# Low-dimensional metal-organic magnets as a route towards the $S=2$ Haldane
phase

Jem Pitcairn  [  Andrea Iliceto  [  Laura Cañadillas-Delgado  [  Oscar Fabelo
[  Cheng Liu  [  Christian Balz  [  Andreas Weilhard  [  Stephen P. Argent  [
Andrew J. Morris  [  Matthew J. Cliffe  [<EMAIL_ADDRESS>
###### Abstract

Metal-organic magnets (MOMs), modular magnetic materials where metal atoms are
connected by organic linkers, are promising candidates for next-generation
quantum technologies. MOMs readily form low-dimensional structures, and so are
ideal systems to realise physical examples of key quantum models, including
the Haldane phase, where a topological excitation gap occurs in integer-spin
antiferromagnetic (AFM) chains. Thus far the Haldane phase has only been
identified for $S=1$, with $S\geq 2$ still unrealised because the larger spin
imposes more stringent requirements on the magnetic interactions. Here, we
report the structure and magnetic properties of CrCl2(pym) (pym=pyrimidine), a
new quasi-1D $S=2$ AFM MOM. We show, using X-ray and neutron diffraction, bulk
property measurements, density-functional theory calculations and inelastic
neutron spectroscopy (INS) that CrCl2(pym) consists of AFM CrCl2 spin chains
($J_{1}=-1.13(4)\;$meV) which are weakly ferromagnetically coupled through
bridging pym ($J_{2}=0.10(2)\;$meV), with easy-axis anisotropy
($D=-0.15(3)\;$meV). We find that although small compared to $J_{1}$, these
additional interactions are sufficient to prevent observation of the Haldane
phase in this material. Nevertheless, the proximity to the Haldane phase
together with the modularity of MOMs suggests that layered Cr(II) MOMs are a
promising family to search for the elusive $S=2$ Haldane phase.

###### keywords:

American Chemical Society, LaTeX

Nottingham]School of Chemistry, University of Nottingham, University Park,
Nottingham, NG7 2RD, United Kingdom Birmingham]School of Metallurgy and
Materials, University of Birmingham, Elms Rd, Edgbaston, Birmingham B15 2TT,
United Kingdom Institut Laue-Langevin]Institut Laue-Langevin, 71 avenue des
Martyrs - CS 20156, 38042 Grenoble, France Institut Laue-Langevin]Institut
Laue-Langevin, 71 avenue des Martyrs - CS 20156, 38042 Grenoble, France
Cambridge]Cavendish Laboratory, Department of Physics, University of
Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom ISIS]ISIS
Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Oxford,
Didcot OX11 0QX, United Kingdom Nottingham]School of Chemistry, University of
Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
Nottingham]School of Chemistry, University of Nottingham, University Park,
Nottingham, NG7 2RD, United Kingdom Birmingham]School of Metallurgy and
Materials, University of Birmingham, Elms Rd, Edgbaston, Birmingham B15 2TT,
United Kingdom Nottingham]School of Chemistry, University of Nottingham,
University Park, Nottingham, NG7 2RD, United Kingdom IR,NMR,UV

##  1 Introduction

Figure 1: Crystal structure of CrCl2(pym) viewed along the (a) _c_ , (b) _a_
and (c) _b_ axes. Cr–Cl bond lengths are labelled and H atoms are omitted for
clarity. (d) ORTEP diagram showing the coordination environment.

Metal-organic magnets (MOM) are assembled from metal nodes bridged by organic
molecular linkers into extended networks.1 This gives them a number of
advantages over conventional inorganic magnets: there is a much wider
diversity of organic than atomic ligands;2 the modularity of their
construction allows for tuning of interactions while retaining the topology3
and their longer lengths facilitate magnetic low-dimensionality,4, 5 and thus
enhanced quantum fluctuations.6 Perhaps most excitingly, it has recently been
demonstrated that redox-active radical ligands can introduce into MOFs both
high electronic conductivity (0.45 Scm-1)7 and strong magnetic interactions,8,
9 despite the long-distances between metal centres. This suggests that MOMs
could form the basis for practical new quantum technology.10, 11, 12, 13, 14

MOM spin chains are now well established as host materials for distinctively
quantum behaviour, from spin fractionalisation in Cu(C6H5COO)2.3H2O15 to the
quantum sine-Gordon physics of Cu(pym)(NO3)(H2O)216 and
[Cu(pym)(H2O)4]SiF6.H2O.17 One of the most striking quantum discoveries in
MOMs was the measurement of the topological Haldane gap in the
antiferromagnetic $S=1$ spin chain MOM Ni(C2H8N2).2NO2(ClO4) 18, 19, 20 and
subsequent efforts have uncovered a number of other high-quality model
systems.21, 22, 23, 24 The Haldane phase is yet to be experimentally realised
for spins $S>1$.

The difficulty of reaching the Haldane phase for $S\geq 2$ is largely because
the size of the Haldane gap relative to the intrachain exchange,
$\Delta/J_{1}$, decreases significantly from $\Delta/J_{1}=0.41$ for $S=1$ to
$\Delta/J_{1}=0.087$ for $S=2$, making the gap both more sensitive to the
presence of single-ion anisotropy and non-Heisenberg exchange interactions,
and harder to detect when present.25 These challenges have meant that although
AFM $S=2$ spin chains which could be candidates to host the Haldane phase have
been identified, the $S=2$ gap has not yet been observed.26, 27, 28, 29, 30
The combination of modularity and low-dimensionality of MOMs means they are an
ideal platform to search for the $S=2$ Haldane phases. However, the most
synthetically accessible $S=2$ transition metal ion is Fe^2+, which typically
possesses large single ion anisotropy due to its partially quenched
${}^{5}T_{2\mathrm{g}}$ ground state, and other $S=2$ ions, Mn^3+ and Cr^2+,
are usually sensitive to reduction or oxidation in ambient conditions. As a
result, the chemistry of MOMs which could host $S=2$ Haldane phases is
comparatively underexplored, and their quantum states thus unrealised.

Here we report CrCl2(pym), a new 2D layered magnetic coordination polymer
consisting of CrCl2 chains bridged by pym ligands with a structure analogous
to that of the other transition metal monopyrimidine chlorides (MCl2(pym), M =
Mn, Fe, Co, Ni, Cu),31 the Mn, Co and Cu analogues of which are reported to
possess antiferromagnetic coupling without order down to $1.8\;$K.32 We first
describe its synthesis and structural characterisation using X-ray
diffraction, where the presence of a pronounced Jahn-Teller (JT) distortion
confirms the presence of Cr^2+. We then go on to show using comprehensive
magnetic characterisation, including bulk magnetisation, heat capacity
measurements, powder neutron diffraction (PND) and powder inelastic neutron
scattering (INS) measurements of fully protonated samples, that CrCl2(pym)
orders into a Néel ground state at $T_{\mathrm{N}}=20.0(3)$ K, with AFM
ordering along the CrCl2 chain, FM coupling of the chains through pym and
interlayer FM correlations. Through detailed analysis of the neutron
scattering data, in combination with density-functional theory (DFT)
calculations, we quantitatively determine the size of the key magnetic
interactions, which suggest that CrCl2(pym) is a well separated $S=2$ AFM with
near isotropic single ion properties. We therefore suggest that through
careful ligand choice this family of MOMs offers a potential route to realise
the Haldane phase for $S=2$.

##  2 Results

###  2.1 Synthesis and structure

We synthesised CrCl2(pym) by reacting CrCl2 with pyrimidine. We found that the
monopyrimidine CrCl2(pym) forms in a wide variety of solvents and
stoichiometries, and even _via_ neat combination and with excess ligand,
although bispyrimidine analogues are known for other transition metals.33, 34,
35 Single crystals suitable for X-ray diffraction measurements were grown
through vapour diffusion. We solved the structure from single-crystal X-ray
diffraction (SCXRD) data and found that CrCl2(pym) crystallises in the
monoclinic space group $P2_{1}/m$ with two formula units in the unit cell
(Tab. S1). The Cr^2+ are coordinated by four Cl^- ligands and two N atoms from
the pyrimidine ligands, which forms a distorted CrCl4N2 octahedron (Fig. 1c &
d). The chromium octahedra edge-share through the Cl^- ligands along the
crystallographic _a_ direction, and these chains are connected by pyrimidine
ligands along the crystallographic _b_ direction with an alternating
orientation to form corrugated layers (Fig. 1a). These layers stack in the
crystallographic _c_ direction through van der Waals interactions (Fig. 1b).
The Cr^2+ ion has a large JT distortion, with a long Cr-Cl bond length of
$d_{\mathrm{Cr-Cl}}=2.761(5)\;$Å, comparable to the complex
Cr^2+Cl2(pyridine)4 $d_{\mathrm{Cr-Cl}}=2.803(1)$ Å,36 confirming the Cr^2+
oxidation state. Powder X-ray diffraction performed after exposure to air for
one month show the lattice distortion resulting from this JT distortion is
retained, demonstrating that the bulk of the sample maintains the Cr^2+
oxidation state after exposure to air (Fig. S4).

###  2.2 Magnetic susceptibility

Figure 2: Magnetic susceptibility, $\chi$, measurements of CrCl2(pym). (a)
$\chi(T)$ measured in zero-field cooled (ZFC) and field cooled (FC) conditions
from 2–300 K. (b) $\chi(T)$ data highlighted for 2–30 K. (c) $\chi T(T)$ in
ZFC and FC conditions 2–300 K, with Curie-Weiss fit carried out over
$300>T>150\;$K. Dashed line shows the $S=2$ spin-only limit. (d) ZFC
$\frac{d\chi}{dT}(T)$ over 2–300 K. Inset: ZFC $\frac{d\chi}{dT}(T)$ over 2–35
K.

As we expected CrCl2(pym) to be an $S=2$ 2D magnet, we measured its
temperature dependent magnetic susceptibility, $\chi(T)$. The sample was
measured under field cooled (FC) and zero-field cooled (ZFC) conditions in a
0.01 T _dc_ field from 2 K to 300 K. These data show a broad peak at 20-25 K
characteristic of short-range ordering and low-dimensional magnetism (Fig.
2a). The $\frac{d\chi}{dT}(T)$ data show a discontinuity at 20 K, indicating a
phase transition from a disordered magnetic state to a long-range ordered AFM
state (Fig. 2d). Fitting $\chi^{-1}(T)$ data to the Curie-Weiss law gave a
Curie constant, $C=3.08(1)$ emu K mol-1, in good agreement with the presence
of high-spin Cr^2+ ($C=3$ emu K mol-1) (Fig. 2c & d). The Curie-Weiss
temperature is significant and negative, $\theta=-54.1(5)$ K, indicating net
antiferromagnetic interactions (Fig. 2d), and isothermal magnetisation
measurements carried out at 2 K show that saturation is not reached at fields
of 5 T (Fig. S7). While $M(H)$ is linear in $\mu_{0}H>1$ T, there is a small
sigmoid feature at $\mu_{0}H<1$ T consistent with minor paramagnetic
impurities.

The rise in $\chi(T)$ below $T=10$ K indicates the presence of small
quantities of paramagnetic spins, which we determined to be 1.1(1) spin % from
fitting of the Curie-like tail (Fig. S13).37 This Curie-like tail may be
caused free-spins at chain-ends or Cr^3+ formed due to surface oxidation (Fig.
2b). Indeed, measurement of the magnetic susceptibility of CrCl2(pym) after
air exposure showed a large increase in the paramagnetic contribution, 15.0(2)
spin % (Fig. S6), and X-ray photoelectron spectroscopy (XPS) of this air-
exposed sample primarily detected oxidised Cr (Fig. S8), with Cr^3+, Cr^6+ and
metallic Cr present, as well as O 1s peaks consistent with the formation of
Cr(OH)3.38

###  2.3 Heat capacity

Figure 3: (a) Heat capacity as a function of temperature, $C_{\mathrm{p}}(T)$,
with the non-magnetic background approximated by a linear fit over the region
10 to 30 K (dashed). (b) $C_{\mathrm{p}}/T(T)$, with non-magnetic background
(dashed). Inset: entropy near $T_{\mathrm{N}}$.

The molar heat capacity, $C_{\mathrm{p}}(T)$, of CrCl2(pym) was measured from
2–60 K. We found a peak in $C_{\mathrm{p}}(T)$ occurred at 20.0(3) K (Fig.
3a), consistent with the magnetic phase transition observed in the magnetic
susceptibility data (Fig. 2a). We obtained an estimate of the entropy of
magnetic ordering by integrating $C_{P}/T(T)$ after subtraction of a linear
background ($10-15$ K and $27-30$ K)(Fig. 3b), to account for phononic
contributions. We found that the measured value of magnetic entropy
($S_{\mathrm{exp.}}=12.7(4)$ Jmol-1K-1) is slightly reduced from the expected
value ($S_{\mathrm{calc.}}=13.4$ Jmol-1K-1). The small features present in the
data between 30–40 K are due to instrumental error.

###  2.4 Neutron Diffraction

Figure 4: (a) The crystal structure of CrCl2(pym), nuclear axes shown. (b) The
magnetic structure, highlighting the three most important exchange
interactions, $J_{n}$, magnetic axes shown. (c) Rietveld refinement of
temperature subtracted neutron scattering data. Data between $Q=1.9$ Å-1 and
$2.1$ Å-1 were excluded from the refinement due to incomplete subtraction of
nuclear Bragg peaks due to thermal expansion.

Our bulk measurements thus strongly suggested the presence of long-range
magnetic order. To determine the nature of this magnetic ground state we
carried out PND using instrument D1B at the ILL on a 5 g non-deuterated sample
of CrCl2(pym). We measured the neutron diffraction pattern at two
temperatures: $T=1.5\;$K below $T_{\mathrm{N}}$, and $T=30\;$K above. We
isolated the magnetic scattering from instrumental background and nuclear
scattering contributions by subtracting the high temperature dataset from the
low temperature dataset (Fig. 4c), which allowed us to identify the magnetic
Bragg peaks. We were able to index these reflections with a propagation vector
$\textbf{k}=\frac{1}{2}00$ and using symmetry-mode analysis in the ISODISTORT
software suite39 we identified there were two possible irreducible
representations (irreps), $mY^{-}_{1}$ and $mY^{-}_{2}$ in Miller and Love’s
notation.40 After calibration of the nuclear scale factor through Rietveld
refinement of nuclear structure against the high temperature dataset, we
carried out Rietveld refinement of the magnetic structure using each irrep
against the temperature subtracted dataset. We found for both nuclear and
magnetic refinement that a $hkl$-dependent peak broadening term was necessary
to account for the variation in measured peak widths. This showed that only
the $mY^{-}_{1}$ irrep was consistent with experimental data (Fig. 4c). The
$mY^{-}_{1}$ irrep lowers the symmetry of the structure to $P_{c}2_{1}/c$ with
the magnetic unit cell relating to the nuclear cell as follows:
$a_{\mathrm{mag.}}=c_{\mathrm{nuc.}}$, $b_{\mathrm{mag.}}=b_{\mathrm{nuc.}}$
and $c_{\mathrm{mag.}}=2a_{\mathrm{nuc.}}$ (Fig. 4a & b).

The magnetic structure derived from this refinement is a collinear structure
consisting of antiferromagnetically correlated CrCl2 spin chains
ferromagnetically correlated through the pym ligands, with interlayer
ferromagnetic correlations (Fig. 4b). The refined magnetic moment was Cr was
determined to be $M_{0}=2.61(7)\mu_{\mathrm{B}}$, significantly less than the
spin-only value of $M=gS=4\,\mu_{\mathrm{B}}$.

The magnetic moments in our model lie within the _ac_ -plane, however
components along the _b_ -direction would be permitted by symmetry. The
presence of a component along _b_ would result in intensity at the
$011_{\mathrm{mag.}}$ peak position ($Q=1.00$ Å-1) which is not seen in our
data and so any non-collinearity must be small, $\theta<8^{\circ}$. The
background of this subtracted $I_{\mathrm{1.5K}}-I_{\mathrm{30K}}$ dataset
contains a broad negative feature characteristic of magnetic diffuse
scattering, which could be modelled by a broad Lorentzian peak centred at the
$101_{\mathrm{mag.}}$ peak position, with an isotropic correlation length at
30 K $\lambda=2.8(2)$ Å.

###  2.5 Inelastic neutron scattering

Figure 5: Time-of-flight powder INS spectra of CrCl2(pym) with
$E_{i}=12.14\;$meV measured at (a) 1.7 K and (c) 25 K. (b) LSWT calculated
scattering intensity fitted to the 1.7 K data, with parameters
$J_{1}=-1.13(4)$, $J_{2}=0.10(2)$, $J_{3}=0.01(1)$ and $D=-0.11(1)$ meV.
Hamiltonian described in Eqn. 1.

To measure the parameters of the magnetic Hamiltonian and search for
signatures of low-dimensional magnetism, we collected INS spectra on the same
powder sample of CrCl2(pym) at 1.7 and 25 K using the LET spectrometer at
ISIS, using rep-rate multiplication to measure at multiple $E_{i}$
simultaneously ($E_{i}=12.14,\,3.70,\,1.77$ meV). The spectra collected at 1.7
K show a clear excitation centred at $\Delta E=4.1(2)\;$meV with an energy gap
of $2.2(1)\;$meV (Fig. 5a) despite the presence of an elevated background due
to the incoherent ^1H scattering. The intensity of this feature rapidly falls
with increasing $Q$, until it is masked by phonons, indicating this excitation
is magnetic in origin. We were able to quantitatively fit these data using
linear spin wave theory (LSWT) (Fig. 5b) as implemented by the SpinW software
package,41 using the following magnetic Hamiltonian,

$\mathcal{H}=\sum_{\langle
ij\rangle}-J_{ij}\mathbf{S}_{i}\cdot\mathbf{S}_{j}+\sum_{i}D(S_{i}^{z})^{2},$
(1)

comprising Heisenberg exchange, $J_{ij}$, for the three nearest neighbours
(_i.e._ along the CrCl2 through the pym ligand and between layers) and a
single ion anisotropy, $D$ (Fig. 4b). We began by estimating the approximate
values for each of $J_{1}$, $J_{2}$, $J_{3}$ and $D$ using our bulk magnetic
measurements and extrapolating from analogous compounds.26 These initial
parameters were then optimised using least square requirements of the
calculated spectrum, including a refined multiplicative scale factor and a
background linear in both $Q$ and $\Delta E$, against the experiment data
which gave $J_{1}=-1.13(4)$ meV, $J_{2}=0.10(2)$ meV, $0<J_{3}<0.01(1)$ meV
and $D=-0.15(3)$ meV. The value of D was corrected for kinematical
consistency42, as by default SpinW uses the inconsistent
$D\textquoteright=D[1-\frac{1}{2S}]=\frac{3}{4}D$. A grid search was
undertaken to confirm this as a unique solution. Our experimental spectra were
consistent with a negligible value for $J_{3}$, however the ground state
determined by PND indicates that $J_{3}$ must be ferromagnetic. The ratio of
$J_{1}/J_{2}=11(2)$ indicates that the magnetic interactions in this materials
are primarily one-dimensional. We therefore decided to investigate the
spectrum of CrCl2(pym) in the short-range ordered regime to search for
coherent excitations (Fig. 5c). Energy cuts, integrated over momentum
transfer, $0.76<Q<1.84\;$Å-1, showed no clear evidence of a gap in the
paramagnetic regime, for both $E_{i}=12.14$ meV and $E_{i}=3.70$ meV,
suggesting this material is not within the Haldane phase (Fig. S3b), although
the comparatively high temperature compared to the expected gap size,
$T/\Delta=25$ will make this challenging.

###  2.6 Density-functional theory

Figure 6: Electronic band structure and projected density of states of the
$2\times 2\times 1$ supercell using CASTEP and the PBE+U+MBD*
($U_{\mathrm{eff}}=3\;$eV) functional. The energy zero has been set at the
Fermi energy and is shown by the dashed line. The projected density of states
has been decomposed by element.

To understand the origin of the observed low-dimensional interactions we
carried out collinear spin-polarized plane-wave density-functional theory
(DFT) calculations, by exploring the electronic structure of the DFT ground-
state spin configuration and calculating the exchange energies using the
broken symmetry approach.43 We first optimised the geometry of the
experimental structure using the PBE functional along with a many-body semi-
empirical dispersion correction (MBD*)44 to describe the weak van der Waals
forces between the layers.45 We found that this structure was both too dense,
with a unit-cell volume of 297.68 Å3, 4.8% smaller than experimental value of
312.75 Å3, and lacked the JT distortion characteristic of Cr(II). We therefore
included an effective Coulomb on-site energy, $U_{\mathrm{eff}}=U-J$ where $U$
is the on-site repulsion and $J$ the exchange energy, to account for the
overly delocalised Cr d-states. A range of values for $U_{\mathrm{eff}}$ have
been previously explored for Cr, from $U_{\mathrm{eff}}=2.1\;$eV to
$U_{\mathrm{eff}}=3.5\;$eV.46, 47 We found that $U_{\mathrm{eff}}=3\;$eV was
able to accurately capture the physics of this system, and produced a
structure with both a JT distortion and, as a bonus, a volume within +0.2% of
experiment.

Exchange interactions were calculated using a $2\times 2\times 1$ supercell of
the optimised structure (_i.e._ containing eight distinct Cr atoms) decorated
with eight distinct magnetic orderings. Single point energy calculations were
then carried out on each configurations, and these DFT+$U$ total energies were
then fitted to the Hamiltonian described in Eqn. 1 with $D=0$, _i.e._ the
Heisenberg limit. We carried out these calculations using a series of values
of $U_{\mathrm{eff}}$ to ensure consistency of behaviour (Fig. S10). For our
optimised value of $U_{\mathrm{eff}}=3\;$eV, we obtained a self-consistent set
of superexchange interactions of $J_{1}=-2.53(5)\;$meV, $J_{2}=0.30(5)\;$meV,
$J_{3}=-0.09(5)\;$meV. To test the robustness of our DFT+U calculations, we
performed hybrid calculations using fraction of Fock exchange as implemented
in the HSE functional48, 49, 50 while maintaining a $U_{\mathrm{eff}}=3\;$eV.
HSE calculations are computationally expensive due to the calculation of Fock
exchange and require the use of norm-conserving pseudopotentials within
CASTEP, which limited the sampling of the Brillouin zone and our ability to
explore geometry optimisations. Nevertheless, we found that using the HSE
functional comparable exchange interactions $J_{1}=-2.39(1)\;$meV,
$J_{2}=0.46(1)\;$meV, $J_{3}=-0.15(1)\;$meV. These energies are comparable in
magnitude to those found experimentally for CrCl2(pym), but are notably
larger, likely due to the unphysically large degree of delocalisation.

Our calculations not only allow us to predict the interaction energies, but
also to explore the electronic structure of this material (Fig. 6). The
predicted thermal band gap is approximately $1.2$ eV, and the projection of
the DOS onto local orbitals shows that the top of the valence band is broadly
Cr and Cl based, whilst the organic linker pym states are the bottom of the
conduction band. This can also be observed in the frontier orbitals, where the
HOMO resembles the Cr $d_{z^{2}}$ orbital antibonding with Cl $p$ orbitals and
the LUMO is an antibonding $\pi$ molecular orbital with a single additional
node, suggesting that the lowest lying excitations will be of MLCT character.
The spin density is predominantly around the Cr, however, there is significant
density on both Cl and pym ligands (Fig. 7). Notably, the spin density on pym
appears to be primarily of $\pi$ character, and alternates in sign round the
ring (Fig. 7b).

Figure 7: Spin density isosurfaces (0.015 e Å-3) highlighting the (a) the
Cr–Cl chain and (b) the Cr–pym chain, derived from our CASTEP PBE+U+MBD*
($U_{\mathrm{eff}}=3\;$eV) and c2x calculations.51

##  3 Discussion

Metal N-heterocycle dihalides are a diverse family of MOMs and our study of
CrCl2(pym) provides one of the most in-depth investigations of the magnetic
properties of these materials. There are two common compositions: MX2L2 and
MX2L. The monoligand analogues usually contain linear MX2 chains, and
therefore tend to show primarily 1D magnetic behaviour, _e.g._ NiCl2(pyrazine)
consists of ferromagnetic NiCl2 chains antiferromagnetically coupled with
$T_{\mathrm{N}}=10.2\;$K,3 CuCl2(pyrazine) is also a very good example of a 1D
magnet with no order reported down to $1.8\;$K, but the strongest interaction
in fact occurs through Cu—pyrazine—Cu bridges ($J=-28\;$K), due to the JT
distortion suppressing exchange in the CuCl2 chain.52 Preliminary studies of
the magnetism of pyrimidine analogues, MCl2(pym) M = Mn, Co, Cu, also detect
no magnetic order down to 1.8 K although there are weak AFM interactions
present.32 The strong interactions, particularly occurring through the CrCl2
chain, and magnetic order found in CrCl2(pym) are therefore in striking
contrast. Additionally, the ferromagnetic exchange we observe occuring through
the pym ligand is relatively uncommon for molecular ligands, for example,
antiferromagnetic interactions are the norm for pyrazine-bridged MOMs.53, 54,
55, 56, 57, 58, 59 This ferromagnetic exchange has been previously observed in
pym-bridged MOMs, _e.g._ M(NCS)2(pym)2 ($M=$Ni and Co),60, 61, 62 and has been
rationalised by a three-atom $\pi$-pathway. Our DFT calculations give further
credence to the importance of this pathway.

The bispyrimidine metal chlorides, MCl2(pym)2 M = Fe, Co, Ni and MBr2(pym)2 M
= Co, unlike most materials in this family adopt 3D chiral diamondoid
structures.33, 34, 35 MCl2(pym) all magnetically order with canted AFM
structures, $T_{\mathrm{N}}$ = 7.4 K, 4.7 K and 16.3 K for M = Fe, Co and Ni
respectively, likely arising from the interplay between the superexchange
interactions and the significant single-ion anisotropy, the principal axes of
which are non-collinear.33 Bulk susceptibility studies have shown enhancement
of $T_{\mathrm{N}}$ at moderate pressure ($\Delta
T_{\mathrm{N}}/T_{\mathrm{N}}=15$% at 0.7 GPa),35 which suggests that high
pressure investigations of Cr-based MOMs may also uncover pressure-switchable
magnetic functionality.63

The presence of a JT distortion is strong evidence of Cr^2+, which stands in
contrast to the related CrCl2(pyrazine)2, in which Cr^2+ spontaneously reduces
the ligated pyrazine to a radical anion, and thereby dramatically enhancing
its conductivity and magnetic superexchange.8 The sensitivity of this metal-
ligand redox to the coordination sphere is shown by Cr(OSO2CH3)2(pyrazine)2,
in which Cr remains as Cr^2+ with a JT distortion.56 Studies of molecular
complexes have shown this non-innocent behaviour is favoured by a strong
ligand-field environment and a low energy ligand LUMO,64 and is consistent
with the observed innocence of CrCl2(pym), which has both weaker ligand field
than CrCl2(pyz)2 and a higher energy ligand LUMO (pyrazine,
$E_{\mathrm{red}}=+1.10\;$V and pym $E_{\mathrm{red}}=+0.84\;$V vs.
Li/Li^+).65

Our data clearly show that CrCl2(pym) has a conventional Néel AFM ground
state, $T_{\mathrm{N}}=20.0(3)$ K, but also that there is significant magnetic
low-dimensionality above $T_{\mathrm{N}}$.

The frustration parameter,
$f=\frac{|\theta_{\mathrm{CW}}|}{T_{\mathrm{N}}}=2.7$, derived from bulk
property measurements hints at suppression of magnetic order. As the magnetic
lattice does not show an obvious mechanism for geometric frustration, this is
likely due to a combination of single-ion anisotropy and low-dimensionality
arising from the large differences in strength of superexchange in different
crystallographic directions.

Additionally, the presence of magnetic diffuse scattering at 30 K not present
at 1.5 K, indicates the presence of short-range magnetic correlations retained
above $T_{\mathrm{N}}$. Finally, our analysis of the INS spectra show that the
AFM superexchange through the Cr–Cl–Cr bridge is an order of magnitude larger
than all other superexchange interactions, $|\frac{J_{1}}{J_{2}}|=11(2)$.

The importance of low-dimensionality can also been seen in the reduction in
the apparent size of the Cr^2+ ordered moment determined via neutron
diffraction. The low-dimensionality of the structure can reduce the refined
moment through disorder, both static short-chain defects and stacking
faults66, 67 and dynamic zero-point fluctuations68. Additionally, as is common
in many metal organic magnets,69 there is appreciable delocalisation of the
spin-density onto the ligands, which Mulliken analysis of the DFT-derived
electron density suggests is approximately 10%. These factors in combination
explain the substantial reduction in the ordered moment (approximately one-
third) from that expected moment size, though it is challenging to evaluate
their relative contributions.

Despite this low-dimensionality, our data indicate that like other $S=2$
candidate AFM chains, CrCl2(pym) does not show clear Haldane physics. The
presence of long range order at $T_{\mathrm{N}}/J_{1}=1.5$ hinders
observations at low temperatures and the non-negligible single ion anisotropy
($D=-0.15(3)$ meV, $D/J_{1}=0.13(2)$) is sufficient to suppress the Haldane
phase, for which the critical value is predicted to be $D/J_{1}=0.04$.25
CrCl2(pym) is therefore comparable to the other identified candidate $S=2$
spin chains in both of these parameters,28, 29, 30 including CrCl2, 26
MnCl3(bipy) 70, 27 and CsCrCl3,71 but none have shown clear evidence of a
gapped inelastic neutron spectrum in the disordered phase.

The compound CrCl2(pym) is most similar to, both structurally and
magnetically, is CrCl2,26 which also has quasi-1D antiferromagnetic CrCl2
chains formed from edge-sharing octahedra ($J_{1}=-1.13(13)$ meV,
$D^{\prime}=-0.11(2)$ meV). However, closer examination reveals significant
structural differences that make these magnetic similarities quite surprising.
In CrCl2(pym) the JT distortion means every superexchange pathway within the
CrCl2 spin chain passes through a significantly lengthened bond, whereas in
CrCl2 the equivalent JT distortion lies out of the spin-chain plane and so all
Cr-Cl bonds in the chain are short. Superexchange through a JT-lengthened
pathway is ordinarily weak, as is indeed found for the direction perpendicular
to the CrCl2 spin chain in inorganic CrCl2, with an order of magntiude weaker
exchange $J_{2}=-0.12(7)$ meV.

A second distinction between these two compounds is the potential for tuning
the interactions through substitution of the ligands. Replacing pyrimidine by
a larger bridging ligand may reduce inter-chain exchange, suppressing long-
range order and allowing access to the paramagnetic $S=2$ quasi-1D AFM at
lower temperatures. For example, in NiCl2L substituting pyrazine for
1,2-bis(4-pyridyl)ethane reduces $T_{\mathrm{N}}$ from 10.2 K to 5.6 K.3
Equally, optimisation of the octahedral coordination environment can minimise
$D$, for example in a family of closely related Ni^2+ compounds, matching of
the ligand field strengths reduces the size of the easy-plane anisotropy by a
factor of 4.72 Our measurements of the INS data already suggest that the
interlayer interactions are not significant, but delamination of these van der
Waals sheets, as demonstrated for other magnetic metal-organic nanosheets,73
may provide an alternative route to better magnetic isolation. These results
suggest therefore that bridging CrCl2 spin chains with organic ligands may
provide promising future candidates for $S=2$ Haldane chains.

##  4 Conclusion

We have reported the crystal structure, bulk magnetic properties, magnetic
ground state and magnetic excitations of a new coordination polymer,
CrCl2(pym). We have shown that the oxidation state of chromium in this
compound is Cr^2+, remaining $S=2$, unlike related CrCl2 derived MOMs which
undergo redox to form triplet Cr^3+-radical ligand pairs. 8, 64 CrCl2(pym) is
found to be a $S=2$ quasi-one-dimensional antiferromagnet, with an order of
magnitude separation in energy scales of superexchange,
$|\frac{J_{1}}{J_{2}}|=11(2)$. However we did not find clear evidence of the
Haldane gap in the disordered phase, suggesting the small $J_{2}$ and $D$ are
sufficient in this compound to either suppress the $S=2$ Haldane phase or mask
it through the stabilisation of long range order. The proximity of CrCl2(pym)
to the Haldane region of the phase diagram, and the modularity inherent to
MOMs suggest that optimising the magnetic properties of these systems,
including both superexchange3 and single-ion-anisotropy, 72 is a new and
promising route to the $S=2$ Haldane phase.

##  5 Experimental

###  5.1 Synthesis

Synthesis and handling of CrCl2(pym) was performed in a dry Ar or N2
atmosphere using a MBraun LABstar glovebox or Schlenk line. The reaction of
CrCl2 (200 mg, 1.63 mmol; Fisher Scientific, 99.9%) and pyrimidine (500 mg,
6.24 mmol; Sigma-Aldrich, $\geq$ 98.0%) in 50 mL methanol (MeOH) rapidly
precipitates an orange-brown microcrystalline powder. The CrCl2(pym) product
was then dried _in vacuo_ giving a ca. 90% total yield. The measured
(calculated) elemental composition was: C, 23.45% (23.67%); H, 1.99% (2.40%);
N, 12.94% (13.80%). This procedure, with quantities scaled up (CrCl2, 3.0 g;
pyrimidine, 4.0 g; MeOH, 300 mL), was used to synthesise the sample used for
neutron-scattering measurements. Crystals of sufficient size for X-ray
diffraction studies ($127\times 46\times 26\;\mu$m) were grown by vapour
diffusion of pyrimidine (100 mg, 1.25 mmol) into a concentrated solution of
CrCl2 in 1 mL MeOH (10 mg, 0.08 mmol).

###  5.2 Powder X-ray diffraction

PXRD data were collected using a PANalytical X’Pert Pro diffractometer
equipped with monochromated Cu K$\alpha$1 radiation ($\lambda=1.5406$ Å). The
tube voltage and current were 40 kV and 40 mA, respectively. Scans were
performed from 2∘ to 60∘ on a zero background silicon crystal plate. Peak
fitting, Pawley and Rietveld refinement were performed using Topas Academic
v6.74

###  5.3 Single crystal X-ray diffraction

A diffraction-quality single crystal of CrCl2(pym) was mounted on a polymer-
tipped MiTeGen MicroMountTM using Fomblin (YR-1800 perfluoropolyether oil).
The sample was cooled rapidly to 120 K in a stream of cold N2 gas, using a
Oxford Cryosystems open flow cryostat. Diffraction data were collected on an
Oxford Diffraction GV1000 (AtlasS2 CCD area detector, mirror-monochromated
Cu-K$\alpha$ radiation source; $\lambda=1.54184$ Å, $\omega$ scans). Cell
parameters were refined from the observed positions of all strong reflections
and absorption corrections were applied using a Gaussian numerical method with
beam profile correction (CrysAlisPro). The structure was solved and refined in
Olex275 using SHELXT76 and SHELXL77, respectively.

###  5.4 Magnetic susceptibility

Magnetic property measurements were carried out on a Quantum Design MPMS
superconducting quantum interference device (SQUID). A polycrystalline sample
of CrCl2(pym) (26.6 mg) was immobilised in eicosane (44.5 mg) and sealed in a
low-paramagnetic-impurity borosilicate glass ampoule under vacuum. Magnetic
susceptibility measurements were performed under field cooled (FC) and zero-
field cooled (ZFC) conditions in a 0.01 T _dc_ field from 2 K to 300 K.
Isothermal magnetisation measurements were performed at 2 K from 0 T to 5 T to
–5 T to 0 T. Data were corrected for the diamagnetism of the sample using
Pascal’s constants.78

###  5.5 Heat capacity

Heat-capacity measurements were carried out on a 4.2 mg pellet of CrCl2(pym)
and silver powder (50 wt. %), using a Quantum Design Dynacool Physical
Property Measurement system (PPMS), between 2 and 60 K. Apiezon N grease was
used to ensure good thermal contact. Contributions to the heat capacity due to
Apiezon N were measuerd separately and subtracted, contributions due to silver
were subtracted using tabulated values.79

###  5.6 Powder neutron diffraction

PND measurements were carried out on the D1B neutron diffractometer at
Institut Laue-Langevin, Grenoble, France. Measurements were collected at 1.5 K
and 30 K with $\lambda=2.52$ Å between $0.77^{\circ}$ and $128.67^{\circ}$
with steps of $0.1^{\circ}$. The nuclear structure determined from single
crystal X-ray diffraction was Rietveld refined against neutron diffraction
data to evaluate phase purity. Due to the low intensity of magnetic
reflections, the magnetic structure was determined by refinement against data
from which background and nuclear Bragg peaks were removed by subtraction of
data collected at 30 K from those collected at 1.5 K. The magnetic Bragg peaks
were indexed to determine the magnetic propagation vector and then the allowed
magnetic irreducible representations were determined using symmetry-mode
analysis on the ISODISTORT software.39 Using the scale factor determined from
Rietveld refinement of the nuclear structure against data at 30 K, and peak
parameters determined from Pawley refinement of the nuclear structure against
data at 30 K, the direction and magnitude of the ordered moment for the
subtracted dataset were refined using TOPAS-ACADEMIC 6.0.74

###  5.7 Inelastic neutron scattering

Inelastic neutron scattering (INS) measurements were performed on the LET
time-of-flight direct geometry spectrometer at ISIS.80 The sample (4 g) was
contained in a thin aluminum can of diameter 15 mm and height 45 mm and cooled
in a helium cryostat. The data were collected at 1.7 K and 25 K, for 10 h and
7 h respectively, with $E_{i}=12.14\;$meV using the rep-rate multiplication
method.81, 82 The data were reduced using the Mantid-Plot software package.83
The raw data were corrected for detector efficiency and time independent
background following standard procedures.84

###  5.8 Density-functional theory

Plane-wave density-functional theory calculations were performed using version
19.1 of the CASTEP code.85 The Brillouin zone was integrated using a
Monkhorst-Pack grid of $k$-points, finer than $2\pi\times 0.05$ Å-1 spacing.86
A Gaussian smearing scheme with a smearing width of 0.20 eV was used during
the electronic minimisation process. Vanderbilt ultrasoft pseudo-potentials
were used for computational efficiency (Tab. S3).87 The basis set included
plane-waves up to an associated kinetic energy of 1100 eV. Geometry
optimisations converged until resultant forces were less than $0.05$ eV/Å. The
OptaDOS post-processing code was used to integrate individual Kohn-Sham
eigenvalues into an electronic density of states,88 and the Matador high-
throughput environment was used to obtain electronic band structure and
density of states plots.89

##  6 Supporting Information

Information on single-crystal and powder X-ray diffraction, additional
inelastic neutron scattering data, powder X-ray and neutron diffraction data,
isothermal magnetisation measurements, magnetic susceptibility analysis, X-ray
photoelectron spectroscopy, transmission electron micrographs and additional
details of DFT calculations (PDF).

CCDC 2213061, crystallographic data (CIF).

Magnetic structure (mCIF).

Additional research data for this Article may be accessed at no charge and
under CC-BY license at the University of Nottingham Research Data Management
Repository https://doi.org/10.17639/nott.7257.

Inelastic neutron scattering data measured at ISIS Neutron and Muon Source is
available at https://doi.org/10.5286/ISIS.E.RB2090119.

CCDC 2213061 contains the supplementary crystallographic data for this paper.
These data can be obtained free of charge via
www.ccdc.cam.ac.uk/data_request/cif, or by emailing
<EMAIL_ADDRESS>or by contacting The Cambridge Crystallographic
Data Centre, 12 Union Road, Cambridge CB2 1EZ, U.K.; fax: + 44 1223 336033.

##  7 TOC

Figure 8: TOC Figure

J.P. and M.J.C. acknowledge the School of Chemistry, University of Nottingham
for support from the Hobday bequest. A.J.M. acknowledges funding from EPSRC
(EP/P003532/1). The authors acknowledge networking support via the EPSRC
Collaborative Computational Projects, CCP9 (EP/M022595/1) and CCP-NC
(EP/T026642/1). Computing resources were provided by the Sulis HPC service
(EP/T022108/1). We acknowledge the ILL for beamtime under proposal EASY-778.
We acknowledge ISIS for beamtime under proposal RB2090119. J.P. acknowledges
Jesum Alves Fernandes for training and assistance with XPS analysis. J.P.
acknowledges Benjamin Weare for TEM analysis. Heat Capacity measurements were
performed using the Advanced Materials Characterisation Suite, funded by EPSRC
Strategic Equipment Grant EP/M000524/1. J.P. and M.J.C. acknowledge Siân
Dutton and Joseph Paddison for useful discussions.

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