LAUSR

We show that a collinear Heisenberg antiferromagnet, whose sublattice symmetry is broken at the Hamiltonian level, becomes a fluctuation-induced ferrimagnet at any finite temperature $T$ below the N\'eel temperature ${T}_{\mathrm{N}}$. We demonstrate this using a layered variant of a square-lattice ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. Linear spin-wave theory is used to determine the low-temperature behavior of the uniform magnetization, and nonlinear corrections are argued to yield a temperature-induced qualitative change of the magnon spectrum. We then consider a layered Shastry-Sutherland model, describing a frustrated arrangement of orthogonal dimers. This model displays an antiferromagnetic phase for large intradimer couplings. A lattice distortion which breaks the glide symmetry between the two types of dimers corresponds to broken sublattice symmetry and hence gives rise to ferrimagnetism. Given indications that such a distortion is present in the material $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ under hydrostatic pressure, we suggest the existence of a fluctuation-induced ferrimagnetic phase in pressurized $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$. We predict a nonmonotonic behavior of the uniform magnetization as function of temperature.