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

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 beta = 0.495, gamma = 1.324, and delta = 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 beta suggests a long-range nature of the exchange interactions, whereas the values of the critical exponents gamma and delta 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 (beta = 0.369, gamma = 1.38, and delta = 4.8) of the critical exponents toward the mean-field values (beta = 0.5, gamma = 1, and delta = 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.