In the Hartree method, it is known that the wavefunction of the system does not obey the antisymmetry principle of fermions - that is when you swap two particles, they don't up a negative sign. Therefore, electrons are filled by making sure that Pauli's exclusion principle is obeyed in every step. A Slater determinant is considered to be an improvement because it does satisfy the many-body antisymmetry nature of fermions, and often takes the form (for say, a 2 particle system):

\begin{aligned}\Psi (\mathbf {x} \_{1},\mathbf {x} \_{2})&={\frac {1}{\sqrt {2}}}\{\chi \_{1}(\mathbf {x} \_{1})\chi \_{2}(\mathbf {x} \_{2})-\chi \_{1}(\mathbf {x} \_{2})\chi \_{2}(\mathbf {x} \_{1})\}\\&={\frac {1}{\sqrt {2}}}{\begin{vmatrix}\chi \_{1}(\mathbf {x} \_{1})&\chi \_{2}(\mathbf {x} \_{1})\\\chi \_{1}(\mathbf {x} \_{2})&\chi \_{2}(\mathbf {x} \_{2})\end{vmatrix}}\end{aligned}

My question is, are Slater determinants found in practice in Kohn-Sham Density Functional theory?