Long-range Ordering in Pr(2)NiO(4+δ) Single Crystals studied by Resonant Soft X-Ray Scattering

1
THE MATERIAL: STRUCTURE AND PROPERTIES
OF PRASEODYMIUM NICKELATE
1.1 introduction
The instability of a metal’s Fermi surface at low temperatures gives arise
to the formation of spin or charge density waves, superconductivity, or
other collective electronic ordering phenomena
[1][2][3][4][5]
.
In such materials, known as strongly correlated materials, the mobility
of the valence-state electrons is suppressed due to the interactions be-
tween their mutual repulsion. The 3d-transition metal oxides (TMOs)
represent an important category of the strongly correlated materials.
In this thesis, the focus will be addressed to praseodymium nickelate, a
transition metal oxide where the reduction of the valence shell leads to
the switch of its behaviour from metallic to insulating and localization of
spins
[6][7][8]
. The Fermi surface is modified depending on the repulsive
interactions between valence-state electrons, leading to the formation
of ordered states, which can be studied by using scattering techniques.
The complexity of these structures requires high-quality and pure sam-
ples and only single crystals can satisfy these conditions. The prepara-
tion can be challenging but thanks to the development of techniques as
the floating zone method (FZM), nowadays the growth of large single
crystals is achievable in a reasonable time.
1.2 the crystal structure
1.2.1 The Perovskites and its derivatives
The basic building block of many TMOs is the perovskite unit cell,
named after the mineral CaTiO
3
, with general formula ABO
[9]
3
(Fig-
ure 1.1). It can be described by a three-dimensional (3D) cubic network
ofcorner-sharingoctahedrawiththelargerAalkaline-earthorrare-earth
metal cations occupying every site created by 8 BO
6
octahedra, where
B is a transition metal, and the symmetry space group is Pm
¯
3m
[10]
.
The perovskite phases are very reactive and flexible in terms of oxygen
stoichiometry and substitution of cations A and B with other cations of
different sizes. In order to accommodate the electrostatic potential of
doping ions, the octahedra rotate or distort their shape by tilting or
elongate/shrink along favourable crystalline directions. These displace-
ments within the unit cell lead to a lower symmetry and the size and
the nature of A and B cations play a key role.
Indeed, an important parameter to take into account the variation of
the equilibrium positions of ions in the octahedra is the Goldschmidt
tolerance factor t (Equation 1.1), which measures the degree of distor-
tion as a function of the interatomic distances between cations and
oxygen ions (d
A−O
and d
B−O
)
[11]
.
t =
d
A−O
√
2d
B−O
(1.1)
17
Fig. 1.1: The ideal cubic perovskite structure: the large grey A-cation is
surrounded by corner-sharing BO
6
octahedra
[9]
.
An ideal perovskite structure has a t value equal or close to 1 and a
cubic structure. The tilting of the octahedra is induced by a smaller
size of A cation than the ideal value, resulting in a t value smaller
than 1. However, in the range 0.89 < t < 1 the cubic structure is kept.
Lower symmetries, i.e. tetragonal or orthorhombic, are present in case
of lower t values and, in rare cases, when the t value is higher than 1 a
low-symmetry hexagonal structure is observed.
The nature of cations is relevant for the variation of chemical and
physical properties of perovskites. One of the most important charac-
teristic of cations is their mixed valence states, allowing high flexibility
in the stoichiometry and offering the possibility to obtain derivative
phases by oxidation (A
n
B
n
O
3n−1
), reduction (A
m
B
m
O
3m+2
), excess of
BO
2
intergrown layers (A
l
B
2l
O
2l+3
) and excess of AO intergrown layers
(A
2i
B
i
O
2i+2
). The latter one, referred to as Ruddlesden-Popper phase
in honour of its discoverers’ names
[12]
, will be discussed in details in
the next paragraph.
1.2.2 The Ruddlesden-Popper phases
The general formula of these layered perovskites is (AO)(ABO
3
)
n
where
A is an alkaline earth or rare earth ion, B is a transition metal ion
and n is a positive integer. The unit cell consists of n consecutive
perovskite layers ABO
3
alternating with rock salt layers AO along the
c-axis (Figure 1.2). When n=1 the formula is A
2
BO
4
and the struc-
ture corresponds to the K
2
NiO
4
type, with a perovskite layer ABO
3
sandwiched between two rock salt AO layers. The minimal thickness of
perovskite layers gives the phase highly anisotropic behaviour.
The ideal structure is tetragonal but the symmetry can be lowered to
orthorhombic due to the tilting of octahedra. Great interest has been
focused on the tunable properties of such class of perovskites, due to
the wide range of doping of all the elements involved in the structure.
18
Fig. 1.2: The ideal structure of Ruddlesden-Popper phases with n=1,2,3
[13]
.
1.2.3 The Ln
2
NiO
4+δ
nickelates
In recent years, the structural, transport and electro-magnetic prop-
erties of Ln
2
NiO
4+δ
(Ln = La, Pr, Nd; 0<δ<0.25), and various sub-
stituted phases Ln
2−x
Sr
x
NiO
4
(Ln = La, Pr, Nd, Gd, Sm; 0<x<1.6)
have been extensively investigated, because of the similarity of their
structural and electronic properties with the high temperature su-
perconducting cuprates (HTSC), La
2−x
Sr
x
CuO
4
phases and because
of reports of incipient superconductivity and antiferromagnetism in
La
2−x
Sr
x
NiO
[14][15][16][17][18][19][20]
4
.
Ln
2
NiO
4+δ
compounds exhibit a wide range of oxygen nonstoichiome-
try. One particularity of these phases is their ability to accept additional
oxygen in the structure readily at room temperature, up to five times
more than cuprates. Several reviews revealed that they can undergo
reversible electrochemical redox reactions in the entire range of oxygen
doping
[21][22][23]
. The intercalated oxygen atoms are located in the
tetrahedral interstitial sites of the Ln
2
O
2
layers, as confirmed by several
Fig. 1.3: The orthorhombic Bmab symmetry represented schematically (left).
Perpendicular view of NiO
6
octahedra, tilted by an angle of -45
◦
from either the a– or b–axes and compressed either along the a– or
b–axes. The dotted lines denote a single unit cell (right).
19
Fig. 1.4: The tetragonal P4
2
/ncm symmetry represented schematically (left).
Perpendicular view of NiO
6
octahedra, tilted by an angle of 45
◦
from
either the a– or b–axes. The dotted lines denote a single unit cell
(right).
Fig. 1.5: The tetragonal I4/mmm symmetry represented schematically (left).
Perpendicular view of NiO
6
octahedra without any tilt angle. The
dotted lines denote a single unit cell (right).
studies
[24][25]
.
Each interstitial site is in double tetrahedral coordination, surrounded
by 4 Ln ions and by 4 O ions at the apex (O
ap
) of the octahedra involved,
i.e. two in the rock salt layer and other two in the perovskite layers.
The stabilization of Ln
2
NiO
4+δ
compounds takes place by reducing
intrinsic charge separation between the electropositive ionic rock salt
Ln
2
O
2
and covalent NiO
2
layers, in cooperation with the minimization
of structural strain arising from the distortion of layers. The gain of an
equilibrium state involves three interconnected mechanisms:
1. The intercalation of oxygen causes the shift of apical oxygen ions
from their original position towards Ln, opening the interstitial
tetrahedral site. Such displacement simultaneously lengthens
the apical oxygen d
Ni−O
(ap)
distance, while it shortens the apical
d
Ln−O
(ap)
distance, maximizing the distances between apical and
interstitial oxygen ions asδ6=0. This effect results in the softening
of anisotropy of chemical bonding between the overbonded NiO
2
equatorial planes and underbonded Ln
2
O
2
planes.
2. The interstitial oxygen ions usually induce a tilt of NiO
6
octa-
hedra and a partial oxidation of Ni
2+
to Ni
3+
in NiO
2
layers,
known as charge disproportionation, which compensates the ex-
cess of negative charge of the interstitial oxygen atoms and shrink
d
Ni−O
(eq)
.
20
Fig. 1.6: The orthorhombic Immm symmetry represented schematically (left).
Perpendicular view of NiO
6
octahedra without any tilt angle and
compressed either along the a– or b–axes. The dotted lines denote a
single unit cell (right).
Fig. 1.7: The orthorhombic Pccn symmetry represented schematically (left).
Perpendicular view of NiO
6
octahedra, tilted by an angle of 45
◦
from
either the a– orb–axes and compressed either along the a– orb–axes.
The dotted lines denote a single unit cell (right).
3. The cooperative tilting of the NiO
6
octahedra about [110] axis, in
addition to the bending of Ni–O–Ni bond angle from 180
◦
, allows
lattice parameter matching of the two layers. The compression of
the Ni–O bond length is never involved in this step.
Several phase transitions can take place modifying the structure of
Ln
2
NiO
4+δ
asafunctionofexcessoxygen. Atroomtemperature, thesto-
ichiometricandnear-stoichiometricLn
2
NiO
4
consistsofanorthorhombic
(Bmab) (Figure 1.3); a distorted tetragonal phase (P4
2
/ncm) (Fig-
ure 1.4) is observed for near-stoichiometry compounds, and the undis-
torted tetragonal symmetry (ideal K
2
NiF
4
with space group I4/mmm)
(Figure 1.5) is seen for intermediate oxygen compositions. An or-
thorhombic phase replaces the latter one (Immm) (Figure 1.6) in highly
nonstoichiometric compounds and biphasic regions are observed between
these line-monophasic structures
[26][27][28][29][31][32][33][34]
.
Phase transitions occurs at the same time as a function of temperature.
All the stoichiometric lanthanide nickelates (δ = 0) exhibit a high-
temperature tetragonal (HTT) phase (I4/mmm) at high temperature.
In this case, the tolerance factor t referred to the Ruddlesden-Popper
phases is equal to 1 and Ni–O–Ni bond angle is 180
◦
. When t is less
than 1, at low temperature the structural strain increases due to the
higher thermal expansion coefficients of Ln–O bond length compared
to Ni–O bond length
[35]
. To reduce the strain, Ln
2
NiO
4+δ
compounds
undergo a second-order structural transition to an orthorhombic sym-
21