Abstract
The critical behavior of Heusler alloy $\mathrm{Co}{}_{2}\mathrm{TiSn}$ is investigated by bulk magnetization study around the paramagnetic to ferromagnetic transition. The precise value of Curie temperature ($T{}_{c}=358\phantom{\rule{4pt}{0ex}}\mathrm{K}$) as well as the critical exponents ($\ensuremath{\beta}=0.527\ifmmode\pm\else\textpm\fi{}0.003, \ensuremath{\gamma}=1.229\ifmmode\pm\else\textpm\fi{}0.002$, and $\ensuremath{\delta}=3.33\ifmmode\pm\else\textpm\fi{}0.002$) were determined by means of different analytical methods such as modified Arrott plot analysis, the Kouvel-Fisher method, and critical isotherm analysis. With these critical exponents the isotherm $M(H)$ curves below and above $T{}_{c}$ collapse into two universal branches, fulfilling the single scaling equation $m={f}_{\ifmmode\pm\else\textpm\fi{}}h$, where $m$ and $h$ are normalized magnetization and field, respectively. The reliability of the critical exponents were confirmed by Widom scaling hypothesis $\ensuremath{\delta}=\ensuremath{\gamma}{\ensuremath{\beta}}^{\ensuremath{-}1}$. Apart from the slight increase in $\ensuremath{\beta}$ and $\ensuremath{\gamma}$, the deduced critical exponents were consistent with the theoretical prediction of the mean-field model, indicating the long range magnetic interaction in $\mathrm{Co}{}_{2}\mathrm{TiSn}$. Additionally, it is obtained that spin interaction decays as $J(r)\ensuremath{\sim}{r}^{\ensuremath{-}4.7}$. We suggest that the competition between localized majority spins and itinerant minority spins magnetic interaction could be responsible for critical behavior in $\mathrm{Co}{}_{2}\mathrm{TiSn}$.
Published Version
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