Trigonal antiprismatic Co(ii) single molecule magnets with large uniaxial anisotropies: importance of Raman and tunneling mechanisms

A trigonal antiprismatic Co(ii) molecule exhibits counterion-dependent relaxation of the magnetization due to the importance of the Raman relaxation process.


Trigonal Antiprismatic Co(II) Single Molecule Magnets with
. Variable-frequency ac magnetic susceptibility data for 1 collected at 1.8 K, an ac field of 5 Oe and dc fields from 0 to 5 kOe. Figure S5. Cole-Cole plots of 1 at 1.8 K, an ac field of 5 Oe and dc fields from 0.25 to 5 kOe. Table S1. Cole-Cole fit values of 1 at 1.8 K, an ac field of 5 Oe and dc fields from 0.25 to 5 kOe. Figure S6. Variable-temperature ac magnetic susceptibility data for 1 collected at temperatures from 2 to 12 K, an ac field of 5 Oe and a dc field of 500 Oe. Figure S7. Variable-frequency ac magnetic susceptibility data for 1 collected at 5.0 K, an ac field of 5 Oe and dc fields from 0.125 to 10 kOe. Figure S8. Cole-Cole diagrams of 1 at 5.0 K, an ac field of 5 Oe and dc fields from 0.125 to 10 kOe. Table S2. Cole-Cole fit values of 1 at 5.0 K, an ac field of 5 Oe and dc fields from 0.125 to 10 kOe. Figure S9. Dependence of τ and τ -1 with the applied DC fields for complex 1 at 5 K. Figure S10. Variable-frequency ac magnetic susceptibility data for 1 collected at temperatures from 2 to 8 K, an ac field of 5 Oe and a dc field of 500 Oe. Figure S11. Cole-Cole plots of 1 from 2.0 to 8.0 K, an ac field of 5 Oe and a dc field of 500 Oe. Table S3. Cole-Cole fit values of 1 from 2.0 to 8.0 K, an ac field of 5 Oe and a dc field of 500 Oe. Figure S12. Cole-Cole diagrams of 1 from 2.0 to 8.0 K, an ac field of 5 Oe and a dc field of 3 kOe. Table S4. Cole-Cole fit values of 1 from 2.0 to 8.0 K, an ac field of 5 Oe and a dc field of 3 kOe.

Dynamic Magnetic Measurements. Compound 2.
Figure S13. Variable-frequency ac magnetic susceptibility data for 2 collected at 1.8 K, an ac field of 5 Oe and dc fields from 0 to 1 kOe. Figure S14. Variable-temperature ac magnetic susceptibility data for 2 collected at temperatures from 2 to 15 K, an ac field of 5 Oe and a dc field of 500 Oe.
Electronic Supplementary Material (ESI) for Chemical Science. This journal is © The Royal Society of Chemistry 2016 S2 Figure S15. Variable-frequency ac magnetic susceptibility data for 2 collected at 6.0 K, an ac field of 5 Oe and dc fields from 0 to 10 kOe. Figure S16. Cole-Cole diagrams of 2 at 6.0 K, an ac field of 5 Oe and dc fields from 0.15 to 10 kOe. Table S5. Cole-Cole fit values of 2 at 6.0 K, an ac field of 5 Oe and dc fields from 0.15 to 10 kOe. Figure S17. Dependence of τ and τ -1 with the applied DC fields for complex 2 at 6.0 K. Figure S18. Variable-frequency ac magnetic susceptibility data for 2 collected at temperatures from 2 to 9 K, an ac field of 5 Oe and a dc field of 300 Oe. Figure S19. Cole-Cole diagrams of 2 from 2.0 to 11.0 K, an ac field of 5 Oe and a dc field of 300 Oe. Table S6. Cole-Cole fit values of 2 from 2.0 to 11.0 K, an ac field of 5 Oe and a dc field of 300 Oe. Figure S20. Variable-frequency ac magnetic susceptibility data for 2 collected at temperatures from 2 to 9.5 K, an ac field of 5 Oe and a dc field of 500 Oe. Figure S21. Cole-Cole plots of 2 from 2.0 to 12.0 K, an ac field of 5 Oe and a dc field of 500 Oe. Table S7. Cole-Cole fit values of 2 from 2.0 to 12.0 K, an ac field of 5 Oe and a dc field of 500 Oe. Figure S22. Cole-Cole plots of 2 from 2.0 to 9.5 K, an ac field of 5 Oe and a dc field of 1500 Oe. Table S8. Cole-Cole fit values of 2 from 2.0 to 9.5 K, an ac field of 5 Oe and a dc field of 1500 Oe.        Table S13. Energy of the first five excited states (cm -1 ) and its main contributions to the D and E values in cm -1 at CAS(7,5) NEVPT2 level.

Single Crystal X-ray Diffraction Studies
Single crystal X-ray data for 1 and 2 were collected at 110 K on a Bruker APEX diffractometer equipped with a CCD detector. The data sets were recorded as ϖ-scans at 1.0° step widths. Integration was performed with the Bruker SAINT software package S1 and absorption corrections were empirically applied using SADABS. S2 The crystal structures were refined using the SHELX suite of programs. S3 Images of the crystal structures were rendered using the visualization software DIAMOND. S4 All of the structures were solved by direct methods and all non-hydrogen atoms were located by alternating cycles of least squares refinements and difference Fourier maps. All hydrogen atoms were placed at calculated positions except for some water molecules whose hydrogen atoms were located by difference Fourier maps. The bond distances in disordered solvent molecules were restrained to chemically meaningful values. Anisotropic thermal parameters were added for all non-hydrogen atoms. A summary of pertinent information relating to unit cell parameters, data collection, and refinement statistics is provided in Table 1. CCDC 1422285 (1) and 1422286 (2) contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.  Figure S4. Variable-frequency in-phase (χ m ʹ, up) and out-of-phase (χ m ʺ, down) components of the ac magnetic susceptibility data for 1, collected at 1.8 K with an ac field of 5 Oe and 0, 250, 500, 750, 1000, 1250, 1500, 2000, 2500, 3000, 4000, and 5000 Oe dc applied fields, respectively. Solid lines are guides for the eye. Figure S5. Cole-Cole diagrams of 1 at 1.8 K with an applied dc field from 0.25 to 5 kOe and ac field of 5 Oe. The solid lines are least-square fittings of the data to a distribution of single relaxation processes with a generalized Debye model. Table S1. Cole-Cole fit values of 1 at 1.8 K with an applied dc field of 0.25 to 5 kOe and ac field of 5 Oe. Values in red have an α value of ~ 0.3 indicating a large distribution of relaxation times.  Figure S6. Variable-temperature in-phase (χ m ʹ, top) and out-of-phase (χ m ʺ, bottom) components of the ac magnetic susceptibility data for 1, collected at temperatures from 2 to 12 K with an ac filed of 5 Oe and 500 Oe dc applied fields. Solid lines are guides for the eye.      Figure S9. Dependence of τ (left) and τ -1 (right) with the applied DC fields for complex 1 at 5 K. Solid lines are guides for the eye. S11 Figure S10. Variable-frequency in-phase (χ m ʹ, top) and out-of-phase (χ m ʺ, bottom) components of the ac magnetic susceptibility data for 1, collected at temperatures from 2 to 8 K with an ac field of 5 Oe and 500 Oe dc applied fields.   Figure S12. Cole-Cole diagrams of 1 from 2.0 to 8.0 K with an applied dc field of 3 kOe and an ac field of 5 Oe. The solid lines are least-square fittings of the data to a distribution of single relaxation processes (≥ 4.0 K) with a generalized Debye model. S13   Figure S13. Variable-frequency in-phase (χ m ʹ) and out-of-phase (χ m ʺ) components of the ac magnetic susceptibility data for 2, collected at 1.8 K with an ac field of 5 Oe and different dc applied fields, respectively. Solid lines are guides for the eye.  Figure S14. Variable-temperature in-phase (χ m ʹ, top) and out-of-phase (χ m ʺ, bottom) components of the ac magnetic susceptibility data for 2, collected at temperatures from 2 to 15 K with an ac field of 5 Oe and 500 Oe dc applied fields. Solid lines are guides for the eye.  Figure S15. Variable-frequency in-phase (χ m ʹ, top) and out-of-phase (χ m ʺ, bottom) components of the ac magnetic susceptibility data for 2, collected at a temperature of 6.0 K with an ac field of 5 Oe and a dc applied field between 0 and 10 kOe, respectively. Solid lines are guides for the eye. S16 Figure S16. Cole-Cole diagrams of 2 at 6.0 K with an applied dc field from 0.15 to 10 kOe and ac field of 5 Oe. The solid lines are least-square fittings of the data to a distribution of single relaxation processes with a generalized Debye model.   Figure S18. Variable-frequency in-phase (χ m ʹ, left) and out-of-phase (χ m ʺ, right) components of the ac magnetic susceptibility data for 2, collected at temperatures from 2.0 to 9.0 K with an ac filed of 5 Oe and 300 Oe dc applied field. Solid lines are guides for the eye. S18 Figure S19. Cole-Cole diagrams of 2 from 2.0 to 11.0 K with an applied dc field of 300 Oe and ac field of 5 Oe. The solid lines are least-square fittings of the data to a distribution of single relaxation processes with a generalized Debye model. Table S6. Cole-Cole fit values of 2 from 2.0 to 11.0 K, ac field of 5 Oe and dc field of 300 Oe. Data for the temperatures in red are not used in analysis of the dynamic magnetic measurements due to having less than half of the semicircle in the Cole-Cole plot.  Figure S20. Variable-frequency in-phase (χ m ʹ, top) and out-of-phase (χ m ʺ, bottom) components of the ac magnetic susceptibility data for 2, collected at temperatures from 2.0 to 9.5 K with an ac field of 5 Oe and 500 Oe dc applied field. Solid lines are guides for the eye. Figure S21. Cole-Cole diagrams of 2 from 2.0 to 12.0 K with an applied dc field of 500 Oe and ac field of 5 Oe. The solid lines are least-square fittings of the data to a distribution of single relaxation processes with a generalized Debye model.  Table S7. Cole-Cole fit values of 2 from 2.0 to 12.0 K, ac field of 5 Oe and dc field of 500 Oe. Data for the temperatures in red are not used in analysis of the dynamic magnetic measurements due to having less than half of the semicircle in the Cole-Cole plot.  Figure S22. Cole-Cole diagrams of 2 from 2.0 to 9.5 K with an applied dc field of 1500 Oe and ac field of 5 Oe. The solid lines are least-square fittings of the data to a distribution of single relaxation processes with a generalized Debye model.

Analysis of dynamic magnetic measurements.
We attempted to fit the dependence of τ -1 with the field using Equation S1, which includes a direct process for Kramers ions and tunneling processes as well as a constant term to include relaxation processes without field dependence. All attempts to fit the dependence of τ -1 with the field were unsatisfactory which indicates the complexity of the dependence of the relaxation time with field for compound 1 and 2.

S1
The dependence of τ -1 with the temperature at different fields has been analyzed. To facilitate the analysis we have not considered: -For compound 1, the values at 3 KOe between 2 and 3.5 K because of the presence of two different relaxation processes.
-For compound 2, the values at temperatures larger than 9.5 K because the Cole-Cole plots are not a semicircle (less than half of the semicircle) making the fit unrealistic.
The Arrhenius fit gives an energy barrier and pre-expotential factors (τ 0 ) of 30.6 and 33.6 cm -1 / 2.0(2)-3.3(7) ⋅ 10 -7 s at 500 and 3000 Oe for 1 and 42.5(6)-44.7(6) cm -1 / 1.0(1)-1.5(2)⋅10 -7 s at 500 and 1500 Oe for 2 ( Figure S23). From the experimental static magnetic data and from the calculations the obtained D values are -92 and -114 cm -1 respectively, which leads to energy differences between states of 184 and 228 cm -1 respectively. It is worth noting that an Orbach process should involve a real state and there is not a state around 30 cm -1 , which indicates that other relaxation processes are predominant at these temperatures. The more common relaxation processes for mononuclear compounds are direct and tunneling (usually predominant at low temperatures), and Raman and Orbach (usually predominant at higher temperatures). A fit including all the possible relaxation pathways (Equation S2) has been performed but the number of parameters are too S24 high resulting in an over-parametrization of the curves ( Figure S24), especially without fixing the direct and tunneling parameters because of the unsuccessful fit of the dependence with the field. Figure S24. τ -1 vs temperature for 1 (left) and 2 (right) at different applied dc fields. The solid line is the best fit obtained using equation S2. At higher temperatures, Raman or Orbach should be the predominant processes. The large D value gives rise to a large energy difference between states, which should lead to a very slow relaxation time (slower than the measurable relaxation times with the ac measurements possible with our SQUID) allowing us to discard this process at higher temperatures. In fact, when we try to fit the high temperature regime with both processes and an energy barrier of 200 cm -1 as a starting parameter, this value remains invariable and the data can be fit exclusively with the Raman term ( Figure 25). Figure S25. τ -1 vs temperature for 1 at 500 Oe (left) and 3000 Oe (right) with the contribution of Orbach, Raman and tunneling processes.
At lower temperatures, direct and tunneling should be the predominant processes. At the applied DC fields (500 and 3000 Oe) τ -1 decreases when we increase the field. This indicates that the predominant process should be tunneling because the opposite trend is expected for a direct process (τ -1 is proportional to H 4 ). After this analysis and to avoid the overparametrization of the curves we decided to fit the dependence of τ -1 with temperature using equation 2 and S3. (1 + 2 2 ) +

S3
The best fit using equation S3 is shown in Figure S26 with the parameters in Table  S10. As can be seen, the low temperature regime is not well described because the error is very small compared with the error produced by the Raman part of the equation. Figure S26. τ -1 vs temperature for 1 (left) and 2 (right) at different applied dc fields. The solid line is the best fit obtained using equation S3.