The yrast band diagram and the reduced magnetic dipole-to-electric quadruple transitions ratio, B(M1)/B(E2), are simulated using a Fortran code and constructed based on the projected shell model (PSM). Calculations using the PSM are applied to study the back-bending phenomena of neutron-rich even–even isotopesof Sm, namely $^{150,152,154,156,158}$Sm. The obtained B(M1)/B(E2) ratios show that around the band-crossing spin, their values are decreased. This phenomenon occurs due to a change in the structure of energy bands. Calculated results reproduce well the variation of moments of inertia as a function of rotational frequency in the presented back-bending figures for the isotopes under consideration. Finally, simulated results are compared with the available experimental data. Good agreement has been achieved from this comparison.