Coherent Manipulation and Decoherence of S=10 Fe8 Single- Molecule Magnets Susumu Takahashi Physics Department University of California Santa Barbara S. Takahashi et al., submitted to Phys. Rev. Lett., arXiv: (2008)

2 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. T 2 will be very short. There are some observations of spin echo from highly diluted molecular magnets. C. Schlegel et al., Phys. Rev. Lett. 101, (2008). A. Ardavan et al., Phys. Rev. Lett. 98, (2007). Fluctuations of SMM spin bath is probably one of major decoherence sources. There are two ways to reduce the spin bath fluctuations 1.Dilute the spin bath 2.Polarize the spin bath

3 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 240 GHz Zeeman energy N

4 N-V N 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, R (2006)) N-V $1 $1M $1k

5 N-V N 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, R (2006)) C nuclear spin flip-flops –L. Childress et al., Science (2008) –T. Gaebel et al., Nature Phys. 2, 408 (2008) N-V $1 $1M $1k 13 C N-V

6 Temperature dependence of T 2 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 N

7 Quenching spin bath decoherence No temperature dependence of T 2 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 T 2 99 % for quenching 1/  res = 250  s 90 % 250  s 99 %

8 13 C nuclear spin bath fluctuations 1/  res = 250  s: Temperature independent relaxation rate Decoherence time caused by 13 C nuclear spin flip-flop process where  nn is NMR linewidth, N is the number of nuclear per volume. T 2 ~ 380  s for 13 C nuclear spin bath fluctuations S. Takahashi et al., Phys. Rev. Lett. 101, (2008) (I. M. Brown, Time domain electron spin resonance, p195, Wiley (1979). A. Schweiger and G. Jeschke, Oxford university press (2001)).  res = 250  s

9 Fe 3 + S=5/ 2 Fe 8 single-molecule magnets S=10 spin system Ground state transition (E -10  E -9 ) ~ 110 GHz, smaller than Mn 12 -ac. {[Fe 8 (O) 2 (OH) 12 (C 6 H 15 N 3 ) 6 ]Br 7 (H 2 O)}Br·8H 2 O 110 GHz

10 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, (2004) 240GHz Quartz

11 cw EPR – temperature dependence B ~ easy axis Indicates the ground state peak at 4.6 T. m S =-10 ↔ m S =-9 High polarization

12 First spin echo measurement T 1 ~ 1 ms >> T 2 Strong temperature dependence indicates electron (Fe8 SMM) spin bath fluctuations T 1 measurement T 2 measurement

13 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) & 57 Fe(I=1/2)) S=10 Fe 8 spin bath fluctuations S. Takahashi et al., submitted to Phys. Rev. Lett., arXiv: (2008)

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 (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: (2008)