  (Fe,Co)$_2$B-based compounds with specified 5$d$ substitutions are considered
as promising materials for permanent magnets without rare-earth elements. We
conducted a combined first-principles and experimental study focused on
(Fe$_{0.7}$Co$_{0.3}$)$_2$B alloys doped with W and Re. First, we used
full-potential local-orbital scheme to systematically investigate (Fe,Co)$_2$B
alloys with 3$d$, 4$d$, and 5$d$ substitutions. Computational analyses showed a
significant increase in magnetocrystalline anisotropy only for the Re doped
sample. Simultaneously, the structural and magnetic properties of the
(Fe$_{0.7-x}$Co$_{0.3-x}$M$_{2x}$)$_2$B ($M$ = W, Re; $x$ = 0, 0.025) alloys
were investigated experimentally. The desired (Fe,Co)$_2$B tetragonal phase was
synthesized by heat treatment of amorphous precursors. We observed that
isothermal annealing increases the coercive field of all samples. However, the
obtained values, without further optimization, are well below the threshold for
permanent magnet applications. Nevertheless, annealing of substituted samples
at 750$^o$C significantly improves saturation magnetization values.
Furthermore, M\"{o}ssbauer spectroscopy revealed a reduction of the hyperfine
field due to the presence of Co atoms in the (Fe,Co)$_2$B phase, where
additional defect positions are formed by Re and W. Radio-frequency
M\"{o}ssbauer studies showed that (Fe$_{0.7}$Co$_{0.3}$)$_2$B and the
W-substituted sample began to crystallize when exposed to an radio frequency
field of 12 Oe, indicating that the amorphous phase is stabilized by Re
substitution. Improvement of thermal stability of
(Fe$_{0.675}$Co$_{0.275}$Re$_{0.05}$)$_2$B alloy is consistent with the results
of differential scanning calorimetry and thermomagnetic measurements.
