Identification of triaxial strongly deformed bands in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Hf</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>168</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

Possible decay pathways associated with three candidates for triaxial strongly deformed (TSD) bands in $^{168}\mathrm{Hf}$ have been investigated. The spin and excitation energy of the strongest band, TSD1, were determined approximately based on $\ensuremath{\gamma}$-ray coincidence relationships. Discrete links were established for the second band. The overall agreement between the observed properties of the bands and cranking calculations using the ULTIMATE CRANKER code provides strong support for an interpretation where band TSD1 is associated with a TSD minimum, $({\ensuremath{\varepsilon}}_{2},\ensuremath{\gamma})~(0.43,{20}^{\ifmmode^\circ\else\textdegree\fi{}})$, involving the $\ensuremath{\pi}({i}_{13/2}){}^{2}$ and the $\ensuremath{\nu}({j}_{15/2})$ high-$j$ orbitals. This constitutes the first identification of a TSD band in Hf isotopes, which has been long-predicted by theoretical studies. The second band is understood as being associated with a near-prolate shape and a deformation enhanced with respect to the normal deformed bands. It is proposed to be built on the $\ensuremath{\pi}({i}_{13/2}{h}_{9/2})\ensuremath{\bigotimes}\ensuremath{\nu}({i}_{13/2}){}^{2}$ configuration.

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