Complex exchange mechanism driven ferromagnetism in half-metallic Heusler Co₂TiGe : Evidence from critical behavior

Abstract

We have investigated the critical phenomenon associated with the magnetic phase transition in the half-metallic full-Heusler Co₂TiGe. The compound undergoes a continuous paramagnetic-to-ferromagnetic phase transition below the Curie temperature T_C=371.5 K. The analysis of magnetization isotherms in the vicinity of T_C, following a modified Arrott plot method, the Kouvel-Fisher technique, and a critical isotherm plot, yields the asymptotic critical exponents β=0.495, γ=1.324, and δ=3.67. The self-consistency and reliability of the obtained exponents are further verified by the Widom scaling relation and scaling equations of state. The mean-field-like value of the critical exponent β suggests a long-range nature of the exchange interactions, whereas the values of the critical exponents γ and δ imply sizable critical spin fluctuations. The half-metallic itinerant character of Co₂TiGe in the presence of magnetic inhomogeneity may result in such a strong deviation from the three-dimensional Heisenberg values (β=0.369, γ=1.38, and δ=4.8) of the critical exponents toward the mean-field values (β=0.5, γ=1, and δ=3). The results suggest the complex nature of exchange couplings that stabilize the long-range ferromagnetic ordering in the system and are consistent with the earlier theoretical studies on the exchange mechanism in Co₂TiGe.