A search for self-consistent solutions for the chiral rotational bands in the

N = 75

isotones

{}^{130}{Cs}

{}^{132}{La}

{}^{134}\Pr

, and

{}^{136}{Pm}

is performed within the Skyrme-Hartree-Fock cranking approach using

{SKM}^{*}

and SLy4 parametrizations. The dependence of the solutions on the time-odd contributions in the energy functional is studied. From among the four isotones considered, self-consistent chiral solutions are obtained only in

{}^{132}{La}

. The microscopic calculations are compared with the

{}^{132}{La}

experimental data and with results of a classical model that contains all the mechanisms underlying the chirality of the collective rotational motion. Strong similarities between the Hartree-Fock and classical model results are found. The suggestion formulated earlier by the authors that the chiral rotation cannot exist below a certain critical frequency is further illustrated and discussed, together with the microscopic origin of a transition from planar to chiral rotation in nuclei. We also formulate the separability rule by which the tilted-axis-cranking solutions can be inferred from three independent principal-axis-cranking solutions corresponding to three different axes of rotation.

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