Correlation between anisotropy, slow relaxation, and spectroscopic behaviour: the Ln(trensal) family

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1 Correlation between anisotropy, slow relaxation, and spectroscopic behaviour: the Ln(trensal) family Lorenzo Sorace Department of Chemistry & INSTM, University of Florence, Italy Acknowledgments E. Lucaccini, J.P.Costes, M. Perfetti, R. Sessoli Karlsruhe 11 October Workshop on magnetic anisotropy ECMM2013

2 Outline Introduction Luminescence and electronic structure EPR and static magnetic behaviour Analysis of dynamic behaviour Correlation to the anisotropy

3 Free ion electronic structure E g m H g J B J J 3 L( L 1) S( S 1) 2 2 J( J 1)

4 Effect of the ligands EPR provides information on wavefunction composition and anisotropy type E=(1/2)g eff B B g g J eff ˆ // 2 J eff g g Jˆ J z

5 Parametrization of ligand field: Stevens formalism Hˆ A q k ˆ q O k k Stev k q k LF Ak r k2,4,6 qk r k Oˆ is a parameter, k is a number (tabulated) q k are operator equivalents of the crystal field potential which can be expanded in terms of J +, J -, J z polynomials Most used in magnetic and EPR studies It becomes too involved for treatment of excited multiplets

6 Parametrization of Ligand field: Wybourne s formalism ˆ q B C ( i) B C ( ) 1 ( ) ' i C i ib C ( i) 1 C ( i) k Wyb 0 0 k k k k k q k H LF 0 0 q q q q q q k0 q1 k B q k Cq are parameters are related to spherical harmonics by: () i The resulting matrix elements are: k 2k 1 k Cq( i) Yq ( i) 4 n k n S L' 2J M 1 1/2 3 3 J k k l SLJM J Cq ( i) l ' ' S ' L' J ' M J ' 1 7 2J 1 2 J ' 1 i J k J ' J J ' k n k n l SL U l ' ' SL ' M J q M J ' L L S Allow direct comparison with luminescence data in literature Easy inclusion of excited multiplets Not much used in molecular magnetism (but see CONDON program)

7 The importance of luminescence spectroscopy Dy(III) Er(III)

8 Ln(trensal) family B. M. Flanagan, P. V. Bernhardt, E. R. Krausz, S. R. Lüthi, M. J. Riley, Inorg. Chem. 2002, 41, Space group: P-3c1 Ln(III) ions on a C 3 axis

9 Luminescence spectra Single crystal data with polarized light Low temperature (no hot bands) Luminescence to ground multiplet levels observed for Er B. M. Flanagan, P. V. Bernhardt, E. R. Krausz, S. R. Lüthi, M. J. Riley, Inorg. Chem. 2002, 41,

10 Luminescence spectra About 50 observed transitions! B. M. Flanagan, P. V. Bernhardt, E. R. Krausz, S. R. Lüthi, M. J. Riley, Inorg. Chem. 2002, 41,

11 Ln(trensal) family C0 0C0 3 C-3 C3 0C C-3 C3 ' C-3 C3 C-6 C6 ' C-6 C6 Hˆ B B B B lf Best fit LF parameters of luminescence data 2 B 0 4 B 0 4 B 3 6 B 0 6 B 3 6 B ' 3 6 B 6 6 B ' 6 Dy Er -671(39) (77) -44(106) -2153(34) -2121(83) 1241(57) 988(36) 439(41) 53(49) -284(83) 92(53) 660(49) 545(34) 145(137) 311(36) B ib B ib B. M. Flanagan, P. V. Bernhardt, E. R. Krausz, S. R. Lüthi, M. J. Riley, Inorg. Chem. 2002, 41, Ground multiplets splittings Dy Er

12 Er(trensal) wavefunction composition Er(trensal) 13/2> component is dominant for the ground state Small m J components are dominant for the excited state

13 Dy(trensal) wavefunction composition Dy(trensal) small m J components are dominant in the ground state Large +3/2> and -9/2> components in the first exc. state

14 EPR spectroscopy g eff g // Dy(trensal) Er(trensal) g // g perp Er(trensal) Dy(trensal) g // x H (Oe) g perp g // H (Oe) Dy(trensal) Er(trensal) exp calc exp calc g // g

15 T (emu K mol -1 ) DC magnetic data/ Er(trensal) exp Er(trensal) sim free ion Er(III) Dy(trensal) exp Dy(trensal) sim free ion Dy(III) T (K) No free parameters. Good reproduction of magnetic data BUT

16 M (emu mol -1 ) DC magnetic data/ Er(trensal) exp Er(trensal) sim Dy(trensal) exp Dy(trensal) sim some discrepancy for the high-field magnetization H (Oe) Dy(trensal) Er(trensal) exp calc exp calc g // g

17 Ground doublet anisotropy g 2 tensor shape Er(trensal) Easy axis Dy(trensal) Hard axis

18 '' (emu mol -1 ) Er(trensal) AC susceptibility '' (emu mol -1 ) T=1.9 K H dc (Oe) Field induced slow relaxation Slowest at 900 Oe (Hz) As expected for an easy axis rare-earth complex, frequency dependence of (T) is observed at low T 0.7 T (K) 0.6 H dc =900 Oe (Hz)

19 '' (emu mol -1 ) Dy(trensal) dynamic behaviour '' (emu mol -1 ) T=1.9 K H dc (Oe) Field induced slow relaxation Slowest at 900 Oe Hz) Quite surprisingly, Dy(trensal) is also slowly relaxing H dc =900 Oe T (K) (Hz)

20 Temperature dependence of relaxation time 1 Er(trensal) = 24.5 K, 0 =130.5 ns calulated for = 50 cm -1 E(cm -1 ) Dy Er (ms) 0,1 Dy(trensal) = 9.8 K, 0 =494.5 ns calulated for = 77 cm ,01 0,25 0,30 0,35 0,40 0,45 0,50 0,55 1/T (K -1 ) Both systems are far from linear (Arrhenius) behaviour The relaxation is not related to magnetic anisotropy barrier

21 ''(emu mol -1 ) (ms) Does dilution affect this behaviour? '' (emu (ms) mol -1 ) Y:Er(trensal) 20:1 Y:Dy(trensal) 32:1 H dc = 800 Oe Er(trensal) fit, = 24.6 K, 0 = s Y:Er(trensal) 20:1 fit, = 39.4 K, 0 = 7.1 s (Hz) 1/T(K -1 ) T(K) H dc =900 Oe Dy(trensal) fit, = 9.8 K 0 =494.5 ns Y:Dy(trensal) 32:1 fit, = 20 K 0 =12.1 ns (Hz) / T (K -1 ) T(K) System is still far from Arrhenius behaviour Slow relaxation persist in diluted system

22 Concluding remarks EPR and DC data confirm the LF parametrization obtained by luminescence spectrscopy Dy(trensal) is hard-axis type, Er(trensal) is easy axis type Both derivatives show field induced slow relaxation of the magnetization in a static magnetic field The thermal activation barrier is not consistent with the energy differences obtained by luminescence data. This observation invalidates the general assumption that the slow dynamics of the magnetization is associated in these systems to the magnetic anisotropy Spectroscopic techniques are fundamental to understand the factors affecting the magnetization dynamics and relaxation mechanisms in these systems