Quasi-2D Heisenberg Antiferromagnets [CuX(pyz)2](BF4) with X = Cl and Br

Article abstract of DOI:10.1021/acs.inorgchem.7b03150

Two Cu²⁺ coordination polymers [CuCl(pyz)₂](BF₄) 1 and [CuBr(pyz)₂](BF₄) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D) [Cu(pyz)₂]²⁺ magnetic networks. The layer connectivity by monatomic halide ligands results in significantly shorter interlayer distances. Structures were determined by single-crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid [Cu(pyz)₂]²⁺ layers that do not expand between 5 K and room temperature, whereas the expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a broad maximum at ～8 K, indicating antiferromagnetic interactions within the [Cu(pyz)₂]²⁺ layers. 2D Heisenberg model fits result in J_∥ = 9.4(1) K for 1 and 8.9(1) K for 2. The interlayer coupling is much weaker with |J_⊥| = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly σ-type exchange through pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below T_N = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis (k = 0, 0, 0.5). The ordered magnetic moments are located in the tetragonal plane and amount to 0.76(8) μ_B/Cu²⁺ for 1 and 0.6(1) μ_B/Cu²⁺ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu²⁺ g-tensor was determined from electron spin resonance spectra as g_x = 2.060(1), g_z = 2.275(1) for 1 and g_x = 2.057(1), g_z = 2.272(1) for 2 at room temperature.

Full text of DOI:10.1021/acs.inorgchem.7b03150

Article
pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Quasi-2D Heisenberg Antiferromagnets [CuX(pyz)2](BF4) with X = Cl
and Br
Mariusz Kubus,†,‡ Arianna Lanza,†,§ Rebecca Scatena,† Leonardo H. R. Dos Santos,†
Bjorn Wehinger,‡,# Nicola Casati,§ Christoph Fiolka,† Lukas Keller,‡ Piero Macchi,*,†
̈
Christian Ruegg,*,‡,# and Karl W. Kramer*,†
̈
̈
†Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
‡Laboratory for Neutron Scattering and Imaging and Laboratory for Synchrotron Radiation−Condensed Matter, Paul Scherrer
§
Institute, CH-5232 Villigen PSI, Switzerland
#Department of Quantum Matter Physics, University of Geneva, Quai Ernest Ansermet 24, CH-1211 Genev
̀
e 4, Switzerland
S
* Supporting Information
ABSTRACT: Two Cu2+ coordination polymers [CuCl(pyz)2](BF4) 1 and [CuBr(pyz)2]-
(BF4) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D)
[Cu(pyz)2]2+ magnetic networks. The layer connectivity by monatomic halide ligands
results in significantly shorter interlayer distances. Structures were determined by single-
crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid
[Cu(pyz)2]2+ layers that do not expand between 5 K and room temperature, whereas the
expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a
broad maximum at ∼8 K, indicating antiferromagnetic interactions within the [Cu(pyz)2]2+
layers. 2D Heisenberg model fits result in J∥ = 9.4(1) K for 1 and 8.9(1) K for 2. The
interlayer coupling is much weaker with |J⊥| = 0.31(6) K for 1 and 0.52(9) K for 2. The
electron density, experimentally determined and calculated by density functional theory,
confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal
plane. The analysis of the spin density reveals a mainly σ-type exchange through pyrazine.
Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional
magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below
TN = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis (k = 0, 0, 0.5). The ordered magnetic
moments are located in the tetragonal plane and amount to 0.76(8) μB/Cu2+ for 1 and 0.6(1) μB/Cu2+ for 2 at 1.5 K. The
moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu2+ g-tensor was determined from
electron spin resonance spectra as gx = 2.060(1), gz = 2.275(1) for 1 and gx = 2.057(1), gz = 2.272(1) for 2 at room temperature.
particular interest in quantum magnetism. Coordination
compounds are rather soft and susceptible to the application
of external pressure, which may induce structural or magnetic
phase transitions.15 The relatively weak magnetic interactions in
these 2D Cu2+ materials result in moderate saturation fields at
low temperature,16 which are experimentally accessible and
allow a direct determination of the coupling parameters by
inelastic neutron scattering.
INTRODUCTION
■
Quasi two-dimensional (2D) S = 1/2 square-lattice Heisenberg
antiferromagnets (AFM) have attracted much attention in
recent years as magnetic model systems due to their relation to
high-temperature cuprate superconductors,1−3 their quantum
́
fluctuations below Neel temperature (TN), and a possible
application in quantum computing.4−6 Molecular magnets play
a major role in this field.7−9 Their versatile composition from
metal ions as spin carriers and ligands as linkers allows the
design of tailored lattices for magnetic model systems.10,11
Composition, configuration geometry, and conjugation of the
linkers influence the exchange between magnetic centers. Often
studied are systems with short linkers, for example, O2−, OH−,
N3−, or conjugated groups, such as oxalate or pyrazine
(pyz).10,12 The search for new magnetic materials for
experimental and theoretical investigations can be based on
modifications of known compounds, for example, the single
and double layer models [CuF2(H2O)2(pyz)]13 and
[(CuF2(H2O)2)2(pyz)],14 respectively, or the exploration of
new systems. Cu2+ ions with their small S = 1/2 spin are of
The family of [CuX(pyz)2]Y compounds has attracted major
attention in this field. These compounds are based on
[Cu(pyz)2]2+ layers that are bridged in the third dimension
by X ligands, and charge is compensated by Y anions. Their
three-dimensional (3D) coordination network hosts quasi 2D
−
magnetic interactions. As examples, X can be NO3 and Y =
16
4
17
4
18
−
−
−
−
−
−
PF6 , or X = HF2 and Y = ClO4 , BF4 , PF6 , SbF6 ,
4
19
−
−
AsF6 , or TaF6 .
Received: December 19, 2017
© XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.7b03150
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
refined using a riding model. Selected crystallographic data and
structural refinement details are summarized in Table 1. Atomic
positions and equivalent isotropic displacement parameters are given
in Table S2 of Supporting Information.
Data available in literature do not allow an easy ration-
alization of the magnetic exchange in this family of compounds.
In particular, the role of interlayer interactions through X
anions or the role of the counterion Y remain unclear. For this
reason, we synthesized further compounds and characterized
their structure/property relationships. Here, we present two
members of the [CuX(pyz)2]Y family [CuCl(pyz)2](BF4) 1
and [CuBr(pyz)2](BF4) 2 with a short monatomic connectivity
between the layers by halide ions. Syntheses and crystal growth
are discussed. The crystal and magnetic structures were
determined by X-ray and neutron diffraction. The experimental
electron density distribution is compared to the density
functional theory (DFT) one. The magnetic properties were
determined by superconducting quantum interference device
(SQUID) and electron spin resonance (ESR) measurements
and discussed in the [Cu(pyz)2]2+ series.
Table 1. High-Resolution Crystal Data and Structure
Refinement of [CuCl(pyz)2](BF4) 1 and [CuBr(pyz)2](BF4)
2 at 100 K
empirical formula
formula weight, g mol−1
temperature, K
crystal system
space group
a, b, Å
[CuCl(pyz)2](BF4) [CuBr(pyz)2](BF4)
345.98
390.45
100(2)
100(2)
tetragonal
P4/nbm (125)
9.74670(10)
5.617 90(10)
533.690(14)
2
tetragonal
P4/nbm (125)
9.75710(10)
5.845 00(10)
556.450(15)
2
c, Å
volume, Å3
Z
ρcalc, g cm−3
μ, mm−1
2.153
2.330
EXPERIMENTAL SECTION
■
Synthesis. The title compounds were obtained via two synthetic
routes.
2.341
5.595
F(000)
342
378
Method 1: [CuCl(pyz)2](BF4), 1, was crystallized from a solution
of stoichiometric amounts of 4.9894 g of Cu(BF4)2·6H2O (Alfa Aesar,
98%), 0.7730 g NH4Cl (Merck, 99.8%), and 2.3148 g of pyrazine
(Acros, 99+%) in 0.5 L of water according to reaction 1. The mixture
was cooled until 1 precipitated (yield 32%).
2θ range, deg
index ranges
5.9−105.3
−21 ≤ h ≤ 21
−21 ≤ k ≤ 21
−12 ≤ l ≤ 12
31 788/1655
5.9−91.2
−19 ≤ h ≤ 19
−19 ≤ k ≤ 19
−11 ≤ l ≤ 11
39 145/1252
collected/independent
reflections
Cu(BF )2 + NH4Cl + 2pyz → [CuCl(pyz)2](BF ) + NH4BF
4
4
4
Rint
Rσ
0.017
0.005
0.027
0.007
(1)
Method 2: [CuCl(pyz)2](BF4), 1, was obtained from an aqueous
solution of 1.9431 g of CuCl2 (Aldrich, ≥99.995%), 2.8134 g of
Ag(BF4) (Strem, 99%), and 2.3148 g of pyrazine (Acros, 99+%)
according to reaction 2. First, CuCl2 was dissolved in 250 mL of H2O,
and Ag(BF4) was added. After 30 min of stirring, the precipitated AgCl
was filtered off. Then the pyrazine dissolved in 250 mL of water was
slowly added. The mixture was cooled until precipitation occurred
(yield 60%). Upon slow evaporation at 5 °C during a few weeks, dark
blue crystals with a tetragonal prismatic habitus were obtained.
spherical atom refinement
1655/0/32
data/restraints/parameters
1252/0/27
1.115
goodness-of-fit on F2
1.145
final R indexes [I ≥ 2σ(I)]
final R indexes [all data]
largest diff peak/hole, e Å−3
R1 = 0.016
wR2 = 0.05
R1 = 0.017
wR2 = 0.05
0.65/−0.69
R1 = 0.017
wR2 = 0.04
R1 = 0.022
wR2 = 0.04
0.64/−0.52
multipole model refinement
CuCl2 + Ag(BF ) + 2pyz → [CuCl(pyz)2](BF ) + AgCl
(2)
4
4
data/restraints/parameters
1655/5/105
R1 = 0.011
wR2 = 0.02
0.28/−0.25
1252/5/103
R1 = 0.019
wR2 = 0.02
0.33/−0.32
final R indexes [all data]
[CuBr(pyz)2](BF4), 2, was synthesized according to method 2 from
CuBr2 (Aldrich, 99.999%).
For powder neutron diffraction measurements deuterated samples
were prepared. They were synthesized from deuterated pyrazine (D4-
pyz, CIL, >98% D) and D2O (ARMAR, 99.8% D). The samples were
dried for 1 h in vacuum at room temperature.
Characterization. The thermal stability range of the compounds
was determined on a Mettler Toledo TGA/SDTA851 thermo-balance.
Samples of ∼20 mg weight were heated by 5 K/min in corundum
crucibles in a N2 gas flow of 20 mL/min. The thermogravimetric
analysis (TGA) curves are shown in Figure S1 of the Supporting
Information.
Fourier transform infrared (FTIR) spectra were measured on a
JASCO FT/IR-4700 spectrometer. An FTIR spectrum of 1 is shown in
Figure S2 of Supporting Information.
Single-Crystal X-ray Diffraction. Crystals were mounted with
grease on a glass fiber and cooled by an Oxford cryostream N2 flow
cryostat. Preliminary measurements were performed at 173(2) K up to
a resolution of 0.67 Å, whereas extensive high-resolution data
collections (dmin = 0.45 Å) were performed at 100(2) K, for
[CuCl(pyz)2](BF4), [CuCl(D4-pyz)2](BF4), and [CuBr(pyz)2](BF4).
All measurements were made on an Oxford Diffraction SuperNova
area-detector diffractometer using mirror optics, monochromated, and
Al filtered20 microsource Mo Kα radiation (λ = 0.710 73 Å). Data
reduction was performed using the CrysAlisPro program.21 Intensities
were analytically corrected for Lorentz and polarization effects and for
absorption with the Gaussian method based on the crystal shape. The
pyrazine H atoms were placed in positions calculated theoretically and
largest diff peak/hole, e Å−3
The conventional structural refinements were performed using
SHELXL.22 Multipole refinements with the Hansen-Coppens formal-
ism23 for accurate charge density determination were performed using
XD2015.24 More details on the multipolar models are given in the
Supporting Information. The highest and lowest residual density peaks
were 0.28 and −0.25 e Å−3 for 1 and 0.33 and −0.32 eÅ−3 for 2 using
in both cases all the data. Residual density maps show only small and
random discrepancies.
The d-orbital occupancies were derived with the assumption of low
sp to d overlap, according to the approach suggested by Holladay,
Leung, and Coppens25 using the XDPROP module. Topological
properties and integrated atomic charges were calculated using the
TOPXD module.
Powder X-ray Diffraction. Powder X-ray diffraction patterns were
measured on a STOE STADIP diffractometer in Debye−Scherrer
geometry at room temperature. Samples were prepared on thin plastic
foil. Diffraction patterns were measured with Cu Kα1 radiation (λ =
1.540 59 Å) from a focusing Ge (111) monochromator and recorded
with a position-sensitive Mythen 1K detector with 0.01° resolution in
2θ.
Low-temperature X-ray diffraction patterns were measured at the
powder diffraction station of the Swiss Light Source at the Paul
Scherrer Institute (PSI).26 The sample was filled in a 0.3 mm capillary
B
DOI: 10.1021/acs.inorgchem.7b03150
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
and cooled in a He flow cryostat. Data were measured between 5 and
290 K at a wavelength of λ = 0.564 96 Å. The temperature-dependent
unit-cell parameters were refined with Topas Academic.27
Powder Neutron Diffraction. Powder diffraction patterns were
measured on the cold neutron diffractometer DMC28 of the Swiss
spallation neutron source at PSI. Powder samples of 3 g of deuterated
[CuX(D4-pyz)2](BF4) with X = Cl and Br were sealed in V cans under
He gas. Neutrons with wavelengths of λ = 4.5040 and 3.8040 Å were
used. The samples were cooled in an ILL-type He cryostat (ILL =
Institute Laue-Langevin) with a base temperature of 1.5 K.
Powder diffraction data were analyzed with the FullProf program
package.29,30
Magnetic Measurements. Magnetic susceptibility data were
recorded on a Quantum design MPMS-5XL SQUID magnetometer in
the temperature range from 1.9 to 300 K and a magnetic field of 0.2 T
for a crystal and deuterated powder of 1, 0.1 T for a powder of 2, and
0.05 T for a powder of 1. Magnetization measurements were done at
1.9 K in fields up to 5 T. Susceptibility data were corrected for
diamagnetic contributions from the sample (−0.45·10−6 cm3/g·molar
weight), the empty sample holder, and the temperature-independent
paramagnetic contribution of Cu2+.
pyrazine in the tetragonal plane and by two halide anions along
the c-axis. The Cu−N distances of 2.054 and 2.056 Å are rather
close, whereas the Jahn−Teller distorted Cu−X distances
increase from 2.809 (1) to 2.923 (2) Å, see Table 2. Both the
Table 2. Atomic Distances (Å) and Angles (deg) of
[CuCl(pyz)2](BF4), 1, and [CuBr(pyz)2](BF4), 2, at 100 K
[CuCl(pyz)2](BF4) [CuBr(pyz)2](BF4)
Cu−N (4×)
Cu−X (2×)
pyz rotation angle
Cu−Cu distances
Cu−pyz−Cu (= |a + b|/2)
Cu−X−Cu (= |c|)
2.0544(3)
2.8089(1)
58.35(2)
2.0559(5)
2.9225(1)
55.01(3)
6.8920(1)
5.6179(1)
6.8993(1)
5.8450(1)
pyrazine and the halide ligands act as bidentate linkers
connecting Cu2+ ions into a 3D coordination network. The
pyz rings are rotated around the Cu−N−N−Cu axis by 58.4°
−
(1) and 55.0° (2) from the tetragonal plane. The BF4 anions
ESR Spectroscopy. ESR spectra of powder and crystal samples
were recorded on a Bruker E-500 spectrometer in the X-band at room
temperature.
occupy voids in the 3D network and are linked by F···H bonds
to pyz molecules.
Electronic Structure Calculations. Periodic DFT calculations
were performed using the software CRYSTAL14.31 The functional
B3LYP was used with basis set 86-411G(41d)32 for the Cu and pob-
TZVP33 for all the other atoms. The theoretical electron density was
analyzed with the TOPOND module of CRYSTAL14. Selected crystal
dimeric/tetrameric units were calculated with Gaussian0934 using
again the B3LYP functional and the basis set 6-311G(2d,2p). More
details about the dimeric/tetrameric units are given in the Supporting
Information.
The 3D structural network explains some of the chemical
properties of these compounds. They have a rather low
solubility in water and rapidly precipitate as powder, which
hardly redissolves. Single crystals of millimeter size and
tetragonal prismatic habitus grew by slow evaporation over
several weeks at 5 °C. The 3D coordination network gives rise
to high thermal stability. 1 and 2 decompose in a one-step
process above 240 and 227 °C, respectively, see the TG curves
in Figure S1 of Supporting Information. The decomposition
product is the respective monovalent copper halide CuX with X
= Cl, Br, as confirmed by powder X-ray diffraction.
RESULTS AND DISCUSSION
■
[CuCl(pyz)2](BF4), 1, and [CuBr(pyz)2](BF4), 2, are iso-
structural and crystallize in the tetragonal space group P4/nbm,
see Figure 1. Room-temperature powder diffraction pattern and
Rietveld fits, see Figures S3 and S4 of Supporting Information,
demonstrate the phase purity of the samples, and they perfectly
agree with single-crystal data. In these structures, the Cu2+ ions
have a distorted octahedral coordination by four N atoms from
Temperature-dependent powder X-ray diffraction measure-
ments provided information on the thermal expansion of
[CuCl(pyz)2](BF4). The relative change of lattice parameters
and molar volume is shown in Figure 2, and more details are
Figure 2. Temperature dependence of the reduced lattice parameters
and molar volume of [CuCl(pyz)2](BF4). The lines are a guide.
given in Table S1 of Supporting Information. The thermal
lattice expansion is very anisotropic. Along the a-axis (= b) one
observes even a slight contraction Δa/a = −0.1%, whereas
along the c-axis the lattice strongly expands by Δc/c = 2.1%.
The molar volume increases by 1.9% from 160.44(1) to
163.63(1) cm3/mol between 5 and 290 K. These results
demonstrate the extraordinary rigidity of the [Cu(pyz)2]2+
Figure 1. View onto the crystal structure of [CuCl(pyz)2](BF4) (a)
along the c-axis and (b) along [110]. Hydrogen atoms are omitted for
clarity. The unit cell is outlined by gray lines.
C
DOI: 10.1021/acs.inorgchem.7b03150
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
a
Table 3. Structural and Magnetic Parameters of Compounds with Tetragonal [Cu(pyz)2]2+ Layers
distance (Å)
space group Cu−N Cu−X
Cu−Cu distance (Å)
J∥
TN
No.
compound
Cu−pyz−Cu Cu−X−Cu pyz rot. angle (deg)
(K)
(K)
ref
b
1
2
[Cu(HF2)(pyz)2](SbF6)
[Cu(HF2)(pyz)2](TaF6)
[Cu(HF2)(pyz)2](AsF6)
[Cu(HF2)(pyz)2](PF6)
[Cu(NO3)(pyz)2](PF6)
[CuCl(pyz)2](BF4), 1
[CuBr(pyz)2](BF4), 2
[Cu(NO2)(pyz)2](ClO4)
[Cu(HF2)(pyz)2](ClO4)
[Cu(HF2)(pyz)2](BF4)
P4/nmm
P4/mmm
P4/mmm
P4/mmm
I4/mcm
P4/nbm
P4/nbm
P4/nbm
P4/nbm
P4/nbm
2.048
2.047
2.046
2.041
2.042
2.053
2.052
2.049
2.040
2.039
2.338
2.367
2.333
2.312
2.413
2.865
2.963
2.285
2.228
2.208
6.876
6.862
6.865
6.854
6.866
6.895
6.894
6.877
6.863
6.852
6.97
81.4
90.0
90.0
90.0
61.4
58.8
55.4
59.8
64.2
59.4
13.4
13.1
12.8
12.4
10.8
9.4
4.3
4.2
4.3
4.3
2.0
3.9
3.8
N/A
1.9
1.5
[18]
c
7.027
6.950
6.893
7.003
5.731
5.926
6.646
6.689
6.619
[19]
[4]
3
4
[4, 35]
d
5
[16, 36]
6
this work
this work
[37]
7
8.9
8
8.9
9
7.3
[4]
10
6.3
[4, 17, 38]
a
b
The pyz rotation angle is the deviation from the tetragonal layer. All data at room temperature, except for No. 5 at 163 K. [4] reports space group
c
P4/mmm and 90° pyz rotation angle at room temperature. At 90 K, the pyz rotation angle is 79.1°. At 90 K, the space group is P4/nmm with a pyz
rotation angle of 79.5°. The structure is highly disordered.
d
layers and the softness of the Jahn−Teller distorted Cu−X−Cu
bonds within the 3D coordination network.
From high-resolution single-crystal X-ray diffraction experi-
ments at 100 K and periodic DFT calculations the electron
density distribution in both compounds was determined. The
coefficients of the experimental multipolar refinement were
converted into occupancies of the d-orbitals.25 In agreement
with periodic DFT calculations, the electron population of the
The crystal structures of 1 and 2 are closely related to
−
−
−
−
[Cu(HF2)(pyz)2]Y with Y = ClO4 , PF6 , SbF6 , AsF6 , or
TaF6, see Table 3. All these tetragonal compounds contain
[Cu(pyz)2]2+ layers as their characteristic structural feature.
Further related compounds with distorted [Cu(pyz)2]2+ square
nets, for example, [Cu(ClO4)2(pyz)2] and [Cu(pyz)2(NO3)]-
NO3·H2O, are summarized in Table S3 of Supporting
Information. In [Cu(pyz)]2+ compounds, the angle between
the tetragonal plane and the pyz ring is close to 90° for bigger
octahedral Y anions, or close to 60° for smaller tetrahedral
2
2
dx −y orbital is distinctly smaller than for all other d orbitals, see
2
2
Table 4. This result confirms that dx −y is, in a first
Table 4. d-Electron Populations from Experimental
Multipolar Refinements (exp MM), Multipolar Refinements
of Theoretical Calculations (calc MM), and Periodic DFT
Calculations (calc)
−
anions; the only exception is Y = PF6 which gives both,
depending on the interlayer linker, see Table 3. We note,
however, when low-T measurements are available, all structures
have a pyrazine rotation angle smaller than 90°. Some
structures at room temperature have been refined in
P4/mmm,4,19,34 therefore with pyz necessarily orthogonal to
the tetragonal layer. However, a careful inspection of atomic
displacement parameters of pyz C atoms in these structures
reveals that these are compatible with a disorder between two
orientations of the pyrazine ring, and therefore the reported 90°
angles are deceptive.
2
2
2
dx −y
dxz
dxy
dyz
dz
[CuCl(pyz)2](BF4), 1
exp MM
calc MM
calc
1.644(3)
1.609
2.102(2)
2.120
1.996(3)
2.114
2.102(2)
2.120
2.196(4)
2.123
1.393
1.981
1.977
1.981
1.986
[CuBr(pyz)2](BF4), 2
exp MM
calc MM
calc
1.631(5)
1.610
2.099(4)
2.128
2.091(5)
2.088
2.099(4)
2.128
2.068(6)
2.135
1.393
1.980
1.978
1.980
1.985
In the [CuX(pyz)2](BF4) compounds 1 and 2, the layers are
linked by monatomic halide ligands, which is unprecedented for
the [Cu(pyz)]2+ structural family. For all other compounds, the
approximation, the single-occupied, magnetic orbital. It is
generally observed that the experimental multipole refinements
exceed the occupation of 2.0 for fully occupied orbitals, see, for
example, ref 39. These parameters were freely refined without a
constraint and represent d-shaped electron density functions,
not directly 3d-orbitals. A comparison with multipole refine-
ments fitted to theoretical data (DFT) is very useful, see Table
4, indicating a good agreement between theory and experi-
ments, when the same multipolar expansion is applied. The
experimental deformation density maps clearly confirm the
charge depletion of the Cu2+ ion along the x and y directions in
the local coordinate system, see Figure 3.
The topological analysis of the experimental and theoretical
electron densities, through quantum theory of atoms in
molecules (QTAIM),40 enables addressing the main bonding
features in the two structures, see Table S4 of Supporting
Information. In particular, we focus the attention on bonds to
Cu and electron sharing, including delocalization between
atoms not directly connected by a bond path. The electron
delocalization indices cannot be derived from the experimental
connection occurs via polyatomic anions, such as FHF−, NO2 ,
−
−
−
−
or NO3 , as well as BF4 and ClO4 for the distorted square
nets. Accordingly, 1 and 2 show the by far shortest interlayer
Cu−X−Cu distances, which are significantly shorter than the
intralayer Cu−pyz−Cu distances, see Table 2.
The Cu−ligand distances in [CuX(pyz)2](BF4) indicate that
the elongated Jahn−Teller axis is located parallel to the c-axis,
2
2
and therefore the unpaired electron of the dx −y orbital
localized in the ab plane. As local coordinate system for the
Cu2+ ion, we adopt x = a + b, y = a − b, and z = c. Therefore,
the magnetic interactions predominantly occur within the
[Cu(pyz)2]2+ layers of the ab plane, resulting in a quasi 2D
magnetic network, despite the 3D nature of the coordination
network and the shorter interlayer Cu−X−Cu distances.
If the Cu−pyz direction was instead Jahn−Teller distorted,
the Cu−N distances would be ∼2.40 Å, see, for example ref 14,
which is distinctly longer than the observed distances reported
in Table 2.
D
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The atomic charges, obtained from the QTAIM partitioning
of the experimental and theoretical electron densities of the
crystals or the theoretical electron density of the dimeric units,
are reported in Table S5 of Supporting Information. In all
cases, the actual charge of Cu is smaller than the formal
oxidation state, and the pyrazine is slightly positive, indicating
that the σ-donation mechanism is dominating. The halide
linkers have a negative charge, though significantly reduced
from the formal −1.0, especially for the experimental multipolar
model. The BF4 anion has a charge of ca. −1.0 (with highly
positive B and negative F atoms), indicating rather perfect ionic
interaction between the cationic [CuX(pyz)2]+ network and the
Figure 3. Static deformation electron density maps of 1. The xy and
x−z planes (in the local Cu2+ coordinate system) are depicted. Blue
and red contours (0.2 e/Å3), respectively, represent the excess and
depletion of electron density with respect to the spherical atom
distribution. The green contour is the zero level.
−
interstitial BF4 anions.
The magnetic structures of 1 and 2 were determined from
deuterated powder samples by neutron diffraction in the
temperature range from 1.5 to 15 K. A neutron diffraction
pattern of [CuBr(D4-pyz)2](BF4) measured on DMC with λ =
4.5040 Å at 1.5 K is shown in Figure 5a, and the magnetic
structure is shown in Figure 5b. The agreement factors for the
Rietveld refinement are Rp = 2.9%, Rwp = 4.3%, Rexp = 0.8%,
electron density, but they are computed from gas-phase
calculations on a dimeric [Cu2X4(pyz)7] unit.
In general, the two compounds show very similar features,
both in the experimental and the theoretical analysis. The
electron density calculated at the bond critical points of Cu−X
bonds is ca. 1/3 that of Cu−N bonds. Similarly, the electron
delocalization indices of Cu−X bonds are ca. 1/2 of Cu−N
bonds. This mainly reflects the Jahn−Teller distortion and the
lower (though not-negligible) electron sharing occurring along
this coordination direction. The 1,3 C−C and C−N
interactions in the pyrazine ring have an electron delocalization
of ca. 0.1 electron pairs due to the large resonance within the
aromatic ligand. Of course, the 1,2 interactions have a much
larger delocalization of ca. 1.3 electron pairs. Instead, the 1,3
Cu−C interaction is much weaker (<0.02 electron pairs). This
confirms the previous suggestion that a π driven Cu−Cu
magnetic exchange through the pyrazine is not favorable; this
would be possible only through a significant Cu−C exchange,
which does not occur, see, for example, the discussion in ref 39.
The Cu−N interaction cannot provide any contribution to a π
driven Cu−Cu magnetic exchange, because the atomic orbitals
2
2
pz of N and dx −y of Cu are necessarily orthogonal to each
other. Accordingly, the large Cu−N exchange can only
contribute via σ-type mechanism to the Cu−Cu exchange.
This is confirmed by the calculated spin density distribution for
the dimer, see Figure 4.
Figure 5. (a) Powder neutron diffraction pattern of [CuBr(D4-
pyz)2](BF4) at 1.5 K (DMC, λ = 4.5040 Å). The graph shows the
diffraction pattern (red dots), the Rietveld refinement (black line), the
nuclear (blue ticks) and magnetic (red ticks) Bragg positions, and the
difference curve (blue line). (b) Magnetic structure with k = (0, 0, 0.5)
in a perspective view along the c-axis. Full lines denote the unit cell,
and dashed lines indicate the Cu2+ ion square nets at heights of z/c =
0, 1, and 2.
Figure 4. Calculated spin density distribution imposes an
antiferromagnetic coupling in the [Cu2Cl4(pyz)7] dimer. Cyan and
green surfaces represent excess and defect of α spin density at values
0.013 eÅ−3.
E
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Article
RBragg = 1.7%, and Rmag = 48.6%. A neutron diffraction pattern
of [CuCl(D4-pyz)2](BF4) and the low-angle diffraction patterns
with the magnetic contributions are shown in Figure S6 of
Supporting Information. Because of the long wavelength the
number of accessible nuclear Bragg peaks was very limited.
Therefore, the atomic parameters were fixed to values obtained
from 15 K neutron data measured with λ = 3.8040 Å. When
cooled from 15 to 1.5 K, weak additional magnetic Bragg peaks
appeared below TN = 3.9(1) K for 1 and 3.8(1) K for 2, which
originate from long-range (3D) antiferromagnetic order of the
Cu2+ spins. For both compounds, the magnetic Bragg peaks are
indexed by the propagation vector k = (0, 0, 0.5); it indicates
that the magnetic unit cell is doubled along the c-axis with
respect to the crystallographic unit cell. Accordingly, the
magnetic unit cell contains four Cu2+ ions, see Table 5. The
Figure 6. Temperature dependence of the integrated intensity of the
(−101) magnetic Bragg peak of 1 (black dots) and 2 (blue dots). Fits
to a power law (red lines) result in TN = 3.9(1) K for 1 and TN
3.8(1) K for 2.
=
Table 5. Cu Atomic Positions in the Magnetic Unit Cell with
k = (0, 0, 0.5) and Ordered Moments μx of
[CuCl(pyz)2](BF4), 1, and [CuBr(pyz)2](BF4), 2, at 1.5 K
́
number of data points. The determined Neel temperatures are
in good agreement with magnetic susceptibility measurements
below.
a
x/a
y/b
z/c
μx/μB, 1
μx/μB, 2
I = I0(1 − T/TN)2β
(3)
Cu1
Cu2
Cu3
Cu4
0.25
0.75
0.25
0.75
0.25
0.75
0.25
0.75
0
0
1
1
0.76(8)
−0.76
−0.76
0.76
0.6(1)
−0.6
−0.6
0.6
The Cu2+ g-values and their anisotropy were determined
from X-band ESR spectra at room temperature, see Figure 7.
a
μy = μz = 0 μB
best fit of the intensities was obtained for a magnetic structure
with ordered moments in the tetragonal plane and AFM
coupling both in the ab plane and along the c-axis, see Figure
5b. Since the Cu−ligand−Cu angles are 180° along all magnetic
exchange paths of the [CuX(pyz)2]+ framework the observed
AFM coupling agrees with theoretical expectations. At 1.5 K the
ordered magnetic moments amount to μx = 0.76(8) μB/Cu2+
for 1 and 0.6(1) μB/Cu2+ for 2. For uniaxial symmetry, as it is
the case for the tetragonal title compounds, neutron powder
diffraction data reveal the magnitude of the ordered magnetic
moment, its angle with the c-axis, and the relative phase
between the magnetic ions. The absolute orientation of the
ordered moment within the ab plane cannot be determined.
Therefore, the calculations were done for magnetic moments
aligned along the a-axis.
Figure 7. Experimental (black dots) and simulated (red line) X-band
ESR spectrum of [CuCl(D4-pyz)2](BF4) powder. The fit results in gx
= 2.060(1) and gz = 2.275(1).
For [CuCl(D4-pyz)2](BF4) a g-value of 2.132 was
determined from ESR measurements, see below. Accordingly,
g·S = 1.07 μB/Cu2+ is expected for a fully ordered moment. The
observed value of 0.76 μB/Cu2+ is reduced but in good
agreement with values of other Cu2+ compounds, for example,
Cu(DCO2)2·4D2O,41,42 indicating quantum fluctuations below
TN. The magnetic contributions to the neutron diffraction
pattern in Figure 5 are rather tiny. This is a result of the small S
= 1/2 spin of Cu2+, since the magnetic intensity is proportional
to the square of the ordered moments. The tiny intensity
manifests in a large Rmag = 48.6% value for the magnetic
refinement. Nevertheless, the AFM magnetic structure was
clearly determined as the best solution with respect to magnetic
peak positions and intensities. Calculations for all other spin
orientations resulted in Rmag > 85% values.
For nondeuterated and deuterated [CuCl(pyz)2](BF4) powder
samples values of gx = 2.061(1), gz = 2.276(1), and gx =
2.060(1), gz = 2.275(1) were obtained, respectively. Within
error limits, the values of the H and D samples are equal. They
result in an average g = 2.132(1) for 1. For the bromide gx =
2.057(1) and gz = 2.272(1) were determined with an average g
= 2.129(1). The ESR spectra are in perfect agreement with the
crystal structure exhibiting a single Cu2+ site of axial symmetry,
see Table S2 of Supporting Information. Similar g values were
reported for related [Cu(pyz)2]2+ compounds.19,34,37,43,44
The anisotropy of the Cu2+ g-value was measured for a
nondeuterated single crystal of 1 at room temperature. The
tetragonal prismatic crystal had almost equal edges of 1 mm
length. Its orientation was verified by X-ray diffraction. Data for
a rotation around the b-axis are shown in Figure 8. A sine fit
results in values of gx = 2.058(1) and gz = 2.274(1). A second
data set (not shown here) for the rotation around the c-axis
resulted in an isotropic value of gx = 2.060(1). These single-
crystal values are in good agreement with powder data. They
The temperature dependence of the integrated intensity of
the strongest magnetic peak (−101) at 35.7° 2θ is shown in
́
Figure 6. A fit to the power law in eq 3 yields the Neel
temperatures TN = 3.9(1) K and 3.8(1) K for the chloride and
bromide, respectively. The critical exponent β = 0.23 for a 2D
Heisenberg magnet was kept fixed in the fits due to the limited
F
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Article
i
⎡
⎢
⎢
⎢
⎤
⎥
⎥
⎥
J
5
i=1
∑
N
i
( )
(k T ) ⎦
kBT
pC
T
C
T
χ =
1 +
(1 − p) +
i
J
1 + ∑i5=1
D
i
⎢
⎣
⎥
B
(4)
The fit results in J∥ = 9.4(1) K for 1 and 8.9(1) K for 2, in
good agreement with the estimation from Tmax. The para-
magnetic impurities are 1.0(1) % for 1 and 1.3(1) % for 2. The
expression g·Bs/J∥ ≈ 6.03 T [4] results in an estimate for the
saturation field along the c-axis of Bs ≈ 25 T for 1 and 24 T for
2. The interplane coupling J⊥ is determined by TN and J∥. For a
quasi-2D Heisenberg antiferromagnet the values are related by
eq 5
|J⊥| = Jeb−4πρ/T
N
s
(5)
Figure 8. Angular dependence α of the g-value (black dots) of 1 in the
ac plane from single-crystal ESR spectra. A sine fit (red line) results in
values of gx = 2.058(1) and gz = 2.274(1).
with b = 2.43 and the spin stiffness ρs = 0.183 J for an S = 1/2
system.46 This results in |J⊥| = 0.31(6) K for 1 and 0.52(9) K
for 2.
Weak magnetic interactions between the [Cu(pyz)2]2+ layers
give rise to 3D order at lower temperature, as proven by
neutron diffraction above. The 3D order appears as a kink in
the magnetic susceptibility below 4 K, see the inset in Figure 9.
The ratios of TN/J∥ = 0.41 for 1 and 0.43 for 2 indicate
significant interactions between the layers. As for the ESR data,
the magnetic susceptibility data for nondeuterated and
deuterated samples of 1 were equal within error limits. Only
small variations in the paramagnetic impurities were observed
between the different samples.
confirm the axial anisotropy of the g tensor in [CuX(pyz)2]-
(BF4) and the gx < gz assignment.
The magnetic susceptibility χ and the χ·T product versus
temperature are shown in Figures 9 and S5 of Supporting
Single-crystal susceptibility data of [CuCl(pyz)2](BF4) for
H∥c and H⊥c coincide from 300 to 190 K (data not shown
here). Toward lower temperature, see the inset in Figure 9, an
anisotropy is observed with higher χ values for H⊥c, which is in
agreement with the magnetic structure, see Figure 5b, and
ordered moments in the ab plane.
Magnetization measurements of 1 and 2 at 1.9 K are shown
in Figure 10. The magnetization increases approximately
Figure 9. Temperature dependence of the magnetic susceptibility χ for
○
○
powder samples of nondeuterated 1 (red ), deuterated 1 (purple ),
○
and 2 (blue ). (inset) Magnification of the low-temperature part,
where single-crystal data of 1 for H∥c (green ) and H⊥c (black
are added. Fits to a 2D Heisenberg model (black lines) are shown for
○
○
)
powder samples of 1 and 2 between 4.3 and 300 K.
Information, respectively. At 300 K the χ·T values of 0.4139
cm3 K/mol for 1 and 0.4123 cm3 K/mol for 2 were determined.
They are in good agreement with the expectation value of χ·T =
0.125 05·g2·S·(S + 1) = 0.4255 cm3 K/mol with S = 1/2 and g =
2.132 from ESR. The χ·T values decrease with temperature and
show a steep decline below 50 K due to antiferromagnetic
interactions.
Figure 10. Magnetization of powder samples of 1 (red) and 2 (blue)
at 1.9 K.
The magnetic susceptibility χ shows a broad maximum at ∼8
K, see Figure 9. The maximum occurs due to predominantly
2D AFM interactions in the [Cu(pyz)2]2+ planes. According to
J∥ = 1.07·Tmax an in-plane coupling parameter of J∥ ≈ 9 K can
be estimated for a 2D Heisenberg system. Data were fitted to a
2D spin 1/2 Heisenberg model between 4.3 and 300 K, see eq
4.45 The model includes a small percentage p of paramagnetic
impurities with coefficients Ni and Di from ref 45.
linearly with the magnetic field up to ∼1 T. For higher fields
the curves show an upturn and rise faster than linear. Such
behavior is typical for low-dimensional AFM coupled Cu2+
compounds with a low-spin (singlet) ground state.4,18,47−49
Spins gradually align with increasing magnetic field resulting in
the upturn of the magnetization. The observed value of 734
cm3 G/mol for 1 at 5 T is far from saturation, where M = N·μB·
g·S = 5954 cm3 G/mol is expected for S = 1/2 and g = 2.132.
G
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−
−
The low experimental value at 5 T is in agreement with the
much higher estimated saturation field of Bs ≈ 28 T from the
2D Heisenberg model. A slightly higher magnetization value of
838 cm3 G/mol is observed for 2 at 5 T. It is in agreement with
the smaller J∥ = 8.9 K for the bromide compared to J∥ = 9.4 K
for the chloride.
X = HF2 by NO2 (no. 8) increases J∥, and the correlation is
already broken by these small variations. These results call for
further measurements and calculations of structural and
magnetic properties under pressure that we are currently
undertaking in our laboratories. Only the study of the same
compound under various external parameters will disentangle
the correlation among variables.
The aim of the present study is to establish magneto-
structural correlations in the [Cu(pyz)2]2+ series by adding the
compounds [CuX(pyz)2](BF4), where X = Cl and Br, with
distinctly shorter Cu−X−Cu distances, see Table 3. For all
compounds the Cu−pyz−Cu distances are located in a very
narrow range from 6.852 to 6.895 Å. Therefore, the Cu−pyz−
Cu distances do not significantly correlate with the magnetic
coupling parameters represented by J∥ (2D) and TN (3D). In
contrast, the pyz rotation angle is quite variable. For longer
Cu−X−Cu distances, an increase of the pyz rotation angle is
expected to reduce the steric hindrance of pyz ligands in the
tetragonal plane. Although this is not valid for 1 and 2, where
the Cu−X−Cu distance is ∼0.2 Å longer in 2, the pyz rotation
angle decreases by more than 3°. In Table 3, the pyrazine
rotation angle ranges from ∼55° to 90°. As discussed above, the
perfectly vertical pyrazines are likely affected by disorder over
two conformations. Again no significant correlation is found
with the magnetic coupling: for example, in the three BF4− salts
the pyrazine rotation angle is 55.4°, 58.8°, and 59.4° for X = Br,
Cl, and HF2, respectively, but J∥ and TN for the chloride and
CONCLUSIONS
■
Two Cu2+ coordination polymers [CuX(pyz)2](BF4) with X =
Cl and Br were synthesized, and single crystals were grown by
controlled evaporation from aqueous solution. The isostruc-
tural tetragonal compounds consist of [Cu(pyz)2]2+ layers
linked by halide anions X− into a [CuX(pyz)2]+ 3D
coordination network. The charge is compensated by interstitial
−
BF4 anions. The monatomic halide linkage is unique among
the reported [Cu(pyz)2]2+ compounds and result in distinctly
shorter interlayer distances. The 3D coordination network gives
rise to low solubility and high thermal stability. Temperature-
dependent diffraction measurements revealed a pronounced
structural anisotropy with rigid Cu−pyz−Cu and much softer
Cu−X−Cu linkage. The shorter Cu−N and longer Cu−X
bonds of the octahedral Cu2+ coordination indicate that the
2
2
dx −y magnetic orbital is located in the tetragonal plane.
Experimentally and theoretically derived d-orbital occupancies
2
2
clearly confirm the location of the dx −y orbital in the ab plane.
These materials are very important for their magnetic
properties, which were characterized by neutron diffraction,
magnetic susceptibility, and ESR measurements. The Cu2+ g-
tensor is close to isotropic with a 10% larger gz value at room
temperature. The χ versus T curves show a broad maximum
below 10 K characteristic for a 2D Heisenberg antiferromagnet.
The intralayer interactions J∥ are much stronger than magnetic
interactions between the [Cu(pyz)2]2+ layers. Below 4 K 3D
antiferromagnetic order sets in, and moments are localized in
the tetragonal plane. Some open questions remain concerning
the correlation of structural and magnetic properties in
[CuX(pyz)2]Y compounds, which may depend on multiple
parameters. The rigidity of the Cu−pyz−Cu linkage implies no
correlation with J∥ and TN. On the contrary, the rotation of
pyrazine about the Cu−N axis is quite variable and strongly
depends on Y anions. However, the σ-type Cu−N exchange
mechanism is necessarily independent of the pyz rotation angle.
The electronic polarizability of the X linker appears less
important; otherwise, a higher TN would be expected for the
bromide. Magneto-structural correlations may be drawn for
narrow subsections only, as discussed for [CuX(pyz)2](BF4)
with X = Cl, Br, and HF2. This fosters further investigations
that are currently in due course in our laboratories. In
particular, given the soft nature of the Cu−X−Cu interlayer
connection, we expect a significant increase of the ratio
between magnetic interactions J⊥/J∥ upon application of
isotropic external pressure. Moreover, further chemical
variations of ligands and counteranions will provide a wider
data basis, which is required for more systematic analyses of
correlations between structural features and magnetic exchange.
−
bromide are much higher than for HF2 . This lack of
correlation agrees well with the topological analysis of the
electron density, which reveals that the Cu−N exchange is
predominantly σ-type and independent from the pyz rotation
angle. Compound numbers 1−4 and 9−10 from Table 3
contain the same [Cu(HF2)(pyz)2]+ 3D coordination network.
Noteworthy, the magnetic interactions in compounds 9 and 10
are distinctly weaker than for 1−4, despite shorter Cu−X−Cu
distances. The contacts between pyz and the interstitial anions
have an important influence on the pyz rotation angle, too, and
break a clear correlation with the Cu−X−Cu distance. Such
observations are not rationalized by present models and ask for
further investigation. Present theoretical modeling qualitatively
explains the magnetic interactions and their dimensionality.
As a result of this multiparameter space, it appears that
magneto-structural correlations can be established in narrow
subsections of the [Cu(pyz)2]2+ family, only. For [CuX(pyz)2]-
(BF4) with X = Cl, Br, and (HF2), cf. numbers 6, 7, and 10 in
Table 3, J∥ and TN are displayed versus the Cu−X−Cu distance
in Figure 11. Both J∥ and TN decrease with increasing Cu−X−
Cu distance. The substitution of Y = BF4− by ClO4− (no. 9) or
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.7b03150.
Figure 11. Correlation of J∥ and TN with the Cu−X−Cu distance for
[CuX(pyz)2]Y compounds 6−10 in Table 3. The dashed lines
−
represent linear fits for compounds with Y = BF4 .
H
DOI: 10.1021/acs.inorgchem.7b03150
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Inorganic Chemistry
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AUTHOR INFORMATION
Corresponding Authors
■
*E-mail: piero.macchi@dcb.unibe.ch. (P.M.)
*E-mail: christian.rueegg@psi.ch. (Ch.R.)
*E-mail: karl.kraemer@dcb.unibe.ch. (K.W.K.)
(14) Lanza, A.; Fiolka, C.; Fisch, M.; Casati, N.; Skoulatos, M.;
Ruegg, C.; Kramer, K. W.; Macchi, P. New magnetic frameworks of
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ORCID
[(CuF2(H2O)2)x(pyz)]. Chem. Commun. 2014, 50, 14504−14507.
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Tsirlin, A. A.; et al. Quasi-two-dimensional S = 1/2 magnetism of
Cu[C6H2(COO)4][C2H5NH3]2. Phys. Rev. B: Condens. Matter Mater.
Phys. 2015, 91, 054409.
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Turnbull, M. M.; Willett, R. D. Two-Dimensional Heisenberg
Antiferromagnets: Syntheses, X-ray Structures, and Magnetic Behavior
of [Cu(pz)2](ClO4)2, [Cu(pz)2](BF4)2, and [Cu(pz)2(NO3)](PF6).
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A. C.; Southerland, H. I.; Manson, J. L.; Schlueter, J. A.; Phillips, M.
D.; Turnbull, M. M.; Landee, C. P. Hydrogen Bonding and
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Twamley, B.; Lancaster, T.; Blundell, S. J.; Baker, P. J.; Pratt, F. L.;
Singleton, J.; Mcdonald, R. D.; Goddard, P. A.; Sengupta, P.; Batista,
C. D.; Ding, L.; Lee, C.; Whangbo, M.-H.; Franke, I.; Cox, S.; Baines,
C.; Trial, D. Strong H···F Hydrogen Bonds as Synthons in Polymeric
Quantum Magnets: Structural, Magnetic, and Theoretical Character-
ization of [Cu(HF2)(pyrazine)2]SbF6, [Cu2F(HF)(HF2)(pyrazine)4]-
(SbF6)2, and [CuAg(H3F4)(pyrazine)5](SbF6)2. J. Am. Chem. Soc.
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Mariusz Kubus: 0000-0002-1764-0376
Arianna Lanza: 0000-0002-7820-907X
Nicola Casati: 0000-0002-4206-9239
Karl W. Kramer: 0000-0001-5524-7703
Notes
̈
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
Part of this work is based on experiments performed at the
Swiss spallation neutron source (SINQ) and the Swiss Light
Source (SLS), Paul Scherrer Institute (PSI), Villigen, Switzer-
land. M.K. and B.W. acknowledge funding from the European
Community’s Seventh Framework Program (FP7/2007-2013)
under Grant No. 290605 (PSIFELLOW/COFUND). The
research leading to these results has received funding from the
Swiss National Science Foundation under Grant Nos.
200020_150257 and 200020_160157.
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