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Evidence of High Critical Temperature Charge Density Wave Transitions in the (PO2)4(WO3)2m Family of Low
Dimensional Conductors for m ≥ 8
Alberto Ottolenghi, Jean-Paul Pouget
To cite this version:
Alberto Ottolenghi, Jean-Paul Pouget. Evidence of High Critical Temperature Charge Density Wave Transitions in the (PO2)4(WO3)2m Family of Low Dimensional Conductors for m ≥ 8. Journal de Physique I, EDP Sciences, 1996, 6 (8), pp.1059-1083. �10.1051/jp1:1996116�. �jpa-00247231�
J. Phys. I £Fance 6 (1996) 1059-1083 AUGUST 1996, PAGE 1059
Evidence of High Critical Temperature Charge Density Wave
lhansitions in the (P02)4(W03)2m Family of Low Dimensional Conductors for m > 8
Alberto Ottolenghi (*) and Jean-Paul Pouget
Laboratoire de Physique des Solides (**), Bâtiment 510, Université Paris-Sud,
91405 Orsay Cedex, France
(Received 22 March 1996, accepted 2 May 1996)
PACS.64.70.-p Specific phase transitions PACS.71.45.Lr Charge-density-wave systems
PACS.77.80.-e Ferroelectricity and antiferroelectricity
Abstract. Trie monophosphate tungsten bronzes with pentagonal tunnels (MPTBp) of gen-
eral formula (P02)4(W03)2m form a family of layered conductors where trie average number of conduction electrons per tungsten atom 2/m can be changed while keeping trie same structural
array. Previous investigation of trie low m
= 4,6 and 7 members of this family bave shown that
this serres is subject to several successive mcommensurate charge density wave (CDW) long
range orders below room temperature (RT). Here
we present an X-ray scattering study of trie
m = 8, 9,10,11,12,13 and 14 members of this family. A very ricin and diverse structural phase diagram is observed. Trie
m = 8 member shows only short range order below RT at two different incommensurate wave vectors while commensurate and/or incommensurate long rpnge order is observed above RT for m > 9. Incommensurate modulations are observed for trie m = 11 and 13 members and commensurate ones for trie other members. In most of trie 7 > m > 13 members trie observation of several harmomcs suggests that trie CDW modulation is non-sinusoïdal, which could be trie fingerprint of electron localization phenomena due either to strong electron-phonon
or electron-electron interactions. These CDW instabilities bave been tentatively attributed to chains a and a ~ b of W06 octahedra into which trie Re03 type layers of (P02)4(W03)2m can
be decomposed. In addition, trie observation for
m > 9 of a commensurate (1/2,0,0)
or (1/2, 0, 1/2) modulation or (1/2, 0, ii diffuse scattering suggests trie occurrence of an mcipient W03 type antiferroelectric mstability which interacts with the CDW for m < 13. We further discuss trie division between high m value and low m value members m relation to trie x dependence of trie
physical properties of some M~W03 tungsten bronzes famines and finally propose a dielectric to magnetic duality between CDW tungsten oxides and superconducting copper oxides.
1. Introduction
Interest in macroscopic quantum phenomena, such as superfluidity, superconductivity (SC), density waves in solids, lasers, has grown larger in recent years as they bring to everyday life fundamental concepts of quantum mechanics [ii. Low dimensional metals have been exten-
sively studied since twenty years because they show an extremely large variety of macroscopic
(* e-mail: [email protected]
(** CNRS-URA 02
© Les Éditions de Physique 1996
quantum phenomena (electron instabilities, such as SC, charge density waves (CDW) and spin density waves (SDW)) and allow a constant and stimulating interaction between high
precision measurements and highly nontrivial theoretical models. The richness of electronic instabilities and the study of the competition between different ground states that can be done
through these materials brings to a deep understanding of the role played by electron-phonon and/or electron-electron interactions and by the dimensionality of the system in establishing
these macroscopic quantum states of matter (quantum condensates of electron-electron pairs
or of electron-hole pairs). Transition metal bronzes and oxides provide a natural Mass of low dimensional materials due to the presence of transition metal planar d orbitals, which are
intrinsically low dimensional, and of oxygen, which preserves the tentacular properties of the transition metal ion by acting as a bridge in the formation of chemical bonds between different metal atoms. By using a basic unit of a square of four oxygens with a central transition metal
ion, nature can built structures which are one, two
or three dimensional (ID, 2D or 3D) with respect to the anisotropy of the chemical bond network (we will refer to this dimensionality
as structural), but which are ID or 2D with respect to the anisotropy of the bonding (we will refer to this second dimensionality as electronic). A lot of oxides fit in this dass of materials and SC copper oxides are the best known example. Molybdenum and tungsten bronzes and
oxides fit also in this class and have received a lot of attention m the past fifteen years [2,3]
as they show CDW transitions. An extremely small variation of thermodynamic conditions
(chemical potential, temperature, pressure, etc. can cause an extremely large variation of the
physical properties of these inorganic matenals. Owing to this "thermodynamic sensitivity"
we can say that these materials are good candidates for all kind of instabilities, implying then
an extremely large variety of physical phenomena.
1.1. TUNGSTEN OxiDEs. The basic structural building block of tungsten oxides is a WD6 octahedron. The binary oxide WD3 furnish the simplest example of these materials: it is an antiferroelectric (AFE) semiconductor at room temperature [4], with a 2.58 eV energy gap [si and an ReD3 type perovskite structure [6] (corner sharing octahedra) with two (metastable?) slightly different modifications [si. WD3 shows a complex structural phase diagram with, in addition to the high temperature AFE displacement of the tungsten atoms, several antiferrodis- tortive transitions related to different kind of rotations of the WD6 octahedra [7]. Dther binary tungsten oxides are known, induding the simple metallic WD2 18] and layered semiconduct- ing oxides with substoichiometric shear phases [9] (WD3-x). Tungsten trioxide can be doped
with Na to give sodium tungsten bronzes [7,10] (Na~WD3), a family of compounds where the
gradual filling of the tungsten trioxide ir* band by the sodium electrons allows an interpolation
between the dielectric behaviour of WD3 and the metallic behaviour of the perovskite type material NaWD3 iii,12] (these two limiting materials are each representative of a larger Mass of materials). The perovskite type structure is maintained both for low and for high sodium
concentration while the tetragonal tungsten bronze (TTB) structure [13] or a mixture of these two structures are found at room temperature for 0. il < ~ < 0.43 [11]. It is important to note that the structural dimensionality of cubic sodium tungsten bronze is equal to three, while its electronic structure reflects a 2D character [14] due to the presence of three perpendicular Planes of planar d orbitals of the WD6 octahedra. As the electronic dimensionality is different from the structural dimensionality we will say that this system possesses a "hidden" low di-
mensionality [15] (the electronic one) and we will use this definition ail throughout the paper.
This concept has been intuitively used by Mattheiss in the analysis of the band structure of ReD3 116].
Many other tungsten bronzes are known I?i, some of which show SC at low temperature [17]:
in NaxWD3 SC has been observed below 0.57 K [18] (TTB phase) and in M~WD3 SC transition
N°8 HTC CDW TRANSITIONS IN (P02)4(W03)2m 1061
b a
1?ig. 1. Structure of trie m = 6 member of the family of monophosphate tungsten bronzes
(P02)4(W03)2m with pentagonal tunnels, MPTBp.
1,emperatures showing strong ~ dependence and with a maximum of 7 K [19] (~
= 0.26 and
M
= Rb: hexagonal bronze) have been reported. In all of these bronzes, lower dimensional
structures built from the juxtaposition of sharing corners WD4 squares can be recognized.
1.2. (PD2)4(WD3)2m. Monophosphate tungsten bronzes with pentagonal tunnels
(MPTBp) of general formula (PD2)4(WD3)2m have been discovered more than ten years
<igo [20] and are a new Mass of materials which exhibit CDW instabilities [21, 22] due to the presence of "hidden" ID electronic dimensionality [15,22]. Figure 1 shows the orthorhombic
structure of (PD2)4(WD3)2m for m
= 6.
This structure is built of layers of tungsten trioxide separated by interlayers of PD4 tetrahedra
so that its structural dimensionality is equal to two. The PD4 groups play the role of charge
ieservoirs and give their excess electron to the insulating tungsten trioxide layers resulting in 2/m electrons on average per tungsten atom. The unit cell includes two symmetry related layers
with different orientation of the WD6 octahedra. ilhe idealized top layer of Figure 1
can be built
by cutting the idealized cubic ReD3 structure along the (Î,1, 2)~ plane, the two perpendicular
directions Il,1, 0]~ and Il,î,1]~ corresponding to a and b directions of MPTBp (the suflix c indicates that we are using here the cubic coordinate system of the Re03 structure). In the
same way the idealized bottom layer in Figure 1 can be built by cutting the idealized cubic
ReD3 structure along the (1,î,É)~ plane, the two perpendicular directions Il,1,0]~ and [î,1,1]~
<,orresponding to a and b directions of MPTBp. The thickness of the top layer along the Ii,1,2]~
direction will depend on the number of WD6 octahedra in the layer (the same number will jjive the thickness along the Il,Î, É]~ direction for the bottom layer). The connection between
]ayers through PD4 tetrahedra forms pentagonal tunnels running along the crystallographic a
direction and is obtained by two kinds of symmetrically equivalent tetrahedra: by running along
the crystallographic b direction one altemates a tetrahedron shanng three corners with the top layer octahedra and one corner with the bottom layer octahedra and a tetrahedron sharing
one corner with the top layer octahedra and three corners with the bottom layer octahedra.
A little more geometrical remarks bring to orthorhombic symmetry and a general formula for trie crystallographic parameters of the idealized structure of the m > 3, m # 5 members [20]:
am "
aRe03à bm
"
aRe036 (2)
where dpo4
" 2.95 À is the thickness of
a PD4 tetrahedra along the c direction and aReo~ =
3.8 À is the parameter of cubic ReD3 (Perovskite cell). The /fi factor is the cosinus of the
angle (35 degrees) between the [0,0,2]~ direction (the octahedra's direction) and the [Î,1,2]~
direction (the c direction of MPTBp) in a cubic lattice. Remark that the three sets of planes of WD4 squares of the original cubic structure have been cut to give three sets of chains (ribbons
of WD4 squares) running along the crystallographic a and a ~ b directions so that each WD6 octahedra participates to three different chains, one of each kind. This system possesses then
a "hidden" one-dimensionality which finds its origin m the "hidden" two-dimensionality of perovskite type Na~WD3, being lowered by one due to the cut of the structure along the Il,1, 2)~ planes delimiting the single layer. The two sets of chains in the a ~ b directions are
equivalent by orthorhombic symmetry and one can move along each of them through a step of width of two octahedra in the cubic ReD3 structure: if we take the top layer in Figure 1 and the a +b direction, the chains are ribbons running in the [2,0,1]~ direction of the cubic lattice and have a width of m/2 corner sharing WD4 squares in the [0,0,1]~ direction and of m corner sharing WD4 squares in the Il,0,0]~ direction (Fig. 1 shows the case of m even; for m odd the
value of the width in the [0,0,1]~ direction alternates between the two values @ and ).
a chains correspond then to ribbons running along the Il,1, 0]~ direction and having a width of
m corner shanng W04 squares m the Il,0,0)c direction an~l of m corner sharing W04 squares
in the [0,1,0]~ direction. Dne can move along them through a step of width of one octalledra
m the cubic ReD3 structure. All type of chains can then be thought as built of segments of
m WD4 squares (with two or one octahedra step type connection between the segments). The
pentagonal tunnel connection between layers increases then the isolation of each single layer:
due to the relative orientation at 70 degrees (twice 35 degrees of the orientation of the cubic
structure in one layer) of the neighbouring layers, there is no ribbon of WD4 squares giving
rise to chains in one layer which is coplanar to ribbons giving rise to chains in the neighbouring layers so that interactions between chains of neighbouring layers is weakened. By decreasmg
m, the structure starts to change from the value m
= 5: this member has a layered type
structure with alternating slabs of the m ='4 and
m = 6 type [23]. The m
= 4 member has again a structure of the type of Figure 1. By further decreasing m the PD4 tetrahedra are
mcreasingly isolating the WD6 octahedra. For m
= 3, PD4 tetrahedra penetrate in the WD6 loyers resulting in a complex 3D network [24]. A further decrease of m results in a drastic
reduction of both structural and electronic dimensionalities: the m
= 2 member has still the structure of Figure 1 but no a ~ b chains can be obtained as the step of width of two octahedra
C°rresP°nding t° this type of chains cannot be completed; the
m = 2 member has then a ID structure [25] (a chains only) and is a semiconductor with an antiferromagnetic (AF) ground
State [26], while the last member (m
= 1) of the family has a cubic zirconium pyrophosphate
structure [27] corresponding to an array of isolated WD6 octahedra (this should be called a
"zero dimensional" structure) and is an insulator at room temperature.
lV°8 HTC CDW TRANSITIONS IN (P02)4(W03)2m 1063
The idealized model of Figure implies orthorhombic symmetry with space group P ) ) )
l'or even members and space group P£ ) ) for odd members. The real structure is slightly
different from this idealized model, showing rotations of the WD6 octahedra [20]. In even m
members these rotations suppress the
m mirror perpendicular to a and the symmetry centers
iesulting in either P21cn or P212121 (P21cn is found for m
= 2, while P212121 for m
= 4, 6,8).
In the m
= 5 member the intergrowth of m
= 4 and m
= 6 slabs results in monoclinic symmetry [23]. In the m = 7 member the same tilting of octahedra suppress the m mirrors ,ind the twc-fold axes normal to the a axis; as a result two possible subgroups P ) can be
onsidered with either c or b as the binary axis (the latter one being observed) [28]. In the
m > 8 members the structure is of the type of Figure 1 [20] no refinement of these structures is available at present and orthorhombic symmetry with space group P212121 for even m and
P2nn for odd m has been proposed [20].
The PD4 groups allow to dope WD3 without adding disorder due to the insertion of atoms within WD3, as is the case in Na~WD3. By formally taking m = oo the chemical formula of MPTBp should then be considered equivalent to WD3, as for ~
= 0 in Na~WD3. Two
<idditional structural constraints with respect to Na~WD3 can be recognised: the electronic
<oncentration (2/m) in MPTBp is a function of the width of the layers (m), while hidden (alectronic one-dimensionality results from the cut of the ReD3 structure that is shown in
Figure 1. Both X-ray diffraction and transport data for the m = 4,6, 7 members show the presence of several incommensurate CDW transitions [21,22, 29, 30] below room temperature j[see Tab. I) which for m
= 4,6 can be explained within the "hidden" nesting properties of their Fermi Surfaces (FS) [15,22]; the m = 7 higher temperature CDW transition is extremely complicated, showing up to seven diffraction harmonics and hysteresis loops in the temperature
dependence of satellite intensities and electrical resistivity. Room temperature resistivity of these materials increases with increasing m [29]. Preliminary results on high m value members have also been published [31,32]: X-ray diffraction data for the m
= 8 member show only
two kinds of CDW short range order (SRD) at low temperature [31]; for the m = 9 member
X-ray satellite reflections can be observed at room temperature and they are related to two iiifferent structural phase transitions at high temperature [31], while no other structural phase
transition cari be observed at low temperature down to 20 K (see also Ref. [22] ). For m = 9
high transition temperatures and commensurate modulations appear. If we take ~ = 2/m to compare MPTBp and Na~WD3, the high m value part of the family (m > 8) corresponds to lhe low electron concentration regime of sodium tungsten bronzes where complex electronic
properties have called for so much attention in the past. The difference between high m
value members (m > 8) and low m value members (m < 8) recalls the division found in the literature between the so-called metal and non-metal phases of Na~WD3 133]. This fact encourages the search for the mechanisms which are responsible of the change of character of the phase transitions in the high m value members of MPTBp. To this extent structural data
allows to measure the modulation wave vectors and the transition temperatures and it is a key
to the understanding of the microscopic interactions between structural and electronic degrees
of freedom of this system. An extensive investigation by X-ray scattering of the structural phase diagram of the high m value (m
= 8 to 14) members of this family of tungstates is then presented.
2. Experimental
Samples of different compositions used in this investigation were prepared as described in the literature [34]. Long annealing times are employed for the preparations corresponding to
high m values. Samples were provided by M. Greenblatt (m = 8) of the Sate University of
Table I. Transition temperatures (TÎ~~) and modulation waue nectars (qÎ~~ ) of trie struc- tural phase transitions of trie MPTBp family. Data for trie m
= 4, 6, 7 members are taken from reference [22].
m lattice
4 80(~1) =(0.330(5),0.295(5),?) 52(~1) =(0.340(5),0.000(5),?)
6 120(~1) =(0.385(5),0.000(5),?) 62(~1) =(0.310(5),0.295(5),?)
r~30
7 188(~l) nql~~=n(0.260(3),0.073(3),0;,27(5))
n = 1, 2, 3,4, 5,6, 7
60(~1) nq[~~=n(0.12(1),0.03(1),0.15(5))
n = 1,3,5 8
r~ 220 SRD: q)~~=(0.47(2),0.02(1),0.15(10))
r~ 200 SRD: nq[~~=n(0.19(2),0.03(1),0.06(03))
n = 1, 2, 3, 4, 5,6
9 565(~5) qÎ~~=(°.5°(1),°.°°(1),°.°(2)) 330(~5) qÎ~~=(0.17(1),0.00(1),0.0(2))
10 r~450 q(~°J(300K)=(0.43(1),0.00(1),0.0(1))
and Q(~°)(300K)=(0.14(1),0.00(1),0.0(1))
11 560(~5) nq(~~)(T) n
= 1, 2,3
q(~~)(300K)=(0.43(1),0.00(1),0.0(1))
12 535(~5) q/~~=(0.12(1),0.00(2),0.0(2)) 500(~5) qi~~~=(0.50(1),0.00(1),0.5(2))
13 550(~5) nql~~~=(0.053(8),0.016(10),?)
n = 1,2
510(~5) 160(~10)
14
New Jersey (Rutgers, U-S-A-); D. Groult (m = 9,10,11,14) of I.S.M.R.A. (Caen, France);
J. Marcus (m
= 12,13) of L.E.P.E.S.-C.N.R.S. (Grenoble, France). Crystal of the m
= 8
member are dark purple red, while for m > 8 they are dark blue. For all selected compositions crystals are platelets, limited by orthorhombic directions Il,1,0], [1,î,0], [1,0,0], of typical size
of1.5
mm x 0.5 mm x ù-1 mm. Samples of the m
= 8 to 14 members have been characterized by rotating crystal and Weissenberg techniques. The value of m can be obtained from the measure of the lattice parameter c using formula (1) of Section 1. The temperature dependence of the X-
ray scattering has been measured, for the m
= 8 member between 35 K and room temperature, for the m
= 9 member between 30 K and 650 K, for the m
= 10,11,12 members between là K and 650 K, for the m
= 13 member between 65 K and 650 K and for the m
= 14 member between là K and 800 K.
To perform low temperature experiments the samples were fixed using Araldite glue on a goniometer head mounted on the cold finger of a closed-circuit helium cryocooler. X-ray diffrac- tion expenments were performed in fixed film and oscillating (5 degrees) crystal geometries
