  Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic
at the same time but for different crystallographic axes. We show that inducing
competition of anisotropic interactions of orthogonal irreducible
representations represents a general route to obtain new exotic magnetic
states. We demonstrate it here by observing the emergence of a continuously
tunable 12-layer spatial spin modulation when distorting the square lattice
planes in the quasi-2D antiferromagnetic Sr2IrO4 under in situ shear strain.
This translation-symmetry-breaking phase is a result of an unusual strain
activated anisotropic interaction which is at the 4th order and competing with
the inherent quadratic anisotropic interaction. Such a mechanism of competing
anisotropy is distinct from that among the ferromagnetic, antiferromagnetic,
and/or the Dzyaloshinskii-Moriya interactions, and it could be widely
applicable and highly controllable in low dimensional magnets.
