Exploring the Correlation Between the Spin-State Configuration and the Magnetic Order in Co-Substituted BiFeO₃

BiFeO₃ is one of the most actively studied multiferroic materials that exhibits a robust ferroelectric order below ~ 1100 K and an antiferromagnetic (AFM) order below ~ 640 K. Numerous researches have been conducted to explore its potential in effecting electric field control of magnetic order for energy-efficient nonvolatile magnetic memory applications. The magnetic order in BiFeO₃ is complex in nature. Close competition between various magnetic interactions, such as isotropic symmetric exchange (SE), antisymmetric Dzyaloshinskii-Moriya (DM) interaction and single ion anisotropy (SIA), lead to the formation of magnetic orders like the (1) G-type AFM order and (2) long period cycloidal order (~62nm). By partial substitution of Co instead of Fe, its cycloidal order disappears, and a spin canted G-type AFM with saturation magnetization about 0.03μ_B/f.u. perpendicular to the electric polarization has been observed. Moreover, magnetization reversal by electric field was observed in BiFe_0.9Co_0.1O₃ thin film. Understanding the effect of Co substitution to magnetic order of BiFeO₃ could give us the guideline to enhance the weak spontaneous magnetization of this system which is critical for magnetic memory application.<br/>In the present study, using density functional theory (DFT) calculations and by employing a constructed model spin Hamiltonian and Monte Carlo simulations, we have studied the stability of the canted G-type AFM as a function Co substitution level. Co³⁺ can exhibit various spin states, such as low spin (LS, S=0), intermediate spin (IS, S=1) and high spin (HS, S=2) states. This ambiguity pertaining to the electronic structure of substituted Co³⁺ further contributes to the complexities of the BiFeO₃ system. Our detailed investigations of various properties of BiFeO₃ system as functions of Hubbard U parameter and the concentration of Co³⁺ show that, the spin state of Co³⁺ ion strongly depends on the U value and the high spin state of Co³⁺ is relatively stable. The calculated volume reductions with increase of Co concentrations are in best agreement with the experimental observations corresponding to the mixing of HS and LS of Co. Finite temperature Monte Carlo results considering a wide range of magnetic parameters, lead to the identification of the factors that enhance the stability of the canted G-type AFM phase. We observe that the strong tendency of the HS Co³⁺ to orient in the {111}_pc plane, which is perpendicular to the direction of the spontaneous polarization, enhances the stability of the canted G-type AFM phase and on the other hand the formation of the IS state contributes to the increase of the magnitude of net magnetization.<br/>Our study indicates the existence of HS and LS Co in the system under investigation and suggests guidelines to enhance the multiferroic properties of BiFeO₃.