  We investigate the non-Fermi liquid (NFL) behaviors at the two-dimensional
(2D) magnetic heterostructure interface between a normal metal and a magnetic
insulator. The normal metal undergoes a Lifshitz transition with van Hove
singularities (VHS) saddle points tuned onto the Fermi surface, which
represents a convex-to-concave geometric transition of the 2D Fermi surface. By
coupling to critical spin fluctuations via interfacial exchange interactions,
we uncover a novel NFL phase at the VHS with the quasiparticle lifetime scaling
as $\sim \omega^{1/2}$. This NFL feature dominates over the rest of the Fermi
surface points in the low-energy limit. At finite energies, it crossovers to
the marginal Fermi liquid. Importantly, we demonstrate the strange metal
behaviors, that includes the linear-in-$T$ resistivity and the $T\ln (1/T)$
specific heat, already present with the spatially uniform interaction, which
broadens the scenario in
\href{https://www.science.org/doi/abs/10.1126/science.abq6011}{Science {\bf
381}, 790 (2023)}. Furthermore, we propose the non-magnetic ARPES can directly
probe the NFL features at heterostructure interface. Our findings explore the
interplay of VHS in lower dimension, disorder and strong interactions, which
paves a novel path to study the quantum critical phenomenon, 2D magnetism and
spintronics.
