Magnetization processes in V15 Awaji : 1 Dec. 2002 Magnetization processes in V15 Univ. Tokyo S. Miyashita and K. Saito

Quantum Dynamics in Nanoscale Molecular Magnets Resonant Tunneling Phenomena Quantum Dynamics in Discrete Energy Levels L. Thomas, et al. Nature 383 (1996) 167. C. Sangregorio, et al. PRL 78 (1997) 4645 I. Chiorescu, et al. PRL 84 (2000) 3454.

Resonant Tunneling Discrete Energy level structure J. M. Hernandez, et al. PRB55(1997) 5858 Discrete Energy level structure J. A.A. J. Perenboom, PRB 58 (1998) 330

Nonadiabatic Transition Quantum Dynamics in Discrete Energy Levels Change in Sweeping Field Landau-Zener-Stueckelberg Mechanism C. Zener, Proc. R. Soc. (London) Ser. A137 (1932) 696. Resonant Tunneling SM, JPSJ 64(1995) 3207, 65(1996) 2734. H. De Raedt et al, PRB56 (1997) 2734

Quantum Dynamics Nonadiabatic Transition: Phase interference LZS, RZ Nontrivial Resonance SM, JPSJ 64 (1995) 3207, H.De Raedt, SM, K. Saito, D. Garcia-Pablos and N. Garcia, PRB 56 (1997) 11761. SM, K. Saito and H. De Raedt, PRL 80 (1998) 1525

Successive LZS transitions Magnetization changes only when H(t) crosses 0 SM & K. Saito, JPSJ (2001) 3238

Dissipation Effect Thernal Bath：Quantum Master equation Random Noise： Quantum Schroedinger equation

Adiabatic transition and Relaxation + Thermal Bath Pure Quantum K. Saito, SM, H.de Raedt, Phys. Rev. B60 (1999) 14553

V15 Adiabatic transition Phonon Bottleneck phenomena I. Chiorescu, et al. PRL 84 (2000) 3454. Adiabatic transition Effective S=3/2 system I. Chiorescu, W. Wernsdorfer, A. Mueller, H. Boegge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454. K. Saito & SM. JPSJ (2001) 3385. H. Nakano & SM, JPSJ 70(2001) 2151

Tunneling in half-odd integer spin systems Tunneling Probability Half-interger、Time　Reversal　Sym. Kramers doublet Single spin mode Multi-spin model + DM Two avoided cross structures Adiabatic change of M(H) SM, &. N. Nagaosa, Prog. Theor. Phys. 106 (2001) 533

５spin-model I. Rudra, S. Ramasesha, and D. Sen, J. Phys. Cond. Mat. 13 (2001) 11717 N. P. Konstantinidis and D. Coffey, cond-mat 0204435 I. Rudra, K. Saito, S. Ramasesha and S. Miyashita, preprint

Effective interaction SM, &. N. Nagaosa, Prog. Theor. Phys. 106 (2001) 533

Energy structure Quasi-degenerate avoided level crossing structures 4 states LZS formula works well

4-dimensional irreducible space Overlap of the wave function

Nonadiabatic Transition in the Field Sweeping Transition probability of Magnetization

Adiabatic process in V15 Phonon Bottleneck phenomena Plateau induced by thermal effect Chiorescu, W. Wernsdorfer, A. Mueller, H. Boegge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454.

Reduced Density Matrix Boson Bath K. Saito, S. Takesue and SM. Phys. Rev. B61 (2000) 2397

Field sweeping with thermal bath Fast sweeping Slow sweeping Magnetic FoehnEffect LZS K. Saito & SM. JPSJ (2001) 3385.

Nonadiabatic Tr. & Heat-inflow LZ transition Magnetic Foehn Effcet

Non-monotonic M(H)

Fe2 Fe-rings Y. Shapira, et al PRB59 (1999) 1046 Y. Ajiro & Y. Inagaki Y. Narumi & K. Kindo H. Nakano & SM, JPSJ 70(2001) 2151

Time scales in the simulation

V15

Diagonalization of L

V15-MFE

V15-magnetization relaxation I. Chiorescu, W. Wernsdorfer, A. Mueller, S. Miyashita and B. Barbara, preprint

Relation to the longitudinal relaxation slow sweeping fast sweeping magnetic Feohn isothermal adiabatic

Effects of doubly degenerate structure Transition from 1/2 3/2

Transition from 1/2 to 3/2 Symmetry change from A to E Matrix elements for ESR

Hidden Conservation Law? Equilibrium process Adiabatic change SM, &. N. Nagaosa, Prog. Theor. Phys. 106 (2001) 533

Hysteresis in field sweep

Resonance on the AC field Non-trivial Resonance F. Grossman,et al. PRL 67 (1991) 516. Y. Kayamuma, PRB 47 (1993) 9940 S.Miyashita, K. Saito, H. De Daedt, PRL 80 (1998) 1525.

AC field and `effective ’ gap

Floquet eigenvalue

Omega=0.1

Omega=0.001 <M(t)> 0.02 t

Quantum Phase Effect Berry phase Control of Energy Gap by The External Field W.Wernsdorfer & R. Sessoli: Science 284 (1999) 133

c.f. Spin-rotation pulse Transverse oscillating filed

Effective gap due to the AC field Reduce the too large gap to observe the quantum oscillation of the magnetization in time AC field effect on the sweeping Y. Kayanuma and Y. Mizumoto: PRA 62 (2000) 061401

Sweep with AC field

Sweep with AC field2 <M(t)> t

Sweep with AC field 3 avalanche ?

Hz resonance

Classical Switching and Quantum Switching Switching：　2-values＋Metastability Classical：　Dissipation Ferromagnetic order＋ Hysteresis　 Quantum : Dynamics Quantum States+ Adiabatic change

Thank you for your attention Look for some intrinsic effects due to the real time quantum dynamics Thank you for your attention

Local magnets due to inhomogeneity Heisenberg AF chain: Haldane state F. D. M. Haldane,Phys. Lett. 93A (1983) 464. Phys. Rev. Lett. 50(1983) 1153 Edge States Impurity Effects P. Roos and SM, PRB59 (1999) 13782 SM, S. Yamamoto, Phys. Rev. B48(1993) 915

Inhomogeneity induced magnetization M. Nishino, H. Onishi, K. Yamaguchi & SM: PRB62 (2000) 9463

Quantum Langevin Equation Non-white random field Noise Amplitude >> Gap

Square-root time dependence Resonat Tunneling Relaxation C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli & D. Gatteschi, PRL 78 (1997) 4645. L. Thomas et al. PRL 83 (1999) 2398. Hole digging phenomena Square-root time Initial decay of M(t) W. Wernsdorfer, et al. PRL 82 (1999) 3903

Phenomenological theory

SQ-phenomeno