Quantum tunneling by Hyperfine interaction Origin of adiabatic change of the magnetization and the symmetry of the molecules Seiji Miyashita, Hans de Raedt and Kristel Michielsen Univ. of Tokyo and Groningen Univ.

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

Control of Quantum State Adiabatic Transition Smooth Change of Magnetization I. Chiorescu, W. Wernsdorfer, A. Mueller, H. Boegge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454. K. Saito & SM. JPSJ (2001) 3385.

DM interaction Extra-degeneracy + Dzyloshinskii-Moriya interaction S: odd (S=1/2) V15 Kramers doublet No tunneling? Extra-degeneracy + Dzyloshinskii-Moriya interaction SM, &. N. Nagaosa, . Theor. Phys. 106 (2001) 533

Energy structure with DM |3/2,3/2> |3/2,-1/2> |1/2,a> |1/2,b> No adiabatic change at H=0

Directionally Independent Energy Gap due to Hyperfine interaction SM, H.de Raedt and K. Michielsen: Prog. Thor. Phys.. 110 (2003) No.11

Change of state

Triangle system

M(t) from the ground state Apparent LZS relation

Finite temperature

M(t) under a sweeping field

Finite temperature

Apparent LZS transition

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

Hysteresis in field sweep

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

Coherence at the crossing

Resonance on the AC field Non-trivial Resonance Y. Kayamuma, PRB 47 (1993) 9940 SM, K. Saito, H. De Daedt, Phys. Rev. Lett. 80 (1998) 1525.

Nontrivial resonance

Decoherence

Dissipation Effect Thernal Bath：Quantum Master equation I. Chiorescu, W. Wernsdorfer, A. Mueller, H. Boegge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454. Random Noise： Quantum Schroedinger equation

Quantum Master Equation H0 HB HI e.g. Photon dissipation and pumping : (SM., H. Ezaki, and E. Hanamura PRA 57 (1998) 2046) Lindblad form  Stochastic Schrodinger Equation　　(antibunching, squeezing photo emission)

General formulation Independent phonon bath K. Saito, S. Takesue and SM. Phys. Rev. B61 (2000) 2397 No feedback effects

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

Effects of environments

Phonon-bottleneck effect (MFE) Electron spin system + DM Hx sweeping No noise Symmetric Noise Nonsymmetric Noise

Effects on the Phonon-bottleneck effect (Magnetic Foehn effect) Hz:sweep

45-degree

Reaction to the nuclear spin

Temperature effect

Fe ring Fe3+ plays a role of a localized spin with S=5/2 and L=0. Fe10 n=6 n=10 n=18 n=12 Fe10 [NaFe6(OCH3)12 (dmb)6]+ : monoclinic 単斜晶系 a \ne b \ne c, alpha=gamma=90degree \ne beta [NaFe6(OCH3)12 (pmdbm)6]+ : trigonal 　菱面体晶系 a=b=c, alpha=beta=gamma \le 120degree or \ne 90degree Fe10 : monoclinic Fe12 : monoclinic Fe18 : trigonal

2 1 Fe10 10 3 4 9 +Reflection 5 8 Mirror symmetry 6 7

A set of D vectors from static regular structure <yM|HDM|yM+1>=0 The DM interaction of the above D vectors is not the origin of the peaks in dM/dH.

Anisotropy of g-tensor Hg-tensor=SiSab mBgabiSibHa <yM|Hg-tensor|yM+1>=0 Anisotropy of single ion Hsingle-ion=SiSab DabiSibSia <yM|Hsingle-ion|yM+1>=0 Inversion symmetry should be broken.

Oscillation of methyl groups Structure is measured at Tst=226 K. Each ellipsoid shows 50% possibility. Oblong thermal ellipsoids with the longer radius a Elastic constant of an elastic energy of a methyl group is briefly estimated as K ～ 0.672 kBTst/a2. H. Nakano and SM: JPSJ 71 (2002) 2580

Thank you for your attention

Quantum Control of state: Non AdiabaticTransitions Non-monotonic magnetization process SM, &. N. Nagaosa, Prog. Theor. Phys. 106 (2001) 533

Quantum Switching Memory： 2-values＋Metastability Quantum : Dynamics Classical：Hysteresis　 Dissipation Nondiabatic change Memory Switch Adiabatic change No Hysteresis loss

1. Gap control Transverse field Nontrivial control Quantum interference Berry phase W.Wernsdorfer & R. Sessoli: Science 284 (1999) 133

2. Sweeping velocity control Switching between different S values

3.Rotation of the field (or sample) Rosen-Zener process

Effect of dissipation

Noise of uniform field does not contribute to the transition between Fluctuation of uniform field does not contribute to the transition between S=0 and S=1

Singlet-triplet transition Light emission Spin flip No emission

4. Anisotropy control Spin control in semiconductors by voltage