Coherent Manipulation and Coherent Manipulation and Decoherence of S=10 Fe8 Single-Decoherence of S=10 Fe8 Single-

Molecule MagnetsMolecule Magnets

Susumu TakahashiSusumu TakahashiPhysics DepartmentPhysics Department

University of California Santa BarbaraUniversity of California Santa Barbara

S. Takahashi et al., submitted to Phys. Rev. Lett., arXiv:0810.1254 (2008)

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Spin decoherence of SMMs

• There are many discussions about spin decoherence, but no published experimental data of spin echo from single-crystal SMMs.

• Limited # of high-frequency pulsed EPR systems.

• T2 will be very short.

• There are some observations of spin echo from highly diluted molecular magnets.

C. Schlegel et al., Phys. Rev. Lett. 101, 147203 (2008).A. Ardavan et al., Phys. Rev. Lett. 98, 057201 (2007).

• Fluctuations of SMM spin bath is probably one of major decoherence sources.

• There are two ways to reduce the spin bath fluctuations1. Dilute the spin bath2. Polarize the spin bath

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Suppression of spin decoherence• Fluctuations of SMM spin bath are caused by

spin flip-flop process.• High-frequency and low temperature can

polarize the spin bath• Significantly reduces spin decoherence

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Decoherence of NV center

1. N electron spin flip-flops – J. A. van Wyk et al., J. Phys. D: Appl. Phys.

30, 1790 (1997).

– T. A. Kennedy et al., Appl. Phys. Lett. 83, 4190 (2003)

– R. Hanson et al., Phys. Rev. B 74, 161203R (2006))

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Decoherence of NV center

1. N electron spin flip-flops – J. A. van Wyk et al., J. Phys. D: Appl. Phys.

30, 1790 (1997).

– T. A. Kennedy et al., Appl. Phys. Lett. 83, 4190 (2003)

– R. Hanson et al., Phys. Rev. B 74, 161203R (2006))

2. 13C nuclear spin flip-flops– L. Childress et al., Science 314 281 (2008)

– T. Gaebel et al., Nature Phys. 2, 408 (2008)

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Temperature dependence of T2

• Hahn echo sequence (echo).

• Single exponential fit

• N-V:– T>11.5 K : 6.7 s → 8.3 s– T < 2 K : ~250 s

• N:– T>11.5 K : 5.5 s → 5.8 s– T = 2.5 K : ~80 s

Temperature (K)

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Quenching spin bath decoherence • No temperature

dependence of T2 at 9.4 GHz

(E. C. Reynhardt et. al., J. Chem. Phys. 109, 8471 (1998))

• N spin flip-flop process(C. Kutter et. al., PRL 74, 2925 (1995))

• 90 % for 10 x T2

• 99 % for quenching

• 1/res = 250 s

resTTTTres ZeZe ee

CPP

T

)1)(1(

1//

2

2

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13C nuclear spin bath fluctuations

• 1/res = 250 s: Temperature independent relaxation rate

• Decoherence time caused by 13C nuclear spin flip-flop process

where nn is NMR linewidth, N is the number of nuclear per volume.

• T2 ~ 380 s for 13C nuclear spin bath fluctuations

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4/12

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49.01

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IIT nenn

n

e

S. Takahashi et al., Phys. Rev. Lett. 101, 047601 (2008)

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(I. M. Brown, Time domain electron spin resonance, p195, Wiley (1979).A. Schweiger and G. Jeschke, Oxford university press (2001)).

resTTTTres ZeZe ee

CPP

T

)1)(1(

1//

2

res= 250 s

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Magnetic field (tesla)

Fe8 single-molecule magnets

• S=10 spin system• Ground state transition

(E-10E-9) ~ 110 GHz, smaller than Mn12-ac.

{[Fe8(O)2(OH)12(C6H15N3)6]Br7(H2O)}Br·8H2O

110 GHz

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cw EPR – angle dependence

• A single crystal was rotated as function of a magnetic field.

• Spin Hamiltonian

g=2.00, D=-6.15 GHz, E=1.14 GHz.

J. van Tol et al., Rev. Sci. Instrum. 76, 174101 (2004)

240GHz

Quartz

)( 222yxzB SSEDSgH 0BS

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cw EPR – temperature dependence

• B ~ easy axis• Indicates the ground state peak at 4.6 T.

mS=-10 ↔ mS=-9 High polarization

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First spin echo measurement

• T1 ~ 1 ms >> T2

• Strong temperature dependence indicates electron (Fe8 SMM) spin bath fluctuations

T1 measurement

T2 measurement

0

200

400

600

800

2

(ns)

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• S=10 spin flip-flop process:

• Spin decoherence is significantly suppressed by spin polarization.

• res is likely to coupling to nuclear moments and phonon (Proton (I=1/2) & 57Fe(I=1/2))

S=10 Fe8 spin bath fluctuations

S. Takahashi et al., submitted to Phys. Rev. Lett., arXiv:0810.1254 (2008)

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14

Summary

• We demonstrated that high frequency EPR can significantly suppress fluctuations of an electron spin bath to increase spin decoherence time T2.

• High-frequency EPR can reveal spin decoherence caused by nuclear spin bath fluctuations.

• We demonstrated quenching spin decoherence of NV center in diamond.S. Takahashi et. al., Phys. Rev. Lett. 101 047601 (2008)

• We observed spin echo of single crystal S=10 Fe8 SMMs for the first time.S. Takahashi et al., submitted to Phys. Rev. Lett. arXiv:0810.1254 (2008)