  Here we present a new perspective to the breakdown of ferromagnetic order in
two-dimensional spin-lattice models employing the rotation of the underlying
lattice. Using an Ising spin system on a square lattice as a prototype, we
demonstrate that an additional low-symmetry interaction may lead to the absence
of the truly long-range order and forms aperiodic structure, such as magnetic
stripes. Employing annealing and entropic Monte Carlo simulations, we show that
our model allows tuning between different phases, magnetically ordered as well
as more exotic nonmagnetic phases such as Ising-nematic by changing only one
control parameter, which is responsible for the arising of magnetic
frustration. In addition, our methodology of considering the coupling between
the magnetic structure and the host material can be extended to the study of
any type of spin-exchange model in two dimensions and has many potential
interesting ramifications and applications.
