Band gap of ion-doped La $$_2$$ 2 NiMnO $$_6$$ 6 nanoparticles

We have studied theoretically the magnetization M and the band gap energy $$E_g$$ E g in dependence on temperature, size and ion doping concentration in the double perovskite La $$_2$$ 2 NiMnO $$_6$$ 6 (LNMO)—bulk and nanoparticles. LNMO is a ferromagnetic semiconductor. Therefore, it is appropriate to use for describing its properties the $$s-d(f)$$ s - d ( f ) model. The method for the calculation of M and $$E_g$$ E g is the Green’s function theory within we are able to make a finite temperature analysis of the excitation spectrum and of all physical quantities. The temperature-dependent Matsubara Green’s function formalism can be used for describing the temperature-dependent behavior of realistic systems in thermal equilibrium. M increases with decreasing the nanoparticle size. $$E_g$$ E g decreases with increasing temperature. For nanoparticles, it is smaller than that of bulk LNMO. Doping with Sr ions at the La site reduces M and enhances $$E_g$$ E g . The band gap decreases by Sc ion doping at the La site. The substitution with different ions at the Ni site can also tune $$E_g$$ E g . For example, doping with Fe or Sc ion increases $$E_g$$ E g , whereas by Co, doping $$E_g$$ E g decreases. Substitution by the same ion at different sites, A or B (La or Ni) leads to different behavior of the band gap. It is shown that Sr-, Ba-, Ca-, and Y-doped LNMO NPs with a band gap of $$\sim $$ ∼ 1.4 eV are appropriate for application in solar cells. Comparison to the existing experimental data is made. Graphic abstract