2002 Agilent Technologies Europhysics Prize Lecture on

2. 2002 Agilent Technologies Europhysics Prize Lecture on Quantum Dynamics of Nanomagnets Bernard Barbara, L. Néel Lab, Grenoble, France Jonathan R. Friedman, Amherst College, Amherst, MA, USA Dante Gatteschi, University of Florence, Italy Roberta Sessoli, University of Florence, Italy Wolfgang Wernsdorfer, L. Néel Lab, Grenoble, France Budapest 26/08/2002

3. the miniaturization process Single Domain Particles coherent rotation of all the spins

4. E 

5. Quantum effects in the dynamics of the magnetization First evidences of Quantum Tunneling in nanosized magnetic particles (difficulties due to size distribution) Quantum Coherence in ferrihydrite confined in the ferritin mammalian protein (inconclusive due to distribution of iron load)

6. = metal ions = oxygen = carbon

8. The molecules are regularly arranged in the crystal

9. Mn12acetate Mn(III) S=2 Mn(IV) S=3/2 Total Spin =10 T. Lis Acta Cryst.1980, B36, 2042.

10. high spin molecules and low spin molecules

11. Uniaxial magnetic anisotropyH=-DSz2

12. Uniaxial magnetic anisotropyH=-DSz2 E If S is large M=S-1 M=-S+1 M=+S H=0 +S 0 -S M

13. H=-DSz2+gBHzSz H0 M=S M=-S

14. return to the equilibrium thermal activated mechanism E= DS2 H=0 M=S M=-S time=0 =0exp(E/kBT) 010-7 E=61 K J. Villain et al. Europhys. Lett.1994, 27, 159

15. return to the equilibrium thermal activated mechanism E= DS2 H=0 M=S M=-S time= 010-7 E=61 K =0exp(E/kBT)

16. Temperature dependence of the relaxation time of Mn12acetate 0=2x10-7 s E/kB=61 K  Sessoli et al. Nature1993, 365, 141

17. Mn12acetate: Hysteresis loop magnetic hysteresis without cooperativity

18. High Spin Clusters Single Molecule Magnets

19. deviations from the Arrhenius law Temperature dependence of the relaxation time of Mn12acetate 0=2x10-7 s E/kB=61 K  Barbara et al. J. Magn. Magn. Mat. 1995, 140-144, 1825

20. return to the equilibriumtunnel mechanism H=0 M=S M=-S terms in Sx and Sy of the spin Hamiltonian

21. return to the equilibriumtunnel mechanism H=0 M=S M=-S terms in Sx and Sy of the spin Hamiltonian

22. What is the difference ? Fe8 Mn12 Stot=10 H= BS.g.B - D Sz2 + E (Sx2-Sy2) + BSz4 + C (S+4+S-4) Four fold axis Tetragonal (E=0)

23. What is the difference ? Fe8 Mn12 H= BS.g.B - D Sz2 + E (Sx2-Sy2) + BSz4 + C (S+4+S-4) Four fold axis Tetragonal (E=0) Two fold axis Rhombic (E0)

24. QTM from a chemistry student point of view

25. Quantum Tunneling of the Magnetization from a chemistry student point of view

27. Hysteresis loops for Mn12 Friedman et al., PRL, 1996; Hernandez et al, EPL, 1996; Thomas et al., Nature, 1996

28. Uniform spacing between steps Step spacing: ~4.5 kOe

29. Hysteresis loops for Mn12

30. Enhanced Relaxation at Step Fields Higher energy barrier Yet faster relaxation!

31. Enhanced Relaxation at Step Fields

32. Fast tunneling Thermal activation m = -9 m = -10 m = 9 m = 10 Thermally Assisted Resonant Tunneling Tunneling occurs when levels in opposite wells align.

33. The field at which (in the left well) crosses (in the right well): Hamiltonian for Mn12 Steps occur at regular intervals of field, as observed. Step occurs every 4.5 kOe D/g = 0.31 K Compare with ESR data: D = 0.56 K, g = 1.93 D/g = 0.29 K (Barra et al., PRB, 1997)

34. Hamiltonian for Mn12 • Spectroscopic studies revealed a 4th-order longitudinal anisotropy term B ~ 1.1 mK. (ESR: Barra et al., PRB, 1997 and Hill et al., PRL, 1998; INS: Mirebeau et al., PRL, 1999, Zhong et al., JAP, 2000 and Bao et al., cond-mat, 2000) • Different pairs of levels cross at slightly different fields. • Allows for the Examination of the Crossover from Thermally Assisted to Pure Quantum Tunneling.

35. Crossover to Ground-state Tunneling Level crossing fields: Abrupt “first-order” transition between thermally assisted and ground state tunneling. Theory: Chudnovsky and Garanin, PRL, 1997; Exp’t: Kent, et al., EPL, 2000, Mertes et al., JAP, 2001.

36. Fe8 Hamiltonian in Zero Field Easy Axis Hard Axis Spin wants to rotate in the y-z plane

37. Two Paths for Magnetization Reversal Easy axis Z A Counterclockwise Clockwise Y j H X B Hard axis

38. Destructive Topological Interference Equivalence between paths is maintained when H is applied along the Hard Axis. Topological (Berry’s) phase depends on solid angle W enscribed by the two paths. Complete destructive interference occurs for certain discrete values of W. Easy axis Z A Solid Angle W Y j H X B Hard axis • Theoretical Prediction: A. Garg., 1993.

39. Destructive Topological Interference Modulation of Tunnel Splitting: where W depends on the field along the Hard Axis. When SW = p/2, 3p/2, 5p/2…, tunneling is completely suppressed! Interval between such destructive interference points: • A. Garg., 1993.

40. Measured Tunnel Splitting calculated with D = -0.29, E = 0.046, C = -2.9x10-5 K experimental W. Wernsdorfer and R. Sessoli, Science, 1999.

41. Parity Effect: Odd vs. Even Resonances W. Wernsdorfer and R. Sessoli, Science, 1999.

42. What Causes Tunneling and Why the Parity Effect in Fe8 • Tunneling is produced by terms in the Hamiltonian that do not commute with Sz. • For Fe8, these terms are • Selection rule: • Every other tunneling resonance is forbidden!

43. n = 0 n = 1 -9 8 9 -9 9 -10 -10 10 10 What Causes Tunneling and Why the Parity Effect in Fe8 Tunneling AllowedTunneling Forbidden

44. Parity Effect: Odd vs. Even Resonances W. Wernsdorfer and R. Sessoli, Science, 1999.

45. Classical Thermal Activation Tblocking Tc-o Ground-state Tunneling Crossover From Classical to Quantum Regime (Mn12-ac) Activated Tunneling Measured ( ) and Calculated ( ) Resonance Fields Barbara et al, JMMM 140-144, 1891 (1995) and J. Phys. Jpn. 69, 383 (2000) Paulsen, et al, JMMM 140-144, 379 (1995); NATO, Appl. Sci. 301, Kluwer (1995)

46. Chiorescu et al, PRL, 83, 947 (1999) Barbara et al, J. Phys. Jpn. 69, 383 (2000) Kent et al, EPL, 49, 521 (2000) Data points and calculated lines Inhomogeneous broadening of Two resonances: Dipolar fields Level Scheme 8-0 8-1 Homogeneous broadening of nuclear spins: Tunnel window • Wernsdorfer et al, PRL (1999) The Tunnel Window: An effect of weak Hyperfine Interactions

47. Tetragonal symmetry (Ho in S4) J = L+S = 8; gJ=5/4 Dipolar interactions between Ho3+ << mT Effects of Strong Hyperfine Interactions: Case of Rare-earth ions: Ho3+ in Y0.998Ho0.002LiF4 HCF-Z = -B20 O20 - B40 O40 - B44 O44 - B60O60 - B64O64 - gJmBJH Blm: acurately determined by high resolution optical spectroscopy Sh. Gifeisman et al, Opt. Spect. (USSR) 44, 68 (1978); N.I. Agladze et al, PRL, 66, 477 (1991)

48. Comparisonwith Mn12-ac Ho3+ Thomas et al, Nature (1996) Giraud et al, PRL, 87, 057203-1 (2001) Friedman et al, PRL (1996), Hernandez et al, EPL (1996) Steps at Bn = 450.n (mT)Steps at Bn = 23.n (mT) Tunneling of Mn12-ac Molecules Tunneling of Ho3+ ion Hysteresis loop of Ho3+ ions in YLiF4 Mn12-ac

49. Induce Tunneling of Electronic Moments 7/2 5/2 3/2 Co-Tunneling of Electronic and Nuclear Spins: Electro-nuclear entanglement Avoided Level Crossings between |, Iz and |+, Iz’ if DI= (Iz -Iz’ )/2 integer Role of Strong Hyperfine InteractionsH = HCF-Z + A.I.J -7/2 -5/2 -3/2 -1/2 1/2 3/2 5/2 7/2 -1/2 1/2 -7/2 -5/2 -3/2

50. Additional steps at fields Bn = (23/2).n (mT) Cross-spin reversal and Co-tunneling of Ho3+ pairs Giraud et al, PRL 87, 057203 1 (2001) Fast sweeping rate ... a different regime 50 mK 0.3 T/s ½, Iz ½, I’z