  We show that coexisting domains of coherent and incoherent oscillations can
be induced in an ensemble of any identical nonlinear dynamical systems using
the nonlocal rotational matrix coupling with an asymmetry parameter. Further,
chimera is shown to emerge in a wide range of the asymmetry parameter in
contrast to near $\frac{\pi}{2}$ values of it employed in the earlier works. We
have also corroborated our results using the strength of incoherence in the
frequency domain ($S_{\omega}$) and in the amplitude domain ($S$) thereby
distinguishing the frequency and amplitude chimeras. The robust nature of the
asymmetry parameter in inducing chimeras in any generic dynamical system is
established using ensembles of identical R\"ossler oscillators, Lorenz systems,
and Hindmarsh-Rose (HR) neurons in their chaotic regimes.
