1. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Suppression of Spin Diffusion: Modeling and Simulations Gennady Berman (LANL), Vyacheslav Gorshkov (LANL), Vladimir Tsifrinovich (Polytechnic University, NY) ABSTRACT Inspired by the recent experiments by R. Budakian, H. Mamin, and D. Rugar, Phys. Rev. Lett., 92, 037205 (2004), we suggested a quasi-classical model for computer simulations of the spin diffusion in the presence of the non-uniform magnetic field. Each spin is treated as a classical magnetic moment with the conserved magnitude. The dipole-dipole interaction between spins provides the energy transfer from the slow relaxing spins to the fast relaxing spins. The non-uniform magnetic field decouples the slow and the fast relaxing spins causing the effective suppression of the spin diffusion. As a result the relaxation rate of the slow relaxing spin as well as the overall relaxation rate of the spin system greatly decreases. The comparison between the numerical simulations and the experimental data is presented. Spin Diffusion and Relaxation in a Nonuniform Magnetic Field. Phys. Rev. B 71, 2005, 184409/ 1-5 Spin Diffusion and Relaxation in Solid State Spin Quantum Computer. Phys. Lett. A 452, p.107-114, 2006

2. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Scheme of the experiment

3. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Mathematical model Equations of motion

4. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA B 0 +  B(z) G zz > 0 Spin with fast relaxation Geometry of the system.

5. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Comparison of the results of numerical simulations with experimental data. The measured data R. Budakian, H. Mamin, D. Rugar Suppression of Spin Diffusion near a Micron-Size Ferromagnet Phys. Rev. Lett., 92, 037205 (2004)

6. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Dynamics of spin diffusion (a).

7. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Dynamics of spin diffusion (b)

8. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Estimation of the critical gradient of the external magnetic field

9. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Spin Diffusion and Relaxation in Solid State Spin Quantum Computer Two possible realizations of a spin quantum computer (SQC) are analyzed: (i)a boundary spin chain in a 2D spin array; (ii)an isolated spin chain. In both cases, spin diffusion and relaxation are caused by a fast relaxing spin (FRS) located outside the SQC.

10. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Formation of a magnetic domain in a large spin system.

11. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Slide 10

12. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Spin relaxation in 1D- spin systems Different ways of relaxation Without magnetic field gradient different mechanism of relaxation exist

13. U N C L A S S I F I E D Operated by the Los Alamos National Security, LLC for the DOE/NNSA Two possible implementations of SQC: (i) a boundary chain in a 2D- spin array, and (ii) an isolated spin chain have been considered. In both cases the FRS can appear outside the SQC spin chain. This causes relaxation in the SQC due to spin diffusion generated by the dipole-dipole interaction between spins. In the first case, when the number of spins does not exceed a threshold value, the processes of spin diffusion and relaxation are similar to the case of a 3D- system, and the influence of the FRS does not depend on its location. In the second case, various scenarios of spin diffusion and relaxation appear that include random distribution of the magnetic moments in SQC as well as formation of the stationary or moving domain walls. The relaxation process can be suppressed by a non-uniform external magnetic field, and the characteristic estimate of parameters for this suppression have been calculated. Conclusion