A small po-laron, which is a self-trapped state of an electron, can be stabilized when the electron-phonon interaction is large enough to trap the electron at the local lattice deforma-t
Trang 1Insulator-to-metal Transition and Magnetism of Potassium Metals Loaded
into Regular Cages of Zeolite LSX
Takehito Nakano, Duong Thi Hanh, Akihiro Owaki and Yasuo Nozue∗ Department of Physics, Graduate School of Science, Osaka University, Osaka 560-0043, Japan
Nguyen Hoang Nam
Center for Materials Science, Faculty of Physics, Hanoi University of Science, Vietnam National University, Hanoi, Viet Nam
Shingo Araki
Graduate School of Natural Science and Technology, Okayama University, Okayama 700-0082, Japan
(Received 6 June 2012)
Zeolite LSX (low-silica X) crystals have an aluminosilicate framework with regular supercages
and β-cages They are arrayed in a double diamond structure The loading density of guest K
atoms per supercage (orβ cage), n, can be controlled from 0 to ≈ 9 At n < 2, samples are nearly
nonmagnetic and insulating The Curie constant has a clear peak at n = 3, and the electrical
resistivity suddenly decreases simultaneously The electrical resistivity suddenly decreases again at
n = 6 and shows metallic phase at n > 6 These properties are explained by the polaron effect
including the electron correlation Ferrimagnetic properties are observed atn ≈ 9 A remarkable
increase in the resistivity is observed at very low temperatures atn ≈ 9, and is discussed in terms
of the hypothesis of a Kondo insulator
PACS numbers: 75.50.Gg, 75.50.Ee, 75.30.Mb, 71.38.-k, 75.20.Hr, 82.75.Vx
Keywords: Alkali metal, Cluster, Ferromagnetism, Ferrimagnetism, Polaron, Kondo lattice, Zeolite
DOI: 10.3938/jkps.63.512
I INTRODUCTION
Alkali metals loaded into the regular nanospace of
ze-olites exhibit exotic electronic properties that depend on
the structure of zeolites, the loading density, and the
alkali metals The aluminosilicate frameworks of
zeo-lite crystals provide different types of regular arrays of
nanocages, such as the double-diamond structure of β
cages and supercages, the CsCl structure of α and β
cages, and the body centered cubic structure ofβ cages in
zeolites LSX (low-silica X), A and sodalite, respectively
The aluminosilicate framework has negative charges by
the number of Al atoms Exchangeable cations (positive
ions), such as K+, are distributed in the space of the
framework for the charge neutrality The s-electrons of
guest alkali metals are shared with the zeolite cations
to form cationic clusters and are confined in the space
of cages of the framework Theses-electrons exhibit
ex-otic magnetisms, although bulk alkali metals are
non-magnetic [1,2] Ferromagnetism, ferrimagnetism and
an-tiferromagnetism have been observed in zeolites A [2–4],
∗E-mail: nozue@phys.sci.osaka-u.ac.jp
LSX [5] and sodalite [6–8], respectively
Zeolite LSX has the FAU framework structure with Si/Al = 1 as shown in Fig 1(a) The chemical formula
of framework is given as Al12Si12O48 per supercage (or
β-cage) In LSX, β cages having the inside diameter of
≈ 7 ˚A are arrayed in a diamond structure by the sharing
of double 6-memberred-rings (D6MRs) Among them, the supercages of FAU with the inside diameter of ≈
13 ˚A are formed and arrayed in a diamond structure by the sharing of 12-membered-rings (12MRs) having the inside diameter of≈ 8 ˚A The distance between adjacent supercages is 10.8 ˚A which is shorter than the inside diameter of supercage Eachβ cage shares
6-membered-rings (6MRs) with adjacent four supercages The chem-ical formula of zeolite LSX containing K cations is given
as K12Al12Si12O48 per supercage (orβ-cage) and is
ab-breviated as K12-LSX, here In the present paper, we
load guest nK-atoms into K12-LSX The total chemical
formula is given as K12+nAl12Si12O48 (abbreviated as
Kn/K12-LSX, here).
When potassium metal is heavily loaded into Na4K8
-LSX, N´eel’s N-type ferrimagnetism has been observed and is explained by assuming two non-equivalent mag-netic sublattices of clusters in β-cages and supercages
Trang 2
-512-Fig 1 (Color online) (a) Schematic illustration of the
alu-minosilicate framework of zeolite LSX having the FAU
frame-work structure β-cages are arrayed in a diamond structure
by the sharing of double 6-membered rings Among them,
su-percages are formed (b) Illustration of alkali-metal clusters
stabilized inβ-cages and supercages of LSX zeolite.
[8–10] When nNa atoms are loaded into Na12-LSX
(Nan/Na12-LSX), the optical spectrum shows an
insu-lating phase up to n ≈ 10 and suddenly changes to a
metallic spectrum atn ≈ 12 [11] The electrical
resistiv-ity dramatically decreases by several orders of magnitude
with increasingn from 11 to 12 [12] Many paramagnetic
moments are thermally excited at n ≈ 12 [12] The
in-sulating and non-magnetic phase atn < 11 is explained
by the polaron effect as follows: An s-electron has a
fi-nite interaction with the displacement of cations, which
is called the electron-phonon interaction A small
po-laron, which is a self-trapped state of an electron, can be
stabilized when the electron-phonon interaction is large
enough to trap the electron at the local lattice
deforma-tion induced by the electron itself [13] If the
electron-phonon interaction is weak, a large polaron is stabilized
and moves freely The small polaron is immobile
be-cause of a large lattice distortion Two electrons can
be self-trapped by the strong electron-phonon
interac-tion, and the small bipolaron in the spin-singlet state
is stabilized If the electron-phonon interaction is large
enough to combine bipolarons, small multiple-bipolarons
can be stabilized They are the case at n < 11 Large
polarons, however, are stabilized atn > 11 in the
metal-lic state, if multiple-bipolarons become unstable due to
the increase in the Coulomb repulsion among electrons
The thermal excitation of the paramagnetic
susceptibil-ity has been observed in the metallic state and is assigned
to paramagnetic moments of thermally excited small
po-larons The anomalous paramagnetic behavior has been
observed in NMR study of 23Na [14] This
insulator-to-metal transition and the thermal excitation of
para-magnetic moments are explained by both the electron
correlation and the electron-phonon interaction in the
deformable structure of cations [13]
In the present research, we have studied the magnetic
property and the electrical resistivity in Kn/K12-LSX A
remarkable increase in the paramagnetic moments and a
sudden decrease in the electrical resistivity are observed
atn ≈ 3 A sudden decrease in the electrical resistivity is
observed again atn ≈ 6, and a metallic phase is observed
at n > 6 Ferrimagnetic properties are observed at n ≈
9 In addition, a remarkable increase in the electrical resistivity is observed at very low temperatures in the metallic phase atn ≈ 9, and a Kondo insulator model is
discussed
II EXPERIMENTAL PROCEDURES
We used synthetic zeolite powder of Na12-LSX which
were checked in terms of the chemical analysis for Si/Al ratio and the X-ray analysis for structural quality and purity We exchanged Na cations with K ones in KCl aqueous solution many times in order to prepare K12
-LSX The complete dehydration of the zeolite powder was made by heating at 500◦C for one day under high
vacuum Distilled K metal and dehydrated zeolite pow-der were sealed in a glass tube, and K metal was adsorbed into zeolite powder at 150 ◦C through the vapor phase
as well as the direct contact with the zeolite powder In order to improve the homogeneity of loading density of K metal, we performed the heat treatment of zeolite pow-der for two weeks Finally, we obtained a homogeneous K-loading The average loading density ofnK atoms per
supercage (or β cage) was controlled by adjusting the
weight ratio of K metal and zeolite No residual K metal was seen in either the optical spectrum or the optical microscope image
Samples for magnetic measurement were sealed in quartz glass tubes The DC magnetization was measured
by using a SQUID magnetometer (MPMS-XL, Quantum Design) in the temperature range 1.8 - 300 K For the electrical resistivity measurements, the sample powder was put between two gold electrodes, and an adequate compression force≈ 1 MPa was applied during the
mea-surements The electrical resistivity of the sample was obtained by multiplying the measured resistance by the dimensional factor (area/thickness) of compressed pow-der Due to the constriction resistance between powder particles, the observed electrical resistivity is about one-order of magnitude larger than the true value The rel-ative values, however, can be compared with each other, because of the constant compression force Because of the extreme air-sensitivity of the sample, the sample powder was kept in a handmade airproof cell These pro-cedures were completed in a glovebox filled with pure He gas containing less than 1 ppm O2 and H2O Then, the
cell was set in the sample chamber of Physical Property Measurement System (PPMS, Quantum Design) The sample temperature was controlled between 300 and 2 K Impedance measurements on the cell were made by the 4-terminal measurement method by using Agilent 4824A LCR meter in the frequency range from 20 Hz to 2 MHz and DC We analyzed the frequency dependence of the complex impedance by the Cole-Cole plot and checked
Trang 3Fig 2 (Color online) (a) Loading density dependence of
the Curie constant in Kn/K12-LSX, and (b) that of the Curie
(T C) and the Weiss (T W) temperatures
the reliability of the resistivity at < 109 Ωcm A very
small background resistivity, originating from the electric
circuit inside the cell, was included at the order of 0.1
Ωcm This background was subtracted from the value
III EXPERIMENTAL RESULTS AND
DISCUSSION
1 Magnetic properties
The Curie-Weiss behavior is observed in the
tem-perature dependence of the magnetic susceptibility of
Kn/K12-LSX The loading density dependence of the
Curie constant is estimated from the Curie-Weiss law
and is plotted in Fig 2(a) If each supercage (orβ-cage)
has the magnetic moment of spin 1/2, the Curie constant
is expected to be 3.21 × 104 Kemu/cm3 The observed
Curie constant atn ≤ 2 indicates that about 20% of
su-percages have magnetic moments of spin 1/2 Electrons
inβ cages are not observed in the optical spectra at low
loading densities [11] In Fig 2(a), the Curie constant has a clear peak atn ≈ 3 and quickly decreases at n ≈
4 The peak value atn ≈ 3 amounts to ≈ 100%
distri-bution of magnetic moments with spin 1/2 The Curie constant gradually increases forn > 4, and has the large
value corresponding to≈ 100% distribution of magnetic
moments atn ≈ 9.
The Weiss temperature (T W) estimated from the
Curie-Weiss law is plotted in Fig 2(b) It shows small negative values up to n ≈ 8.5, and quickly decreases
down to –10 K atn ≈ 9 Spontaneous magnetization is
clearly observed atn ≈ 9 The extrapolated Curie
tem-perature (T C) is plotted in the same figure From the
negative value of the Weiss temperature, the existence
of an antiferromagnetic interaction is very clear Hence, the observed spontaneous magnetization is assigned to the ferrimagnetism, where two non-equivalent magnetic sublattices, possibly clusters in supercage- and
β-cage-networks, have an antiferromagnetic interaction through 6MRs, likely, N´eel’s N-type ferrimagnetism observed in
Kn/Na4K8-LSX [8–10].
2 Electrical resistivity
The electrical resistivity at 300 K is quiten-dependent
as shown in Fig 3(a) The resistivity at n ≤ 2 is very
high, as expected from the optical spectrum [15], but suddenly decreases atn > 2 in Fig 3(a) The resistivity
gradually increases up ton = 6 However, the resistivity
suddenly decreases again atn ≈ 6 and shows very small
values atn > 6 As shown in Fig 3(b), the resistivity
at n = 6.2 is very low even at low temperatures This
result implies that some amounts of carriers exist at low temperatures, indicating that a nearly metallic phase is realized at n > 6 With the increase in n, the
resistiv-ity decreases at higher temperatures (T > 20 K), but
quickly increases at very low temperatures (T < 20 K).
Atn = 9.0, the value at the lowest temperature is more
than 100 times of those at higher temperatures This re-sult clearly indicates that a very small gap, such as≈ 1
meV, exists at the Fermi energy Samples showing these strange temperature dependences exhibit ferrimagnetic properties as well
3 Polaron effects
In order to explain the high Curie constant and the low resistivity atn ≈ 3 found in Figs 2(a) and 3(a),
re-spectively, we propose the polaron effect fors-electrons
in zeolite According to the theory of self-trapping of an electron in the deformable lattice [13], the self-trapped
Trang 4Fig 3 (Color online) (a) Loading density dependence of
the electrical resistivity at 300 K in Kn/K12-LSX, and (b)
the temperature dependence of the electrical resistivity at n
= 6.2, 8.4, 9.0
Fig 4 (Color online) Schematic illustration of adiabatic
potentials for polarons expected at n < 6 and n > 6 in
Kn/K12-LSX See the text for the details
state (small polaron), can be stabilized in the case of
a strong electron-phonon interaction In the small po-laron, the depth of the deformation potential for electron must be deeper than the kinetic energy If the Coulomb repulsive interaction U between two electrons bound in
the deformation potential well is smaller than the energy gain by the lattice distortion for two electrons atn < 2,
the small bipolaron will be stabilized, as shown in Fig 4, where adiabatic potentials for different types of polarons are illustrated for n < 6 and n > 6 Small bipolarons
have a heavy effective mass and are immobile They have a very small contribution to the electrical conduc-tivity Small bipolarons have a closed electronic shell and are non-magnetic (spin-singlet) Hence, the hopping of
an electron to neighboring small bipolaron states will be suppressed The small Curie constant and the high resis-tivity atn < 2 in Figs 2(a) and 3(a), respectively, can be
explained by small bipolarons However, atn ≈ 3, small
tripolarons become more stable than small tetrapolarons, because the Coulomb repulsion energy among four elec-trons is significant in small tetrapolarons Tripolarons are paramagnetic and can contribute to the hopping con-duction because of the open electronic shell Adiabatic potentials of these small multiple-polarons are illustrated schematically in Fig 4 The increases in the Curie con-stant and the hopping conduction at n ≈ 3 can be
ex-plained
With increasingn, small multiple-polarons are
gener-ated successively These small multiple-polarons can be-come unstable suddenly above a certain critical value of
n, and large polarons, which are mobile, may become
sta-ble, indicating that the stability of large polarons show the to-metal transition This type of insulator-to-metal transition has been observed in Nan/Na12-LSX
at n ≈ 12 [12] In K n/K12-LSX, a similar
insulator-to-metal transition may occur atn ≈ 6 The smaller critical
value ofn in the K-system is due to the weaker
electron-phonon interaction compared with the Na-system The electrons (polarons) in supercages mainly contribute to the electrical conductivity, because of the large windows (12MRs) of supercages Electrons inβ cages, however,
may have no contribution to the conductivity, because
of both the well-localized wave functions inβ cages and
the high potential barriers by D6MRs between them, as shown in Fig 1 An electron in β cage can have
mag-netic moment and contribute to the remarkable increase
in the Curie constant at higher loading densities in Fig 2(a) A sudden decrease in the resistivity atn ≈ 6,
how-ever, has no correlation to the Curie constant Hence, the insulator-to-metal transition is independent ofβ cage
clusters, but occurs in the clusters in the supercage net-work
The localized electronic state in β cage can have a
finite hybridization with supercage electrons through 6MRs In order to explain the ferrimagnetism observed
atn ≈ 9, an antiferromagnetic interaction through 6MRs
is supposed between non-equivalent magnetic sublattices
of clusters in β cages and supercages This interaction
Trang 5Fig 5 (Color online) Schematic illustration of density
of states at the supercage network and the localized state
at β-cage One-electron and two-electron states of β-cage
cluster are located at below and above the Fermi energy of
the supercage metallic network, where the Fermi energy is
located at the center of the narrow band
and the electron correlation in narrowβ cage can lead to
the model of the Kondo lattice, as discussed in the next
section
4 Possibility of a Kondo insulator
As seen in Fig 3(b), the electrical resistivity at the
metallic phase shows a remarkable increase at very low
temperatures At least, a very narrow gap may exist at
n ≈ 9, but no gap at n ≈ 6.2 Such a narrow gap at
n ≈ 9 is hardly expected from the ordinary electronic
model Hence, we propose a model shown in Fig 5 [5],
where the Fermi energy is located at the center of the
narrow band provided by the clusters in the supercage
network, and the localized state at β cage is located
be-low (above) the Fermi energy for one- (two-) electron
state The Coulomb repulsion energy U is supposed for
two electrons in the β cage Differently from the
ordi-nary Kondo scheme, metallic electrons at the supercage
network have the spin polarization, because both of the
supercage and the β-cage networks have magnetic
mo-ments in the ferrimagnetic state If a small gap can be
opened at the Fermi energy, likely a Kondo insulator,
the electrical resistivity increases at very low
tempera-tures This model is quite speculative, and further study
is needed
IV CONCLUSION
Remarkable loading-density dependences are observed
in the Curie constant and the electrical resistivity in
Kn/K12-LSX The Curie constant has a clear peak at
n ≈ 3, and the electrical resistivity suddenly decreases
simultaneously A sudden decrease in the electrical resis-tivity is observed atn ≈ 6, and a metallic phase appears
atn > 6 These properties are explained by the polaron
effect Ferrimagnetic properties are observed atn ≈ 9 A
remarkable increase in the resistivity is observed at very low temperatures atn ≈ 9 This result is interpreted in
terms of the hypothesis of the Kondo insulator
ACKNOWLEDGMENTS
This work was supported by Grant-in-Aid for Scien-tific Research (24244059 and 19051009) and by G-COE Program (Core Research and Engineering of Advanced Materials-Interdisciplinary Education Center for Materi-als Science)
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