  The identification of materials supporting complex, tunable magnetic order at
ambient temperatures is foundational to the development of new magnetic device
architectures. We report the design of Mn2XY tetragonal inverse Heusler alloys
that are capable of hosting magnetic antiskyrmions whose stability is sensitive
to elastic strain. We first construct a universal magnetic Hamiltonian
capturing the short- and long- range magnetic order which can be expected in
these materials. This model reveals critical combinations of magnetic
interactions that are necessary to approach a magnetic phase boundary, where
the magnetic structure is highly susceptible to small perturbations such as
elastic strain. We then computationally search for quaternary Mn2(X1,X2)Y
alloys where these critical interactions may be realized and which are likely
to be synthesizable in the inverse Heusler structure. We identify the
Mn2Pt(1-z)X(z)Ga family of materials with X=Au, Ir, Ni as an ideal system for
accessing all possible magnetic phases, with several critical compositions
where magnetic phase transitions may be actuated mechanically.
