Macroscopic quantum effects generated by the acoustic wave in molecular magnet 김 광 희 ( 세종대학교 ) Acknowledgements E. M. Chudnovksy (City Univ. of New York, USA) D. A. Garanin (City Univ. of New York, USA)

Macroscopic Quantum Phenomena

H H H N microscopic, seen macroscopic, not seen

Classical Dynamics Quantum Mechanics

Why is Quantum Cat not seen? - Rash answer - maybe quantum mechanics does not hold for macroscopic bodies such as cats - Careful answer - Quantum mechanics is OK, but - maybe states are not degenerate - maybe tunneling rate is too small - maybe temperature is too high - maybe the environments know the states of the system DECOHERENCE!!

What is a good candidate to show macroscopic quantum phenomena? Josephoson junction-based system: phase difference of the order parameter –A. O. Caldeira and A. J. Leggett, Ann. Phys. (NY) 149, 374 (1983) –J. Clarke et al, Science, 239, 992 (1988) Magnetic system: Magnetization S.C

Outline Review of magnetization reversal in magnet –Giant spin approximation –Stoner-Wohlfarth model in classical magnet –Landau-Zener model in quantum magnet Rabi spin oscillations generated by ultrasound in solids Macroscopic quantum effects generated by the acoustic wave in molecular magnet –Macroscopic quantum beats of magnetization Spintronics in molecular magnet Summary

Magnet Molecular magnet

Cobalt cluster of 3 nm Blue:1289-atoms truncated octahedron Grey: added atoms, total of 1388 atoms Truncated octahedron with 1289 atoms for diameters of 3.1nm HRTEM [110] direction, Fcc-structure, faceting

Hystersis Loop in a Magnet M s H -M s M h +1 (anisotropy energy +external field)

[Wernsdorfer et al. PRL (2001)]

[Zurek, QP ]

Classical vs Quantum

Quantum Steps in Mn12 At resonance, or (uniaxial symmetry) H=0

Quantum Steps in Mn12 = 0.44 T D = 0.60 K cf) 0.61 K [Sessoli et al. ’93] = 0.44 T

[Barra et al. EPL (1996)] Governed by Quantum dynamics !!

Source (coherent laser) Phase interference Figure (interference) Young experimentAharovnov-Bohm effect and ……

Is Aharonov-Bohm effect is expected in molecular magnets ?

hard axis

[Wernsdorfer and Sessoli, Science (1999)]

To study quantum spin-rotation effects in solid, we need to estimate the magnetic field due to rotation. the phonon displacement field the local rotation of the crystal lattice

Rabi Spin Oscillation (Cont’d) For displacement field in a surface acoustic wave, one obtains In the presence of deformation of the crystal lattice, local anisotropy axes defined by the crystal field are rotated by the angle. Laboratory frame Lattice frame

Rabi Spin Oscillation (Cont’d) The lattice-frame Hamiltonian The Rabi oscillation between the two lowest states of sound wave

Rabi Spin Oscillation (Cont’d) Project the Hamiltonian on the “Rotating wave approximation” states at

Rabi Spin Oscillation (Cont’d) The probability to find the spin in the state

Rabi Spin Oscillation (Cont’d) The expectation value of the projection of the spin onto the Z axis

Rabi Spin Oscillation (Cont’d) The Rabi oscillations ofhave a wave dependence on coordinate !!

How can you obtain the global Rabi oscillations averaged over the whole sample ? Longitudinal Field Sweep.

Field sweep(cont’d) where

Field sweep(cont’d) The field is changing at a constant rate  and  a pulse of sound is introduced shortly before reaching the resonance between  [G-H Kim and Chudnovsky, PRB (2009)]

To study the electronic and magnetic properties of a SMM and eventually to develop electronic devices Molecular spintronics using molecular nanomanet [G-H Kim and T-S Kim, PRL (2004)]

Idea is simple! But, dynamics is not simple!!

What do we expect in the electronic devices? Tunneling of electrons scattered by the spin of SMM Direct tunneling between two electrodes Electric current ? :Hamiltonian of SMM [J.A. Appelbaum, PRL, 1966; P.W. Anderson, PRL 1966 ]

Example: Fe8(cont’d) hard axis easy axis

Molecular spintronics

Summary - Classical vs. quantum dynamics in molecular magnet - Rabi oscillation generated by the ultrasound in molecular magnet - Applying a longitudinal magnetic field, we can generate quantum beats of the magnetization in molecular magnet - Possibility of molecular nanomagnet for molecular spintronics

[T. W. Hansch, Nobel lecuture 2005]

Field sweep (cont’d) The final magnetization on crossing the step

Field sweep (cont’d) Another possible situation corresponds to the system initially saturated in the |-S> state, after which the acoustic wave is applied to the system and maintained during the sweep. the level that provides significant probability of the transition

Field sweep (cont’d)

The optimal condition for pronounced beats What does the above condition mean for experiment? The validity of the continuous elastic theory

Field sweep(cont’d) Since experiments on MM require T~O(K), we should be concerned with the power of the sound. It should be sufficiently low to avoid the unwanted heating of the sample. (ex) Fe8

Field sweep(cont’d)

Disorder produces randomness in the local field. The critical strength of disorder at which the beats disappear

-The field sweep in MM is accompanied by the self-organization of the dipolar field such that the external field in the crystal maintains a very high degree of uniformity. [Garanin and Chudnovsky, PRL (2009)] -Regardless of this effect, our prediction that the asymptotic value of exhibits a significant decrease in the presence of the sound, is not affected by disorder.

Field sweep