  We study coherent dynamics in a system of dipolar coupled spin qubits diluted
in solid and subjected to a driving microwave field. In the case of rare earth
ions, anisotropic crystal background results in anisotropic g tensor and thus
modifies the dipolar coupling. We develop a microscopic theory of spin
relaxation in transient regime for the frequently encountered case of axially
symmetric crystal field. The calculated decoherence rate is nonlinear in Rabi
frequency. We show that the direction of static magnetic field that corresponds
to the highest spin g-factor is preferable in order to obtain higher number of
coherent qubit operations. The results of calculations are in excellent
agreement with our experimental data on Rabi oscillations recorded for a series
of CaWO4 crystals with different concentrations of Nd3+ ions.
