1. NMR Studies of nanoscale molecular magnets Y. Furukawa Y. Fujiyoshi S. Kawakami K. Kumagai F. Borsa P. Kogerler Hokkaido University (Japan) Pavia University (Italy) Ames Laboratory (USA)

2. Outline ① Introduction Review of level crossing phenomenon in nanoscale molecular magnets AF ring clusters (Fe6, Fe10 and Cr8) ② 1 H-NMR measurements in V15 system ・ level crossing phenomenon ・ spin dynamics ③ 57 Fe-NMR measurements in Fe8 system ・ Spin dynamics in magnetic field parallel and perpendicular to the magnetic easy axis. ④ Summary

3. Fe O C Cr O C (Fe 10 (OCH 3 ) 20 (C 2 H 2 O 2 Cl) 10 ) [ LiFe 6 (OCH 3 ) 12 (C 15 H 11 O 2 ) 6 ]ClO 4 Cr 8 (OH) 12 (C 2 H 3 O) 12 Fe 3+ (S=5/2) or Cr 3+ (S=3/2) ions in ring configuration J ~ 21 K J ~ 14 K J ~ 17 K AF exchange interactions between nearest neighbor spins lead to S=0 ground state. AF ring clusters Fe6Fe10Cr8

4. Level crossing in AF ring clusters Advantages of clusters for the studies of level crossing phenomenon ・ Completely isolated system (w/o 3D magnetic ordering) ・ Very homogenous We can investigate “purely” level crossing phenomenon Fe6(Na) Hysteresis loop Quantum hysteresis O. Waldmann et al., PRL 89 (2002) 246401

5. M.Affronte, Phys.Rev.Lett. 88, 167201 (2002) M.Affronte, Phys.Rev.B 68, 104403 (2003) Specific heat measurements at low temperature Two level Schottky model Fe6 Cr8 ⊿ i ～ 0.86K for Fe6 ⊿ i ＜ 0.2K for Cr8 T=0.9K

6. M.Affronte et al., PRL 88 167201 (2002) LAC (level anti-crossing) B c1 =11.7T, Δ 1 /k B =0.86K B c2 =22.4T, Δ 2 /k B =2.36K true level crossing (or very small LAC) Energy diagrams for Fe6 and Fe10 Fe6Fe10 Origin of LAC is still open question Possibility of Dzyaloshinskii-Moriya interaction

7. Difference for the level crossing as seen by NMR ⊿ １ ～０．８６Ｋ （ by heat capacity data ） M. Affronte et al., PRL 88(2002)167201 Ｓ＝ 0 Ｓ＝ １ ⊿ ① Fe6(Li) ② Fe10 Ｓ＝０ Ｓ＝１ M-H Julien et al., PRL 83 (1999)227 Y. Fujiyoshi et al. unpublished level anti-crossing true level crossing 1/T 1 constant at H c 1/T 1 depends on T at H c We may distinguish by 1/T 1 measurements

8. Ｖ１５ Ｋ ６ ［Ａｓ ６ Ｖ １５ Ｏ ４２ （Ｈ ２ Ｏ）］・８Ｈ ２ Ｏ At low temperature three s=1/2 triangle system (frustrated system) Number of states (2×1/2+1) 3 = 8 states Ground state : S=1/2 two S=1/2 states (four states) First excited state : S=3/2 (four states) Fifteen V 4+ (s=1/2) ions Strong AF interactions of V 4+ spins in hexagon. Ｊ＝－ 800 Ｋ Ｊ＝－ 2.5 Ｋ Ｊ 2 ＝－ 150 Ｋ

9. E S=3/2 -E S=1/2 ~3.6K (at H=0) Level crossing between S=1/2 and S=3/2 at H~2.7T One of the good candidate for the studies of level crossing phenomena Spin frustrations at S=1/2 ground state To investigate ･ level crossing phenomena comparison with AF ring cluster ･ spin dynamics We have carried out 1 H-NMR S=1/2 S=3/2 Energy diagram in V15 system

10. Magnetic field dependence of proton 1/T 1 at T=1.5K and 4.2K H. Yoneda, T. Goto et al., Physica B 329-333 (2003) 1176. Observation of peak of 1/T 1 at level crossing field (~2.7T)

11. Comparison with different three clusters (powder samples) Level anti-crossing in V15 similar to the case of Fe6(Li) true level crossinglevel anti-crossing Ｖ １５

12. Possible origin for level anti-crossing Existence of Dzyaloshinskii-Moriya interaction (Miyashita et al.) Most important term for mixing of the levels d ･ S z S x H//d → biggest gap H ⊥ d → smaller gap To elucidate the origin of LAC, measurements on a single crystal are highly required. Energy gap should be depend on angle between H and d

13. Magnetic field dependence of proton 1/T 1 at T=1.5K and 4.2K Thermal fluctuations of the magnetization due to spin-phonon interaction Not include :effects of level crossing and spin frustrations Transition probability 1/T 1 was sum up for S=1/2 and S=3/2 states, respectively, with each Boltzmann factor S=1/2 S=3/2 C=1×10 7 (Hz/K 3 ) Experimental data at high magnetic field is reproduced by the calculations. Large deviations between data and the fitting at low magnetic field regions. A. Lascialfari, et al., PRL 81 (1998) 3773 H. Yoneda, et al., Physica B 329-333 (2003) 1176.

14. Temperature dependence of 1/T 1 at low field region At low field 1/T 1 shows constant behavior This can not be explained by the spin-phonon interaction Existence of strong spin fluctuations (not depend on temperature) Quantum fluctuations due to spin frustrations in the S=1/2 ground state At low H, the ground state is frustrated S=1/2 state

15. Summary of spin dynamics in V15 cluster ② Around level crossing field Enhancements of 1/T 1 due to level crossing ③ High magnetic field region Thermal fluctuations of S=3/2 originated from spin-phonon interactions ① Low magnetic field region Strong spin fluctuations

16. Eight Fe 3+ (S=5/2) ions are almost coplanar Strong AF interaction between Fe 3+ spins →a total spin S=10 ground state (S=5/2×6-5/2×2=10) A magnetic easy axis is perpendicular to the plane formed by Fe 3+ ions Spin Hamiltonian for the S=10 ground state D= ~ ‐ 0.27K E= 0.046K medium hard axis 57 Fe-NMR study in Fe8 cluster crystal structure of Fe8 cluster [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 8 ･ 9H 2 O) Superparamagnetic state at low temperature

17. Quantum tunneling of magnetization (QTM) tunneling Step-wise increase at ⊿ H ~ n×0.22T Magnetization curve in Superparamagnetic state W. Wernsdorfer et al. J. Appl. Phys. 87,5481 (2000)

18. Transverse field dependence of 1 H-1/T 1 (H//medium axis) Transverse field dependence of 1 H-1/T 1 (H//medium axis) Transverse field dependence of tunnel splitting Transverse field dependence of tunnel splitting Tunnel splitting ⊿ T increases with increasing the transverse field 1/T 1 shows a peak, which originated from the large increases of ⊿ T in the transverse field Y. Furukawa, et al., PRB (in press) NMR energy More detail information 57 Fe-NMR investigation in Fe8 cluster

19. 57 Fe-NMR spectrum 57 Fe-NMR core-polarization Observation of eight 57 Fe-NMR signals under zero magnetic field P5 ～ P8 P3,P 4 P1,P 2 Apical sites Central sites Lateral sites P5 ～ P8 P3,P4 P1,P2 Parallel field dependence of resonance frequencies Parallel field dependence of resonance frequencies H//easy axis 57 Fe: γ/2π=1.3757 (MHz/T) Y. Furukawa, et al., PRB 68 (2003) 180405(R)

20. Parallel field dependence of 57 Fe-1/T 1 measured at T=1.5K （ H//easy axis ） spin phonon interaction Calculated results reproduced the experimental observation except for H~0T

21. Transverse field dependence of 1/T 1 and 1/T 2 （ H//medium axis ） The behavior can not be explained by the spin-phonon interaction model at all. There seems to be a peak in a region of 2-4 Tesla Originated from tunneling dynamics ? (as in the case of 1 H-1/T 1 )

22. S u m m a r y ① 1 H-NMR measurements in V15 system ・ low magnetic field region 1/T 1 does not depend on temperature, suggesting the quantum fluctuation in frustrated S=1/2 state or effects due to level crossing at H~0. ・ around level crossing field 1/T 1 shows a peak Temperature dependence of 1/T 1 suggest level anti-crossing. ・ high magnetic field region Temperature and magnetic field dependence of 1/T 1 could be explained by the thermal fluctuations of S=3/2 due to spin-phonon interactions. ② 57 Fe-NMR in 57 Fe8 system ・ Internal spin structure of Fe8 cluster is revealed directly by NMR ・ Parallel field dependence of 1/T 1 can be explained by spin-phonon model except for H~0. ･ Transverse field dependence of 1/T 1 and T 2 shows large peaks in the region of H=2~4 Tesla.

23. H=0 Ｔ～ 0.1 Ｔ H=0.1T ～ Thermal fluctuations due to spin-phonon interaction Sublevels degenerated at H=0 Parallel field dependence of 1/T 1 （ H//easy axis ） Parallel field dependence of 1/T 1 （ H//easy axis ）