Non-collinear magnetism in the post-perovskite thiocyanate frameworks CsM(NCS)3

AMX3 compounds are structurally diverse, a notable example being the post-perovskite structure which adopts a two-dimensional framework with corner- and edge-sharing octahedra. Few molecular post-perovskites are known and of these, none have reported magnetic structures. Here we report the synthesis, structure and magnetic properties of molecular post-perovskites: CsNi(NCS)3, a thiocyanate framework, and two new isostructural analogues CsCo(NCS)3 and CsMn(NCS)3. Magnetisation measurements show that all three compounds undergo magnetic order. CsNi(NCS)3 (Curie temperature, TC = 8.5(1) K) and CsCo(NCS)3 (TC = 6.7(1) K) order as weak ferromagnets. On the other hand, CsMn(NCS)3 orders as an antiferromagnet (Néel temperature, TN = 16.8(8) K). Neutron diffraction data of CsNi(NCS)3 and CsMn(NCS)3, show that both are non-collinear magnets. These results suggest molecular frameworks are fruitful ground for realising the spin textures required for the next generation of information technology.


List of Figures
Variable temperature magnetic susceptibility product measured over the range 2-300 K (zero-field cooled). The high temperature spin only Curie value, C, is indicated with a dashed line for a) CsNi(NCS) 3  Inverse of magnetic susceptibility (zero-field cooled) between 1.5 and 300 K. The high temperature data was modelled using the Curie-Weiss law (180 < T < 300 K for Ni; 100 < T < 300 K for Co and Mn), black line. . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Inverse of magnetic susceptibility for CsNi(NCS) 3 . The high temperature data was modelled using the Curie-Weiss law for a) 100 < T < 300 K, θ CW = +1.5 (4) and b) 200 < T < 300 K, θ CW = −12.7 (8)  Rietveld fits (black line) for CsNi(NCS) 3 data (green circles) collected with the D1b diffractometer at a) 10 K and b) 1.5 K. The black markers indicate the position of nuclear Bragg reflections and green markers for magnetic Bragg reflections. Data at 0.85 Å have been omitted due to the presence of an impurity. . . . . . . . . . . . . . . . . . . 8 6 CsNi(NCS) 3 lattice parameters between 1.5 and 10 K, obtained from Rietveld refinements of neutron diffraction data measured using the D1b diffractometer (ILL). The verical dashed black line indicates the magnetic ordering temperature (T C = 8.5 K). A linear fit (dark green line) was used to calculated the coefficient of thermal expansion. As the change in sin(β) is at least one of magnitude smaller than the change in the a, b and c axes, the thermal expansion tensor will not significantly rotate over this temperature range. a) a axis, Other AM(NCS) 3 structures with perovskite-analogue structure types: a) CsCd(NCS) 3

Single Crystal X-ray Diffraction
Single crystals were selected and mounted using Fomblin® (YR-1800 perfluoropolyether oil) on a polymer-tipped MiTeGen MicroMountTM and cooled rapidly to 120 K in a stream of cold N 2 using an Oxford Cryosystems open flow cryostat. 4 Single crystal X-ray diffraction data were collected on an Oxford Diffraction GV1000 (AtlasS2 CCD area detector, mirror-monochromated Cu-Kα radiation source; λ = 1.541 Å; ω 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). 5 The structure was solved within Olex2 6 by dual space iterative methods (SHELXT), 7 least squares refinement of the structural model was carried using (SHELXL). 8 Structures were checked with checkCIF (https://checkcif.iucr.org).

Single Crystal Neutron Diffraction
Monochromatic single crystal neutron diffraction data for CsMn(NCS) 3 and CsNi(NCS) 3 were collected on the four-circle D19 diffractometer at the Institut Laue Langevin (ILL) Grenoble, France, using neutrons with a wavelength of 1.455 Å (CsMn(NCS) 3 ) and 1.457 Å (CsNi(NCS) 3 ) provided by a flat Cu monochromator using the 220 reflection at 2θ M = 69.91°take-off angle. The samples were each placed in a closed-circuit displex cooling device, which was operated following a ramp of 2 K min −1 . NOMAD software from the ILL was used for data collection. Unit cell determinations were performed using PFIND and DIRAX programs, and processing of the raw data was applied using RETREAT, RAFD19 and Int3D programs. [9][10][11][12] For CsNi(NCS) 3 , the data were corrected for the absorption of the low-temperature device using the D19ABS program 13 and for the size and composition of the crystal. For CsMn(NCS) 3 the data were corrected for the absorption of the low-temperature device using the D19ABS program. Structural models were solved using the SUPERFLIP program and refined using Jana2006. 14,15

Powder Neutron Diffraction
Constant wavelength powder neutron diffraction data for CsMn(NCS) 3 and CsNi(NCS) 3 were collected on the high-intensity medium resolution D1b diffractometer 16 at ILL, France. The incident wavelength was λ = 2.52 Å and the scattering was measured over an angular range of 2 < 2θ < 128°. Thermal diffractograms for CsMn(NCS) 3 were collected between 1.5 K and 20 K heated with a programmed ramp of 0.06 K min −1 . Long acquisition measurements were collected at 1.5 K and 20 K.
Thermal diffractograms for CsNi(NCS) 3 were collected between 1.5 K and 10 K heated with a programmed ramp of 0.025 K min −1 . Long acquisition measurements were collected at 1.5 K and 10 K. NOMAD software from the ILL was used for data collection. Refinements of the magnetic model were completed using the FullProf program. 17

Magnetic Measurements
Measurements of the magnetic susceptibility were carried out on samples of CsNi(NCS) 3 (34.5 mg) and CsCo(NCS) 3 (14.3 mg) using a Quantum Design Magnetic Property Measurements System (MPMS) 3 Superconducting Quantum Interference Device (SQUID) magnetometer, and for CsMn(NCS) 3 (9.6 mg) using an MPMS XL. The zero-field-cooled (ZFC) and field-cooled (FC) susceptibility was measured in an applied field of 0.01 T over the temperature range 2-300 K. As M(H) is linear in this field, the small-field approximation for the susceptibility, χ(T) ≃ M H , where M is the magnetisation and H is the magnetic field intensity, was taken to be valid. Isothermal magnetisation measurements were carried out at 2 K over the field range −7 to +7 T for CsMn(NCS) 3 and CsCo(NCS) 3 , and a range of −6 to +6 T for CsNi(NCS) 3 . Data were corrected for diamagnetism of the sample using Pascal's constants. 18

Density Functional Theory Calculations
We have performed density functional theory (DFT) calculations to probe the structures and energetics of spin order of the compounds considered in this study. The spin-polarised DFT+U method (with Grimme's D3 van der Waals correction) 19 was employed in structural optimisations and energy calculations, using the Vienna Ab initio Simulation Package (VASP 5.4.4). 20 In our DFT+U calculations, we used U values of 3.6, 5.0 and 5.1 eV for d-electrons of Mn 2+ , Co 2+ and Ni 2+ cations, 21,22 respectively, and a range of ferromagnetic and anti-ferromagnetic spin solutions were considered for divalent magnetic cations (Table 1). We used a plane-wave basis set with a kinetic energy cutoff of 520 eV to expand the wave functions. The Perdew-Burke-Ernzerhof functional 23 in combination with the projector augmented wave method 24,25 were used to solve the Kohn-Sham equations. An energy convergence threshold of 10 −4 eV was used for all total energy calculations, and the structural optimisations, including cell parameters and atomic positions, were considered converged if all interatomic forces fall below 0.01 eV Å −1 . All DFT calculations have been performed in the 2 × 1 × 1 supercell (8 formula units per cell) using a 6 × 5 × 5 k-grid (which corresponds to a k-points spacing of around 0.1 Å −1 ).   Figure 2: Inverse of magnetic susceptibility (zero-field cooled) between 1.5 and 300 K. The high temperature data was modelled using the Curie-Weiss law (180 < T < 300 K for Ni; 100 < T < 300 K for Co and Mn), black line.         . Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. ** Absorption correction was applied using D19ABS program for the low-temperature device 13 and the size and composition of the crystal.  . Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. **Absorption correction was applied using D19ABS program for the low-temperature device. 13