Electronic configuration of $\mathrm{Mn}^{3+}=[\mathrm{Ar}] 3 d^4$

Electronic configuration of $\mathrm{Mn}^{2+}=[\mathrm{Ar}] 3 d^5$

Electronic configuration of $\mathrm{Cr}^{3+}=[\mathrm{Ar}] 3 d^\beta$

Electronic configuration of $\mathrm{Cr}^{2+}=[\mathrm{Ar}] 3 d^4$

As $\mathrm{Mn}^{3+}$ from $d^4$ configuration goes to more stable $d^5$ configuration (Half filled), due to more exchange energy in $d^5$ configuration.