In this study, we have calculated the effective magnetic moments of decuplet baryons as a function of external magnetic field for different values of the baryonic densities focusing on \(\varDelta ^-\) baryon in particular. The impact of the magnetic field has been realised through the chiral SU(3) quark mean field model which considers quarks as the fundamental degrees of freedom. We have studied the impact of varying the magnetic fields on the quark masses and hence the masses of the decuplet baryons and have used these masses as an input to calculate individual contributions coming from valence quarks, quark sea and orbital angular momentum of the quark sea towards the total magnetic moment of the decuplet baryons. These individual contributions have been calculated using chiral constituent quark model. Studying the magnetic moment of baryons provides crucial insights into their internal quark structure and interactions thus helping to refine models of strong force dynamics.