Room-temperature structural phase transition in the quasi-2D spin-\nicefrac{{1}}{{2}} Heisenberg antiferromagnet Cu(pz){}_{2}(ClO{}_{4}){}_{2}

Room-temperature structural phase transition in the quasi-2D spin- Heisenberg antiferromagnet Cu(pz)(ClO)

N. Barbero nbarbero@phys.ethz.ch Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zurich, Switzerland    M. Medarde Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland    T. Shang Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland    D. Sheptyakov Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland    C. P. Landee Department of Physics, Clark University, Worcester, Massachusetts 01610, USA    J. Mesot Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zurich, Switzerland Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland    H.-R. Ott Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zurich, Switzerland Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland    T. Shiroka tshiroka@phys.ethz.ch Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zurich, Switzerland Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
Abstract

Cu(pz)(ClO) (with pz denoting pyrazine CHN) is a two-dimensional spin- square-lattice antiferromagnet with  K. Due to a persisting focus on the low-temperature magnetic properties, its room-temperature structural and physical properties caught no attention up to now. Here we report a study of the structural features of Cu(pz)(ClO) in the paramagnetic phase, up to 330 K. By employing magnetization, specific heat, Cl nuclear magnetic resonance, and neutron diffraction measurements, we provide evidence of a second-order phase transition at  K, not reported before. The absence of a magnetic ordering across in the magnetization data, yet the presence of a sizable anomaly in the specific heat, suggest a structural order-to-disorder type transition. NMR and neutron-diffraction data corroborate our conjecture, by revealing subtle angular distortions of the pyrazine rings and of ClO counteranion tetrahedra, shown to adopt a configuration of higher symmetry above the transition temperature.

Two-dimensional systems, pressure-dependent phase transitions, antiferromagnetism, nuclear magnetic resonance

I Introduction

As a notable physical realization of a quasi-2D Heisenberg antiferromagnet, Cu(pz)(ClO) has been a test case for investigating the competition between long-range magnetic order and quantum fluctuations Darriet et al. (1979); Choi et al. (2003). Its structure consists of stacks along the -axis of well-isolated nearly-square layers of Cu ions in the -plane, rotated by 45 with respect to the in-plane primitive vectors, as shown schematically in Fig. I. Along the -axis, each layer is shifted by half a unit cell along the - and -axes. Each Cu ion is bridged to its four nearest-neighbors (NN) by CHN pyrazine ligands, which provide the intralayer superexchange interaction. Two ClO perchlorate counteranions, linked to Cu ions via one of the oxygen atoms in the O tetrahedra, provide a sufficient interlayer separation along the -axis, hence implying a negligible interlayer interaction. Overall, this results in a Cu-ion arrangement of nearly-tetragonal symmetry Landee and M.Turnbull (2013). The 3D antiferromagnetism (AFM) of Cu(pz)(ClO) has been extensively studied by inelastic neutron scattering (INS) Tsyrulin et al. (2010), muon-spin rotation (SR) Lancaster et al. (2007), and nuclear magnetic resonance (NMR) Barbero et al. (2016) measurements. It has also been shown that applied magnetic fields along the -axis strengthen the AFM order by suppressing the quantum fluctuations, hence enhancing above its zero-field value of 4.24 K Tsyrulin et al. (2010). On the other hand, external hydrostatic pressure reduces Barbero et al. (2016), most likely by enforcing 1D-type interactions Mermin and Wagner (1966), as suggested by results of density-functional theory (DFT) calculations on similar compounds Vela et al. (2013); Wehinger et al. (2018).

The crystal structure of Cu(pz)(ClO) was determined at 163 and 293 K from single-crystal x-ray diffraction data Woodward et al. (2007), obtaining a better refinement with the space group in the first case and with the space group in the latter. It was also observed that the four pyrazine moieties form two sets at low temperature, each of them characterized by a different tilting angle with respect to the -plane. The values of these angles are distinct at 163 K, but they become identical (65.8) at 293 K. Along with x-ray diffraction patterns, Choi et al. Choi et al. (2003) reported also infrared-spectroscopy data, used to track the evolution of the vibrational modes as a function of temperature. Upon heating, the latter measurements indicated a softening of the vibrational modes starting at approximately 180 K, related to the out-of-plane deformations of the pyrazine rings.

In this work, by combining data from NMR, specific-heat and neutron-diffraction experiments, we provide clear evidence for a structural phase transition occurring at = 294(1) K, not reported before in the literature. Our results indicate that the two initially different Cl sites become equivalent above and that the symmetry of the individual pyrazine rings increases upon heating above .

After introducing the experimental details in Sec. II, in Sec. III.1 and III.2, we describe the material characterization via magnetization and specific-heat measurements. From these data, we identify the onset of the AFM order at and of the structural transition at , respectively. The Cl NMR results discussed in Sec. III.3 clearly show the merging of the two lines upon heating, reflecting an increase in structure symmetry and allowing for an evaluation of the isotropic hyperfine coupling. Finally, to precisely identify the variations in bond lengths and angles, we employed neutron powder diffraction measurements, whose results are reported in Sec. III.4. The combined data of our investigations indicate that the second-order structural phase transition is accompanied by subtle transformations in both the ClO tetrahedra and in the CHN pyrazine ligands.

Figure 1. : A layer of Cu(pz)(ClO), whose structure (space group no. 12) was determined from neutron diffraction data at 294 K. Each Cu(II) atom (blue) is linked via pyrazine rings (C = brown, N = gray) to four other copper ions, all lying in the -plane. The layers are spaced by perchlorate counteranions (Cl = green, O = red), lying along the interlayer -axis direction. As described in the text and in Table 1 (see Appendix), the N and C atoms in the pyrazine rings and the O atoms in the perchlorate counteranions have different Wyckoff positions. Each counteranion contains a Cl site at the center and four O atoms at its vertices.

Ii Experimental details

The Cu(ClO) crystals were synthesized by dissolving Cu(ClO)6HO and pyrazine in water with a drop of dilute HClO(aq), in order to prevent the precipitation of Cu(OH) and of CuCO. The solution was then partially covered and left to evaporate slowly, with the crystals growing over several weeks. Finally, the mixture was filtered, the recovered crystals were washed in deionized water at 10C, and dried in air. Since the samples are hygroscopic, they were stored in an inert-gas atmosphere Woodward et al. (2007). Single crystals with a typical mass of 80 mg were aligned with the -axis (hard axis) parallel to the applied magnetic field, for both the magnetization- and NMR experiments. Given the easily identifiable -planes, delimited by smooth surfaces, the visual crystal alignment was achieved with an uncertainty of about 5. For the neutron diffraction measurements, we used deuterated powder synthesized by following the same protocol, but employing deuterated reagents. The magnetization measurements were performed with a commercial magnetic property measurement system (MPMS) XL setup from 2 to 310 K in an applied magnetic field of 5 mT. The heat-capacity data were collected by means of a Quantum Design physical property measurement system (PPMS-9 T) by using the relaxation method, both upon heating and upon cooling, in a temperature range between 250 and 330 K.

The Cl-NMR study comprised lineshape and spin-lattice relaxation time measurements in a 7.063-T field, corresponding to a Larmor frequency of 29.4664 MHz for the spin-3/2 Cl quadrupolar nuclei. NMR signals were detected by employing a standard spin-echo sequence, consisting in and pulses of 2 and 4 s, respectively, with recycle delays ranging from 0.6 to 0.2 s for temperatures in the 4–310 K range. The NMR lineshapes were obtained from fast Fourier transforms (FFT) of the echo signals. The spin-lattice relaxation times were measured via the inversion-recovery method using a -- pulse sequence.

Neutron diffraction experiments were performed at the HRPT diffractometer (high-resolution powder diffractometer for thermal neutrons) at the SINQ facility of the Paul Scherrer Institute (PSI) in Villigen, Switzerland. Several patterns were recorded between 260 and 330 K, using two different wavelengths ( = 1.494 Å and 1.886 Å) of the high-intensity mode (24’ primary-beam collimation) Fischer et al. (2000). The sample was placed in an 8-mm-diameter vanadium cylinder under helium atmosphere and sealed with indium wire. The cylinder was then introduced into a cryofurnace whose contribution to the neutron-count background was minimized by means of an oscillating radial collimator. All the patterns were refined by using the Rietveld refinement FullProf suite Rodríguez-Carvajal (1993).

Figure 2. : , as measured at 5 mT. The linear fit (red line) to the data in the paramagnetic regime ( K) implies an effective magnetic moment of 0.5(1) , while the negative intercept on the axis indicates AFM interactions among the Cu ions. Inset: low-temperature 1/ data. The arrow at  K indicates the inflection point, considered as the onset of AFM order Barbero et al. (2016).

Iii Results and discussion

iii.1 Magnetization measurements

The inverse magnetic susceptibility 1/ measured at 5 mT (see Fig. II) indicates an effective magnetic moment, = 0.5(1) . Its value, far smaller than the corresponding Cu single-ion spin-only magnetic moment (1.73 ), suggests the presence of strong quantum fluctuations. As previously reported Tsyrulin et al. (2010), an enhancement of in higher magnetic fields may be interpreted as a field-induced suppression of the quantum fluctuations. Besides the clear anomaly at  K, the response remains paramagnetic up to 300 K, thus excluding the magnetic nature of the transition observed at  K (see below).

iii.2 Specific-heat measurements

The heat capacity data vs. temperature, collected between 250 and 330 K upon both heating and cooling, are shown in Fig. III.2. The significant and overlapping (i.e., hysteresis-free) anomalies both peak at 293 K and indicate the existence of a previously unnoticed second-order phase transition in this temperature range. The independence of the transition from the applied magnetic field (of 5 T in this case, see inset in Fig. III.2) and the absence of an anomaly in the magnetic susceptibility (see Fig. II), rule out a magnetic origin of the transition and suggest the transition at to be of structural character. From the heat-capacity data, we calculated numerically the entropy , with being a reference temperature. Since across we find ( JKmol), this suggest an order-to-disorder (i.e., a non displacive) type of structural transition (see below).

Figure 3. : The temperature dependence of the heat capacity measured upon heating and cooling showing the lack of hysteresis. The arrow indicates = 294 K. Inset: the coinciding 0- and 5-T datasets rule out heat-capacity changes in the applied magnetic field range.

iii.3 Nuclear magnetic resonance measurements

Cl NMR peak positions vs. temperature (a). Despite a general increase in frequency with
temperature, the peak separation (b) stays mostly constant
(ca. 
The Clogston-Jaccarino
Cl NMR spin-lattice relaxation rate
A typical neutron-diffraction pattern measured at 294 K
using
(a) Structural fragment of the
pyrazine ring with labels identifying each atom.
(b) Thermal ellipsoids of oxygen atoms in the ClO

Figure 9. : (a) Structural fragment of the pyrazine ring with labels identifying each atom. (b) Thermal ellipsoids of oxygen atoms in the ClO perchlorate anions at 294 K. Note the large displacements of the two O1 atoms.

iii.4 Neutron diffraction

The magnetization, specific-heat, and NMR results shown in the previous sections suggest a structural origin for the two transitions at  K and  K. To closely monitor the evolution of the crystal structure between 260 and 330 K we performed systematic neutron powder-diffraction measurements. The initial structure refinement at 295 K, i.e., just above the transition, was carried out by assuming as valid the space group, previously proposed in the literature for the structure at 293 K Darriet et al. (1979). A representative Rietveld fit is shown in Fig. III.3.

Temperature dependence of the diagonal
Temperature-dependence of the N–D1 distance (a) and of the
atomic coordinates of the N atoms (b). In all cases, the crossing of
parabolic- (linear-) and linear fits (black solid lines)
was used to define the position of the anomaly at
Figure 12. : Temperature-dependence of the N–D1 distance (a) and of the atomic coordinates of the N atoms (b). In all cases, the crossing of parabolic- (linear-) and linear fits (black solid lines) was used to define the position of the anomaly at  K (vertical line). In (b), the and coordinates cross at about 308 K. For clarity, the values were vertically offset by 0.647 Å. The dihedral angle, also shown in (a), decreases with temperature and exhibits an inflection point at  K.

As shown in Fig. III.4, the transition at also involves subtle structural anomalies related to a distortion and reorientation of the four pyrazine rings. For instance, the N–D1 distance first increases up to 288 K and then saturates, whereas the and atomic coordinates of the N atoms first rapidly decrease down to and then continue decreasing with a reduced rate or saturate, respectively. We recall that , , and are the atomic coordinates, referred to the basis vectors , , and , respectively. As for the coordinate, it increases linearly across the covered temperature range, without showing any evident anomalies. Incidentally, the crossing of the - and coordinate values at about 308 K suggests a more regular in-plane arrangement of the pyrazine ligands above the second, yet much weaker, transition at . This corresponds to the pyrazine rings becoming closer to regular undeformed hexagons. We note also that such rings are not perfectly flat. Nevertheless, considering the small deviatiations from an ideal plane, we still can define a dihedral angle between the average plane of the pyrazine rings and the basal plane of Cu octahedra. The temperature dependence of the dihedral angle is shown in Fig. III.4(a) (right scale). This angle, very close to the values reported in the literature Woodward et al. (2007), decreases with temperature. Albeit weakly, the structural transition at  K is here reflected in an inflection point in .

In any case, such modifications are subtle and modest in magnitude. We also note that the small mismatch between the transition temperature , established as outlined in Secs. IIIB and IIIC, and the anomalies in the neutron-diffraction data is most likely due to temperature control and calibration issues, difficult to control exactly in experiments at room temperature. Moreover, we recall that the Cu–N and Cu–O3 distances do not exhibit clear anomalies at and that the ratio (Cu–N)/(Cu–O3), reflecting the degree of the Jahn-Teller distortion of the octahedra centered at Cu sites, has a constant value of . Finally, both the in-plane N–Cu–N- and the apical O–Cu–N angles are close to 90 and tend to the exact value of 90 upon increasing temperature. The absence of significant changes in these angles, which control the overlap of the CuN and CuO orbitals, indicates that the phase transition reported here does not imply sizable changes in the strength of the superexchange interactions.

To provide a possible explanation for the above observations, we recall that structural phase transitions can be classified as either displacive or order-disorder, usually considered as mutually exclusive. The latter consists in the transition from a configuration where one or more sites exhibit split occupancies to a more ordered one within the same set of atomic positions. From our neutron-diffraction and measurements, we conclude that the observed transition is a second-order structural transition of the order-disorder type (with some possible residual displacive effects). In fact, below , two locally different Cl sites can be distinguished and, hence, the system is disordered. Above , despite the established equivalence of the two Cl sites, some residual disorder persists, most likely due to the co-existence of two similar configurations of the perchlorate subunits.

Iv Conclusion

By combining the results of magnetization-, specific-heat-, NMR-, and neutron-diffraction experiments, we identified a previously unnoticed second-order phase transition at = 294 K in Cu(pz)(ClO) and determined its order-to-disorder structural character. Cl NMR measurements indicate the presence of two inequivalent Cl sites which persists, upon heating, up to the transition temperature. Interestingly, the distance in frequency between the two Cl NMR lines starts reducing from 175 K, i.e., the temperature at which a softening of the vibrational modes related to the pyrazine rings was previously observed. Above , the measured NMR orbital shift is compatible with typical values of the Cl nucleus in a tetrahedral environment. Below , instead, it assumes two significantly different values, with opposite signs for the two distinct sites, thus revealing strong deviations from the ideal tetrahedral geometry. The spin-lattice relaxation-rate data allowed us to precisely identify and to observe also a minor anomaly at  K, attributable to secondary structural distortions. The refinement of the neutron-diffraction patterns, assuming the validity of the space group, was used to monitor the temperature dependence of all the structural parameters. A detailed analysis indicates that the reported transition affects the perchlorate ClO tetrahedra, which adopt a more regular and ordered arrangement above . The relatively high values of the atomic displacements indicate the persistence of some positional disorder also above the transition, most likely due to the competition between two possible oxygen-site positions, almost degenerate in energy. Similarly, reorentations of the pyrazine rings, occurring at the transition, are reflected in anomalies in the N–H distance and in the nitrogen atomic coordinates. As shown by magnetization- and specific-heat data, these subtle structural modifications do not affect the magnetic properties of Cu(pz)(ClO) in the covered temperature range. Future DFT calculations, which account for positional disorder and geometric distortions, are expected to provide further insight into the significance of the structural phase transition reported here.

Acknowledgments

This work is based on experiments performed at the Swiss spallation neutron source SINQ and the Swiss Light Source SLS, both at the Paul Scherrer Institute, Villigen, Switzerland. A special thank goes to N. Casati for supporting our preliminary x-ray experiments at the Materials Science Beamline (SLS). The authors thank M. Chinotti, D. Gawryluk, and M. Turnbull for helpful discussions and assistance. This work was financially supported in part by the Schweizerische Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNF), Grant no. 200021-169455.

Appendix

iv.1 Structural refinement comparison between the and space groups at 294 K

 K model model
(Å) 9.78047(9) 9.78070(7)
(Å) 9.77594(9) 9.77589(7)
(Å) 8.16470(9) 8.16488(7)
120.8361(7) 120.8353(6)
Cu [0, 0, 0] [0, 0, 0]
0.0118(9) 0.0126(9)
Cl [0.2402(4), 0, 0.5391(5)] [0.2599(4), 0.4925(16), 0.4607(5)]
0.012(3) 0.0292(10)
O1 [0.2052(9), 0.1075(9), 0.6031(11)] [0.3071(18), 0.588(3), 0.388(3)]
0.057(5) 0.031(7)
0.393(14) 0.48(5)
0.128(6) 0.100(13)
0.061(6) 0.051(14)
0.030(4) 0.035(7)
0.195(7) 0.21(2)
0.193(8) 0.20(2)
O1’ [0.2713(19), 0.374(3), 0.397(3)]
0.061(10)
0.217(16)
0.176(18)
0.006(10)
0.012(11)
0.173(14)
0.151(15)
O2 [0.4010(7), 0, 0.5868(9)] [0.1025(6), 0.504(2), 0.4146(9)]
0.015(3)
0.069(5)
0.067(5)
0.005(6)
0.009(3)
0.003(7)
0.042(4) 0.047(4)
O3 [0.1363(7), 0, 0.3366(8)] [0.3643(6), 0.503(2), 0.6617(8)]
0.0311(13) 0.0335(13)
C1 [0.8968(3), 0.7691(3), 0.1448(4)] [0.8948(10) 0.2307(14) 0.1506(11)]
0.0145(7) 0.0168(5)
C2 [0.7985(3), 0.6701(3), 0.1524(4)] [0.2996(9) 0.8400(15) 0.1504(12)]
0.0190(7) 0.0168(5)
C3 [0.0997(10), 0.7683(14), 0.8572(11)]
0.0168(5)
C4 [0.7037(9), 0.1779(14), 0.8445(12)]
0.0168(5)
D1 [1.0197(5), 0.7807(4), 0.2700(6)] [0.0283(9), 0.2351(14), 0.2558(9)]
Occ 0.978(2) 0.961(7)
0.0428(12) 0.0254(9)
D2 [0.8379(5), 0.6088(4), 0.2768(5)] [0.3453(8), 0.9067(14), 0.2672(9)]
Occ 0.978(2) 0.961(7)
0.0372(10) 0.0254(9)
D3 [0.9892(8), 0.7973(14), 0.7166(10)]
Occ 0.961(7)
0.0254(9)
D4 [0.6732(8), 0.1254(14), 0.7153(10)]
Occ 0.961(7)
0.0254(9)
N1 [0.6505(2), 0.65082(20), 0.0041(3)] [0.8503(6), 0.1551(15), 0.9987(8)]
0.0096(4) 0.0141(5)
N2 [0.1512(6), 0.8534(15), 0.0060(8)]
0.0141(5)

( Å)
1.494 1.886 1.494 1.886
5.18 8.54 3.27 5.06
4.50 3.49 4.48 3.48
10.2 10.2 8.10 7.82
9.37 9.14 7.53 7.25
.




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  • (27) We recall that ADPs, which describe the anisotropic thermal motion through a symmetric rank-2 tensor, consist of six independent parameters. In the isotropic case, the off-diagonal terms clearly vanish. Most often are used to express ADPs, since they represent directly the mean-square atomic displacements (some values relevant to our case are reported in Table 1). An alternative, closely related quantity is . Computer programs generally output the values, defined as , since these minimize computation time and can be related directly to the reciprocal-cell parameters and . The diagonal ADPs describe displacements along three mutually perpendicular axes of the ellipsoid and, hence, are always positive. On the other hand, since the other elements of the ADP tensor establish the orientation of the ellipsoid with respect to the crystal-lattice coordinate system, the off-diagonal elements can be either positive or negative, under the structural constrain , which is confirmed from our data and is a necessary requirement for the physical validity of the refinement.
  • (28) The quantities marked with (*) in Table I were constrained to be identical for the same atomic species. The occupation of the D sites was found to be very close to 100%. The occupation of the remaining atomic sites was 100%.
  • (29) The Supplemental Material available at [URL] includes the two structural .cif files used for refining the neutron-diffraction patterns at 295 K, by assuming as valid the space groups and , respectively.

Table 1.: Structural parameters as determined from neutron powder diffraction at  K, using the space groups and , respectively 333The quantities marked with (*) in Table I were constrained to be identical for the same atomic species. The occupation of the D sites was found to be very close to 100%. The occupation of the remaining atomic sites was 100%. For the last group, that is non-centrosymmetric, the origin is floating. For that reason the -coordinate of Cu has been fixed to zero, matching the Cu postion in . To further facilitate comparisons, the setting for the monoclinic cell was chosen to be the same as in reference Woodward et al. (2007). For every space group the fits were carried out using a single structural model to refine simultaneosly the data recorded at and 1.886 Å. The related .cif file with the refinement parameters can be found in the Supplemental Material 444The Supplemental Material available at [URL] includes the two structural .cif files used for refining the neutron-diffraction patterns at 295 K, by assuming as valid the space groups and , respectively..
Figure 11. : Temperature dependence of the diagonal (blue diamonds) and (green squares) O1 ADPs and of the absolute value of the off-diagonal term (red circles). The crossing of the parabolic- and linear fits (black solid lines) was used to better define the position of the anomaly at  K (vertical line).
Figure 11. : Temperature dependence of the diagonal (blue diamonds) and (green squares) O1 ADPs and of the absolute value of the off-diagonal term (red circles). The crossing of the parabolic- and linear fits (black solid lines) was used to better define the position of the anomaly at  K (vertical line).
Figure 10. : Relative variation of the lattice parameters , , and (inset) and of the monoclinic angle (main panel) with temperature. The interlayer axis () is almost constant, the axis increases smoothly, whereas the axis exhibits a tiny kink close to (vertical line). The monoclinic angle , too, shows a clear change of slope across the transition (arrow).
Figure 10. : Relative variation of the lattice parameters , , and (inset) and of the monoclinic angle (main panel) with temperature. The interlayer axis () is almost constant, the axis increases smoothly, whereas the axis exhibits a tiny kink close to (vertical line). The monoclinic angle , too, shows a clear change of slope across the transition (arrow).
Figure 8. : A typical neutron-diffraction pattern measured at 294 K using = 1.8857 Å. The orange circles correspond to the observed pattern and the black solid line to the Rietveld fit obtained using the space group. The positions of the Bragg reflections and the difference between the observed and calculated patterns are shown in blue.
Figure 8. : A typical neutron-diffraction pattern measured at 294 K using = 1.8857 Å. The orange circles correspond to the observed pattern and the black solid line to the Rietveld fit obtained using the space group. The positions of the Bragg reflections and the difference between the observed and calculated patterns are shown in blue.
Figure 7. : Cl NMR spin-lattice relaxation rate vs. temperature measured upon heating (red circles) and cooling (blue squares). Both datasets exhibit a main peak (I) at 295 K and a smaller secondary peak (II) at 304 K. To compensate for a known calibration offset, data measured upon heating were shifted by  K.
Figure 7. : Cl NMR spin-lattice relaxation rate vs. temperature measured upon heating (red circles) and cooling (blue squares). Both datasets exhibit a main peak (I) at 295 K and a smaller secondary peak (II) at 304 K. To compensate for a known calibration offset, data measured upon heating were shifted by  K.
Figure 6. : The Clogston-Jaccarino vs.  plot for the two inequivalent chlorine sites. The almost identical slopes result in the same hyperfine coupling value,  mT/. The purely linear behavior is modified when the NMR signals start to merge. The arrow indicates the direction of increasing temperature.
Figure 6. : The Clogston-Jaccarino vs.  plot for the two inequivalent chlorine sites. The almost identical slopes result in the same hyperfine coupling value,  mT/. The purely linear behavior is modified when the NMR signals start to merge. The arrow indicates the direction of increasing temperature.
Figure 5. : Cl NMR peak positions vs. temperature (a). Despite a general increase in frequency with temperature, the peak separation (b) stays mostly constant (ca. 30 kHz), to smoothly go to zero at  K (see arrows). The line is a fit to , with . Inset: upon heating, the NMR linewidth shows a clear drop at (dashed line) indicative of a transition to a configuration with higher local symmetry.
Figure 5. : Cl NMR peak positions vs. temperature (a). Despite a general increase in frequency with temperature, the peak separation (b) stays mostly constant (ca. 30 kHz), to smoothly go to zero at  K (see arrows). The line is a fit to , with . Inset: upon heating, the NMR linewidth shows a clear drop at (dashed line) indicative of a transition to a configuration with higher local symmetry.
Figure 4. : Evolution of the Cl NMR line shape and position with temperature. Note that at room temperature Cu(pz)(ClO) exhibits a positive paramagnetic shift of 0.1%, with respect to the Larmor frequency (29.466 MHz in a 7.063-T magnetic field). At  K, the two NMR lines resulting from the two inequivalent chlorine sites merge into a single peak, indicating that the structural transformation of the ClO tetrahedra is complete.
Figure 4. : Evolution of the Cl NMR line shape and position with temperature. Note that at room temperature Cu(pz)(ClO) exhibits a positive paramagnetic shift of 0.1%, with respect to the Larmor frequency (29.466 MHz in a 7.063-T magnetic field). At  K, the two NMR lines resulting from the two inequivalent chlorine sites merge into a single peak, indicating that the structural transformation of the ClO tetrahedra is complete.
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