  Discovery of the large magnetocaloric effect in HoB$_2$ has highlighted the
practical advantage of heavy rare-earth ions. Other holmium compounds are of
interest, and we here report the synthesis and the magnetic properties of
HoSi$_{1.67}$ and HoGe$_{1.67}$ which form the same AlB$_2$-type structure but
with vacancies. They are found to show the antiferromagnetic order with the
Neel temperature 17.6(2)K for HoSi$_{1.67}$ and 9.9(2)K for HoGe$_{1.67}$, and
the magnetic entropy changes at the temperature are 0.05(1)J/cm$^3$K for
HoSi$_{1.67}$ and 0.08(1)J/cm$^3$K for HoGe$_{1.67}$. Magnetic orders were
suppressed by replacing vacancies with nickel, resulting in an increase of
magnetic entropy changes. Distance between the in-plane Ho$^{3+}$ ions appears
to be an important parameter leading to the transition between the
antiferromagnetic (HoSi$_{1.67}$) and the ferromagnetic (HoB$_2$) order. The
finding may aid the exploration of other heavy rare-earth compounds for similar
applications.
