We have investigated the structural, electronic, and topological band structures and the linear coefficient γ of the electronic-specific heat and magnetic properties for ferromagnetic phase of CePdBi in bulk and nanolayers using density functional theory. The total energies as a function of volume are calculated and the bulk modulus and their pressure derivatives are determined. Also, the total energy calculation within generalized gradient approximation (GGA), local density approximation (LDA), and (LDA + U) indicate that at zero pressure the ferromagnetic phase of CePdBi compound is the most stable phase. This result is in agreement with the experimental results. The GGA and Engel-Vosko generalized gradient approximation have been used to obtain the band inversion strength and band order. The effect of hydrostatic pressure on the band inversion strength, band order, and total and local magnetic moments of CePdBi in bulk has been investigated. The magnetic moment decreases with the increasing pressure. The calculations of the structural, electronic properties, topological band structures, magnetic moment, and the linear coefficient γ of the electronicspecific heat have been performed under the presence of spin-orbit coupling. As far as we know, this is the first report on the pressure dependence of the magnetic moment
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