Magnetoelastic paradox: Absence of symmetry-breaking distortions below T_N in antiferromagnetic systems without orbital moment

Phase transitions are often associated with symmetry breaking. In case of magnetic order time reversal symmetry is broken and this leads to magnetostriction. For magnetic systems without orbital moment (L = 0) the only source of magnetostriction is believed to be the exchange striction (ES). If the systems, for instance Gd³⁺-based compounds (S = 7/2, L = 0), order ferromagnetically (fm) no lattice distortions are expected from the standard model of rare-earth magnetism, whereas in the antiferromagnetically (afm) ordered compounds symmetry-breaking lattice distortions should occur. These latter prediction of the theory is in complete contrast to all available experimental data on Gd³⁺ antiferromagnets. They show in many cases large magnetostrictive effects, but no symmetry breaking. Thus we can formulate the "magnetoelastic paradox": in afm systems without orbital moment (L = 0) symmetry-breaking distortions below the Néel temperature are expected, but have not been found. New experimental data indicates, that the magnetoelastic paradox is only present in zero field and may be lifted by a small magnetic field.