  Altermagnetism refers to a wide class of compensated magnetic orders
featuring magnetic sublattices with opposite spins related by rotational
symmetry rather than inversion or translational operations, resulting in
non-trivial spin splitting and high-order multipolar orders. Here, by combining
theoretical analysis, electrical transport, X-ray and optical spectroscopies,
and nonlinear optical measurements, we establish a phase diagram in hybrid
molecular beam epitaxy-grown RuO2/TiO2 (110) films, mapping the broken
symmetries along the altermagnetic/electronic/structural phase transitions as
functions of film thickness and temperature. This phase diagram features a
novel altermagnetic metallic polar phase in strained 2 nm samples, extending
the concept of multiferroics to altermagnetic systems. These results provide a
comprehensive understanding of altermagnetism upon epitaxial heterostructure
design for emergent novel phases with multifunctionalities.
