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We study non-supersymmetric truncations of $\omega$-deformed ${\cal N}=8$gauged supergravity that retain a $U(1)$ gauge field and three scalars, ofwhich two are neutral and one charged. We construct dyonic domain-wall andblack hole solutions with AdS$_4$ boundary conditions when only one (neutral)scalar is non-vanishing, and examine their behavior as the magnetic field andtemperature of the system are varied. In the infrared the domain-wall solutionsapproach either dyonic AdS$_2 \times \mathbb{R}^2$ or else Lifshitz-like,hyperscaling violating geometries. The scaling exponents of the latter are$z=3/2$ and $\theta = -2$, and are independent of the $\omega$-deformation. New$\omega$-dependent AdS$_4$ vacua are also identified. We find a rich structurefor the magnetization of the system, including a line of metamagneticfirst-order phase transitions when the magnetic field lies in a particularrange. Such transitions arise generically in the $\omega$-deformed theories.Finally, we study the onset of a superfluid phase by allowing a fluctuation ofthe charged scalar field to condense, spontaneously breaking the abelian gaugesymmetry. The mechanism by which the superconducting instability ceases toexist for strong magnetic fields is different depending on whether the field ispositive or negative. Finally, such instabilities are expected to compete withspatially modulated phases.

Superfluid and Metamagnetic Phase Transitions in $\omega$-deformed Gauged Supergravity