  The nucleus $^{180}$Hf is one of the most primary of examples of an axially
symmetric prolate rotor. Combined with the presence of high-$K$ isomers,
spectroscopic studies can provide important information on the nature of its
single-particle levels. Precise measurements are essential for constraining
nuclear models and interpreting the nature of such isomeric states. In this
work, the nucleus $^{180}$Hf was populated using the proton pick-up reaction
$^{181}$Ta($^{11}$B,$^{12}$C)$^{180}$Hf at beam energy of 47 MeV at Horia
Hulubei National Institute of Nuclear Physics and Engineering (IFIN-HH). The
spin of the 1374 keV state and the mixing ratio of the $1066$ keV transition
have been measured, the latter with an increased precision compared to the
previous value from literature. The presently measured spin of the 1374 keV
state, currently assigned a tentative value of $(4^-_1)$, favors one of the two
different values reported in the literature. The particular state constitutes
the band-head of a rotational band in $^{180}$Hf. The measured multipolarity
mixing ratio of the inter-band transition $1374 \rightarrow 309$ keV can
provide important information for the testing and constraining of theoretical
nuclear models used for the study of the intrinsic properties of $^{180}$Hf as
well as its neighboring isotopes.
