Magnetic behaviour of the MTbF6 fluoroterbates (M=Cd, Ca, Sr, (α/β)-Ba)

Article abstract of DOI:10.1016/j.jssc.2011.10.030

Neutron powder diffraction has been performed on the MTbF₆ fluorides (M=Cd, Ca, Sr, (α/β)-Ba). Four of these fluorides (Cd, Ca, Sr, β-Ba) are built of a (pseudo-) tetragonal packing of [TbF ₆]^2- chains and only differs by the chains relative orientations. Thus this series represents a valuable opportunity to evaluate the Tb⁴-Tb⁴ magnetic interactions. All the compounds displayed antiferromagnetic order (T_N=2.70 K (Cd), 2.15 K (Ca), 2.60 K (Sr), 2.10 K (β-Ba)), except for the α form of BaTbF₆. The crystal structure of this latter fluoroterbate has also been investigated by means of high-resolution neutron powder diffraction. From Neutron Powder Diffraction data, CdTbF₆ and β-BaTbF₆ magnetic structures were determined, together with the metamagnetic behaviour of β-BaTbF₆ as a function of an external magnetic field. A tentative phase diagram is then given for β-BaTbF₆. Advantage was taken of the polymorphism of the BaTbF₆ fluoroterbate to analyse, on the basis of topological parameters such as bond distances and angles, the magnetic behaviour of its α and β forms. It was shown that superexchange interactions are present in β-BaTbF₆, and that these interactions may also rule the magnetic behaviour of the other MTbF ₆ (M=Ca, Sr, Cd) tetravalent terbium fluorides.

Full text of DOI:10.1016/j.jssc.2011.10.030

Journal of Solid State Chemistry 185 (2012) 229–237
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry
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Magnetic behaviour of the MTbF6 fluoroterbates (M¼Cd, Ca, Sr, (
a/b)-Ba)
n
a
b
b
c
M. Josse a,d, M. El-Ghozzi a, , D. Avignant , G. Andre , F. Bouree , O. Isnard
´
´
a
ꢀ
Laboratoire des Mate´riaux Inorganiques, UMR 6002 CNRS, Universite´ Blaise Pascal, 63171 Aubiere, France
b Laboratoire Le´on Brillouin, CEA-CNRS, CEA-Saclay, 91191 Gif-sur-Yvette, France
c Institut N´eel, CNRS/Universite´ Joseph Fourier, UPR2940, 38042 Grenoble, France
d CNRS, Universite´ de Bordeaux, ICMCB, Pessac, France
a r t i c l e i n f o
a b s t r a c t
Article history:
Neutron powder diffraction has been performed on the MTbF6 fluorides (M¼Cd, Ca, Sr, (
a/b)-Ba). Four
of these fluorides (Cd, Ca, Sr,
b
-Ba) are built of a (pseudo-) tetragonal packing of [TbF6]2ꢀ chains and
Received 24 June 2011
Received in revised form
3 October 2011
only differs by the chains relative orientations. Thus this series represents a valuable opportunity to
evaluate the Tb4þ-Tb4þ magnetic interactions. All the compounds displayed antiferromagnetic order
Accepted 17 October 2011
Available online 11 November 2011
(TN¼2.70 K (Cd), 2.15 K (Ca), 2.60 K (Sr), 2.10 K (
structure of this latter fluoroterbate has also been investigated by means of high-resolution neutron
powder diffraction. From Neutron Powder Diffraction data, CdTbF6 and -BaTbF6 magnetic structures
were determined, together with the metamagnetic behaviour of -BaTbF6 as a function of an external
magnetic field. A tentative phase diagram is then given for -BaTbF6. Advantage was taken of the
polymorphism of the BaTbF6 fluoroterbate to analyse, on the basis of topological parameters such as
bond distances and angles, the magnetic behaviour of its and forms. It was shown that
superexchange interactions are present in -BaTbF6, and that these interactions may also rule the
magnetic behaviour of the other MTbF6 (M¼Ca, Sr, Cd) tetravalent terbium fluorides.
& 2011 Elsevier Inc. All rights reserved.
b-Ba)), except for the a form of BaTbF6. The crystal
Keywords:
b
Tetravalent terbium
Fluorides
b
b
Neutron diffraction
Magnetic structure
Metamagnetism
Superexchange
a
b
b
1. Introduction
fluoroterbates incommensurate square-modulated magnetic
structures are observed at low temperature (below 2.1 K).
The ordering temperature observed have been correlated to the
efficiency of the dipolar interactions to relay the frustration
induced by the pseudo-hexagonal packing of magnetic [TbF6]2ꢀ
chains, while the magnetic behaviour of Li2TbF6 suggests non-
dipolar interactions in these chains.
The magnetic properties of paramagnetic lanthanides ions are
related to their partially filled 4f shell, which is known to have a
pronounced internal character. Because of their limited spatial
extension and of the screening of the 5d and 6s shells, 4f electrons
hardly interact with the electronic shells of neighbouring atoms,
especially with other 4f electrons. Thus chemical bonding of rare-
earths in oxides and fluorides is predominantly ionic, and their
magnetism is usually dominated by dipolar interactions, espe-
cially in fluorides.
To supplement our investigations, in order to bring further
evidences of these non-dipolar interactions, we investigated the
magnetic behaviour of the MTbF6 (M¼Cd, Ca, Sr, (
a/b)-Ba)
fluorides.
However structural studies of tetravalent terbium fluorides
suggest that the singular crystal-chemistry of this class of fluor-
ides (a propensity of the Tb4þ ions to adopt an 8-fold coordina-
tion) may be influenced by the half-filled 4f shell of the Tb4þ ion
[1,2], i.e. that 4f electrons influence the Tb–F chemical bonding in
these compounds.
Similarly, the magnetic behaviour of fluoroterbates, studied for
many years in our laboratory, tends to demonstrate that non-
dipolar interactions occur in these materials and may rule their
magnetic behaviour [3–5], as for example, the recent study of the
magnetic behaviour of M2TbF6 (M¼Li, K, Rb) fluorides [6]. In these
The crystal structures of a and b polymorphs of BaTbF6 were the
first, among fluoroterbates, to be determined from single-crystal
X-ray diffraction (XRD) [7,8]. SrTbF6 was reported to be isomorphic
to b-BaZrF6 [9]. CaTbF6 and CdTbF6 adopt an anti-KSbF6 [2] and are,
after Li2TbF6 [1], new examples of the singular crystal-chemistry of
fluoroterbates. The remarkable feature of the MTbF6 fluorides is that
they are all, except a
-BaTbF6, built of [TbF6]2ꢀ chains (Fig. 1). These
chains adopt different orientation, depending on the size of the
associated alkaline earth, yielding different symmetries for the
corresponding crystal structure. This series represents a valuable
opportunity to evaluate the Tb4þ–Tb4þ magnetic interactions, due
to the homogeneity of the polyhedral frameworks ([TbF6]2ꢀ chains)
on one hand, and to the polymorphism of BaTbF6 on the other hand,
which should allow more insight the structural parameters influen-
cing the magnetic behaviour of fluoroterbates.
n Corresponding author.
E-mail address: Malika.EL-GHOZZI@univ-bpclermont.fr (M. El-Ghozzi).
0022-4596/$ - see front matter & 2011 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2011.10.030

230
M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
Fig. 1. Crystal structure of CaTbF6 and CdTbF6 viewed along the c-axis (top left) and the b-axis (top right), Tb4þ polyhedra in green, Ca2þ/Cd2þ polyhedra in blue. Crystal
structure of SrTbF6 and
-BaTbF6 viewed along the a-axis (bottom left) and the c-axis (bottom right), Tb4þ polyhedra in green, Sr2þ/Ba2þ as spheres. (For interpretation of
the references to color in this figure legend, the reader is referred to the web version of this article.)
b
The present work deals with a neutron diffraction study of the
magnetic behaviour of the titles compounds. The magnetic
oxidation state of terbium ions in the title compounds. NDP
under magnetic field for the -BaTbF6 fluororterbate were
b
structures of CdTbF6 and
b
-BaTbF6 were determined. The crystal
recorded on the super-D2B instrument at the Institut Laue
Langevin (ILL, Grenoble). The data were analysed with the FULL-
PROF program [11], using the magnetic form factor of Gd3þ for
the magnetic refinements, as this ion is isoelectronic to Tb4þ for
which no magnetic form factors are available. The dipolar mag-
structure of -BaTbF6 was also investigated by means of high
a
resolution powder neutron diffraction to benefit from the most
accurate description of its anionic framework.
The magnetic behaviour in these MTbF6 (M¼Cd, Ca, Sr, Ba)
compounds will be discussed with respect to crystal-chemical
netostatic energy of
b-BaTbF6 has been obtained using the
considerations, with a particular focus on the
of BaTbF6. The nature of the magnetic interactions involved in
these fluoroterbates will be investigated.
a
and
b
polymorphs
concept of non-overlapping charges developed by Bertaut [12]
to account for the long range character of the dipolar interactions.
The results in Section 3.1.3 are for Tb4þ magnetic moments equal
to 7 mB (theoretical value).
2. Material and methods
3. Results and discussion
Polycrystalline samples of the title compounds were obtained
by heating overnight stoichiometric mixtures of MF2 (Strem
chemicals) (M¼Cd, Ca, Sr, Ba) and TbF4 (prepared by fluorination
of Tb4O7, (Merck)), under pure fluorine gas, at 500 1C. The samples
were then annealed for 12 h at temperatures ranging from 540 to
720 1C.
3.1.
a and b-BaTbF6 fluorides
3.1.1. Nuclear structure
3.1.1.1. a–
were recorded on the G4-1 diffractometer in the temperature
range 1.4–5 K. The nuclear structure of -BaTbF6 at 5 K was
refined on the basis of the model determined from single-
crystal X-ray diffraction [8], leading to conventional RBragg¼3.0%
(Table 1). Refined atomic coordinates, in good agreement with
those obtained from single-crystal X-ray data, are presented in
b–BaTbF6:. Neutron Powder Diffraction (NPD) patterns
Neutron powder diffraction patterns were recorded at the
Leon Brillouin Laboratory (LLB, Saclay, France) on the two-axis
˚
b
G4.1 diffractometer (
l
¼2.4266 A) down to 1.4 K, without any
magnetic field, for the determination of the magnetic structure
˚
[10], and on the 3T2 high resolution diffractometer (
l¼1.2251 A)
at 300 K for the refinement of the crystal structure of a-BaTbF6. It
is worth mentioning that all the structural refinements performed
were fully consistent with the previously reported crystallo-
graphic data [2,4,7,8], and thus confirmed the tetravalent
Table 2. The crystal structure of b-BaTbF6 is built of infinite
[TbF6]2ꢀ linear chains arising from [TbF8]4ꢀ polyhedra sharing
opposite and almost orthogonal edges. These chains adopt a

M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
231
pseudo-tetragonal packing and are linked by the Ba2þ ions, which
are surrounded by four [TbF6]2ꢀ chains. In this structure, the
[TbF6]2ꢀ chains are rigorously linear (Tb–Tb–Tb angles are equal
to 1801 in the chains).
3.1.1.2. b–
a
-BaTbF6:. The crystal structure of
a
-BaTbF6 has been
previously determined from single-crystal X-ray diffraction [7],
but the low symmetry (space group Pı) lead us to record a NPD at
300 K, using thermal neutron
resolution diffractometer 3T2, in order to confirm the positional
parameters of the fluorine atoms. As shown by Fig. 2, the Rietveld
refinement unambiguously confirmed the triclinic symmetry,
with RBragg¼4.0% (Table 1). The refined atomic coordinates
gathered in Table 3 show the good agreement between X-ray
ꢁ
˚
(
l
¼1.2251 A), on the high
Table 1
Characteristics of the neutron powder diffraction Rietveld refinement of
(300 K) and -BaTbF6 (5K) nuclear structures.
a-BaTbF6
b
a
-BaTbF6
b
-BaTbF6
and neutron data. The crystal structure of
a-BaTbF6 is based on
10ꢀ
(nuclear, 3T2)
(nuclear, G4-1)
tetrameric units [Tb4F26
]
built by corner sharing between
6ꢀ
[Tb2F14
]
dimers, themselves built of [TbF8]4ꢀ polyhedra
ꢁ
System and space group
Refined cell parameters:
Orthorhombic Cmma
(no. 67)
Triclinic P ı (no. 2)
10ꢀ
sharing an edge, as displayed by Fig. 3(a). These [Tb4F26
]
a¼7.760(1),
b¼11.600(1),
c¼5.485(1)
Z¼4
a¼7.348(1),
tetramers are further linked together by two common corners,
leading to the formation of corrugated layers of [TbF6]2ꢀ formula
that expand along the a and b-axes. The Ba2þ ions lie between
these corrugated layers.
b¼8.448(1), c¼8.675(1)
˚
(A and deg.)
a
b
g
¼101.62(1),
¼96.83(1),
¼114.65(1)
Z¼4
3.1.2. Magnetic studies
2.4266
1.2251
˚
Wavelength (A)
range/step
8–881 ꢁ 0.1
6–125.71 ꢁ 0.05
2
y
3.1.2.1. a–
At low temperature, several purely magnetic Bragg peaks
appear in the -BaTbF6 NPD diagram, that can be indexed in the
b-BaTbF6. (i) Zero field study
Number of independent
reflections
30
3190
Number of intensity
dependent parameters
11
48
b
orthorhombic (a b 2c) magnetic unit cell, with h even, k and l odd
indices. As a direct consequence of these selection rules, two
magnetic moments separated by [1/2 0 0] in the crystal unit cell
are identical, and opposite when they are separated either by
[1/2 1/2 0] or [0 0 1]. The resulting magnetic structure is then
antiferromagnetic, with ferromagnetic [TbF6]2ꢀ chains, and anti-
ferromagnetic coupling between neighbouring [TbF6]2ꢀ chains.
The thermal variation of the intensity of the most intense
magnetic Bragg peak (Fig. 4) lead to TN¼2.1(1) K.
Conventional rietveld reliability factor (%)
Rp
11.3
10.7
8.06
7.97
4.02
2.06
1.78
Rwp
RBragg
RF
w2
2.98
3.04
8.25
Table 2
Let us note that this magnetic structure can also be described
using the commensurate propagation vector k¼(0 1 1/2). Bertaut’s
representation analysis [13] for Cmma space group, k¼(0 1 1/2)
propagation vector and (4a) Wyckoff position, leads first to an
8-dimensional Gk group (all the rotational symmetry elements of
the space group Cmma (D22h1) leave k invariant) and then to eight
one-dimensional irreducible representations for Gk (Table 4). For
the (4a) Wyckoff position, only two Tb4þ in the crystal unit-cell
Atomic positions refined at 5 K (from G4-1 data) for
b
-BaTbF6.
Atom
X
Y
Z
Ba
0
1/4
0
0.4436(1)
0
Tb
1/4
F(1)
F(2)
0
0.4300(4)
0.3719(3)
0.1557(8)
0.2541(6)
0.3060(4)
Fig. 2. Rietveld plot for the refinement of
a-BaTbF6 nuclear structure at 300 K (3T2 data).

232
M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
Table 3
(Table 6 and Fig. 5). Each Tb4þ magnetic moment is directed along
Atomic positions (300 K) refined from single-crystal XRD data (top) [7] and from
the a-axis of the crystal structure, i.e. along the direction of the
[TbF6]2ꢀ chains, and equal to 6.68(3)
mB, as compared to the 7 mB
high resolution neutron powder diffraction data (bottom, in italic) for
a-BaTbF6.
theoretical gJJ value (Table 4). This magnetic structure can be
described by the magnetic group CImma.
2
Atom
Tb1
X
Y
Z
˚
B (A )
(ii) Neutron diffraction under magnetic field
0.18367(8)
0.25951(7)
0.28111(7)
0.430(8)
0.1836(6)
0.2579(5)
0.2815(5)
0.51(4)
In order to evaluate the stability of the antiferromagnetic
structure under external magnetic field, we undertook a neutron
diffraction study under magnetic field (H). As powder samples
may exhibit superparamagnetic behaviour, we prepared sintered
Tb2
Ba1
Ba2
F1
0.22918(8)
0.78338(7)
0.06120(7)
0.387(7)
0.2286(5)
0.7823(5)
0.0615(4)
0.51(4)
0.2988(1)
0.31428(9)
0.76950(9)
0.66(1)
pellets (to avoid grain reorientation) of
b-BaTbF6 that were
0.2971(8)
0.3130(8)
0.7691(6)
0.62(6)
broken into millimetric parts (to avoid preferred orientation due
to pellet texturation) and then placed in the 8 mm diameter
cylindrical sample holder (applied magnetic field was parallel to
the sample holder axis).
0.7072(1)
0.2311(1)
0.45645(9)
0.72(1)
0.7067(8)
0.2294(7)
0.4559(6)
0.62(6)
0.095(1)
0.236(1)
0.027(1)
1.0(1)
0.0975(8)
0.2364(7)
0.0258(7)
1.07(3)
NPD data obtained in zero-field cooled process confirmed the
antiferromagnetic transition previously observed at TN¼2.1 K
(see Fig. 4).
F2
0.119(1)
0.383(1)
0.496(1)
1.0(1)
0.1171(7)
0.3833(7)
0.4956(1)
1.07(3)
F3
1/2
0
0
1.3(2)
The progressive application of magnetic field at 1.4 K (in the
antiferromagnetic state) first induced a reduction of the intensity
of antiferromagnetic contributions in the NDP. Around 0.15 T,
small contributions associated with the onset of ferromagnetic
order were observed, and grew with increase of the applied
magnetic field. At 1 T a small amount of the antiferromagnetic
phase was still present, while at 4 T the sample was completely
ferromagnetic (Fig. 6).
1/2
0
0
1.07(3)
F4
0.087 (1)
0.754(1)
0.258(1)
1.2(1)
0.0877(8)
0.7542(7)
0.2589(6)
1.07(3)
F5
0.292(1)
0.534(1)
0.288(1)
1.1(1)
0.2928(8)
0.5355(6)
0.2873(6)
1.07(3)
F6
0
1/2
0
1.2(2)
0
1/2
0
1.07(3)
F7
0.527(1)
0.108(1)
0.726(1)
1.0(1)
The same procedure repeated at higher temperatures did not
reveal significant changes in the onset of this magnetic transition.
It is worth to note that the ferromagnetic ordering could be
stabilised above TN by applying magnetic field, for example at
T¼2.34 K with H¼1 T. After heating the sample up to 20 K, the
antiferromagnetic ordering could be observed again below 2.1 K
after a zero field cooling.
0.5262(8)
0.1078(7)
0.7247(7)
1.07(3)
F8
0.396(1)
0.638(1)
0.001(1)
1.1(1)
0.3924(8)
0.6350(7)
0.0011(6)
1.07(3)
F9
0.310(1)
0.177(1)
0.469(1)
1.2(1)
0.3120(8)
0.1772(7)
0.4693(6)
1.07(3)
F10
F11
F12
F13
0.869(1)
0.284(1)
0.199(1)
1.1(1)
0.8692(9)
0.2830(8)
0.1978(6)
1.07(3)
This experience both confirmed the zero field antiferromag-
netic ordering in
b-BaTbF6 and revealed its metamagnetic beha-
0.082(1)
0.960(1)
0.703(1)
1.4(2)
0.0814(8)
0.9612(7)
0.7018(6)
1.07(3)
viour, which originates from the weakness of interchains
˚
magnetic interactions, with Tb–Tb distances exceeding 5.5 A.
0.236(1)
0.041 (1)
0.145(1)
1.2(1)
A tentative H–T magnetic phase diagram (Fig. 7) has been built
0.2350(8)
0.04047(7)
0.14688(7)
1.07(3)
from our observation of the evolution of
structure under magnetic field.
b-BaTbF6 magnetic
0.497(1)
0.6230(1)
0.702(16)
1.4(2)
0.4943(8)
0.6296(7)
0.7029(6)
1.07(3)
3.1.2.2. b–a-BaTbF6. NPD diagrams were recorded on the G4-1
have to be characterised from a magnetic point of view: Tb1 in [1/
4 0 0] and Tb2 in [3/4 0 0]. From their magnetic moments, S1 and
S2 respectively, one immediately gets the magnetic moments for
all Tb4þ ions in the magnetic (a b 2c) unit-cell, as [1/2 1/2 0] and
[0 0 1] translations are associated to a change of sign for the
diffractometer, for increasing temperatures in the range 1.4–10 K.
No long-range magnetic ordering was observed at T¼1.4 K, but
only a significant modulation of the paramagnetic background,
which is the signature of short-range magnetic correlations. These
correlations probably arise from weak magnetic interactions
between Tb4þ ions within the tetramers. The location of this
magnetic diffusion signal, close to the (0 1 0) nuclear Bragg
magnetic moment components. The magnetic representation
G is
associated to 6 ꢁ 6 matrices, characteristic of the transformations
of the spin components of Tb1 and Tb2 by Gk symmetry elements
˚
position (d¼7.37 A), suggest that magnetic interactions may
(Table of
representation can be reduced as
The basic vectors associated with each representation appear-
ing in correspond to six possible magnetic structures, namely
G characters: 6 2 2 ꢀ2 0 0 0 0). This 6-dimensional
also take place between these tetramers, within the corrugated
[TbF6]2ꢀ layers previously described, although its important
width indicate a relatively short correlation length.
G¼t1þt2þt3þt4þt5þt6.
G
three ferromagnetic [TbF6]2ꢀ chains and three antiferromagnetic
[TbF6]2ꢀ chains, the Tb4þ magnetic moments within a chain being
parallel either to the a or b or c axis (Table 5). Let us recall that the
resulting magnetic structure for the 8 Tb4þ in the magnetic unit
3.1.3. Magnetic interactions in BaTbF6 fluorides
a
and b-BaTbF6 possess the same elements and the same
stoichiometry, so that the striking difference in their magnetic
behaviour is closely related to their structural characteristics and
allows for the investigation of the magnetic interactions involved
in these fluoroterbates. Correlation between polyhedral linking
and magnetic behaviour of fluoroterbates was previously outlined
by a systematic study of their magnetic properties, and led to the
notion of ‘‘Polyhedra Connection Mode’’ (PCM) [5]. From this
cell is antiferromagnetic, whatever t1–6, as [1/2 1/2 0] and [0 0 1]
translations are always associated to a change of sign for the
magnetic moment components from one chain to the neighbouring
ones. The best agreement between observed and calculated NPD
diagrams for the magnetic structures described above [
t
i, i¼1–6] is
unambiguously obtained for
t1, a structure based on ferromagnetic
arrangement of Tb4þ magnetic moments within the [TbF6]2ꢀ
chains and antiferromagnetic interactions between these chains
point of view the magnetic behaviours of
a and b BaTbF6 are both
coherent with the PCM phenomenological rule: the necessity to

M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
233
10ꢀ
Fig. 3. (a) Crystal structure of
a
-BaTbF6 viewed along the b-axis. Enlightened tetrameric building unit [Tb4F26
]
in clear blue, Ba2þ in cyan. (b): three-dimensional
framework formed by Tb4þ ions less than 5.76 A from one another, viewed along the b-axis (atoms in green: Tb1, in red: Tb2, in blue, edge-sharing connexion, in green,
corner sharing connexion, in purple unconnected Tb4þ ions separated by 5.13 A.). (For interpretation of the references to color in this figure legend, the reader is referred to
˚
˚
the web version of this article.)
Table 5
b
-BaTbF6 magnetic structure: basis vectors as determined from Bertaut’s repre-
sentation analysis and refined values for the Tb4þ magnetic moment components
(representation t1 from NPD data refinement).
I.R
B.V
Tb4þ S1
Tb4þ S2
Tb4þ S1
Tb4þ S2
at [1/4 0 0]
Mx My Mz
at [3/4 0 0]
Mx My Mz
Refined values (mB
{Mx My Mz}
)
t1
t2
t3
t4
t5
t6
100
100
010
010
001
001
100
Mx¼6.68(3)
c1
c2
c3
c4
c7
c8
ꢀ100
010
Mx
My
Mz
ꢀMx
ꢀMy
ꢀMz
My
Mz
0ꢀ10
001
00ꢀ1
have either at least 50% of edges in the connection between
terbium polyhedra, or a continuous edge pathway, to observe
long range magnetic order at low temperature. These criteria are
fulfilled for
polyhedra). In the case of
b
-BaTbF6 (infinite chains of 100% edge-connected
a
-BaTbF6, the Tb4þ polyhedra are only
33.3% edge-connected, and with no infinite edge pathway
Fig. 4. Thermal variation of the (0 1 1/2) magnetic reflection integrated intensity
of -BaTbF6.
10ꢀ
b
(connections within a [Tb4F26
]
tetramer).
In order to investigate the magnetic interactions involved in
these compounds, Table 7 recalls the relevant distances and angles
for both forms of the BaTbF6 fluoride. Clearly, two types of
magnetic interaction can be considered there: magnetic exchange
and dipolar ones. Let us examine them both consecutively.
Table 4
Irreducible representations associated to the Gk group (Kovalev’s notation [14]).
h1
h4
h3
h2
h25
h28
h27
h26
Let us first now examine the case of exchange interactions
between neighbouring Tb4þ ions, either direct or indirect. Firstly,
direct exchange interactions are highly unlikely, considering the
large Tb4þ–Tb4þ distances in both compounds. We shall then
focus our interest on indirect exchange, via Tb–F–Tb super-
exchange paths, and analyse the Tb–F distances in both BaTbF6
s1
s2
s3
s4
s5
s6
s7
s8
1
1
1
1
1
1
1
1
1
1
1
1
ꢀ1
1
1
ꢀ1
1
1
ꢀ1
ꢀ1
1
1
ꢀ1
ꢀ1
1
1
1
1
ꢀ1
ꢀ1
1
1
ꢀ1
ꢀ1
ꢀ1
ꢀ1
1
1
ꢀ1
1
ꢀ1
ꢀ1
1
ꢀ1
ꢀ1
ꢀ1
ꢀ1
1
ꢀ1
1
1
ꢀ1
1
ꢀ1
ꢀ1
1
compounds,
a and b. In b-BaTbF6, the four Tb–F distances
ꢀ1
ꢀ1
ꢀ1
1
1
associated to edge-shared polyhedra are identical and equal to
˚
2.28 A. Something similar is observed for a-BaTbF6, but with less
1
ꢀ1
ꢀ1

234
M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
Table 6
Characteristics of the Rietveld refinement of
structures at 1.4 K.
b-BaTbF6 and CdTbF6 magnetic
CdTbF6
b-BaTbF6
(magnetic, G4-1)
(magnetic, G4-1)
System and space group
Refined cell parameters
Orthorhombic Cmma
Triclinic, P1 (no. 1)
(no. 67)
˚
˚
a¼7.756(1) A,
a¼b¼10.348(2) A
˚
˚
b¼11.593(1) A
c¼7.691(2) A
˚
2c¼10.965(1) A
Z¼8
Wavelength
˚
˚
2.4266 A
2.4266 A
8–881 ꢁ 0.1
8–881/0.1
352
1
2y range/step
Independent reflections
Intensity dependent
parameters
531
7
Rietveld reliability factor (%)
Rp
10.0
10.9
4.39
49.4
Rwp
RBragg
42.4
Magnetic pattern
Fig. 7. Tentative magnetic phase diagram for
b-BaTbF6. The dashed lines are
only
34.1
6.56
2.31
hypothetical boundaries extrapolated from our experimental observations.
Rmag
RF
w2
1.37
4.16
22.0
distances corresponding to shared corners in
a-BaTbF6, either
within the tetrameric unit or between two neighbouring tetramers,
are all shorter than or equal to Tb–F distances for edged shared
polyhedra in the same compound. From experimentally observed
magnetic properties, either in
a-BaTbF6 (long-range magnetic
order) or -BaTbF6 (short-range magnetic correlations), the mag-
b
netic behaviour of the polymorphic fluoroterbate BaTbF6 is then
consistent with the existence of superexchange interactions.
Of course dipolar interaction are always involved in magnetic
ordering, and the large distance separating the spin chains in
b-BaTbF6 unambiguously indicates that their coupling rely on
dipolar interactions. A potential Tb–F – – F–Tb super–
(Ba)
superexchange coupling should be inexistent considering the
already weak superexchange interaction taking place between
Tb4þ magnetic moments in
b-BaTbF6, as suggested by the low
ordering temperature: TN¼2.1 K. Dipolar interactions couple the
spin chains antiferromagnetically and allow for the existence of a
long range, three-dimensional, magnetic order. The easy reversal
of one of the magnetic sublattices of antiferromagnetic b-BaTbF6
by an external magnetic field shows their relative weakness,
yielding the observed metamagnetic behaviour. Furthermore,
dipolar energy calculations show that in b-BaTbF6, ferromagnetic
chains are more stable with magnetic moments oriented along
the a-axis (ꢀ1265 mK (a-axis) vs þ560 mK (b-axis) and
þ700 mK (c-axis)), which is the orientation actually observed in
this work. However the striking difference between the magnetic
Fig. 5. Rietveld plot of the refinement of the magnetic structure of
1.4 K. The most intense magnetic reflexions are marked by *. Inset: magnetic
structure of -BaTbF6 viewed along the a-axis.
b-BaTbF6 at
b
behaviours of
a and b forms of BaTbF6 requires the consideration
of superexchange interactions to be explained.
3.2. CaTbF6 and CdTbF6 fluorides
3.2.1. Nuclear structure
The room temperature crystal structures of CaTbF6 and CdTbF6
have been determined and presented in details in a previous study
[2], the results of which were used in the present work. The anti-
KSbF6 structure of these compounds is represented in Fig. 1. How-
ever neutron diffraction has revealed the polymorphic behaviour of
CaTbF6.
On cooling the sample on the G4-1 diffractometer, a first order
phase transition was observed in CaTbF6. The transition occurs
around 220 K on cooling and around 250 K on heating. Attempts
to determine the unit cell were unsuccessful, and thus the low
temperature crystal-structure could not be determined at the
moment.
Fig. 6. Evolution of the magnetic diffraction pattern of b-BaTbF6 with a vertical
magnetic field (0, 0.04, 0.08, 0.16, 0.4, 1 and 4 T from top to bottom) at 1.4 K.
regular edge-shared polyhedra (two Tb–F distances smaller and
˚
two higher than 2.28 A, with the same mean distance value), and
no continuous edge-pathway. Let us also note that the Tb–F

M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
235
Table 7
Topological data for
a and b-BaTbF6 at 300 K.
Shared edges
Shared corners
Others
Angle (deg.)
Tb–F–Tb
Angle (deg.)
Tb–F–Tb
˚
˚
˚
Distances (A)
Distances (A)
Distances (A)
Tb–Tb
Tb–F
Tb–Tb
Tb–F
Tb–Tb
a
-BaTbF6
3.83
Tb1
Tb1–F–Tb2
116.21
Tb2–F–Tb1
112.21
Tb1–Tb2
4.26
Tb1
Tb1–F–Tb2
161.4
Tb1–Tb2
5.07–5.61
Tb1–Tb1
5.13–5.35
2.17/2.44
Tb2
2.18
Tb2
Tb2–Tb2
4.36
Tb2–F–Tb2
180.0 ꢁ 2
2.17/2.34
2.13
2.18
2.28
Tb2–Tb2
4.56
b-BaTbF6
3.88
2.27
117.41
–
–
–
5.52
5.76
magnetic order around 2.15 K (CaTbF6, Fig. 8) and 2.70 K
(CdTbF6). In both cases the observation of purely magnetic
contributions in the NDP accounts for the onset of an antiferro-
magnetic order. Since the crystal structure of the low-tempera-
ture form of CaTbF6 remains unknown, the determination of the
magnetic structure of CaTbF6 could not be undertaken.
In the case of CdTbF6, however, considering that the structural
rearrangement is minor and does not affect the cationic sublat-
tice, phenomenological considerations allowed us to determine
the magnetic structure of this tetravalent terbium fluoride.
First, the magnetic diagram was obtained in form of the difference
diagram (1.83–4.13 K). This revealed a quite simple magnetic diffrac-
tion pattern, but since the structural distortion was not elucidated,
the actual symmetry of the material remains unknown and thus
representational analysis could not be performed.
Fig. 8. Evolution of CaTbF6 neutron diffraction pattern between 5 K (front pattern)
and 1.4 K (rear pattern).
However, the [TbF6]2ꢀ chains arranged in a tetragonal packing
in CdTbF6 crystal structure may be compared to the corrugated
chains (edge-sharing antiprisms) observed in the M2TbF6 (M¼Li,
K, Rb) series of terbium fluorides [6]. In these latter compounds,
Tb4þ magnetic moments are coupled ferromagnetically within
the chains, the interchain interactions being antiferromagnetic.
By analogy, we envisaged for CdTbF6 a magnetic structure built of
ferromagnetic [TbF6]2ꢀ chains coupled antiferromagnetically.
Since there are two Tb4þ ions in the nuclear unit cell, located
at (1/2 1/2 1/4) and (1/2 1/2 3/4), such a magnetic structure,
as the chains expand along the
z direction, require a
!
k ¼ ð1=2 1=2 0Þ propagation vector, i.e. a fourfold magnetic cell
as compared to the nuclear cell.
The simulated NDP corresponding to this hypothesis revealed
a perfect agreement with the observed magnetic pattern (Fig. 9).
Rietveld refinement of this hypothesis, using the difference
pattern previously mentioned, confirmed this magnetic structure,
with a refined magnetic moment of 6.5 mB for the Tb4þ ion
Fig. 9. Rietveld plot of the difference pattern (1.83 K–4.13 K) refinement of the
magnetic structure of CdTbF6. Inset: magnetic structure of CdTbF6 viewed along
the c-axis.
(theoretical value: 7.0 mB).
Given the important absorption cross-section of Cadmium
(2520 barns), which necessitates long counting times to obtain a
good statistic, NDP have been recorded at room and low tem-
peratures (To5 K) only for this sample. Comparison of these
diagrams suggests a small modification of the crystal structure
Table 6 gathers the details of this refinement, for which the
elevated values of Rp, Rwp et Rexp arise from the weak signal to
noise ratio of our data, due to the presence of cadmium in our
sample.
(two small additional contribution at 2
satisfying structural hypothesis could be elaborated from our
experimental data.
y¼601 and 771), but no
3.3. SrTbF6
3.3.1. Nuclear structure
Although SrTbF6 was one of the first tetravalent terbium
fluorides synthesised, its crystal structure has never been inves-
tigated. Burns et al. [9] reported SrTbF6 to be isotypic to RbPaF6,
3.2.2. Magnetic studies
NDP recorded at low temperature on CaTbF6, and also on
CdTbF6 revealed that these two fluoroterbates exhibit long range
i.e. to
b-BaTbF6, but our attempts to fit the neutron diffraction

236
M. Josse et al. / Journal of Solid State Chemistry 185 (2012) 229–237
The inset of Fig. 11 displays the pre-ordering magnetic diffusion
signals observed in this family. These signals are identical for all
representatives, and some of their features (signal around 321 (2 ))
y
are characteristics of one-dimensional systems, as previously exem-
plified during the study of Li2TbF6 fluoroterbate, the structure of
which is also based on [TbF6]2ꢀ chains.
Thus, from the similarities of their magnetic behaviour, it is
likely that the magnetic order in these compounds relies on the
establishment of superexchange interactions, as we demonstrated
from the study of the polymorphic fluoroterbate BaTbF6.
4. Conclusion
Fig. 10. Evolution of the neutron diffraction pattern of SrTbF6 between 5 K
In this work the magnetic behaviour of the MTbF6 fluorides
(front pattern) and 1.4 K (rear pattern).
(M¼Ca, Sr, (
powder diffraction. A magnetic order was observed in all com-
pounds except -BaTbF6, the crystal structure of which was inves-
tigated by high-resolution neutron powder diffraction.
The magnetic structures of CdTbF6 and -BaTbF6 were deter-
mined from phenomenological considerations, consistently with
Bertaut’s representational analysis in the case of -BaTbF6.
A neutron diffraction study under magnetic field emphasised
the metamagnetic behaviour of -BaTbF6.
a/b)-Ba, Cd) was investigated by means of neutron
a
b
b
b
In previous works, the study of fluoroterbates with various
dimensionalities [5] correlated the ordering temperature to the
Polyhedra Connection Mode and suggested that non-dipolar
interaction may occur in tetravalent terbium fluorides.
The analysis of the magnetic behaviour of the polymorphic
fluoroterbate BaTbF6, on the basis of topological parameters,
reveals the existence of superexchange interactions. These mag-
netic interactions are likely to be involved in the other member of
a/b
)-Ba, Cd) family, all built of [TbF6]2ꢀ
Fig. 11. Magnetic diffraction pattern of
CdTbF6 (rear) at 1.4 K. Inset: diffusion signal ascribable to short range magnetic
correlations detected in -BaTbF6 (blue), SrTbF6 (red) and CaTbF6 (cyan). Grey
b-BaTbF6 (front), SrTbF6, CaTbF6 and
the MTbF6 (M¼Ca, Sr, (
chains, as suggested by their similar magnetic behaviours. This
work confirm the fact that dipolar interactions only are not
sufficient to explain the magnetic order in one-dimensional
fluoroterbates, as was suggested by the study of M02TbF6 (M0 ¼Li,
K, Rb) fluorides [6], and demonstrate the existence of super-
exchange interactions, promoted by Tb4þ polyhedra edge sharing.
To complete these studies, the magnetic properties of tetra-
valent terbium fluorides with other dimensionalities for their
polyhedral framework (for example two-dimensional matrices)
will be presented in a future article.
b
rectangle: 1D signal. (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
data using this hypothesis were unsuccessful, as several signifi-
cant contributions were not simulated.
Upon cooling, in order to study the magnetic properties of
SrTbF6 at low temperature, a nuclear phase transition was
observed around 210–220 K. Similarly to the case of CaTbF6, the
unit cell could not be determined from our diffraction data.
The study of the magnetic properties of fluoroterbates, initially
engaged after the observation of a favoured capacity for the Tb4þ
ion to assume eight-coordination, will also be worth of interest
concerning the recently discovered fluoroterbates in which the
Tb4þ ion adopt a seven-coordination [15]. The topological differ-
ences associated with such an environment could allow for a
better understanding of the magnetic ordering in tetravalent
terbium fluoride.
3.3.2. Magnetic studies
NDP recorded between 1.40 and 5 K revealed the appearance
of a long range antiferromagnetic order in SrTbF6 below 2.6 K
(Fig. 10). Although the magnetic diffraction pattern of SrTbF6
is relatively simple, the magnetic structure could not be
solved given the absence of structural model for its low
temperature phase.
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