Magnetic correlations and Griffith-like phase in Co₂TiSi0.5Al0.5 Heusler alloy

We present a comprehensive study aimed at elucidating the complex magnetic correlations in Co₂TiSi0.5Al0.5 Heusler alloy having the partial B2-type structure amid L2₁ cubic main phase. The thermo-magnetization measurements at 100 Oe reveal the presence of two magnetic transitions at TC1=278~K and TC2=270~K, respectively, with saturation magnetization of around 1.2 μ _ B/f.u. at 5~K. Our magnetic field dependent studies reveal the dominance of TC1 transition at lower fields (μ₀ H 0.03~Tesla); however, at higher fields the TC2 transition becomes more pronounced. The observation of remnant magnetization above Curie temperature suggests the development of Griffiths-like phase, which is extensively analyzed through { ac} and { dc}- magnetic susceptibility (χ) data. The evaluation of magnetocaloric potential indicates second order phase transition with notable Δ SM= 2.22 Jkg⁻¹K⁻¹ at 7 Tesla. The low-field (μ₀ H 0.1~Tesla) magnetic entropy (Δ SM) curves exhibit two non-identical positive peaks. The nature and range of spin interactions near TC were scrutinized through rigorous critical phenomenon analysis, and the values of exponents α, β, γ and δ to be $0.063, 0.361, 1.108$ and $3.943$, respectively, which are found to be slightly deviating from mean-field theory towards 3D Heisenberg model. Additionally, the exchange magnetic interactions are found to decay as J(r) ~ r-4.6. Furthermore, the density functional theory results reveal the half-metallic nature exhibiting 100% spin polarization (SP). However, the electronic and magnetic properties are greatly affected by the incorporation of structural disorder, which results in drastic reduction of SP to mere 8.3%.