Significance of the structural configuration of B2 disorder in Co and Ti based Heusler alloys

We investigate here structural (at local and global levels) and transport properties for ${X}_{2}\mathrm{MnAl}$ ($X=$ Co and Ti). Additionally, the magnetic properties were also studied for ${\mathrm{Ti}}_{2}\mathrm{MnAl}$. Our x-ray diffraction results show that both the compounds stabilize in B2 disordered phase with cubic structure of $Pm\overline{3}m$ space group. Further, the structural configuration of the above disordered phase for both the compounds was identified using combined studies of x-ray absorption spectroscopy and multiple scattering calculations at the transition metal $K$ edges. Upon such identification, in the case of ${\mathrm{Co}}_{2}{\mathrm{Mn}}_{1\ensuremath{-}y}{\mathrm{Cr}}_{y}\mathrm{Al}$ ($y=$ 0, 0.05, 0.1, 0.2) with change in $y$, we are able to establish a better connection quantitatively between the inverse of Mn-Co bonds and peak in the temperature-dependent resistivity. This highlights the crucial importance of a detailed understanding of the nature of B2 disorder. In the case of $y=0$, in the temperature range of study, the resistivity is driven by the functional form associated with (a) three-dimensional enhanced electron-electron Coulomb interaction scattering mechanism and (b) an unconventional one-magnon process. For ${\mathrm{Ti}}_{2}\mathrm{MnAl}$, the transport shows metallic glasslike behavior at high temperature, while at low temperature it follows both the Cote-Meisel's model and quantum correction model. In this compound, the magnetic studies suggest the formation of superparamagnetic clusters in the paramagnetic matrix at low temperatures. Our density functional theory results are in line with the transport and magnetic properties. In literature, the spin polarization percentage ($P$) for $X=$ Co in B2 disordered phase is $76%$. However, the present results emphasize the fact that in B2 disordered phase, the value of $P$ can range from $90%$ to $71%$ depending on the structural configuration introduced by swapping of the atomic positions of Mn and Al. For the compound under study, the value of percentage spin polarization obtained ranges between $82%$ to $85%$. In addition, we also identify the origin of the difference in the shape of the Mn $3d$ density of states for both the alloys. Our results for $X=$ Co alloy highlights the importance of identifying the specific structural configuration associated with a particular disorder category especially in the estimation of ${T}_{c}$ and $P$ and for $X=$ Ti, the physical properties can be tuned by varying the position of ${E}_{F}$ and thereby its utilization in device applications.