Journal of the Physical Society of Japan 84, 104703 (2015)
http://dx.doi.org/10.7566/JPSJ.84.104703

Investigating Orbital Magnetic Moments in Spinel-Type MnV2O4Using X-ray Magnetic Circular Dichroism
Jun Okabayashi1+, Shigeki Miyasaka2, Kazuhiro Hemmi2, Kiyohisa Tanaka2,3, Setsuko Tajima2,
Hiroki Wadati4, Arata Tanaka5, Yasumasa Takagi3, and Toshihiko Yokoyama3
1

Research Center for Spectrochemistry, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan2
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
3
Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
4
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 227-8581, Japan
5
Department of Quantum Matter, Hiroshima University, Higashihiroshima, Hiroshima 739-8530, Japan(Received March 13, 2015; accepted July 23, 2015; published online September 7, 2015)

Element-speciﬁc magnetic structures, particularly orbital magnetic moments, of spinel-type MnV2O4 were
investigated using X-ray magnetic circular dichroism (XMCD). X-ray absorption and XMCD spectra clearly revealthat the Mn2+ (d 5) and V3+ (d 2) states are coupled antiferromagnetically. Analyses of XMCD spectra using magneto
optical sum rules revealed that small but ﬁnite orbital magnetic moments remain in both V and Mn 3d states, which
accounts for the antiferro-type orbital ordering in the V sites of MnV2O4 with coexisting complex and real orbital states.
Additionally, the Cr doping eﬀect in MnV2O4 was examined. The XMCD spectra of Cr 3+ (d 3) L-edges exhibited thesubstitution of Cr ions to the V sites ferromagnetically, with low conductivity through the suppression of the orbital
ordering.

1.

Introduction

Couplings between orbital and spin degrees of freedom intransition metal (TM) oxides exhibit a wide variety ofinteresting physical phenomena studied in strongly correlated
electron systems.1) The orbital degeneracy of t2g or eg
orbitals, split by the crystal ﬁeld in TM oxides, gives riseto the orbital ordering phenomena in perovskite-type Mn or
V oxides accompanied by Jahn–Teller distortion.2,3) Spineltype vanadium oxides (AV2O4) are one of the candidates used
to investigate the orbital ordering phenomena using charge,
spin, and orbital degrees of freedom. These materials haveattracted considerable attention owing to the topologicallyfrustrated pyrochlore lattices of V atoms, which induce
orbital ordering through structural transition from cubic totetragonal symmetries. The orbital degeneracy of d 2 systems
in octahedrally coordinated TM 3d t2g orbitals allows for thecontrollability of orbital states through local lattice distortion.
Interesting physics in the long-range orbital ordering using
the Jahn–Teller active d 2 electrons in V3+ states has been
extensively investigated for AV2O4 (A: Zn, Cd, Mg),4–6)
MnV2O4,7–11) and FeV2O4.12,13) MnV2O4 is a good candidate
for studying orbital ordering since the orbital magnetic
moments of Mn2+ (d 5 ) are nearly quenched with relatively
large spin moments in high spin states. Extensive studies oforbital ordering in MnV2O4 have been performed using X-ray
diﬀraction,14) neutron diﬀraction,15,16) optical conductivity,17)Raman spectroscopy,18) nuclear magnetic resonance of
51 19)V, and ﬁrst-principles calculations.20,21) X-ray diﬀraction
using synchrotron radiation shows that the structural
 to tetragonal I41 =a symmetrytransition from cubic Fd3m
occurs as the temperature decreases from the spin transition
temperature above 59 K to the orbital ordering temperature
below 54 K.14) On the basis of neutron scattering, the total(spin and orbital) magnetic moments of Mn and V atoms
were estimated to be 4.2 and 1.3 B , respectively,15) although
the spin and orbital components were not distinguished. In
addition, functional properties such as magneto caloric eﬀects
and magnetic shape memory eﬀects in MnV2O4 were also

demonstrated in the interval temperature between spin andorbital orderings.22,23)
An unresolved issue related to the orbital ordering ofspinel-type vanadium oxides is the relationship between theorbital magnetic moments in vanadium sites and the orbital
ordering. In particular, the type of orbital ordering that occurs
has been under dispute. One type is the antiferro-orbital
ordering with alternate occupations of yz and zx along thec-axis proposed by Motome and Tsunetsugu,24) which resultsin the space group I41 =a and the real wave functions dyz =dzx
due to the quenching of orbital angular momentums. The
presence of this type of ordering suggests that the spin–orbit
interactions in V 3d states are negligible. The other type isthe ferro-orbital ordering with occupied degenerated orbitals
proposed by Tchernyshyov,25) shown as dyz þ idzx , which
results in complex wave functions of the space group
I41 =amd symmetry. Large orbital moments are expectedwith this type of ordering. In order to determine the type oforbital ordering in MnV2O4, element-speciﬁc and quantitative measurements of orbital magnetic moments are essential.
Although the spin magnetic moments summing the antiparallel coupling between Mn2+ (d 5 , S ¼ 5=2) and V3+ (d 2 ,S ¼ 1) were estimated from magnetization measurements,10)
the element-speciﬁc orbital magnetic moments of each ion
have not been investigated. Additionally, I41 =amd complex
wave functions are considered to occur in FeV2O4 because
the tetrahedral coordinated high-spin d 6 systems in Fe sites
involve the doubly degenerate e states with orbital ordering.14) The Orbital-Peierls model with the space group
P41 21 2 was also proposed by Khomskii and Mizokawa26)
for related spinel-type compounds, although this model does
not exhibit the mirror, glide, and face-centered symmetries ofthe spinel structure. First-principles calculations for MnV2O4
predict collinear orbital chains along the V sites in apyrochlore lattice.20,21) Sarkar et al. proposed that the large
trigonal distortion in the VO6 octahedra modulates the orbital
ordering type.20) Local density approximations (LDAs)
including the intra-atomic Coulomb interaction (U) andspin–orbit interaction reveal that the mixing states of the real

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J. Phys. Soc. Jpn. 84, 104703 (2015)

J. Okabayashi et al.

and complex wave functions are essential for the ground-state
conﬁgurations.20) Strong exchange interactions between theV sites and the large U values are expected with complex
orbital ordering. The Coulomb-enhanced spin–orbit eﬀects
are also candidates for the generation of orbital magnetic
moments.20) Optical conductivity measurements17) using
multiplet spectral analysis suggest the mixing of real andcomplex orbital orderings. Therefore, the investigation ofelement-speciﬁc orbital magnetic moments in MnV2O4 isstrongly desired in order to clarify the physics behind theorbital ordering phenomena.
X-ray magnetic circular dichroism (XMCD) with X-ray
absorption spectroscopy (XAS) using polarized synchrotron
radiation is a powerful technique for investigating themagnetic and electronic states, particularly element-speciﬁc
spin and orbital moments. The analysis of XMCD using
magneto optical sum rules enables us to deduce the precise
orbital magnetic moments.27) The spin sum rules are notapplicable to spin magnetic moments in early 3d TMs owing
to the failure of the separation of core-hole spin–orbit
interactions and the existence of magnetic dipole terms.28)
These rules are applicable empirically only for the late 3d
TMs such as Mn, Fe, Co, and Ni compounds. On the other
hand, for orbital magnetic moments, the orbital sum rule is inprinciple applicable even in vanadium compounds because
the overlap between the core-hole spin–orbit splitting cancels
out in the orbital sum rule analysis. For the analysis of XAS
and XMCD spectra, the cluster-model simulation including
the conﬁguration interaction (CI) approach was used todetermine the electronic structure parameters accompaniedby spin and orbital magnetic moments. We employed not
only sum rules but also cluster-model calculations with CI,
which are suitable for deducing the electronic structure
parameters and spin and orbital magnetic moments.
Recently, Hemmi et al.11) reported that Cr or Mo impurities in MnV2O4 suppressed the orbital ordering owing to thet2g orbitals being fully occupied. We examined if the Cr3+
or Mo3+ impurities (d 3 ) substituted the V3+ sites withadditional electron numbers, resulting in metallic conductivity. We found that the critical temperature for orbital ordering
decreased from 59 to 40 K after 13% Cr doping, suggestingthat orbital ordering occurred in V3+ ions. However, the spin
conﬁgurations of each element need to be determined
explicitly. Investigations of the eﬀects of impurity doping
on element-speciﬁc magnetic moments enable us to discuss
the modulation of orbital ordering.
In this study, we investigated the element-speciﬁc
electronic and magnetic properties of MnV2O4 using XAS
and XMCD, and examined the relationship between orbital
magnetic moments and orbital ordering. We employedmagneto optical sum rules and cluster-model calculations
for the analysis of XMCD to deduce the orbital magnetic
moments. We found that the ﬁnite orbital magnetic moments
in V sites contribute to the orbital ordering type through themixing of real and complex wave functions. Furthermore, we
examined the Cr doping eﬀect in MnV2O4 using XMCD.
2.

Methods

Polycrystalline samples of MnV2O4 were synthesized by asolid-state reaction method. Single crystals were grown fromthe polycrystalline samples by the ﬂoating-zone method.

Details of the sample preparation and the fundamental
physical properties are provided in Ref. 11. The magnetic
and orbital ordering temperatures of MnV2O4 were estimatedto be 59 and 54 K, respectively. The XAS and XMCD
measurements were performed at BL-4B, UVSOR, Instituteof Molecular Science, Japan. The XAS spectra with diﬀerent
helicities were obtained by switching the magnetic ﬁelds inthe parallel and antiparallel directions along the incident
beam. The total photoelectron yield mode by directly
detecting the sample current was adopted. The extent ofcircular polarization (P) was evaluated to be 71  0:5%. The
photon energy resolution was set at 100 meV. The XAS andXMCD measurements were performed at a sample temperature of 5 K. A magnetic ﬁeld of 5 T, produced using a
superconducting magnet, was applied in the direction of theincident polarized soft X-ray.29) MnV2O4 rods were scraped
into a powder in air prior to the XAS and XMCD
measurements, in order to prevent the charge-up eﬀect
during the photoelectron emission process. Since the probing
depth of photoelectrons was approximately 5 nm in the
TM L-edge photon energy regions, some contamination on
the surfaces was expected in the oxygen K-edge XAS
spectrum. However, we could assume that the XMCD
signals were derived from the intrinsic magnetic propertiesof MnV2O4 from the XAS line shapes of both Mn and
V L-edges.
3.

Results and Discussion

Figure 1(a) shows XAS, XMCD, and the integrated
XMCD spectra of V L2;3 -edge regions taken at 5 K, which
is suﬃciently lower than the orbital ordered transition
temperature. Comparing the XAS line shapes with referenceline shapes in vanadium oxides possessing other valence
states such as V2O3, VO2, and V2O5,30,31) we infer fromthe XAS spectra that V3+ states are formed. Several ﬁne
structures were observed in the V L-edge XAS spectrum, andclear diﬀerences depending on the magnetic ﬁeld, i.e., photon
helicities, were observed in the XMCD signals. The XMCD
intensities were estimated to be approximately 5% of the
XAS intensities at the L3 main peak of 518 eV depending on
the helicities of þ and  . The complicated XMCD signals
were derived from the ﬁnal-state multiplet structures of V3+
ions. In previous studies of V3+ states, using XMCD, in
FeV2O4 measured at 80 K, similar complicated line shapes ofboth XAS and XMCD have been observed.32) Although spin
sum rules cannot be adopted for the V L-edge XMCD
because of the small spin–orbit splitting of V L2;3 edges,28)
asymmetric intensities in the XMCD spectra between V L2and L3 edges can be evaluated by the integration of XMCD
spectra. The orbital sum rule for XMCD spectral analysis
implies that the orbital magnetic moments are proportional tothe integrals of XMCD signals along L2;3 edges and the 3delectron numbers.27) The positive and negative asymmetric
XMCD signals at L3 and L2 edges, respectively, can beobserved in Fig. 1(a). The resulting residuals (q) from the
XMCD integrals for both L2 and L3 edges are shown at thebottom of Fig. 1(a), suggesting that the ﬁnite values of orbital
magnetic moments remained in the V3+ states. The integralof XAS (þ þ  ) after subtracting the background is also
shown in the third panel of Fig. 1. Using the integrals over
XAS spectra (r) and assuming that the V 3d electron number

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J. Phys. Soc. Jpn. 84, 104703 (2015)(a)J. Okabayashi et al.

(b)

Table I. Spin and orbital magnetic moments of V and Mn in MnV2O4
estimated from the magneto optical sum rules of XMCD spectra shown in
Fig. 1. The spin sum rule for V L-edge cannot be adopted. The electronic
structure parameters used in the cluster-model calculations of V and Mn in
MnV2O4 shown in Fig. 2 are also listed. Error bars are about 10% for eachvalue.

σ+
σ−

σ+
σ−

Elements

XMCD and sum rules

Electronic structure parametersin cluster-model calculations

mspin [ B ] morbital [ B ] Δ (eV) U (eV) pd (eV) 10Dq (eV)V
Mn

σ+ − σ−

—
4.17

0.150
0.058

4.0
4.0

5.0
5.0

1.7
1.5

1.0
0.0

σ+ − σ−deduced as the less-than-half 3d TM systems. Applying thespin sum rules for Mn L2;3 -edge XMCD with the correlation
factor (C ¼ 0:68) of Mn2+ considering the L3 and L2 edge
overlap:35,36)
mspin ¼

Fig. 1. (Color online) XAS, XMCD, and their integrated spectra in
MnV2O4 for (a) V and (b) Mn L-edges at a temperature of 5 K andmagnetic ﬁeld of 5 T. þ and  denote the helicities depending on themagnetic ﬁeld direction.

(ne ) is 2  0:2, we deduced the orbital magnetic moments(morb ) in the expression of the orbital sum rule:33)
morb ¼

1 4q
ð10  ne Þ:
P 3r

morb is deduced to be 0:150  0:023 B =(V atoms) from theorbital sum rule. The ﬁnite morb indicates that unquenched
orbital magnetic moments contribute to complex wave
functions in V sites. The physical origins of the ﬁnite but
small amplitudes of the orbital magnetic moments in V sites
are discussed below.
Mn L2;3 -edge XAS and XMCD spectra are also shown in
Fig. 1(b). The XAS spectral line shapes with multiplet
structures are similar to those of Mn2+ compounds with Td
symmetry such as (Ga, Mn)As ferromagnetic semiconductors
in the tetrahedral Mn2+ situations.34) The XMCD intensities
in Fig. 1(b) were estimated to be approximately 23% at theL3 -edge main peak of 639 eV by comparison with those of
XAS. The XMCD intensities of Mn L2;3 edges are higher
than those of the V L2;3 edges. Also, the sign of the XMCD
signals is opposite to that of the V L-edge XMCD signal.
This clearly indicates the antiparallel coupling of totalmagnetic moments between Mn2+ and V3+ ions, consistent
with the well-known ferrimagnetic properties of MnV2O4,10)
which is also analogous to the case of FeV2O4.32) The integral
over the XMCD spectrum along the Mn L2 and L3 edges
converged to a small positive value, as shown in the bottom
panel in Fig. 1(b), because the areas of the positive andnegative intensities were almost equivalent. This suggeststhat the quite small orbital magnetic moments of Mn are

1 6p  4q
ð10  ne Þ;PCrwhere p is the integral of XMCD for only the L3 edge, we
obtained mspin ¼ 4:17  0:63 B =Mn and morb ¼ 0:058 
0:009 B =Mn, which indicates the ratio of morb =mspin ¼
0:013, suggesting the quite small contribution of orbital
magnetic moments because we assume a 3d 5 conﬁguration
with ne ¼ 5. The spin and orbital magnetic moments arelisted in Table I.
For the analysis of XAS and XMCD spectra, we employedcluster-model calculations including the CI for Mn2+ and V3+sites in MnV2O4 as tetrahedral (Td ) MnO4 and octahedral(Oh ) VO6 clusters, modeled as a fragment of the spinel-type
structures. The Hamiltonian included the electronic structure
parameters of full on-site TM 3d–3d (valence–valence) and
2p–3d (core–valence) Coulomb interactions (U) and the Td
or Oh crystal ﬁelds (10Dq) in the TMs, along with thehybridization between the TM 3d and O 2p wave functions.
The charge-transfer energy was deﬁned as  ¼ Eðd nþ1 LÞ Eðd n Þ, where L denotes a hole in a ligand p orbital. The
hybridization between the TM 3d and O 2p states was also
parameterized in terms of the Slater–Koster parameters ( pd)and ( pd), where the relation ðpdÞ ¼ ð pdÞ=2 wasused.37) The parameters ( pp) and ( pp) were always set
to zero. In all cases, a Gaussian broadening was used tosimulate spectral broadening.
Figure 2 shows the calculated XAS and XMCD spectra of
V and Mn L-edges obtained using the cluster models with
CI. We assumed that the V3+ (d 2 ) states had Oh symmetry
and the Mn2+ (d 5 ) states had Td symmetry. The electronic
structure parameters were chosen to reproduce the experimental results and are listed in Table I. In ﬁrst-principles
calculations using the LDA+U method, the Coulombinteraction Udd ¼ 4:5 eV was adopted to model the orbital
ordering physics.20) We also use similar U values for thecluster-model calculation (U ¼ 5 eV). The electronic structure parameters Δ, U, 10Dq, and ( pd) used for the
calculations are plausible parameters for spinel-type oxides.
In the case of Mn ions, the cluster-model simulations
reproduce the spectral line shapes of both XAS and XMCD
qualitatively, as shown in Fig. 2(b). Because of the d 5
electron system in high-spin states, the orbital magnetic
moments in Mn sites are almost quenched. Spin magnetic
moments of approximately 4:5  0:4 B are consistent with

104703-3©2015 The Physical Society of Japan

J. Phys. Soc. Jpn. 84, 104703 (2015)

(a)
σ+
σ−

J. Okabayashi et al.

(b)
σ+
σ−

Fig. 2. (Color online) Cluster-model calculations of XAS and XMCD in
MnV2O4 for (a) V and (b) Mn L-edges. Dot curves at the bottom panels are
the experimental spectra shown in Fig. 1 for comparison.

the Mn d 5 states deduced from the XMCD analysis. The CI
contributions of the ground states are estimated to be d 5 :80.2%, d 6 L: 19.3%, and d 7 L3 : 0.02%. These results support
the claim that the obtained parameters reasonably model thephysical phenomena for MnV2O4.
In the case of V L-edges, qualitatively similar spectral line
shapes with both XAS and XMCD spectra in Fig. 1 werereproduced by the cluster-model calculation. Tetragonal local
lattice distortion around the V sites must also be considered.
The t2g states are split into two levels by the tetragonal
distortion, and the lowest xy states are occupied by one of theelectrons. The other electron occupies the yz or zx states. We
determined the tetragonal distortion for the V 3d states (Dtet )to be 0.02 eV in order to reproduce the complicated XMCD
spectral line shapes qualitatively. The best ﬁtted parameter
sets reveal the spin magnetic moment of 1:2  0:2 B , which
is not sensitive to the electronic structure parameters. At
least, the peak positions in each multiplet structure are
reproduced by the calculations. Since the intensities in thecalculated spectrum do not perfectly coincide with the
XMCD spectrum, particularly for the L2 and L3 intensity
ratios, the orbital magnetic moment is not deduced from thecluster-model calculation explicitly. The CI contributionsof the ground states are estimated to be d 2 : 42.8%, d 3 L:
44.9%, d 4 L2 : 11.4%, and d 5 L3 : 0.88%. Spin–orbit interaction
coeﬃcients (λ) also become the parameters, where thenonzero value of 0:5 is adopted for the ﬁtting. The λ valuesof 0 or 1 have been reported in Ref. 32. Therefore, theorbital mixing of V yz and zx orbitals in MnV2O4 induces
the small but ﬁnite orbital magnetic moments in V sites fororbital ordering.
In view of the above results, we discuss the site speciﬁc
spin and orbital magnetic moments of MnV2O4 deduced fromthe XMCD analysis. By comparing the XMCD intensities
between Mn and V spectra, the smaller intensities of the V Ledge XMCD compared with those of Mn reveal the spincanted geometry in V sites, consistent with the noncollinear
magnetic structures with the 2-in and 2-out spin conﬁgurations as reported in the literature. The XMCD integrals for

Mn converge to a small value while those for V remain ﬁnite.
This clearly suggests the existence of the small but ﬁnite
orbital magnetic moments in the V sites, which can be
explained by the (i) complex orbital ordering as discussed in
the case of FeV2O4, (ii) domain formation, and (iii) mixing of
the real and complex orbital orderings due to the trigonal
distortion around the V sites. First, as reported usingsynchrotron radiation X-ray diﬀraction measurements, thecomplex orbital ordering is related to the high symmetry of
I41 =amd in FeV2O4.14) The diﬀerent nature of the orbital
ordering between MnV2O4 and FeV2O4 is a result of thecrystal symmetry. As expected in the complex orbital
ordering cases, unquenched large orbital magnetic momentsof 1 B with the spin magnetic moments of 2 B with the
opposite sign should be anticipated. Therefore, the simple
complex orbital ordering is not an acceptable model for
MnV2O4. Although the previous reports of XMCD in
FeV2O4 resulted in quenched orbital magnetic moments in
V sites, the measurement temperature might be far above thecritical temperature for the orbital ordering, indicating thediﬃculty in comparing and discussing the types of orbital
ordering.32) We note that in FeV2O4, the high-spin d 6
conﬁguration of Fe2+ ions is twofold degenerate in e orbitals
resulting in unquenched orbital moments, which trigger
further complex orbital ordering when combined with V ions
resulting in physical properties diﬀerent from those of
MnV2O4. Second, since the samples were scraped to powder,
for the XMCD measurements, some domains might beintroduced. However, the reasonable values of spin andorbital magnetic moments of Mn guarantee to clarify thephysics from the obtained XMCD spectra. Therefore, thescenario of the domain formation is a minor eﬀect. Third, thetheoretical calculations and some experiments fail to suggest
a simple real orbital ordering scenario in MnV2O4.15,19,20)
Although the crystal symmetry of MnV2O4 possesses theI41 =a, the trigonal distortion in VO6 octahedra modulates
the orbital ordering. Therefore, the ﬁnite orbital magnetic
moments deduced from XMCD analysis can be explained
as the mixing of real and complex orbital orderings. Asan element-speciﬁc direct observation of orbital ordering,51
V NMR measurements become comparable for the discussion.19) It also supports the antiferro-type orbital orderingwith a small amount of the ferro-type one through the local
lattice distortion, although the I41 =a space symmetry of theantiferro-type one is maintained. The small but ﬁnite orbital
magnetic moments in V sites deduced from XMCD measurements are consistent with the theoretical proposal by Sarkar
et al.20) and other experiments,17) that is, the mixing of realand complex orbital orderings is essential for the orbital
ordering picture in MnV2O4.
Finally, we discuss the eﬀects of Cr doping in MnV2O4.
Figure 3 shows the Cr L-edge XAS and XMCD spectra for
13% Cr doped MnV2O4. Clear XMCD signals were observedwith a positive sign at the L3 edge and a negative sign at theL2 edge, which is the same sign direction as that for the V
XMCD spectra. The XAS spectral line shapes in comparison
with the XAS spectra of other Cr compounds indicated that
Cr 3+ (3d 3 ) states were formed.38) These results suggest that
the Cr ions shift to V sites with 3+ valence states and arecoupled ferromagnetically with V ions. We note that the XAS
and XMCD line shapes of Mn and V L-edges remain

104703-4©2015 The Physical Society of Japan

J. Phys. Soc. Jpn. 84, 104703 (2015)

J. Okabayashi et al.

σ
σ

σ

σ

Fig. 3. (Color online) XAS and XMCD spectra of the Cr L-edges in 13%
Cr-doped MnV2O4.

unchanged (not shown). The Cr 3+ states can explain the
suppression of orbital ordering temperature because 3d 3electrons in Cr 3+ states fully occupy the t2g states and theorbital degree of freedom is quenched.
4.

Summary

We investigated element-speciﬁc magnetic structures ofspinel-type MnV2O4 using XMCD. X-ray absorption and
XMCD spectra along with theoretical cluster-model analysis
clearly revealed that Mn2+ (d 5 ) and V3+ (d 2 ) states arecoupled antiferromagnetically. Analysis of XMCD spectrausing sum rules revealed that small but ﬁnite orbital magnetic
moments remain in V 3d states, indicating that the complex
and real orbital ordered states coexist. Furthermore, the Cr Ledge XMCD revealed that the Cr doping in MnV2O4 enabled
the substitution of the V site with the same spin direction.
Acknowledgements
This work was performed under the approval of the
UVSOR facility programs at the Institute of Molecular
Science, Japan. This work was partly supported by the
Nanotechnology Platform Program (Molecule and Material
Synthesis). We thank Professor Takashi Mizokawa (Waseda
University) for fruitful discussion.

+

jun@chem.s.u-tokyo.ac.jp
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