Magnetic self-frustration from spontaneous structural distortion

In frustrated magnetism, lattice distortions mediated by magnetoelastic coupling are commonly invoked as an escape route from extensive degeneracy toward an ordered ground state and, in some cases, the onset of multiferroicity. Here we present a minimal classical model that illustrates the converse phenomenon, which we term ``magnetic self-frustration''. Monte Carlo simulations reveal that a kagom\'e lattice with trivial magnetic interactions -- namely, nearest-neighbor Ising ferromagnetism -- undergoes a magnetostructural transition into a breathing-like phase, characterized by irregular bond dimerization along the three kagom\'e directions. Structurally, the equilateral triangles belonging to one of the two kagom\'e sublattices spontaneously distort, expanding into isosceles triangles. An analysis to first order in the magnetoelastic coupling constant $\alpha$ shows that the shape of these triangles is remarkably robust. Acting like rigid building blocks in a puzzle, their vertices determine the geometry of the second sublattice, giving rise to contracted ferromagnetic triangles with a variety of shapes. The magnetic sector can be mapped onto an effective antiferromagnetic triangular lattice, which remains disordered down to low temperatures and retains a finite residual entropy of one third of that of Wannier. This self-frustrated phase takes place at intermediate values of $\alpha$, separating the conventional undistorted ferromagnetic phase at weak coupling from a strongly coupled ordered phase characterized by a regular dimerized up-up-down-down antiferromagnetic pattern along the three kagom\'e directions, built from ferromagnetic triangles and hexagons.