Neutron diffraction study of quasi-1D Ising ferromagnet [Co(NCS)2(pyridine)2]n

Article abstract of DOI:10.1016/j.jpcs.2018.11.001

The quasi-one-dimensional [Co(NCS)₂(pyridine)₂]_n coordination polymer built of ferromagnetic chains of Co(II) ions linked by (NCS)₂ anions is known as an Ising ferromagnet that magnetically orders at T_C = 3.9 K. We performed a neutron diffraction study and show that the magnetic structure is collinear ferromagnetic, static, and without any glassy component. The magnitude of the ordered magnetic moment of Co(II) is 3.65(15) μ_B, which points to a relatively large contribution of the orbital moment. The direction of the moment is close to the direction of the Co–N(pyridine) bond, which confirms literature ab initio calculations. We show that dipolar interactions are mainly responsible for the magnetic interchain coupling.

Full text of DOI:10.1016/j.jpcs.2018.11.001

Accepted Manuscript
Neutron diffraction study of quasi-1D ising ferromagnet [Co(NCS)2(pyridine)2]n
Stanisław Baran, Andreas Hoser, Michał Rams, Serghei Ostrovsky, Tristan Neumann,
Christian Näther, Zbigniew Tomkowicz
PII:
S0022-3697(18)31020-5
https://doi.org/10.1016/j.jpcs.2018.11.001
PCS 8787
DOI:
Reference:
To appear in: Journal of Physics and Chemistry of Solids
Received Date: 18 April 2018
Revised Date: 8 November 2018
Accepted Date: 9 November 2018
Please cite this article as: Stanisł. Baran, A. Hoser, Michał. Rams, S. Ostrovsky, T. Neumann, C. Näther,
Z. Tomkowicz, Neutron diffraction study of quasi-1D ising ferromagnet [Co(NCS)2(pyridine)2]n, Journal
of Physics and Chemistry of Solids (2018), doi: https://doi.org/10.1016/j.jpcs.2018.11.001.
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ACCEPTED MANUSCRIPT
Neutron diffraction study of quasi-1D Ising ferromagnet [Co(NCS)2(pyridine)2]n
Stanisław Baran,a Andreas Hoser,b Michał Rams,a Serghei Ostrovsky,c Tristan Neumann,d
Christian Näther,d,1 Zbigniew Tomkowicza,1
aM. Smoluchowski Institute of Physics, Jagiellonian University, Prof. S. Łojasiewicza 11, 30-
348, Kraków, Poland
bHelmholtz-Zentrum Berlin für Materialen und Energie GmbH, Hahn-Meitner Platz 1, 14109
Berlin, Germany
cInstitute of Applied Physics, Academy str. 5, MD-2028 Chisinau, Moldova
dInstitut für Anorganische Chemie, Christian-Albrechts-Universität zu Kiel, Max-Eyth-Straße
2, 24118 Kiel, Germany.
Keywords:
A. Ferromagnetic coordination polymers
D. Ising ferromagnets
D. Magnetic structure
C. Neutron diffraction
D. Dipolar interactions
Abstract
The quasi-one-dimensional [Co(NCS)2(pyridine)2]n coordination polymer built of
ferromagnetic chains of Co(II) ions linked by (NCS)2 anions is known as an Ising
ferromagnet that magnetically orders at TC = 3.9 K. We performed a neutron
diffraction study and show that the magnetic structure is collinear ferromagnetic,
static, and without any glassy component. The magnitude of the ordered magnetic
moment of Co(II) is 3.65(15) µB, which points to a relatively large contribution of the
orbital moment. The direction of the moment is close to the direction of the Co–
1 Corresponding authors: z.tomkowicz@uj.edu.pl, cnaether@ac.uni-kiel.de
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N(pyridine) bond, which confirms literature ab initio calculations. We show that
dipolar interactions are mainly responsible for the magnetic interchain coupling.
1. Introduction
Quasi-one-dimensional magnets are interesting objects of scientific research from
the perspective of basic science and applications, such as photoswitchable magnetic
nanowires or extremely dense memories [1,2,3,4]. With sufficiently small interchain
interactions and sufficiently large uniaxial anisotropy, such magnets may exhibit very
slow magnetic relaxations. Then they behave like superparamagnets but have a
single relaxation time that is strictly determined by intrachain ferromagnetic
interactions and uniaxial anisotropy. Because of the very slow relaxations, they were
called single-chain magnets (SCMs). This fascinating property was first demonstrated
by Caneschi et al. [5] in 2001, many years after it was theoretically predicted (in
1963) by Glauber [6] for ferromagnetic Ising chains. Many such materials were
synthesized and investigated from various points of view, including the different
conditions of their existence, which did not necessarily have to be Glauber-like. In
particular, Miyasaka et al. [7] showed that for weakly antiferromagnetically coupled
ferromagnetic chains, slow relaxations may develop below the Néel temperature (i.e.,
in a magnetically ordered state). On the other hand, for ferromagnetically coupled
chains, ferromagnetic three-dimensional (3D) domains are formed. In this case SCM
relaxations are also present but are difficult to observe in the presence of the 3D
domain wall relaxations. However, they may be observed in an applied magnetic field
[8].
Näther and coworkers [9,10,11,12,13,14] studied a series of polymeric
compounds of the form [Co(NCS)2L2]n, where L is an organic ligand that is a pyridine
derivative. These compounds are composed of ferromagnetic cobalt chains. Each
Co(II) ion is in the center of a distorted octahedron built from two equatorial nitrogen
atoms, two equatorial sulfur atoms, and two apical nitrogens atoms of the ligand.
Depending on the ligand, the packing of chains in the crystal structure can be
different, and consequently various magnetic properties are observed. Some
compounds are antiferromagnets [9,10,11,12] and others are ferromagnets [13,14].
The recently studied compound [Co(NCS)2(py)2]n, where py is pyridine [15] (Fig. 1), is
a ferromagnet with a Curie temperature (TC) of 3.9 K [16]. This compound crystallizes
ꢁ
in the triclinic space group ꢀ1 with three Co(II) ions in the unit cell. In this structure,
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the two lateral Co–Npy vectors are not parallel relative to the middle one, but are
instead tilted in opposite directions at an angle of 7°. There is some orientation
disorder of the pyridine rings, with 15% minor orientation.
Detailed crystallographic data can be found in [17]. It has been shown [15] that
[Co(NCS)2(py)2]n has a strong Ising anisotropy as evidenced by magnetic
measurements and high field–high frequency ESR (HF-ESR) studies. The g factors
obtained from HF-ESR are g║ = 7.0 and g┴ = 2.4, and the intrachain exchange
integral J║ is 28 K. For comparison, J║ determined by the Fisher model [18] from
∑
magnetic measurements and with use of the Ising Hamiltonian ℋ = −ꢂ ꢄ ꢃꢅꢃꢅ
+
ꢄꢆꢇ
ꢄ
∑
ꢈꢉ ꢄ ꢊ ⋅ ꢋꢌ ⋅ ꢍꢄ with s = 1/2 is 28 ± 1.5 K. The interchain exchange integral zJ’ was
estimated to be 0.40(10) K. This is relatively high, which may suppress the SCM
behavior. However, taking into account that the shortest interchain Co–Co distance is
8.58 Å (the intrachain distance is 5.64 Å) and that there is no chemical bonding
between chains, a question arises as to what kind of interchain interactions
determine that the interchain coupling is noticeable and ferromagnetic.
The shortest interchain distance is between hydrogens of neighboring chains
(3.05 Å). However, the shortest path for possible hydrogen bonds is C─H···Npy, with
a bond length of 3.72 Å and a bond angle of 159.4°. The next shortest path is
C─H···Nbr (where Nbr is the bridging N), with a bond length of 3.81 Å and a bond
angle of 133.6°, and there are some other longer paths, such as C─H···S. These
shortest paths are listed in Table 1. The C and H atoms that were considered are
shown in Fig. 2. The aforementioned bond lengths are on the order of van der Waals
distances and cannot bring about magnetic exchange. Spin polarization through the
flat pyridine rings is an unlikely option because the distance between face-to-face
rings (~8.5 Å) is too great. Besides, that would lead rather to an antiferromagnetic
interaction. Thus, it seems very likely that dipolar interactions are responsible for the
ferromagnetic interchain coupling.
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In this work neutron diffraction experiments were undertaken to determine the
magnetic structure, in particular, the magnitude and orientation of the magnetic
moment of the Co(II) ion, and to compare these experimental findings with theoretical
predictions [15]. The aim is to finally evaluate the predicted direction of the easy-axis
anisotropy relative to the Co–Npy vectors. Additionally, supplementary magnetic
measurements were undertaken to identify any difference due to deuteration.
Calculations of the energy of the dipolar interactions were performed to determine
whether they are compatible with the magnetic structure found.
2. Synthesis and methods
2.1. Synthesis of deuterated [Co(NCS)2(py)2]n
Co(NO3)2·6H2O and KSCN were purchased from Merck and deuterated pyridine was
purchased from Carl Roth. All chemicals were used as purchased. For the synthesis
of [Co(NCS)2(py)2]n, Co(NO3)·6H2O (90.0 mmol, 26.19 g) was reacted with KSCN
(180 mmol, 17.49 g) in 300 mL of ethanol. The resulting white precipitate of KNO3
was filtered off. Deuterated pyridine (30.0 mmol, 2.410 mL) was added to a solution
of Co(NCS)2, and ethanol was removed in a vacuum. The residue was filtered off and
washed with demineralized water, leading to a microcrystalline powder of
[Co(NCS)2(py)2]n. The phase purity of this compound was examined by elemental
analysis, atomic absorption spectroscopy (AAS), and X-ray powder diffraction.
Elemental CHNS analysis (%) for C12D10CoN4S2 (343.4 g/mol): calcd. C 42.07, D
5.87, N 16.32, S 18.68; found C 42.15, H 5.71, N 16.75 S 18.58 (performed with a
vario MICRO cube elemental analyzer manufactured by Elementar). AAS (Co, %):
found 17.28; calcd. 17.16 (performed with a vario MICRO cube elemental analyzer).
AAS (Co, %): found 17.28; calcd. 17.16 (performed with a PerkinElmer AAnalyst
300).
.
2.2. Methods
The X-ray power diffraction measurements were performed at room temperature with
a Stoe transmission powder diffraction system (STADI P) equipped with a linear
position-sensitive detector and a Ge(111) monochromator (Cu Kα1 radiation).
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Specific heat measurements were performed by the relaxation method with Quantum
Design PPMS. The samples were pressed for measurements. Other details may be
found in [12].
Magnetic measurements were performed with a Quantum Design MPMS-XL
magnetometer.
Neutron diffraction experiments were performed at the E6 focusing powder
diffractometer at Helmholtz-Zentrum Berlin. The powder sample was put into a
vanadium thin-walled tube of radius R=3 mm and placed in a cryostat. The
wavelength of the neutron beam was 2.432 Å.
3. Results of subsidiary measurements
3.1. X-ray powder diffraction
The X-ray powder pattern of the deuterated compound is shown in Fig. 3. For
comparison, the experimental and calculated patterns for the nondeuterated
compound are also shown in Fig. 3. To visualize that the first reflection is definitely
split a simulated line diagram showing only peak positions is added (Fig. 3(d). Thus,
it can be seen that there is practically no difference between the patterns for the
deuterated and nondeuterated compounds and that the deuterated compound is
phase-pure.
3.2. Specific heat and magnetic properties
Specific heat and magnetic DC measurements were performed for deuterated
[Co(NCS)2(py)2]n. Experimental data for the temperature-dependent specific heat are
shown in Fig. 4, and the data for the temperature-dependent magnetic susceptibility
are shown in Fig. 5. The measured characteristics practically do not differ from those
already published [15,16] for the nondeuterated compound.
We also present magnetization (M) data, which we need for subsequent
comparison of the magnetic moment of the Co(II) ion with that obtained from neutron
diffraction. Measurements were performed at 1.8 K for a ground deuterated sample
and deuterated and nondeuterated samples pressed into a tablet, and also for a
sample sunk in eicosane (see Fig. 6). It is seen in Fig. 6 that the highest observed
magnetic moment is 3.15 µB for the ground sample, for which it is expected that
grains have freedom of reorientation in a magnetic field. However, the stated value
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may decrease with respect to the true value when individual grains are not single
crystals, even for the well-ground sample.
4. Neutron diffraction results
Powder neutron diffraction patterns were acquired at two temperatures: 10.2 K (i.e.,
above TC) and 1.7 K (i.e., below TC). Analysis of the patterns was performed by the
Rietveld method [19] with the FullProf suite of programs [20]. To this aim, the
absorption parameter µR had to be calculated, and it was determined to be 0.031.
Firstly, the pattern taken at 10.2 K was analyzed. The initial model of the crystal
structure obtained from the single-crystal X-ray diffraction (at 170 K) [17] of the
nondeuterated compound did not perfectly match the neutron data and needed
refinement. Because, as previously stated, the X-ray diffraction powder patterns of
the deuterated and nondeuterated compounds do not differ, deuterium atoms
seemed to be mainly responsible for this disagreement. Therefore, we initiated
refinement by fitting deuterium positions as well as positions of other pyridine atoms.
The disorder from the second (minor) orientation of the pyridine rings (see [17]) was
also taken into account. Because of the large number of coordinate parameters, it
was necessary to use constraints assuming 1% limits for changes. In the refinement
process the parameters were not changed all at once, but were changed in turn for
D, C, and Npy atoms. Because of no improvement, the parameters of all other atoms
were also varied. Correctness of the structural model was checked at each stage with
use of the program Mercury (Cambridge Crystallographic Data Centre). However, the
best fit was not satisfactory. Therefore, we tried to fit the structure model again
assuming no disorder. This time, relatively good agreement was obtained even
without fitting, and after a slight refinement, the Rp factor was approximately 5 (Fig.
7). Because of the successful determination of the nuclear structure, the scale factor
was well determined and was later used to refine the magnetic structure.
Crystallographic data for the nuclear structure are given in the Appendix. It is noted
that the crystallographic structure obtained for deuterated [Co(NCS)2(py)2]n is
isomorphic with the structure of [Ni(NCS)2(py)2]n [21].
The lattice constants obtained from the refinement are a = 8.536(2) Å,
b = 8.417(2) Å, c = 15.611(3) Å, α = 93.917(20)°, β = 95.902(20)°, γ = 114.226(20)°,
and V = 1009.8(7) Å3 at 10.2 K. For comparison, the data from the single-crystal X-
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ray diffraction obtained at 170 K for the nondeuterated compound are
a = 8.5816(13) Å,
b = 8.6752(12) Å,
c = 15.520(2) Å,
α = 92.700(17)°,
β = 96.254(17)°, γ = 114.754(15)°, and V =1037.5(3) Å3.
Fig. 8 shows the difference pattern obtained by subtraction of the pattern
recorded at 10.2 K from that recorded at 1.7 K. All observed Bragg reflections are of
magnetic origin and fall at the same positions as the nuclear ones as expected for a
ferromagnetic structure. The magnetic reflections are very small in comparison with
the nuclear ones (in our case the intensity of the strongest magnetic reflection is
about 5% of the strongest nuclear one). This is the well-known disadvantage of
neutron diffraction when applied to organometallic compounds, where the magnetic
elements are surrounded by a large number of organic moieties. In such a situation,
the magnetic scattering is only a small fraction of the nuclear scattering [22].
Starting models for refinement are very limited because from magnetic studies
is known that the compound studied is ferromagnetic and no extra reflections of pure
magnetic origin appear that could not be indexed with use of the nuclear
crystallographic unit cell. Therefore, the wave vector of the magnetic structure is
k = (0, 0, 0). In this case the application of group theory representation analysis is
trivial. It predicts equal values and parallel or antiparallel orientation of the Co2
magnetic moments, but the mutual orientation of the Co1 magnetic moment with
respect to Co2 magnetic moments is arbitrary. During refinement it was found that
the model with the magnetic moments parallel to the chain axis could definitely be
rejected because of a large discrepancy between experimental and refined patterns.
The model in which the magnetic moments are all parallel and directed along the Co–
Npy vector gave the best agreement between the aforementioned patterns, with an Rp
factor of 1.4. The calculated pattern is shown in Fig. 8 with the solid line. The
uncertainty of the common orientation of the magnetic moments is ±25°.
Differentiation of the Co1 magnetic moment with respect to the Co2 magnetic
moments (as to their magnitudes and directions) did not lead to better agreement.
The magnitude of the magnetic moment of the Co(II) ion, as determined by
refinement, is 3.65(15) µB. The magnetic structure obtained is shown in Fig. 9.
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5. Discussion
Using neutron powder diffraction, we refined the crystallographic structure of
deuterated [Co(NCS)2(py)2]n and found no orientation disorder of the pyridine rings in
contrast to the X-ray diffraction experiments for the nondeuterated compound, which
were performed at high temperatures. However, the magnetic properties, which were
studied at low temperatures, showed no difference between deuterated and
nondeuterated compounds. The reason for the disagreement may be that the
orientation disorder observed for the nondeuterated compound is only a dynamic
effect that appears only at high temperatures and is independent of deuteration.
The magnetic structure was refined with the difference pattern obtained from the
patterns recorded at 1.7 K and 10.2 K. As a result, a collinear magnetic structure was
obtained with a relatively large ordered magnetic moment (3.65 µB) and with the
moment direction along the Co–Npy vector, which is consistent with ab initio
calculations [15]. It may be concluded that there is no canting, no glassy component
in the sample, and no prominent relaxations at 1.7 K.
The value of the moment is close to the expected g║s value (3.5 µB, with g║ = 7
and s = 1/2) [15]. An easy-axis anisotropy for the Co(II) ion corresponds to the
4
4
4
splitting of the T1g orbital triplet into A2g and Eg terms, with the latter being the
ground one. The orbital angular momentum is partially quenched, with only the axial
component being nonzero. The corresponding wave functions of the lowest Kramers
doublet are |MS = ±3/2, ML = ∓1>, where the components of the orbital angular
momentum are written with use of the so-called T-P isomorphism [23]. Thus, the
magnetic moment has only an axial component and consists of both spin and orbital
contributions. One can easily estimate that for the compound studied the orbital
contribution to the total magnetic moment is about 0.65 µB.
The magnitude of the ordered magnetic moment may be compared with the
values obtained directly from the magnetic experiments (see Fig. 6). In this case, the
greatest value (3.15 µB) was obtained for the ground sample in a field of 50 kOe, and
a possible reason for this inconsistency was provided in Section 3.2. However, it can
also be compared with the experimental value for the pressed sample with
immobilized grains. Namely, for a ferromagnet with the Ising anisotropy occurring in a
field large enough to have one-domain grains, the averaging of directions over half of
a sphere produces the factor ½ in the calculation of the magnetization, leading in our
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case to 3.65/2 = 1.82 µB. This is very close to the value of 1.8 µB obtained from the
M(H) data in Fig. 4 by extrapolation to a zero field from the field range of 10–20 kOe.
With regard to the magnetic moment direction, the direction along the Co–Npy
vector was reported for a similar compound, [CoCl2(py)2]n, by de Jonge et al. [24].
Their results were obtained by a nuclear magnetic resonance (NMR) study for a
single-crystal sample. Measurements were performed at a low temperature of around
1.5 K. [CoCl2(py)2]n has a crystal structure different from that of [Co(NCS)2(py)2]n and
its interchain magnetic coupling is antiferromagnetic but it is also composed of
ferromagnetic chains of Co(II) ions that are doubly bridged by chlorine. These results
were somewhat questioned by Foner et al. [25] in that the phase studied by de Jonge
et al. was the α phase, which is not stable at low temperatures. However, de Jonge
et al. argued that the NMR lines of the α phase still existed at low temperatures.
There have also been magnetic [26] and HF-ESR [27] studies of the halogenated
compound [CoCl2(3,5-Br2py)2], where two hydrogen atoms in [CoCl2(py)2]n were
replaced by Br. Then, the local anisotropy becomes easy-plane anisotropy (the plane
is formed by four bridging Cl ions); however, a combination of orthogonal easy planes
causes overall easy-axis anisotropy along the chain axes. Thus, it is seen how a
small modification of the molecular structure may change the anisotropy and even its
character.
Assuming that dipolar interactions are responsible for the interchain magnetic
interactions, it would be interesting to check if the identified direction (along the Co–
Npy vector) of the magnetic moments is consistent with the ferromagnetic ordering of
ferromagnetic chains. The calculations of the dipolar energy were performed for a
ferromagnetic arrangement and several antiferromagnetic arrangements of the
magnetic moments of Co(II) ions. Details of the calculations are presented in the
Appendix. As seen, the calculated energy of the antiferromagnetic spin alignment is
lower than that for the ferromagnetic configuration; however, the minimal energy
corresponds to structures that can be regarded as composed of ferromagnetic
domains. The domain formation releases the demagnetizing energy, thus leading to
a ground ferromagnetic configuration in the compound studied. The results obtained
are in good agreement with those published for manganese porphyrin chains with a
similar 3D chain arrangement [28] as well as with the results of simulations
performed for the chain lattices with different packing of chains in the 3D space [29].
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Thus, the ferromagnetic structure identified for [Co(NCS)2(py)2]n is consistent with
dipolar interactions and can be caused by these interactions. If the dipolar
interactions are really responsible for interchain coupling for this type of compound,
then the question arises about the SCM phenomenon: how to diminish this coupling
or, at least, make it antiferromagnetic to observe the SCM behavior. It is known that
in the case of magnetic moments being parallel to the chain direction, the dipolar
coupling is antiferromagnetic and vanishes [29]. However, in the family of compounds
studied, where the ligand is a pyridine derivative, the local easy axes are almost
perpendicular to the chain direction. In this case, there is another strategy to achieve
the goal; namely (except for the obvious increase of interchain distance), through an
appropriate 3D arrangement of the chains. The 3D structure of the reported
compound can be obtained by the translation of the rhombus composed of four
chains with its smaller angle at approximately 60° (pseudohexagonal lattice of
chains; Fig. 9). Modeling the behavior of this type of structure [29] demonstrates that
the nature of the ground state (ferromagnetic or antiferromagnetic) depends on that
angle. When this angle is close to 90° (square lattice of chains), the ground-state
configuration corresponds to the antiferromagnetic coupling of chains. Although the
coupling energy is not very small, with the antiferromagnetic coupling, SCM
observations may be possible because of the lack of ferromagnetic 3D domains, as
mentioned in Section 1.
6. Conclusions
A deuterated sample of quasi-one-dimensional [Co(NCS)2(py)2]n was synthesized
and characterized by X-ray diffraction, magnetic and specific heat measurements,
and neutron diffraction. As shown, deuteration does not influence the magnetic
properties. The magnetic structure, as determined by neutron diffraction, is collinear
ferromagnetic. The ordered magnetic moment is directed along the Co–Npy axis,
which is consistent with the direction of the easy-axis anisotropy known from ab initio
calculations reported in the literature. The magnitude of the moment is 3.65 µB,
including the orbital contribution of 0.65 µB. We showed that ferromagnetic interchain
magnetic coupling is due to dipolar interactions. The role of dipolar interactions was
discussed with respect to SCM properties.
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Appendix
Calculation of the energy of the dipolar interactions
It is assumed that the intrachain spin alignment is governed by the exchange
interaction, while the interchain arrangement occurs because of the dipole-dipole
interaction between spins of different chains. At a given temperature, each Co chain
can be described with use of the correlation length, which depends on the value of
the intrachain exchange interaction and diverges at 0 K. Within the correlation length,
all individual magnetic moments are oriented parallel to each other (and parallel to
local easy axes), while magnetic moments from the neighboring correlated blocks are
assumed to be independent and can be either parallel or antiparallel to each other.
The energy of the dipole-dipole interaction between two spins is
µB2 g|2|


3 s r s r
(
ij )(
)
i
j
ij
ij
dip
E
=
sisj −
,
(A1)
r3
r2




ij
ij
with µB and g|| being the Bohr magneton and the component of the Landé factor
along the local easy axis, respectively.
Let us assume that because of the intrachain exchange interaction all magnetic
moments within n unit cells along the chain are correlated. The big cell presented in
Fig. A.1 is considered. This cell consists of 4n3 elementary unit cells (n unit cells
along the chain direction and 2n unit cells in the two other directions). Since the
diagonal of the unit cell (along which the chain is aligned, see Fig. 1) is about two
times longer than the unit-cell parameters a and b, the size of the big cell in all three
directions is approximately the same and corresponds to the in-chain correlation
length. All individual spins are oriented along the local easy axes that coincide with
the Co–Npy directions. In the subsequent calculations, we ignore the small deviation
of Co–Npy vectors and assume that all local easy axes are parallel to each other and
coincide with the easy axis of the central Co ion. The energy of the dipole-dipole
interaction between some spin placed in the middle of this big cell and all other spins
within the cell (except those belonging to the same chain and coupled by the
exchange interaction) is calculated by assuming ferromagnetic or antiferromagnetic
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spin alignment. To obtain the energy of the dipolar interaction per spin in the uniform
medium the value calculated as described above is divided by 2.
For the antiferromagnetic spin alignments, it was assumed that chains form planes.
All spins within each plane are parallel to each other, while spins from the
neighboring planes are oppositely directed. Three antiferromagnetic spin alignments
were considered; namely, planes parallel to the a unit-cell direction, parallel to the b
unit-cell direction, and oriented along the bisection between these two directions. The
minimal energy for the antiferromagnetic configurations considered corresponds to
the magnetic structure presented in Fig. A.2 (planes parallel to the a unit-cell
direction).
J||
Calculations were performed for n = 270, which for
= 28 K corresponds to the in-
chain Ising correlation length at 2.5 K. This means that interactions with all spins
located closer than 2300 Å are taken into account. To check if the result of the
calculations depends on the size of the big cell (Fig. A.1), all calculations were
repeated for n = 500 (in this case the interactions between all spins located closer
than 4200 Å are taken into account). The difference is smaller than 0.06%, which
indicates that convergence is achieved. The corresponding energies per spin are -
0.0117 cm-1 and -0.0258 cm-1 for ferromagnetic and antiferromagnetic configurations,
respectively.
To investigate the possibility that the actual ground state of the compound
corresponds to a multidomain ferromagnet, we consider the system consisting of one
central big cell (Fig. A.1) and 26 neighboring big cells that enclose this one. As
before, the size n of each big cell is equal to the in-chain correlation length. The
energy of the dipole-dipole interaction is calculated for the interaction of all spins from
the central big cell between themselves (except those belonging to the same chain)
as well as for the interaction of each spin from the central cell with each spin from the
26 neighboring cells. During these calculations it was assumed that within each of the
27 big cells all spins are parallel to each other (and parallel to the local easy axis),
while spins from the different big cells can be either parallel or pointed in the opposite
directions. The average dipolar energy per spin in the central big cell is calculated.
Calculations were performed for n = 270. Several configurations with energies lower
than the energy of the antiferromagnetic configuration were found. They are
schematically shown in Fig. A.3. Areas where all spins are parallel to each other are
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marked with the same color. In the areas of different colors, spins are pointed in the
opposite directions. The corresponding energies are -0.0369 cm-1, -0.0473 cm-1, and
-0.0369 cm-1 for the left, middle, and right configurations, respectively. The planes
and stripes presented can be regarded as ferromagnetic domains that release the
demagnetizing energy. Of course, the particular shape of the domains appears only
because of the initial assumptions of the model, while nature prefers more
complicated types of surfaces.
Crystallographic data for [Co(NCS)2(py)2]n obtained by means of neutron
diffraction at 10.2 K
ꢁ
Table A.1. Space group ꢀ1.
Atom x
y
y
Atom x
y
z
Co1 0.5
0.5
0.5
N21 1.0724 0.9272 0.7828
Co2 0.8290 0.8262 0.8355 C21 1.1047 1.0425 0.7259
S1
C1
N1
S2
C2
N2
S3
C3
N3
0.5523 0.8146 0.5451 D21 1.0183 1.0803 0.7077
0.6416 0.8350 0.6469 C22 1.2596 1.1096 0.6919
0.7009 0.8465 0.7192 D22 1.2785 1.1905 0.6505
0.7855 0.5169 0.7888 C23 1.3894 1.0552 0.7202
0.6759 0.4886 0.7888 D23 1.4980 1.0999 0.6991
0.5986 0.4697 0.6220 C24 1.3535 0.9378 0.7781
0.8669 1.1348 0.8773 D24 1.4371 0.8975 0.7978
0.9701 1.1681 0.9773 C25 1.1954 0.8761 0.8087
1.0422 1.1905 1.0477 D25 1.1732 0.7942 0.8497
N11 0.5919 0.7230 0.8928 N31 0.7599 0.5884 0.4646
C11 0.5847 0.7819 0.9747 C31 0.9001 0.7029 0.5162
D11 0.6865 0.8720 1.0053 D31 0.8847 0.7434 0.5711
C12 0.4398 0.7187 1.0156 C32 1.0641 0.7651 0.4947
D12 0.4417 0.7636 1.0730 D32 1.1592 0.8476 0.5334
C13 0.2904 0.5877 0.9712 C33 1.0888 0.7046 0.4145
D13 0.1865 0.5435 0.9967 D33 1.2001 0.7481 0.3962
C14 0.2958 0.5220 0.8881 C34 0.9486 0.5816 0.3635
D14 0.1966 0.4297 0.8570 D34 0.9622 0.5341 0.3100
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C15 0.4464 0.5929 0.8523 C35 0.7879 0.5260 0.3891
D15 0.4484 0.5475 0.7957 D15 0.6919 0.4401 0.3891
The overall temperature factor is 0.57.
Table A.2. Lattice constants at 10.2 K.
a (Å)
b (Å)
c (Å)
α (°)
β (°)
γ (°)
8.536(2) 8.417(2) 15.611(3) 93.917(20) 95.202(20) 114.226(20)
Acknowledgements
This project was supported by the Deutsche Forschungsgemeinschaft (project no. Na
720/5-1) and the state of Schleswig-Holstein. ZT thanks the National Science Centre
(Poland) for financial support granted under decision DEC-2013/11/B/ST3/03799. SO
gratefully acknowledges the support by STCU (project 6219) and the Supreme
Council for Science and Technological Development of the Republic of Moldova
(project 15.817.02.06F). We thank Helmholtz-Zentrum Berlin for giving us the
opportunity to perform neutron diffraction experiments.
Conflicts of interest
The authors declare that they have no conflicts of interest.
Figures captions
Fig. 1. Visualization of the chain structure of [Co(NCS)2(pyridine)2]n. The
crystallographic unit cell is also shown. The central cobalt atom in the unit cell is Co1,
the lateral ones (crystallographically equivalent) are Co2.
Fig. 2. Carbon and hydrogen atoms that were considered to participate in possible
hydrogen bonding.
Fig. 3. X-ray diffraction patterns for [Co(NCS)2(py)2]n: (a) deuterated, (b)
nondeuterated, (c) nondeuterated, simulated on the basis on the lattice parameters
obtained by a Pawley fit using powder data measured at room temperature, (d) a line
diagram added to visualize that the first intense reflection is split.
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Fig. 4. Comparison of temperature dependencies of specific heat measured for
deuterated and nondeuterated [Co(NCS)2(pyridine)2]n.
Fig. 5. Comparison of magnetic susceptibilities measured for deuterated and
nondeuterated [Co(NCS)2(pyridine)2]n in the field-cooling and zero-field-cooling
regimes.
Fig. 6. Comparison of the magnetization data recorded at 1.8 K as a function of
magnetic field for deuterated versus nondeuterated samples and samples with
immobilized grains versus a well-ground sample.
Fig. 7. Neutron diffraction pattern recorded at 10.2 K for [Co(NCS)2(pyridine)2]n (black
points). The calculated profile is drawn with a solid red line and the difference
between the calculated and observed profiles is drawn with a blue line at the bottom.
Vertical short green lines represent the Bragg positions.
Fig. 8. Difference neutron diffraction pattern for [Co(NCS)2(pyridine)2]n. The
calculated profile is drawn with a solid red line and the difference between the
calculated and observed profiles is drawn with a blue line. Vertical short green lines
represent the Bragg positions. In the 2θ region between 40° and 45°, a number of
strong overlapping Bragg reflections of nuclear origin give rise to the increased noise
observed in the differential pattern; therefore, this region was excluded from the
refinement of the magnetic structure.
Fig. 9. Magnetic structure of [Co(NCS)2(pyridine)2]n. The view is along the [111]
direction (i.e., along the chain axis).
Fig. A.1. Big cell for the calculation of the energy of the dipole-dipole interaction. In
one of the corners of this big cell, the orientation of the unit cell is shown.
Fig. A.2. Antiferromagnetic spin alignment with the lowest energy (section
perpendicular to the chain direction).
Fig. A.3. Possible spin alignments that can be regarded as ferromagnetic domain
structures.
Table 1. Distances and angles for atomic paths considered as possible interchain
hydrogen bonds (symmetry equivalents are not given). The C–H distance is
approximately 0.95 Å. Atom numbers are according to the CIF file [17]. Nbr means the
N atom belonging to the bridge, and Npy means the N atom of pyridine.
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Distance (Å)
Angle (°)
H···N or H···S
Path C─H···N or
C─H···S
2.77
2.86
2.90
2.95
2.98
159.4
133.6
129.4
144.2
143.7
C24─H24···Npy (N11)
C24─H24···Nbr (N1)
C22─H22···Nbr (N2)
C34─H34···S2
C14─H14···S3
References
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[29] P. Panissod, M. Drillon, in: J.S. Miller, M. Drillon (Eds.), Magnetism: Molecules to
Materials IV. Wiley-VCH, Weinheim, 2002, pp. 233-270.
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Figures
Fig.1.
Fig.2.
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Fig.3.
8
6
4
2
0
deuterated
nondeuterated
2.5
5.0
7.5
10.0
T (K)
Fig.4.
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25
20
15
10
5
deuterated
nondeuterated
100 Oe
0
2.5
5.0
7.5
10.0
T (K)
Fig.5.
4
3
2
1
0
deuterated, ground
deuterated, pressed into a tablet
nondeuterated, pressed into a tablet
nondeuterated, sunk in eicosane
-1
-2
-3
0
10
20
30
40
50
H (kOe)
Fig.6.
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Yobs
Ycal
Yobs-Ycal
Bragg positions
80
60
40
20
0
0
20
40
60
80
100
120
2
θ
(deg)
Fig.7.
20
18
16
14
12
Yobs
Ycal
Yobs-Ycal
Bragg positions
10
20
30
40
50
60
70
80
90
2θ (deg)
Fig.8.
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Fig.9.
Fig.A1.
5

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Fig.A2.
Fig.A3.
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Highlights
•
•
Coordination polymer [Co(NCS)2(pyridine)2]n is composed of ferromagnetic
Ising chains.
The magnetic structure, as determined by neutron diffraction, is collinear
ferromagnetic.
•
•
The direction of the magnetic moment confirms literature ab initio calculations.
Dipolar interactions are responsible for magnetic interchain coupling.
1