Relationship between crystal structure and multiferroic orders in orthorhombic perovskite manganites

Orthorhombic rare-earth manganites, o-$R$MnO${}_{3}$ ($R$ is a rare-earth cation or Y), are typical representatives of multiferroics in which ferroelectricity is induced by magnetic order. They are of interest because their magnetic and ferroelectric properties can be strongly modified by small external perturbations. Here, the authors use resonant and nonresonant x-ray diffraction measurements, density functional theory, and Monte Carlo simulations to investigate how their properties can be manipulated using chemical pressure and epitaxial strain. The authors extract the evolution of the internal lattice parameters of o-$R$MnO${}_{3}$ under chemical pressure and epitaxial strain as well as the corresponding variations of the microscopic exchange interactions and long-range magnetic order. They demonstrate that chemical pressure and epitaxial strain are accommodated differently by the o-$R$MnO${}_{3}$ crystal lattice, which is key for understanding the difference in the magnetic properties and electric polarizations of bulk samples and strained films.