θ1 (θ2) denotes the angle between the direction ofincident (emitted) X-ray and that of the magnetization M. The MCD
in RXES is a difference of RXES spectra for incident photons with +and – helicities, where the helicity of the emitted photon is not detected.

recently been a subject of remarkable progress due to theadvent of high-brilliance synchrotron radiation sources.
RXES is a photon-in and photon-out process, which is represented theoretically by a coherent second-order opticalformula. [1]. The formula includes, in general, both real andvirtual processes. In the real process, RXES consists of two
successive processes, X-ray absorption from a ground state
to a core-excited state and X-ray emission from this intermediate state to a final state. In the virtual process, on the other
hand, two channels from the ground state to the final state
via different intermediate states interfere each other, so that
this is called interference process. Until very recently, therole of the interference process in RXES was not wellunderstood, but very recently we have revealed theoreticallythat the interference process plays an essential role in magnetic circular dichroism (MCD) of RXES in a special geometry for ferromagnetic materials [2], and this finding has
been confirmed by experimental observations [2].
Let us consider the situation shown in Figure 1. The
magnetization of a thin-film is parallel to the sample surface
and the angle between the incident X-ray (emitted X-ray)and the magnetization is θ1 (θ2) . The MCD in RXES
(referred to as MCD-RXES) is defined by the difference of
RXES spectra for incident photons with + and - helicities,
where the helicity of the emitted photon is not analyzed.

Within the atomic model, we have calculated the dependence of MCD-RXES on θ1 and θ2 . By group theoreticalconsideration, we have obtained a quite general analytic
expression, and the result shows the following remarkablefacts: The intensity of the real process is proportional to cos
θ1, while that of the interference process to sinθ1.
Therefore, when the incident X-ray direction is parallel tothe magnetization (denoted by the longitudinal geometry),
we have the 100 % real process contribution to MCD-RXES
spectrum, while for the incident X-ray perpendicular to themagnetization (denoted by the transverse geometry) we havethe 100 % interference process contribution. This result issurprising, because the interference effect in RXES is often
considered to be negligibly small. Another remarkable pointof the calculated result is that theθ2 dependence of MCDRXES intensity in the transverse geometry is proportional tosin 2θ2.
Experimental observations of MCD-RXES spectra forlongitudinal and transverse geometries have been made by
Iwazumi et al. for the Gd 2p3/2-5d excitation and the
3d-2p3/2 de-excitation of ferromagnetic Gd-Co amorphousalloy. The observed results are in good agreement with thecalculated ones both in the spectral shape and the spectral
intensity ratio in the longitudinal and transverse geometries.
Furthermore, the θ2 dependence of MCD-RXES spectra in
the transverse geometry has also been measured and compared with the calculated result. The result is shown in
Figure 2, where A(●) , B(+) and C(○) are intensities of a
MCD-RXES peak by the 3d3/2-2p3/2 transition, and of two
MCD-RXES peaks by the 3d5/2-2p3/2 transition, respectively, and they are displayed as a function of the angleθ2. The
theoretical result (sin 2θ2) is also shown with the solid
curves, and is found to be in reasonable agreement with theexperimental result. This is the evidence that almost pureinterference process has been observed in MCD-RXES
experiments in the transverse geometry.
We would like to thank Dr. Iwazumi and his collaborators for their fine experiments.
References[1] A. Kotani and S. Shin, Rev. Mod. Phys. 73, 203 (2001).
[2] K. Fukui, H. Ogasawara, A. Kotani, T. Iwazumi, H. Shoji and T.
Nakamura, J. Phys. Soc. Jpn. 70, 3457 (2001).

Authors

A. Kotani, H. Ogasawara and K. Fukuia
aRIKEN/SPring-8

Lifting of Degeneracy of the Spin-1
Pyrochlore Antiferromagnets
K. UedaFig. 2. Experimental result ofθ2 dependence of MCD-RXES in thetransverse geometry for three different emitted photon energies A(closed circle), B (cross) and C (open circle). The solid curves are thecalculated ones.

10

ISSP Activity Report A 2001

Since the pioneering work by Anderson [1] on the classical spin system with a disordered ground state, geometrically frustrated spin systems have been a fascinating subject.
The pyrochlore lattice which is the network of the cornersharing tetrahedrons (see Fig.1) is the typical three dimensional frustrated system. This structure is found in a numberof compounds including spinels, pyrochlores and C15-type
Laves phase. For the spin-1/2 antiferromagnetic Heisenberg
model, the quantum spin-liquid ground state is proposed
based on the series expansion [2], but concerning the lowlying spin-singlet states below the spin gap a consistent picture has not emerged yet.
For spin-1 Heisenberg antiferromagnets, in contrast toFig.1. The primitive cell of the pyrochlore lattice (left panel) and its
projected view from the origin to [111] direction (right).

the spin-1/2 cases, numerical methods are not powerfulenough to draw definitive results and we need some analytic
approach to solve the problem. Recently we proposed theidea of the tetrahedron-unit decomposition of the pyrochlore
lattice [3], which is a natural generalization of the valencebond-solid(VBS) state approach developed for the onedimensional spin-1 antiferromagnets [4]. In this approach
the ground states of the fundamental unit are the tetrahedronspin singlets which form the two-dimensional E representation of the tetrahedral group (Td). Because of this degeneracy, the constructed variational wave functions for the groundstate manifold have a macroscopic degeneracy.
Therefore, for the physics of the spin-1 pyrochlore antiferromagnets, it is essential to understand how the degeneracy is lifted. In principle, this degeneracy may be lifted within the model itself without introducing additional couplings.
However, physically relevant ways of lifting may be throughthe couplings with other degrees of freedom. One plausible
scenario is through the coupling with the local lattice distortion belonging to the same irreducible representation E:
spin-driven Jahn-teller effect [3]. Actually the structuraltransition observed in some spinel compounds is consistent
with this picture. Another relevant coupling may be theinteractions between the tetrahedrons next to each other. For
this case, the effective interaction can be mapped to aneffective Hamiltonian of XY model, leading to a parity-broken ground state.
References[1] P.W. Anderson: Phys. Rev. 102, 1008 (1956).
[2] B. Canals and C. Lacroix: Phys. Rev. B 61, 1149 (2000).
[3] Y. Yamashita and K. Ueda: Phys. Rev. Lett. 85, 4960 (2000).
[4] I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki: Phys. Rev. Lett.
59, 799 (1987).
[5]Y. Yamashita, K. Ueda, and M. Sigrist: J. Phys.:Condens. Matter
13, L691 (2001).

Authors

Y. Yamashita, K. Ueda and M. SigristaaTheoretische Physik, ETH Zurich (Switzerland)

Quantum Melting of Charge and Spin
OrdersM. Imada
Regular alignments of charge and/or spin densities ofelectrons are universally observable phenomena in electronic systems. These include charge (spin) density waves,charge orders including stripes, and antiferromagnetic (spiral) orders. A common feature in these phenomena is spontaneous breaking of the translational symmetry, where theFig. 1. Solid-liquid phase boundary in plane of the filling n = 1/l withinteger l and electron gas parameter rs defined by the ratio of electronmean distance and the Bohr radius. The square indicates the Wignertransition point in the continuum limit. The path-integral renormalization group results (filled and open red circles for spinless and spin1/2 fermions, respectively) are compared with the Hartree-Fockresults (purple crosses for spinless and green triangles for spin-1/2
electrons). The red solid curves are guides for the eye. The dottedcurves show contour lines for the ratio of the dielectric constant andthe effective mass scaled by the bare values being at 1, 2, 3, 4 and 5
from up to down. The inset enlarges small rs region. When the electron filling is changed with condition n = 1/l, and with fixed ratio ofthe dielectric constant and the effective mass, the system follows acontour line. With increasing l, the system undergoes a phase transition from a charge ordered insulator to a metal when crossing the red
curve. Namely, the charge order undergoes a quantum melting when
the fractional number of the commensurability becomes complicated.
The Hartree-Fock calculation does not reproduce this trend of thequantum melting.

main origin of the periodicity formation is in many cases
ascribed to electron-electron Coulomb interaction. In particular, the periodic alignment of charge and spin becomesremarkably stable if the electron concentration satisfies“commensurability condition”, where the electron filling, n(namely, the number of conduction electrons in a unit cell)
is a simple fractional number or integer. The Mott insulator
is the most conspicuous example of such commensurate
insulators, where the filling is an odd integer. Other many
examples are found in charge orders of transition metalcompounds and organic systems, where the filling is a simple fractional number such as 1/2 and 2/3. It is known thatvarious dramatic and unsolved phenomena such as cupratehigh-Tc superconductivity and colossal magnetoresistance inmanganese oxides are observed closed to and under theproximity of such commensurate orders. For clarification of
the mechanisms of such dramatic phenomena, it clearlyrequires elucidating mechanisms of commensurate insulator
formation and its quantum melting. However, the stability ofspin/charge orders only at some simple commensurate fillings is not well understood, which also means that theprocess of the quantum melting of these orders remains an
open question.
We have studied the physics of quantum melting transitions of charge and spins. It has turned out that these transitions can indeed be successfully described only when taking
account full quantum mechanical fluctuations beyond themean-field level. For this purpose, we have developed new
numerical as well as analytical tools, since the available
tools have various types of difficulties in attacking them.
The minus sign problem is known to be one of such difficulties, because of which, for example, most of numericalmethods are not feasible for analysis of geometrically frustrated systems. The effects of frustrations have crucial
importance in clarifying the quantum meltings as we see
below. We have developed the path-integral renormalization

ISSP Activity Report A 2001

11

Fig.2. Phase diagram of the Hubbard model at half filling in the planeof the onsite Coulomb interaction scaled by the electron transfer U/t
and the degree of the frustration t'/t for two choices of different lattice
structures, namely the square lattice with next-nearest neighbor transfer (top panel) and anisotropic triangular lattice (bottom panel).
AFI,NMI and PM represent AF insulator, nonmagnetic insulator, andparamagnetic metal, respectively. Green dashed curve in the upper
panel shows the Hartree-Fock results for the metal-insulator phaseboundary[8].

group method for numerical calculations [1,2] and the correlator projection method [3,4] for analytic treatments andhave overcome the difficulties. In the path-integral renormalization group calculations, metal-insulator transitions,magnetic transitions and other possibilities of transitions arecarefully examined with finite size scalings and extrapolations to the thermodynamic limit. With the newly developed
tools, we have obtained the following remarkable insight.
(1) The charge order is indeed stabilized only at commensurate fillings with some simple fractions such as 1, 1/2,
1/3, 2/3, …, while quantum fluctuations destroy the ordering
at other fillings [5]. For example, at n = 1/4, the chargeorder is stable at two-orders of magnitude larger electron
density than the quantum melting point of the Wigner crystal in a 2D electron system in the continuum space (Figure1). When the fraction k/l (with k and l being irreducible
integers) becomes complicated with large l, the charge order
quantum mechanically melts depending on the ratio of theeffective mass and the dielectric constant. The Hartree-Fockcalculation fails in accounting for such quantum melting andmore elaborate calculations such as our method are crucial.
Although the band theory predicts a simple distinction
between metals and insulators, the real structure with longrange Coulomb interaction becomes much richer and more
complicated than the band theory, because the simple metala la the band theory actually has a rich and complex hierarchy structure with commensurate insulator phases contained.
(2) The spin orders in commensurate charge orderedstate melt quantum mechanically when the geometrical frustration effects get large [6,7]. Quantum spin liquid phasethen appears in a wide area adjacent to the metal-insulatortransition and sandwiched by the metal and the antiferromagnetic insulator phases (Figure 2). In this spin liquid
insulator phase, none of translational symmetry breakings
such as dimer, and (staggered) flux state are stabilized and it
is likely that the phase is not adiabatically continued to theband insulator.
(3) The order of metal-insulator transitions becomesfrom the first order to continuous when the geometrical frus-

12

ISSP Activity Report A 2001

tration effects get large. This may be accounted for by the
reduction of the spin correlations in the spin liquid phase.
The reduction makes the interactions among the sites ofholes and doubly occupied electrons (doublon) relatively
small. This suppresses the phase segregation into the phasewith rich doublons and holes, namely the liquid, and thephase with fewer doublons and holes, insulator. When themetal-insulator transition is the first-order type at zero temperature, it accompanies a first-order boundary line at finite
temperature. This line starts at zero-temperature transition
point and ends at a second-order critical point at a nonzero
temperature. When the first-order transition is transformed
to a continuous one at zero temperature, the accompanied
first-order transition line at finite temperatures shrinks andits critical end point merges to zero temperature. Since thecompressibility generally diverges at the critical end point,
this causes the divergence of the compressibility at the zerotemperature metal-insulator transition point. Then the metalinsulator transition at zero temperature bears a marginal
character between the first-order and continuous, since thecompressibility divergence is the signal of the phase separation and the emergence of the first-order transition.
(4) Because of the compressibility divergence, the marginal character of the continuous metal-insulator transition
alters the nature of the quantum critical phenomena (QCP)
from the usual QCP expected with simple scaling laws to amore drastic one with structural formation, and self-organization, which is typical in complex systems. The divergenceof the compressibility necessarily triggers the differentiationof electrons in the momentum space at the marginal point
between localization and itinerancy. This yields sensitivity
to external perturbations and serious competitions among
instabilities to various orders such as superconductivity,
charge/spin orders and ferromagnetism. Then these drastic
effects now eventually accounts for the underlying physics
of the high-Tc superconductivity and colossal magnetoresistance. This underlying physics is summarized by the emergence of extreme sensitivity of the systems to tiny perturbations such as magnetic fields and pressure as exemplified in
the response in the colossal magnetoresistance. The sameunderlying physics generates coexisting instability to various orders as superconductivity and charge orders as wellknown in the high-Tc cuprates.
References[1] M. Imada and T. Kashima: J. Phys. Soc. Jpn. 69 2723-2726 (2000).
[2] T. Kashima and M. Imada: J. Phys. Soc. Jpn. 70 2287-2299 (2001).
[3] S. Onoda and M. Imada: J. Phys. Soc. Jpn. 70 632-635 (2001).
[4] S. Onoda and M. Imada: J. Phys. Soc. Jpn. 70 3398-3418 (2001).
[5] Y. Noda and M. Imada: preprint (cond-mat/0203024).
[6] T. Kashima and M. Imada: J. Phys. Soc. Jpn. 70 3052-3067 (2001).
[7] H. Morita, S. Watanabe and M. Imada: preprint (condmat/
0203020,J.Phys. Soc. Jpn. 71 NO9).
[8] W. Hofstetter and D. Vollhardt: Ann. Physik, 7 48 (1998).

AuthorM. ImadaΓ Method for the Self-Energy of a
GWΓ
Many-Electron System
Y. TakadaIn the last two decades, we have witnessed the power ofquantum Monte Carlo (QMC) simulations that allow us toobtain virtually exact information on the static properties
associated with the ground-state wave function of a quantum

many-body system. However, QMC cannot be used to evaluate dynamical properties, because dynamics requires information on excited-state wave functions as well. Thus weneed to develop an alternative algorithm for dynamics.
Four decades ago, Baym and Kadanoff proposed a conserving approximation scheme by formulating the dynamical problem in terms of an energy functional Φ[G] with G
the full Green's function. The self-energy Σ is obtained by
Σ=δΦ[G] /δG. One can choose Φ[G] at one’s disposal.
Although it is found to be very useful in many cases, thisscheme never provides the exact Σ, because no algorithm isknown to give exact Φ[G].
In 1995, I developed a conceptually new scheme toobtain the exact Σ, named the self-energy revision operator
theory [1]; instead of pursuing Φ[G], I paid attention to theexact functional relations between Σ and the vertex function Γ, obeying the microscopic conservation law. In particular, Γ is determined through the Bethe-Salpeter equation with an irreducible electron-hole interaction given by
the functional derivative, δΣ/δΓ. Starting from an arbitrary input, both Σ and Γ are iteratively revised towards
self-consistency through the functional relations. Note thatthe number of terms representing Σ generated in this iterative process rapidly increases, eventually covering all terms
derivable from the exact Φ[G] when the self-consistency isachieved.
In a numerical algorithm, however, the functional differentiation δΣ/δΓ is not feasible, prompting me to invent
an alternative scheme to revise G on a computer in an accurate and efficient way. Recently such a scheme is provided,
giving an accurate enough result for Σ, in which the Wardidentity is satisfied automatically [2,3]. This method allows
us to obtain accurate results for the dynamical quantities,
promising us to open a new dimension to the quantum
many-body problems.
My calculation scheme is schematically shown in Figure
1, which indicates that this method may be regarded as anextension of the Hedin’s GW method by including Γ that isdetermined self-consistently with Σ. Thus it is named the
GWΓ method.
As an illustration, my method is implemented in thehomogeneous electron gas at the density parameter rs = 4
corresponding to sodium. The obtained single-electron spectral function A(p,ω) (which is given by –ImG(p,ω)/π) is
shown in Figure 2. The main peak represents the structure ofa quasiparticle. Its width is very sharp at and near the Fermi
surface [Case (a)], indicating the existence of a well-definedquasiparticle. However, it is very broad far away from theFermi surface [Case (b)]. In fact, its tail connects continuously with the plasmon-side band or the plasmaron (an enti-

Fig 1. Schematic representation of my self-consistent calculation
scheme for the self-energy Σ, where V is the bare Coulomb interaction, G(0) is the bare Green’s function, π is the polarization function,and fxc is the exchange-correlation kernel appearing in the timedependent density functional theory.

Fig 2. A(p,ω) for the homogeneous electron gas at the sodium density (a) at the Fermi surface (p = pF) and (b) at the band bottom (p = 0).

ty composed of the real plasmon and the quasiparticle),
implying a strongly decaying nature of the quasiparticle.
Note that without Γ satisfying the Ward identity or the
microscopic conservation law, this plasmaron peak does notcome to the right energy position.
My result of A(p,ω) discloses the intriguing complexityof the single-electron spectral function even in such a simple
system as the electron gas, urging us to make a moredetailed analysis of the experimental data obtained by angleresolved photoemission spectroscopy (ARPES) in various
materials widely ranging from simple to transition metals.
References[1] Y. Takada, Phys. Rev. B 52, 12708 (1995).
[2] Y. Takada, Int. J. Mod. Phys. B 15, 2595 (2001).
[3] Y. Takada, Phys. Rev. Lett. 87, 226402 (2001).

AuthorY. TakadaSpin-Triplet Superconductivity
in Quasi-One Dimension
M. Kohmoto
In recent years the signs for unconventional superconductivity in many compounds have been accumulated.
Examples include high superconductors, heavy fermions,organic conductors, Sr2RuO4, etc. The common features of
those compounds are quasi-low dimensionality and proximity of antiferromagnetic (AF) order.
Here we consider seemingly the simplest quasi-onedimensional systems which are realized in (TMTSF)2X family where X = PF6, AsF6, SbF6, ClO4, etc. (Bechgaard salts).
At ambient pressure, most of these extremely anisotropic
compounds undergo metal-insulator transition at low temperature and have a spin-density-wave(SDW) fundamental
state. Under moderate pressure, the SDW instability is suppressed and replaced by a superconducting transition at a
critical temperature of order of 1 K [1]. (One exception tothis is (TMTSF)2ClO4 which is superconducting at ambientpressure.) Thus these compounds may be characterized bycompetition between superconducting and SDW groundstates [2].

ISSP Activity Report A 200113

For the interaction, we consider AF magnetic coupling
and weakly screened phonon-mediated interaction. In contrast to the previous works, we assume that the weakly
screened phonon-mediated interaction is the driving force ofsuperconductivity [3].
We also assume that AF fluctuation is not strong enough togive SDW gap. The spin-triplet superconductivity is possible because the Fermi surfaces are disconnected in quasione dimensional systems.
The weakly screened phonon-mediated interaction of
spin-triplet pairing has the same magnitude as that of spinsinglet one. In many systems, however, only the spin-singlet
superconductivity is realized. This is because the Fermi surfaces of usual matters are connected. In a system of connected Fermi surface, the requirement of parity and continuity
does not admit the constant spin-triplet gap. Therefore, thes-wave superconductivity is favored from the kinematic reason. The quasi-one-dimensional system we consider, however, has disconnected Fermi surfaces, so it admits constantspin-triplet gap. Therefore, there is no reason to prefer swave superconductivity. In the case of constant gap, theinteraction due to AF fluctuations act against the spin-singlet superconductivity more than the spin-triplet one, so thespin-triplet superconductivity is realized. This spin-triplet
gap is nodeless.
To calculate the transition temperature Tc, we apply the
BCS weak coupling theory. Since Tc of (TMTSF)2X israther low, one can expect that the strong coupling corrections do not change our results qualitatively. For the sake ofsimplicity, the cutoffs of the phonon-mediated interaction
and AF one are taken to be same and denoted byωD and thewidth of the peaks of these interactions are taken to be sameas Γ. The open Fermi surface is given by kx=±c .We
approximate the spin-singlet gap ψ by= constand the spin-triplet gap= const. If we denotethe density of states on the Fermi surface as
and thestrength of phonon interaction and AF interaction as f (0)and f (Q), the critical temperature of the spin-singlet superconductivity becomeswhere, and that of spin-triplet becomes

Quantum Hall Systems under Lateral
Modulation Potential
Y. IyeThe quantum Hall effect (QHE) system ---- two-dimensional electron gas (2DEG) subjected to a quantizing magnetic field ---- provides an experimental stage for ever fascinating physics. There are many different regimes of Landaulevel filling factor, ν, each of which involves characteristic
length scales. Therefore, by imposing an external modulation potential with periodicity close to such length scales,
one can perturb the QHE system in a non-trivial way, andhence extract useful piece of information, or even create
new states.We have studied magnetotransport in 2DEG subjected to a short period (a = 92 nm) one-dimensional modulation potential as shown in Fig.1.
Geometrical resonance of composite fermions
The concept of composite fermions (CFs), first advanced
by J.Jain and elaborated by many subsequent studies, one of
the most successful models to describe some aspects of thequantum Hall systems in a pictorial way. One of the unsettled issues is the spin state of CFs. As for the ν= 1/2 CFs, it
is established that they are fully spin polarized. For ν= 3/2,
however, the existing data are somewhat contradictory.
Figure 2 shows the magnetoresistance trace for a modulated 2DEG sample, in comparison with a plain 2DEG. The
former trace exhibits commensurability oscillation featuresnear ν= 3/2, which arise from geometrical resonance of CF
cyclotron radius with the modulation period. Detailed analyses of the positions of the resistance dips shown in Fig.3
indicate that the ν= 3/2 CFs are fully spin polarized.
Stripe phase in half-filled higher Landau levels
The fractional QHE and CF Fermi liquid behavior occur
in the lowest Laudau levels (LLs). In higher LLs, the electronic ground states are quite different. Recently, anisotropic
states are discovered at half-filled higher LLs in ultrahighquality 2DEG samples with mobility in excess of
1000m2/Vs. The anisotropic state is attributed to occurrence
Fig. 1. GaAs/AlGaAs 2DEG
sample with periodic potential modulation.

where=-f (0) + 3J (Q) .From the above equations, theconditionis always satisfied in the present case.
Thusand spin-triplet superconductivity is present
if=-f (0) + J (Q)<0. This result shows that this superconductivity disappears if AF fluctuations dominate. On theother hand spin-triplet superconductivity is realized if
phonon-mediated interaction dominates. Since
is an odd
function, the gaps at the open Fermi surfaces kx=±c have
opposite signs and there is no node in the gap.
References[1] For a review, see T. Ishigro, K. Yamaji and G. Saito, Organic
Superconductors (Spring-Verlag, Berlin) 1998.
[2] D. Jérome, A. Mazaud, M. Ribault and K. Bechgaard, J.
Phys.(Paris) Lett., 41 L95 (1980) .
[3] M. Kohmoto and M. Sato, Europhys. Lett., 56 (5), 726-740 (2001).

Principal Publication and Authors
M. Kohmoto and M. Sato

14

ISSP Activity Report A 2001

Fig.2. Magnetoresistance traces for a plain (red) and a modulated(black) 2DEG. The difference is most conspicuous around the filling
ν= 3/2.

Fig.3. Expanded view of the traces near ν= 3/2. The positions of theresistance dips are consistent with those predicted by assuming fully
spin polarized CFs.

Fig.4 Magnetoresistance traces obtained for different current directions in a modulated 2DEG over the range, 5 <ν< 14. The featuresindicated by arrows and circles correspond to stripe phase at half
filled higher Landau levels.

of stripe phase, or a kind of charge density wave state.
Although the mobility of our 2DEG samples is about
100 m2/Vs, similar features have been observed in modulated samples as shown in Fig.4. This finding suggests that the
stripe phase can be stabilized by external modulation potential of appropriate periodicity. We have found that such features at fillings as high as ν= 25/2, and also at ν= 7/2 and
5/2, for which the ground state of plain 2DEG is known tobe an even denominator FQHE.
References[1] A. Endo, M. Kawamura, S. Katsumoto and Y.Iye
Phys. Rev. B63 113310-1-4 (2001).
[2] A.Endo and Y.Iye
Solid State Commun. 117 249-254 (2001).

Fig.1. Scanning electron micrograph of the sample. The ring structure
was fabricated by electron-beam lithography and wet-etching. The
bright yellow regions indicate gate-electrodes made of Au. They areplaced to constitute quantum dot (or single-electron transistor) on
each path of the AB interferometer

metallic islands (quantum dots or Coulomb islands).
While the charging effect represents the particle-side ofelectrons, the interference effect reveals the other side, i.e.,electrons as waves. The interference of two partial waves isdetermined by the phase difference, which can be tuned by
the magnetic flux threaded inside the loop consists of theirtrajectories. This is a kind of Aharonov-Bohm effect, which
is observable as an oscillation of electric conductancethrough metallic rings of mesoscopic size against external
magnetic field.
Then a natural question is “ what happens when a quantum dot is placed on a metallic loop, i.e., an AharonovBohm (AB) interferometer? ” Into the language of energy
spectrum, this question is interpreted as “what happens
when a system with discrete energy levels is embedded in
the continuum?” A basic answer to the question was theoretically given by Fano in 1961 [1]. The two states merge into
a new state (Fano resonant state), which sits in between thetwo extremes of a quantum.
The simplest natural realization of the above question isa single atom embedded in delocalized states. This results incharacteristic asymmetric line-shapes of resonance peaks,
which are widely observed in various physical systems andknown as the Fano effect. However, these natural systems
have little controllability and the examination beyond theline-shape has been an untouched issue. We have observed

Authors

A. Endo, S. Katsumoto, Y. Iye

Continuum Meets Discrete in an
Aharonov-Bohm Interferometer
S. Katsumoto
An electron is a quantum, which is a particle and at thesame time, a wave. The charge of single electron (namely
the basic charge) was first measured by Millikan in 1911
(till 1913), by using tiny oil-droplets, which are maybe thefirst “quantum dots”. In modern experiments such singleelectron charging effect appears in so called “single-electrontransistors”, which are composed of electrodes and small

Fig.2. Conductance through an AB interferometer with a quantum dot
in one of its arms. The two axes in plane are the external magnetic
field and the gate voltage of the dot. The oscillation along the voltage
is Coulomb oscillation and that along the magnetic field is AB oscillation. Note that the asymmetry in the Coulomb-line-shape changes
its parity when the field passes the maxima of the AB oscillation.

ISSP Activity Report A 200115

and examined the Fano effect for the first time in an artificial quantum dot – AB ring hybrid system and obtained anessentially new insight that the Fano parameter which is the
key variable in the effect should be complex number.
Figure 1 shows a scanning electron micrograph of thefabricated device. A two dimensional electron gas at a
(Ga,Al)As/GaAs hetero-interface was mesa-etched into asmall ring (AB interferometer) structure, and thin wires ofAu were placed to form quantum dots interrupting the electron paths and to control the electro-static potential of them.
The sample was cooled down to 30 mK and the magnetic
field up to 7 T was applied.
Figure 2 displays the conductance through the ring as afunction of the applied magnetic field and the gate voltage.
For this measurement, the gate-voltages were adjusted toform a quantum dot in one arm and to open the other to form
continuous a ring-interferometer. The oscillation versus thegate voltage is due to the discrete levels formed by singleelectron charging effect and called “Coulomb oscillation”.
Unlike usual Coulomb oscillation, the line-shapes are asymmetric manifesting a Fano state are formed.
At the same time, an oscillation versus magnetic field isobserved, which is the AB oscillation. Hence the systemshows the both aspects of electrons as “quanta”. What isremarkable here is the parity of the asymmetric line-shapechanges when the magnetic field passes the maxima of theAB oscillation. The parity as well as detailed line-shape isdetermined by so called the “Fano parameter” q, which has
been conventionally treated as a real variable. However thedata shown in Fig.2 manifest that q is a function of at least
two parameters. And the simplest way to treat the situation
is to treat q as a complex variable. Further study to clarify
the many-body effects on the Fano state is now under way.
References[1] U. Fano, Phys. Rev. 124, 1866 (1961).

Authors

K. Kobayashi, H. Aikawa, S. Katsumoto and Y. Iye

Fig. 1. STM images of 0.35 ML Ag deposited Ge(001) surface at 90
K, observed at 65 K after 13 hours annealing at RT. The 2D island (a)and the 1D chain (b) are formed on this surface. The former elongatesalong the Ge dimer row direction and occupies three dimer rows. The
latter elongates along the Ge dimer direction and has mono-atomic
width.

We have studied Ag on Ge(001) surfaces by STM attemperatures between 65 K and RT to understand theprocesses of Ag island formation and their intermixing into
the Ge surface by increasing the temperature. Silver wasalways deposited at 90 K. The deposited Ag atoms or theirsmall aggregates are randomly located at various sites on
Ge(001) at 78 K, and are observed as small and large brightdots in the STM images. Some of the dots move on the surface with keeping the phase of the substrate Ge dimer buckling. By increasing the sample temperature, the bright dots
diffuse, transform and assemble into small clusters, which
are still one mono atomic layer thick. Finally, above 200 K,
the clusters occupying three Ge dimer rows transform into
the 2D islands with small corrugation. The images inside
the 2D island and the 1D chain were found not to be thecluster types of the bright dots. This suggests Ag dots moveon the surface and intermix or alloy with the substrate Ge
atoms during the annealing.
On 0.2 ML Ag deposited Ge(001) after annealing at 180
K for 2 hours, we found the clusters made of the large dots

Correlated Motion of Small Ag Clusters
and Ge Dimer-Bucklingon Ge(001) as a
Precursor Process of Surface Alloying
F. KomoriThe motion of atoms and small clusters at surfaces is an
important subject not only for the fundamental understanding of the stability of material but also for the fabrication ofnovel and functional materials by such as alloying or chemical reactions. Still the dynamical processes prior to thealloying at surfaces have not been well studied.
Among various surface alloys and compounds, Ag on
clean Ge(001) has attained a special interest since the discovery of superconductivity below 2 K.[1] This system is acandidate for the superconducting surface alloy because Ag
and Ge are immiscible and not superconductors in the bulk.
The growth of Ag on Ge(001) has been previously studied
by scanning tunneling microscopy (STM) at room temperature (RT). [2] When sub-monolayer (ML) Ag is depositedon Ge(001) surfaces at 90 K, they form 1 ML thick two
dimensional (2D) islands and one-dimensional (1D) chains
after annealing at RT as shown in Fig. 1. The 2D island isstable at RT and the corrugation on the island is small in
STM observations. This suggests that alloying occurs at the
Ag-Ge interface during the annealing to RT.

16

ISSP Activity Report A 2001

Fig. 2. (a-c) Successive STM images at 180 K with about 5 min interval including a cluster made of two kinds of the Ag dots on three Ge
dimer rows.(d-f) Schematic diagram of the dots and the cluster
motion in (a-c). In (a, d), two bright dots indicated by 1, 2 are locatedin the trough between Ge dimer rows, and an ellipsoidal dot, indicated as 3-4, is located in the lower left adjacent trough between therows. Next in (b, e), the location of the ellipsoidal dot moves to thelower right side along the Ge dimer row. In the third (c, f), the locations of the two bright dots and an ellipsoidal dot are exchanged. The
isolated large dot indicated by 5 in the figures also moves along the
Ge dimer row.

as well as isolated large dots. Figures 2 show successive
STM images with 5 min interval, and their models. As in themodels, the thermally-activated motion of the Ag dots causes the buckling change of the Ge dimer and vice versa at thistemperature. Especially, the movement of the bright dots
along the dimer row in the cluster induces the simultaneous
formation and separation of the ellipsoidal dots with correlated change of the buckling phase at the Ge dimer rows
under the cluster. These correlated motions are precursor
processes to the formation of the 2D alloy islands above 200
K.
References[1] M.J. Burns, J.R. Lince, R.S. Williams and P.M. Chaikin, Solid
State Commun. 51 865 (1984).
[2] F. Komori, K. Kushida, K. Hattori, S. Arai and T. Iimori, Surf. Sci.
438 123 (1999).

Authors

Y. Naitoh, K. Nakatsuji and F. Komori

Spectroscopic Evidence for
Asymmetric Dimer of Si(100)at Very Low Temperature
J. Yoshinobu
Surface atoms on Si(100) are reconstructed to form a(2 × 1) dimer row structure [1]. Many experimental andtheoretical studies have supported the buckled (asymmetric)
dimer with c(4 × 2) phase as a ground state. However,recently, several low temperature STM studies have reported symmetric dimer images [2-5], and the origin of symmetric images is still controversial. In this study [6], using highresolution Si 2p photoelectron spectroscopy [7,8], we haveinvestigated the electronic states of Si(100) at 140 K, 100 K
and 55 K.
The experiments were performed in an ultrahigh vacuum(UHV) chamber, where the base pressure was 7 × 10-11

Torr. Boron-doped p-type Si(100) wafers (3~5 Ωcm) wereused in the experiments. Clean Si(100) surfaces were prepared after being outgassed at ~ 900 K for 12 hours, flashed
up to 1550 K several times, and cooled slowly from ~ 1000
K to 140 K, 100 K or 55 K. High resolution Si 2p PES measurements were performed at BL-16B with an undulator
radiation source of Photon Factory in KEK. The photoelectrons were collected with a hemispherical analyzer. The total
instrumental energy resolution of the present experiments
was below 80 meV when the photon energy was 129 eV. It
should be noted that in our LEED measurements sharpc(4 × 2) patterns were observed at 55 K, 100 K, and 140 K.
Figure 1 shows the Si 2p PES spectra for the Si(100) surface at 140K, 100 K and 55K. By carefully analyzing thespectra and the plots of relative area intensity of each component as a function of emission angle, we can decompose
the spectrum into five components and assign them [6-8]:
the components B is due to the bulk Si atoms; the components Su and Sd correspond to the up and down Si atoms of
the asymmetric dimers, respectively; the component SS is
assigned to second layer Si atoms. The component X is stillunidentified. The split of 550 meV between the up and down
dimer components comes from a substantial charge transfer
within the dimer atoms, indicating that the asymmetricdimers have some ionic character. The peak positions andthe angle dependence of intensity ratios agree well with theprevious results [7].With decreasing the temperature, thespectral shapes become sharper due to reduced thermal
broadening, but the spectra at 140 K, 100 K, and 55 K arebasically similar. Thus the local structure of Si(100) surface
at 140 K, 100 K, and 55 K must be the same. The intensity
ratio of the up and down dimer peaks are almost the same inthis temperature range, indicating that the asymmetric dimer
structure of Si(100) does not change between 55 K and 144
K. Thus, we conclude that the dimer on Si(100) is asymmetric down to 55 K, and the origin of symmetric images in
STM is due to dynamic or extrinsic effects.

Table I. Summary of relative area intensities ofeach component at normal emission.
140K
100K
55K

Su
0.15
0.15
0.15

Sd
0.15
0.15
0.14

B
0.39
0.38
0.37

SS
0.24
0.24
0.27

X
0.07
0.08
0.07

References[1] R. E. Schlier and H. E. Farnsworth, J. Chem. Phys. 30, 917 (1959).
[2] H. Shigekawa et al. , JJAP part2 39, (1997) L1081, and JJAP par1
39 3811 (2000).
[3] T. Yokoyama and K. Takayanagi, Phys. Rev. B61, R5078(2000).
[4] T. Mitsui and K. Takayanagi, Phys. Rev. B 62, R16251 (2000).
[5] Y. Kondo et al, Surf. Sci. 453, L318 (2000).
[6] Y. Yamashita, S. Machida, M. Nagao, S. Yamamoto, Y. Kakefuda,
K. Mukai and J. Yoshinobu, Jpn. J. Appl. Phys. 41, L272 (2002).
[7] E. Landemark et al, Phys. Rev. Lett.69, 1588 (1992).
[8] E. Pehlke and M. Scheffler, Phys. Rev. Lett. 71, 2338 (1993).

Authors

Y. Yamashita, S. Machida, M. Nagao, S. Yamamoto, Y. Kakefuda, K.
Mukai and J. Yoshinobu

Magnetoresistance in Fractional-Layer
Oxide Superlattices
Fig. 1. Si 2p PES spectra for the Si(100) surface (a) at 140 K, (b) 100
K, (c) 55K. The emission angle was 0° and the photon energy was
129 eV.

M. Lippmaa

ISSP Activity Report A 2001

17

Transition metal oxides are well known for the wide
variety of interesting and useful physical properties. Our
work is aimed at understanding the growth process of oxidethin films and the properties of oxide surfaces and interfaces.We mainly concentrate on the perovskite-type materials that have similar structures and lattice constants. Thissimilarity leads to the possibility of artificially constructing
lattices in thin film form. Crystal growth by pulsed laser
deposition (PLD) is possible even when the growth conditions are far from thermodynamic equilibrium. It is thus
feasible to build lattices which can not be grown in bulkform.
An example structure of an artificial material is shown in
Figure 1. This particular structure, also known as a fractional layer superlattice or an epitaxial nanocomposite, consistsof a matrix material, shown in red, and nanodots (blue),
which are embedded at regular intervals in the matrix. We
haveselectedaferromagnetic
metallicoxide,
La 0.6 Sr 0.4 MnO3 for the matrix layers and La 0.6 Sr 0.4 FeO3,
which is antiferromagnetic in bulk form, for the nanodots.
As shown in the model image in Figure 1(a), the ferromagnetic order, and thus also metallic conductivity, is lost in
the matrix layers immediately surrounding the nanodots,
forming insulating bubbles in the lattice. The size of suchbubbles is reduced when an external magnetic field isapplied (Figure 1(b)) due to the partial restoration of metallic conductivity in the atomic layers which are not in directcontact with the nanodots. If the nanodot density is carefully
adjusted, it is possible to grow a thin film which is close to apercolative metal to insulator transition [1]. Without anexternal field the nonconducting bubbles touch, and the lattice is insulating. When an external field is applied, the bubbles shrink and conduction paths open (Figure 1(b)).
This behavior can be seen in the resistivity vs. temperature plots measured at various magnetic fields, as shown in
Figure 2. The largest magnetoresistance effect was achievedin a lattice containing nanodots with an average diameter of
25 nm at a coverage of 0.5 monolayers. The nanodot layers
were separated from each other by three layers of the matrix
material. As shown in the plot, the material is an insulator
when no field is applied. Metallic behavior, i.e. drop of
resistivity with decreasing temperature, appears when an
external magnetic field of 1 Tesla or more is applied.
When nanodots with a smaller diameter are used, such as
5 nm, conduction paths do not form even in a field of 7
Tesla. The magnetoresistance behavior of the constituent

Fig. 1. A cross section of a fractional layer superlattice consisting of aferromagnetic and metallic matrix (red) and embedded nanodots(blue). Each nanodot has a thickness of just 0.4 nm, i.e. a single unit
cell. Regions of reduced conductivity, which surround the nanodots,
become smaller when an external field is applied, opening conduction
paths.

18

ISSP Activity Report A 2001

Fig. 2. Magnetoresistance in fractional layer superlattices. The average nanodot diameter in the two samples was 25 nm and 5 nm.
Temperature behaviors of the two component materials are also
shown for comparison.

materials, La 0.6 Sr 0.4 MnO3 and La 0.6 Sr 0.4 FeO3, are also
shown for comparison. Fractional layer superlattices offer a
new way of creating thin film materials with properties thatcan be tuned by changing the shape, size, or density of thenanostructures used. Due to the local nature of interactions
that determine the bulk transport properties, these superlattices can also be used for studying the electronic structure ofoxide heterointerfaces in general. It is particularly important
to distinguish between various competing mechanisms
which are present close to the interface, such as exchangeinteractions, cation diffusion, and charge transfer.
References[1] N. Nakagawa, M. Lippmaa, K. Shibuya, H. Koinuma, and
M. Kawasaki, Jpn. J. Appl. Phys. 41, L302 (2002).

Authors

M. Lippmaa, N. Nakagawaa, K. Terai and K. Shibuya
aBell Laboratories (USA)Generation and Application of theWorld Highest Magnetic Fields
N. MiuraAt the Megagauss Laboratory (MGL) of ISSP, two techniques have been so far developed to generate very highmagnetic fields in the megagauss range (>100 T). They are
the single-turn coil technique and electromagnetic flux compression. The former technique is useful for handy experiments in the 100-200 T range, as the samples are preserved
intact in each shot in spite of the violent destruction of thecoil. Electromagnetic flux compression, on the other hand, isa powerful technique for even higher magnetic fields. By
compressing the magnetic flux with an imploding metal ring(liner) driven by a large pulsed primary current through a
one-turn coil (primary coil), we can generate a field exceeding 500 T.
Recently, we have developed a new device called “feedgap compensator” by which we improved the symmetry of
the liner deformation resulting in a considerable increase of
the maximum available field. One of the serious problems
which restricted the maximum field was the existence of the“feed gap” in the primary coil. This causes an asymmetricliner deformation, and the protrude towards the feed gap
induces a generation of plasma jet which often destroys the
sample before the maximum field is reached. By employing

Fig. 1. (Left) Sketch of a primary coil and a liner for electromagnetic
flux compression with a feed gap compensator in between. When we
supply a large pulsed current of the order of 5 MA to the primarycoil, a secondary current is induced in the liner in the opposite direction, and the repulsive force between the two currents rapidly
squeezes the liner. This motion of the liner towards the inward direction compresses the magnetic flux inside which has been injected
beforehand. 6 pieces of Cu blocks that are inserted between the primary coil and the liner being electrically insulated are the feed gap
compensator. Without the compensator, the magnetic field near the
feed gap is always weaker than the other part, and this causes anasymmetric deformation of the liner. With the compensator, the symmetry was much improved.
(Right) High speed photograph of the imploding liner (shadow
graph). Reflecting the 6 slits in the compensator, the deformed liner
has a hexagonal symmetry. The deformation without the compensatoris very different, involving a protrude and the shift of the center ofgravity towards the feed gap.

the feed gap compensator as shown in Fig. 1, we found thatthe liner symmetry was much improved. As a result, we succeeded in generating a magnetic field up to 622 T. Figure 2
shows the waveforms of the magnetic field and the primary
current when we obtained 622 T. This is the highest magnetic field which has ever been produced by indoor experiments in the world.
Such a high magnetic field is an extremely powerfulexperimental tool for investigating solid state physics, since
it will drastically alter electronic states in solids. We can
expect that it will open up a new area of physics beyond theexisting theory. In fact, we have found many new phenomena in a variety of materials under the extremely high magnetic fields [1-3]. As an example, we show in Fig. 3 themagneto-optical spectra in a GaAs/AlAs quantum well in amagnetic field above 500 T. The data show the exciton line
and many absorption lines due to the inter-Landau leveltransitions. A number of new features are observed in theFig. 3. Magneto-absorption spectra in GaAs/AlAs quantum wells.
The thickness of the layers is 9.0 nm and 5.0 nm for GaAs and AlAs,
respectively. The temperature was 23 K. The line at the lowest photon energy is due to the exciton absorption. The exciton line shows a
discontinuity at about 240 T. This field corresponds to the magnetic
field at which the wave-function extension along the magnetic field is
reduced to the thickness of the layers of GaAs. The study of excitonsin very high magnetic field is of interest in connection with the fundamental problem of physics concerning hydrogen atoms in extremely high magnetic fields such as those existing in neutron stars (~108
T). Although the field available in our experiments today is several
orders of magnitude less, its effect on excitons is comparable withthat the field in neutron stars gives on hydrogen atoms due to thelarge dielectric constant and the small effective mass of the material.

spectra, such as the broadening, discontinuity, sudden emergence and disappearance of the absorption lines.
References[1] T. Hayashi, N. Miura, K. Noda, H. Kuwahara, S. Okamoto, S.
Ishihara and S. Maekawa: Phys. Rev. B 65 024408 (2002).
[2] Y. H. Matsuda, T. Ikaida, N. Miura, S. Kuroda, F. Takano and K.
Takita: Phys. Rev. B 65 115202 (2002).
[3] N. Miura, H. Nakagawa, T. Sekitani, M. Naito, H. Sato and Y.
Enomoto: to be published in Physica B 319 (2002) 310.

Principal Publication and Authors

N. Miura, Y. H. Matsuda, K. Uchida, S. Ikeda and F. Herlach:
Proceedings of the 4th International Conferences on the PhysicalPhenomena in High Magnetic Fields (Santa Fe, 2001). (World
Scientific, 2002) P.513.

Development of Advanced Experimental
Techniques under Pulsed Ultra-High
Magnetic Fields
T. Osada

Fig. 2 Waveforms of the primary current I and the magnetic field B,
generated by electromagnetic flux compression. The signals from 2
pick up coils are shown for B (red and green curves). The 2 graphs
coincide almost precisely until the pick up coils are destroyed atabout 46 μs. showing the accuracy of the field measurement. Just
before the destruction of the coils, the turn-around effect ( the fieldstarts decreasing after taking the maximum) is seen in the bothcurves.

We have developed two novel experimental techniques
for use in pulsed high magnetic fields at the megagauss laboratory (MGL) of ISSP. One is the direct magnetotransportmeasurement under pulsed ultra high magnetic fields up to
600 T using RF bias and PSD technique. The other is thehigh sensitivity torque-meter under 50 T-class pulsed magnetic fields with use of a micro-cantilever.
Ultra-high magnetic fields exceeding 100 T can beobtained only as a single-shot pulse using destructive methods. At MGL, ultra-high magnetic fields are generated byuse of two types of methods. One is the single-turn coilmethod generating the maximum field of 200 T, and theother is the electromagnetic flux compression method generating the maximum field of 620 T, which is the world recordof the in-house high magnetic fields. However, their effective pulse width is so short (several μsec) that experiments

ISSP Activity Report A 2001

19

has been applied to the oxide superconductor Sr2RuO4,
organic conductor α-(BEDT-TTF)2KHg(SCN)4, etc.
Principal Publication and Authors

T. Osada, E. Ohmichi, S. Ikeda, M. Kuraguchi, T. Inokuchi, K.
Kobayashi, M. Saito and M. Kobayakawa

Maturity of Non Magnetic 4GPa ClassHigh Pressure Cell
Y. Uwatoko

Fig. 1. Magnetoresistance of single crystal graphite under pulsed
ultra-high magnetic fields generated by the electromagnetic flux
compression device (inset). Large arrows indicate the new
Shubnikov-de Haas structures.

are very difficult because of huge discharge noise, huge
induced voltage, and self-heating of samples.
In order to overcome these difficulties, we have
employed RF bias (f = 30~100 MHz) and phase sensitive
detection (PSD) technique. Temperature increase due toself-heating can be suppressed by decreasing sample size.
The magnetoresistance of single-crystal graphite andquasi-twodimensionalorganic
conductor
α-(BEDT-TTF)2KHg(SCN)4 was successfully measured
under vertical magnetic fields up to 200 T generated by theflux-compression method. In graphite, new Shubnikov-de
Haas oscillations were observed at unexpected positions inhigh magnetic fields. This result suggests the importance ofcorrelation effects in graphite in ultra-high magnetic fieldregion.
The other technique is the high sensitivity micro-scale
magnetic torque measurement. A high-sensitive miniature
torque-meter is developed with use of a commercial piezoresistive micro-cantilever for atomic force microscope(AFM). A sample mounted at the end of a cantilever beam
produces magnetic torque τ= M × B in a magnetic field,
and the resultant deflection of the beam is detected electrically. Resistance through a piezo-resistive path is precisely
measured with a Wheatstone bridge circuit. This makes it
possible to detect a small change in magnetization of samples of less than 1 mg, and the sensitivity is evaluated as theorder of m ~10-13 Am2 at 40 T, which is superior to conventional induction methods. The micro-cantilever techniqueFig. 2. Scanning electron microscope image of the micro-cantileveron which a small sample crystal is mounted. Inset: de Haas-van
Alphen oscillations measured in Sr2RuO4.

20

ISSP Activity Report A 2001

Undoubtedly, the study of the physical properties at highpressure, high magnetic field and low temperature is one of
the important subjects for the understanding of highly correlated electron systems, in which the various attractive phenomena such as superconductivity and magnetically ordered
non-Fermi liquid have been induced under pressure. Until
now, many scientists have designed a nonmagnetic piston
cylinder type high pressure cell made of nonmagnetic Cu-Be
alloy [1]. Unfortunately, the pressure limit should be only up
to 20 kbar due to the limit of the tensile strength of Cu-Be
alloy. Recently, however, the new high pressure cells madeof Ni-Cr-Al alloy (Russian alloy) and Co-Ni-Cr-Mo alloy(MP35N) have been tested successfully up to a pressure of
31.5 kbar and 35 kbar, respectively. These strong non-magnetic materials Ni-Cr-Al and MP35N have been introducedby Eremets et al. [2] and Walker [3]. In the field of thesolid state physics at low temperature the mechanical andmagnetic properties of Ni-Cr-Al alloy seems to be better
than those MP35N alloy.
For optimum mechanical properties which were obtainedat aging condition of 700℃ for 2 hours, the hardness
became about 57 HRC.
The alloy showed the ultimate tensile strengths of over 2
GPa, which is almost similar to that of MP35N alloy [3],and the true strain of about 2 %.
We have analyzed the magnetic properties of a sample ofa heat-treated Ni-Cr-Al alloy, MP35N and Cu-Be alloy by
SQUID magnetometer (Quantum Design). The magnetic
susceptibility of Ni-Cr-Al alloy is almost ten times lager
than that of Cu-Be alloy. The Ni-Cr-Al shows no temperature dependence in susceptibility, while the MP35N has

Fig. 1. Design of 4GPa Class Non Magnetic High Pressure Cell. The
dimensions of inner NiCrAl cylinder are 25, 14 and 5 mm, in length,
outer diameter and inner diameter. Basic idea of cell is similar to theformer designed hybrid cells [2,3]. The high pressure sample space
was sealed by Teflon cell technique. As a pressure transmitting fluid

Fig. 2. Pressure versus applied force. There is one linear variation atroom and low temperature up to 4 GPa.

large temperature dependence. In this respect the Ni-Cr-Al
is conclusively better material for high pressure cell at highmagnetic field and low temperature. These materials are notferromagnetic at least down to 2 K.
We have designed a conventional piston cylinder cell,which consists of a nonmagnetic WC and the Ni-Cr-Al innercylinder inserted into the Cu-Be outer sleeve. A schematic
drawing of the pressure cell is shown in Fig. 1.
The pressure at room temperature and liquid helium temperature were determined from P-T phase diagram for Bi,
Tl, and Te and the superconducting transition temperature
TC(P) for Pb, which have well known pressure dependence.
From the data measured in this study, at room and low temperaturs pressure is shown as a function of applied force in
Fig. 2. There is one linear variation at room and low temperature up to 4GPa. As a final results, it has been found that amaximum working pressure could be raised constantly up to
P = 4 GPa at T = 30 mK without any trouble.
References[1] H. Fujwara, H. Kadomatsu and K. Tohma: Rev. Sci. Instrum. 51,
1345 (1980).
[2] M. Eremets: High Pressure Experimental Methods, Oxford
University Press 1996.
[3] I.R. Walker: Rev. Sci. Instrum. 70, 3402 (1999).

Authors

Fig.1. Temperature dependence of the positive ion mobility at 32 barfor various magnetic fields. The slope of the Log (1/T) dependence

ered to explain a Log (1/ T ) dependence of positive ion
mobility below 100 mK, the magnetic exchange scattering
between the ion and the quasi-particles could be relevant to
it. To clarify the scattering mechanism, the positive ion
mobility has been measured under higher magnetic fields up
to 15 T at various pressures and temperatures.
The temperature dependence of the mobility at P = 32
bar is given for various magnetic fields in Fig.1. Below 20
mK, the Log (1/T) dependence does exist even at high magnetic fields up to 14.8 T. The magnetic field dependence atconstant temperature is more surprising. The mobility
exhibits a small broad peak followed by a large decrease at
3.2 mK. The behavior is seriously affected by the liquidpressure as shown in Fig.2. The peak shifts to the high fieldside with decreasing the pressure, and is followed by a large
decrease above 25 bar. On the other hand no magnetic fielddependence is observed for the negative ion called electron bubble in the same pressure and temperature region.
Therefore the field dependence in the positive ion mobility
is attributable to the magnetic interaction between the 3He
quasi-particles and the localized spins on the ion surface.
What is a microscopic mechanism? Variation of the bulk

M. Hedo, S. Todo, Y. Uwatoko, M. Kosakaa, N. Moria and T.
Matsumotob.
aDepartment of Physics, Saitama University, Urawa 338-8570, JapanbNational Institute for Materials Science, Tsukuba 305-0047, Japan

Positive Ion Mobility in Normal Liquid
3He under High Magnetic Fields
H. Ishimoto

The ion in liquid 3He is a powerful tool not only forstudying elementally excitations but also for understanding
the behavior of heavy charged particle in neutral Fermi liquid. The positive ion called snowball is a cluster of
3He atoms attracted to the core (3He) + by its large local
2
electric field. Existence of the localized 3He spins on the ion
surface makes the positive ion a sort of magnetic impurity
which is intentionally produced in extremely pure Fermi liquid. The radius is the order of 1 nm, which grows with anapplied liquid pressure. At low temperatures below 100 mK,
the ion interacts with Landau quasi-particles, and hence thesituation resembles a Kondo effect in metal. However in liquid 3He, the ionic recoil is important because of the absenceof lattice. Although the inelastic energy exchange is consid-

Fig.2. Magnetic field dependence of the positive ion mobility at 3.2
mK for various pressures.

ISSP Activity Report A 200121

liquid 3He properties and the melting pressure with magnetic field is not large enough to explain it. The other possible
origin could be the localized 3He spins on the snowball,which causes a large magnetization under high magnetic
field. It should suppress a spin flip exchange scattering of
the quasi-particles, resulting into the increase of the mobility. At the same time, it induces a polarized spin density arising from the RKKY spin oscillation in the vicinity of thesnowball, leading the enhancement of the scattering crosssection and hence the decrease of the mobility. A delicatecompetition between these two factors seems to cause acomplicated field dependence of the mobility. To understand clearly the scattering of the snowball under high magnetic fields, a new theoretical treatment is eagerly desired.
Principal Publication and Authors

K. Obara, D. Ueno, V. Efimov, R. Masutomi, A.Yamaguchi and H.
Ishimoto, Phys. Rev. Lett. 87 235301 (2001) .

THz-Electron Spin Resonancein a Big-Bang
H. Nojiri and N. Miura

Fig. 2. A spin-phonon coupled mode of CuGeO3 (red arrows) isobserved at 107 T in the middle of incommensurate magnetic phase.
The strong-polarization dependence indicates that the mode is not apure spin resonance mode. Field dependence the mode is analyzed inconnection with previous data taken at low fields [1].

middle (the saturation field is about 250 T) of the magnetic
phase where no other microscopic spin probe can access.
ReferenceTHz-electron spin resonance is a unique method toinvestigate magnetic as well as electronic property of solid.
THz-regime is a new developing field of spectroscopy and it
is useful to investigate a strong spin-phonon coupling in low
dimensional magnets and strongly correlated electron systems.
Since a resonance field exceeds 100 T, a use of nondestructive field generator is necessary for such experiments. A very short interval of a field pulse as well as anoisy environment have prevented a realization of such
experiment. Use of a high power far-infrared laser and an
advanced shielding system have enabled us to perform THzelectron spin resonance in mega-gauss fields. Very clean
spectrua can be observed at low temperatures as shown in
Fig. 1.
As the first experiment, a spin-phonon coupled mode in
CuGeO3 is observed. A splitting of the mode in low fieldhas been interpreted as the change of incommensurate lattice
distortion in the magnetic phase. The present result shows
how the incommensurate wave vector changes in the very

Fig. 1. Example of ESR spectrum (red) in FeF2 at 25 K with afreguency ν= 2.52 THz and a field trac e (blue). Inset shows a photograph at the instance of field generation. In the big explosion of asingle-turn coil, a very clean signal is obtained and the sample can berecovered undestroyed.

22

ISSP Activity Report A 2001

1)K. Takehana et al., J. Phys. Soc. Jpn., 70 3391 (2001).

Authors

H. Nojiria , Y. H. Matsuda and N. Miura

Dynamical Study on Room-Temperature
Huge Magnetoresistance Effect
H. Akinaga and N. MiuraaDepartment of Physics, Okayama University

There has been increasing interest in magnetoresistance(MR) effect with a view to its application in various magnetic devices, such as a magnetic field sensor. The spin-dependent MR effect in artificial structures, such as metallic multilayers and tunnel junctions, have attracted much attention,
raising scientific and technological issues. Rapid increase in
the recording density of hard disk drives requires the continuous development of the magneto-electronics devices.
Recently, we developed successfully new MR materials
consisting of nanoscale metal islands that are grown on a
GaAs substrate [1]. The material shows more than thousand-Fig. 1. The current evolution as a function of time, under an influenceof the pulsed magnetic field. The MR ratio calculated from the current change reaches more than 3000 %.

fold MR change under a relatively low magnetic field, evenat room-temperature (RT). The new MR material shows thehighest magnetic-field sensitivity compared with the existent MR materials and devices in the magnetic-field range ofa few hundred Oe. We termed the new phenomenon
Magnetoresistive switch. In the fiscal year of 2001, we haveinvestigated the dynamics of the magnetoresistive switch
effect. The magnetic-field sensitivity and the response timeof the effect are decisive parameters for the sensor application. As a result of the investigation, we have found amethod to improve the dynam-ic properties of the new MR
material [2].
This work was partly supported by the New Energy andIndustrial Technology Development Organization (NEDO).
References[1] H. Akinaga, M. Mizuguchi, K. Ono and M. Oshima, Appl. Phys.
Lett. 76, 357-9 (2000).
[2] H. Akinaga, N. Miura and K. Uchida, Patent pending.

Authors

H. Akinagaa, K. Uchida, Y. Matsuda and N. MiuraaResearch Consortium for Synthetic Nano-Function Materials Project(SYNAF), National Institute of Advanced Industrial Science andTechnology (AIST)

Measurement of the Intensity-Dependent
Atomic Dipole Phase of a High
Harmonic by
Frequency-Resolved
Optical Gating (FROG)
S. WatanabeHigh harmonics generated by nonlinear interaction
between the intense laser field and atoms are of great interest for the potential application to science and technology invacuum ultraviolet (VUV), extreme ultraviolet (XUV) andsoft x-ray regions. Recently, theoretical analyses and experiments in the strong field approximation reveal that high harmonic pulses have an intensity-dependent phase, i.e. atomic
dipole phase, inducing negative chirp in a high harmonic
pulse [1]. Thus, appropriate phase compensation compresses
the high harmonic pulses to the attosecond regime.
However, the phase of a high harmonic pulse has never beenmeasured so far. One of the techniques commonly used forcharactering the ultrashort pulses fully is frequency-resolved
optical gating (FROG) [2], involving the measurement of
the time-dependent spectrum of the autocorrelation or crosscorrelation (spectrogram) and the solution of the pulse
retrieval problem mathematically. In this work, we havedeveloped two-photon-ionization (TPI) FROG and mea-

Fig. 2. Retrieved pulse shape and phase of the fifth harmonic of
Ti:sapphire laser after a 2-mm thick CaF2 plate. The phase is constantwithin the pulse duration, indicating that the pulse is almost Fouriertransform limited.

sured the temporal profile, including the phase, of the fifth
harmonic of Ti:sapphire laser for the first time, from which
the negative chirp of a high harmonic was confirmed.
Figures 1 and 2 show the spectrogram constructed fromthe time-dependent TPI photoelectron spectra and retrieved
pulse profile of the fifth harmonic of Ti:sapphire laser after
a 2-mm thick CaF2 plate, respectively. The temporal duration of the pulse was 50 fs. The phase shown in Fig. 2 isalmost flat within the pulse duration, indicating that thepulse is almost Fourier-transform limited. Because TPI is
the second order process, a TPI spectrogram is symmetricwith respect to time reversal and the temporal direction cannot be determined by one spectrogram. Thus, the thicknessof the CaF2 plate, i.e. phase dispersion, was changed to 0.5
or 4 mm and the pulse profiles were measured. The temporal
direction was determined to be consistent among theretrieved pulses, taking account of the phase dispersion. Thechanges in the pulse profiles are explained well, confirmingthat TPI FROG measurement is valid. From these results,
the temporal shape just after the generation of the harmonic
pulse was calculated and the pulse was found to have negative chirp. The amount of the chirp agrees with the estimation by a theoretical model in the strong field approximation. This work supports the theoretical description of highharmonic generation and suggests the attosecond pulse generation by appropriate phase compensation. By using ashorter laser pulse and generating higher harmonics, attosecond pulses will be obtained, revealing unprecedented phenomena, such as electronic motions in materials.
References[1] M. Lewenstein, P. Salières, and A. L'Huillier, Phys. Rev. A 52,
4747 (1995).
[2] R. Trebino, et al., Rev. Sci. Instrum. 68, 3277 (1997).

Principal Publication and Authors

T. Sekikawa, T. Katsura, S. Miura, and S. Watanabe
Physical Review Lett 88, 193902 (2002).

Direct Phase Measurement of the X-Ray
Specular Reflection Using Modulation
under the Bragg Condition
T. Takahashi

Fig. 1 TPI photoelectron spectrogram of the fifth harmonic of
Ti : sapphire laser.

Specular reflectivity of X-rays, giving information on
the electron density distribution perpendicular to the surface,
is a helpful method in studying the structure of surfaces,

ISSP Activity Report A 2001

23

Fig.1. Illustration of experimental condition where specular reflection
is measured when a Bragg reflection is excited (a). When the surface
layer has no periodicity in the direction parallel to the surface or has aperiodicity different from that of the substrate crystal, the specularreflection of the surface layer is excited only by the incident wave
while that of the bulk is excited both by the incident and diffracted
waves (b).

interfaces, and thin films. However, as is the case in X-ray
intensity measurements, one is faced with the so-calledphase problem due to lack of phase information on reflected
waves through the detection of X-rays as intensities. For thisreason one must construct a number of structural models
until a model explains experimental results well.
Nevertheless, one can directly get a structural model fromexperimental results if one could obtain phase informationfrom the experimental results.
In the structure analysis of 3D crystals, such studies getting phase information have been made extensively. In contrast, in the structural analysis of surface layers only a few
studies have been done. In this report we show a new
method to obtain directly the phase of X-ray specular reflection using its intensity modulation by exciting a Braggreflection on the substrate crystal, particularly useful for surface layers without the same lateral periodicity as the substrate crystal. Figure1 shows a basic idea of the present
work. When a Bragg diffraction condition except the symmetric Bragg diffraction is satisfied by the substrate crystal,
the Bragg diffracted wave is excited only in the substrate
crystal as illustrated in Fig.1 (b). In this situation, specularreflectivity is given as a sum of three components, A_0(substrate) +A_h (substrate) +A_0 (surface). Since the structure of the substrate crystal is known, the amplitudes of theincident wave A_0 (substrate) and the diffracted wave A_h(substrate) are known. When the substrate is a nearly perfect

Fig.2. Intensity changes of X-rays as a function of incident angle of
X-rays. Filled and open circles respectively correspond to the intensities of specular reflection and 113 Bragg reflection.

24

ISSP Activity Report A 2001

crystal such as silicon, the phase of the diffracted wave A_h(substrate) changes as a function of incident angle aroundthe Bragg angle according to the dynamical theory [1]. Thus
the measurement of intensity modulations of specular reflectivity under the diffraction condition gives information of
the amplitude and the phase of specular reflected wave by
the surface layer, A_0 (surface).
We applied the method to a Si(001) single-crystal whose
surface was covered with a layer of native oxide a few
nanometers thick, that is considered to be amorphous in its
structure [2]. Figure 2 shows an experimental result of X-ray
intensities as a function of incident angle. From the intensity
modulation of specular reflection indicated by filled circles,
the phase and the amplitude of A_0 (surface) were determined to be 6.36x10∧-3 and 0.26x2π, respectively. Itshould be noted that the absolute value of the modulus of
A_0 (surface) is obtained without measuring absolute reflectivities.
This result indicates that in principle one can determine
the structure of the surface layer by the Fourier transform ofa set of A_0 (surface)’s if one repeats such measurements byscanning the wavelength of the incident wave to vary theperpendicular momentum transfer of specular reflection. A
preliminary result supporting the present method has beenobtained, which will be described elsewhere.
References[1] T. Takahashi and S. Nakatani, Surf. Sci. 326 347 (1995).
[2] W. Yashiro, K. Sumitani, K. Hirano, T. Takahashi, Jpn. J. Appl.
Phys. 41 L592 (2002).

Authors

T. Takahashi, W. Yashiro, K. Sumitani and K. Hiranoa

Nonmagnetic-Impurity-Induced
Antiferromagnetic Long-Range Order inQuantum-Disordered Antiferromagnets
H. Takayama
aPhoton Factory, KEK

In low dimensional antiferromagnets, such as a bondalternating antiferromagnetic (AF) chain, or a 2 dimensional(2D) antiferromagnet consisting of bond-alternating AF
chains coupled with AF interchain interactions, a pair of
spins coupled with a stronger interaction forms a singlet andso their ground state is non-magnetic and associates with afinite excitation energy, the so-called spin gap. Here we callthem quantum-disordered antiferromagnets. We have determined the ground-state phase diagram of the 2D antiferromagnet above-mentioned in the parameter space of thestrengths of bond-alternation and interchain coupling bymeans of the quantum Monte Carlo simulation with the continuous-imaginary-time loop algorithm (CITLA-QMC).
Our interest of the present work is to reveal what happens on the nonmagnetic, spin-gapped ground state when
non-magnetic impurities are introduced. We have considered two effects of the latter; one is site dilution, i.e., a nonmagnetic atom is substituted for a magnetic atom, and theother is bond dilution, i.e., a non-magnetic atom breaks an
exchange interaction between spins.
Site-dilution effect
For the site dilution, it is natural for us to imagine thefollowing scenario. Since the spin system of our present

Fig.1 Real-space distribution of magnetic moments in the groundstate of a site-diluted 2D AF Heisenberg model consisting of bondalternating (-J-J'-J-J'-) AF chains coupled with AF interchain interactions J". The values of the parameters are J=1, J'=J"=0.5, and 30
diluted sites on a 64×64 lattice. The upper (lower) figure is the 3D(2D) representation. The magnetic moments are peaked at sites connected by a strong bond with diluted sites. Each of them has a significant spatial extent whose size is the AF coherence length of the medium, i.e., the sea of singlets.

interest is not frustrated, a spin which loses its partner of asinglet by dilution behaves as an almost free (or classical)
spin. Between these free spins the residual interactions exist
through paths connecting them. The interactions are exponentially small as a function of the distance between two
free spins, but they keep the staggeredness with respect tothe original lattice since the dilution does not induce frustrations. Consequently, in the ground state the AF long-rangeorder (AF-LRO) carried on these free spins is expected evenwith an infinitesimal concentration of dilution.
By the CITLA-QMC simulation we have thoroughly justified the above-mentioned scenario, which we call that ofthe dilution-induced AF-LRO on a sea of singlets [1]. In
Fig. 1 the real-space distribution of magnetic moments isshown. The AF-LRO is ascertained by examining the staggered spin correlation function. The staggered magnetization

Fig.2 Concentration dependences of the staggered magnetization Ms
in the site- and bond-diluted systems with J = 1 and J' = J" = 0.5.
There exists the critical concentration xc of about 0.05 in the bonddiluted system. The arrows with xp's indicate the percolation thresholds on the site and bond dilution problems, at which Ms is expected
to vanish.

depends on the concentration of dilution as shown in Fig. 2,
from which we conclude the critical concentration xc above
which the AF-LRO appears is zero.
Bond-dilution effectWe may think that the above scenario of the AF-LRO on
a sea of singlets can be applied also to the bond-dilution
case if we take into account one difference that there appear
two, instead of one, free spins at both ends of a diluted
strong bond. However this is not the case, since these two
spins are coupled antiferromagnetically by interaction Jaf via
the shortest paths which are proportional to JJ"J". If thestrength of Jaf is larger than that of the effective interactions
between free spins at different strong bonds diluted, Jeff,
which is certainly the case for a small concentration of dilution, the two spins reform a singlet by Jaf. Thus the criticalconcentration xc is expected to be finite for the bond-diluted
system in contrast to xc = 0 for the site-diluted system.
The staggered magnetization data obtained by the
CITLA-QMC simulation [2] and shown in Fig. 2 clearly
indicate the existence of a finite critical concentration xc forthe bond-dilution case. We have also confirmed a new spin
gap proportional to Jaf within the original spin gap of thenon-diluted system. A further interesting phenomenon coming out from the competition between Jeff and Jaf is a possible existence of the quantum Griffiths phase. Our datastrongly suggest that the spin gap vanishes at concentration
xc' which is smaller than xc. Detailed simulations to specify
the properties of the phase between xc' and xc are now inprogress.
References[1] C. Yasuda, S. Todo, M. Matsumoto, and H. Takayama, Phys. Rev.
B 64 092405 (2001).
[2] C. Yasuda, S. Todo, M. Matsumoto, and H. Takayama, Prog.
Theor. Phys. Suppl. 145 399 (2002).

Discovery of Missing Link:
II. A Spin-1/2 Pyroxene Compound
NaTiSi2O6
A.N. Vasil'ev and Y. Ueda
Authors

C. Yasuda , S. Toda , M. Matsumoto and H. Takayama

The alkali metal pyroxene family denoted as AM3+B2O6(A = alkali metal; B = Si, Ge) was previously studied from amineralogical standpoint. The compound NaAlSi2O6 named
jadeite or "hisui" in Japanese and LiAlSi2O6 called "kunzite" after the mineralogist Dr. G. F. Kunz have been very
precious stones since ancient times. Recently, the pyroxene
compounds with transition metal ions M3+ have drawn great
attention as one-dimensional (1D) magnets. In the crystal
structure of pyroxene (Figure 1), the M3+O6-octahedra form
1D chains along the c-axis by sharing edges and alkali metal
ions A+ occupy the tunnel sites in the framework formed by
M3+O6-octahedra and BO4-tetrahedra. Since each chain isbridged by SiO4- or GeO4-tetrahedra, the magnetic interchain interaction is considered to be much weaker than theintrachain interaction. Many transition metal compounds ofthe pyroxene family have been reported and they exhibits
Néel ordered states as the ground state. Although the search
for a spin-1/2 compound has been motivated by its intriguing quantum phenomena, it has been missing in the pyroxene family.

ISSP Activity Report A 2001

25

Fig.1. The magnetic susceptibility of spin-1/2 1D magnet NaTiSi2O6
is well fitted to the Bonner-Fisher equation above 250 K and at 210
K it shows a spin-Peierls-like transition. The transition, however,occurs at a temperature higher than that at the maximum point of theBonner-Fisher curve, indicating that the intrinsic magnetoelastic
instability of a 1D system cannot be considered as a driving force forthe transition. The structural feature that the 1D chain is made up of
skew edge-sharing Ti3+O6 octahedra suggests an important role ofthe orbital degree of freedom, that is, the orbital order on the transition.

In the present study a powder sample of NaTiSi2O6 thatis a spin-1/2 compound in the pyroxene family has been successfully synthesized and a novel phase transition was
found. As can be seen in Figure 1, the magnetic susceptibility (χ) is well fitted to the Bonner-Fisher equation above
250 K and rapidly decreases below 210 K. The ground stateis spin-singlet. The most significant feature of this spinPeierls-like transition is that the transition occurs at a temperature higher than that at the maximum point of theBonner-Fisher curve. This means that the short-range magnetic correlations within the chain are not fully developedand intrinsic magnetoelastic instability of a 1 D system cannot be considered as a driving force for the transition. The
structural feature that the 1 D chain is made up of skew
edge-sharing Ti3+O6 octahedra (Figure 1) suggests animportant role of the orbital degree of freedom, that is, theorbital order on the transition.
Principal Publication and Authors

M. Isobe, E. Ninomiyaa, A. N. Vasil'evb and Y. Ueda
J. Phys. Soc. Jpn. 71 1423-1426 (2002).
aChiba University (Japan)
bMoscow State University (Russia)

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ISSP Activity Report A 2001