W. Grochala et al.
FULL PAPER
Thermal analysis was performed with an STA 409PG TGA/DSC
analyzer from Netzsch coupled with an Aëolos QMS 403C mass
spectrometer (Netzsch) for evolved gas analysis. Samples (ca.
10 mg) were loaded into alumina crucibles. Heating rates of 1, 5
and 10 Kmin–1 were applied.
sulting in a quasi-3D magnetic character of this system at low tem-
peratures.
Phonon frequencies at the centre of the Brillouin zone were calcu-
lated with VASP at the PAW LDA and PAW GGA-PBE level using
atomic displacement of 0.002 Å with forces preoptimized down to
10–4 eVÅ–1 (for comparison of LDA phonon DOS and of experi-
mental IR and Raman spectra, see the Supporting Information).
Magnetic measurements were conducted with a superconducting
quantum interference device magnetometer MPMS-XL-5 from
Quantum Design equipped with a 50 kOe magnet, and operating
in the temperature range 2–300 K.
Supporting Information (see footnote on the first page of this arti-
cle): More computational DFT results including the phonon den-
sity of states and assignment of vibrational bands are given.
ESR spectra were taken with an ESP 300E spectrometer (frequency
9.5 GHz; X-band) from Bruker for samples sealed in Ar atmo-
sphere inside a 4 mm thick quartz capillary.
Acknowledgments
Solid-state density functional theory (DFT) calculations were per-
formed using the VASP code[35] with the projector-augmented wave
method (PAW)[36] as implemented in the MedeA package. For the
exchange-correlation part of the Hamiltonian, the local density
approximation (LDA) in its local spin density approximation
(LSDA) variant was applied, since we have noticed previously that
LDA allows for much better reproduction than generalized gradi-
ent approximation (GGA) of the unit-cell parameters of related
AgSO4[37] (for the GGA-PBE and GGA-PW91 results, see the Sup-
porting Information). During the full geometry optimization (cell
and atomic parameters), the ionic relaxation was continued until
the forces on individual atoms were less than 0.002 eVÅ–1. The
electronic iterations convergence was set to 10–7 eV per atom by
using the standard blocked Davidson algorithm and reciprocal
space projection operators. The spacing between the points for the
k-points mesh generation was around 0.5 Å–1 (Monhorst pack of
5ϫ5ϫ5). The valence electrons were described by plane waves
with a kinetic energy cutoff of 600 eV, thereby yielding satisfactory
convergence of total energy. Four different schemes of magnetic
ordering were tested: one ferromagnetic: (i) further denoted as FM,
with FM intrasheet and FM intersheet coupling, and three antifer-
romagnetic ones: (ii) AFM1 with AFM intrasheet and AFM in-
tersheet coupling, (iii) AFM2 with AFM intrasheet and FM in-
tersheet coupling, (iv) AFM3, with FM intrasheet and AFM in-
tersheet coupling, as well as (v) a nonmagnetic cell. Total optimiza-
tions at the LSDA level for the above-mentioned unit cells have
showed that the FM solution corresponds to a global energy mini-
mum with all AFM solutions higher in total energy, and the non-
magnetic solution pushed above the FM one at as much as
35.4 meV per FU. For this reason, the unit cell of the FM solution
optimized at the LSDA level was used for subsequent single-point
calculations of energy of all magnetic ordering schemes in question.
This work is dedicated to Professor Felix Aubke in recognition of
his significant contribution to chemistry of fluorosulfates. The pro-
ject “Quest for Superconductivity in Crystal-Engineered Higher
Fluorides of Silver” is operated within the Foundation for Polish
Science “TEAM” Program cofinanced by the EU European Re-
gional Development Fund. This work has been partly supported
by the Slovenian Research Agency (ARRS) within the research
program P1-0045 Inorganic Chemistry and Technology. Calcula-
tions have been performed on ICM supercomputers.
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The spin-polarized LSDA and LSDA+U single-point calculations
were performed to derive the electronic and magnetic structure of
Ag(SO3F)2 as well as the intrasheet magnetic superexchange con-
stant, J. To mimic the strongly correlated nature of the 4d electrons
of Ag and the interacting p electrons of the bridging “oxide anions”
(within the superexchange Ag–O–O–Ag path), the value of the
Coulomb integral U was set to 4 eV and Hund’s exchange J to 1 eV
for both of these ions; the respective values for S(3p) electrons were
2 and 1 eV, thus allowing direct comparison with results obtained
earlier for AgSO4.[7,37] The value of J was approximated by the
difference of energy of FM and AFM2 configurations (which differ
only in the spin flip within the sheets) as customary for 2D systems
(this value was divided by the number of AgII cations per unit cell,
z = 4). The appreciable difference in energy between the FM and
AFM3 configurations (which differ only in sign of the intersheet
magnetic coupling) of 0.3 meV per FU (LSDA+U) suggests that
intersheet superexchange is quite strong for Ag(SO3F)2 (only one
order of magnitude weaker than the intrasheet coupling), thus re-
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submitted.
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[15] Typical bond lengths and angles in the SO3F– anion were taken
from published crystal structures of fluorosulfates with ionic
and more covalent metal–oxygen bonds, such as LiSO3F,
Sn(SO3F)2, Au(SO3F)3, FXe(SO3F) and (FXe)2(SO3F)(SbF6).
The angles were restrained at 113 (O–S–O) and 105° (O–S–F),
whereas the distances at 1.42 Å (for S=O bonds, O is attached
weakly to Ag at separation Ͼ2.4 Å), 1.48 Å (for S–O bonds, O
is attached stronger to Ag at separation Ͻ2.2 Å) and 1.55 Å
(for S–F bonds). The strength of the restraints allowed for a
typical deviation of bond lengths of 0.005 Å and up to 5° for
bond angles.
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Eur. J. Inorg. Chem. 2011, 2499–2507