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We study an extended central spin model with an isotropic nearest-neighbour spin-exchange interaction among the bath spins. The system is controllable by external magnetic fields applied on the central spin and the bath, respectively. We construct a basis set of the Hilbert space and express the Hamiltonian of the extended model into a series of 2 × 2 block matrices to obtain the exact solution of the model successfully. Therefrom, the coherence and the spin polarization of the central spin are investigated. We find that if the couplings among the bath spins are antiferromagnetic, the central spin has good coherence and polarization at low temperatures. Moreover, the decoherence is greatly suppressed at the critical point where the strengthes of the central and the bath magnetic field take the same value. A dephasing phenomenon is identified when the initial state of the central spin is unpolarized.

Density-functional with generalized gradient approximation (GGA) for the exchange-correlation potential has been used to calculate the energetically globalminimum geometries and electronic states of Ni n Al (n ϭ 2-8) neutral clusters. Our calculations predict the existence of a number of previously unknown isomers. All structures may be derived from a substitution of a Ni atom at marginal positions by an Al atom in the Ni nϩ1 cluster. Aluminum atom remains on the surface of the geometrical configurations. Moreover, these species prefer to adopt three-dimensional (3D) spacial forms at the smaller number of nickel atoms compared with the pure Ni nϩ1 (n Ն 3) configuration. Atomization energies per atom for Ni n Al (n ϭ 2-8) have the same trend as the binding energies per atom for Ni n (n ϭ 3-9). The stabilization energies reveal that Ni 5 Al is the relatively most stable in this series. In comparison with the magnetic moment of pure metal nickel (0.6 B ), the average magnetic moment of Ni atom increases in NiOAl clusters except the Ni 3 Al. Moreover, except the case of Ni 5 Al, Ni average magnetic moment decreases when alloyed with Al atoms than that in pure Ni clusters, which originate the effective charge transferring from Al to Ni atoms.