Interplay of rare earth and iron magnetism in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mtext>FeAsO</mml:mtext></mml:mrow></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mtext>La</mml:mtext></mml:mrow></mml:math>, Ce, Pr, and Sm): Muon-spin relaxation study and symmetry analysis

We report zero-field muon spin relaxation $(\ensuremath{\mu}\text{SR})$ measurements on $R\text{FeAsO}$ with $R=\text{La}$, Ce, Pr, and Sm. We study the interaction of the FeAs and $R$ (rare-earth) electronic systems in the nonsuperconducting magnetically ordered parent compounds of $R{\text{FeAsO}}_{1\ensuremath{-}x}{\text{F}}_{x}$ superconductors via a detailed comparison of the local hyperfine fields at the muon site with available M\"ossbauer spectroscopy and neutron-scattering data. These studies provide microscopic evidence of long-range commensurate magnetic Fe order with the Fe moments not varying by more than 15% within the series $R\text{FeAsO}$ with $R=\text{La}$, Ce, Pr, and Sm. At low temperatures, long-range $R$ magnetic order is also observed. Different combined Fe and $R$ magnetic structures are proposed for all compounds using the muon site in the crystal structure obtained by electronic potential calculations. Our data point to a strong effect of $R$ order on the iron subsystem in the case of different symmetry of Fe and $R$ order parameters resulting in a Fe spin reorientation in the $R$-ordered phase in PrFeAsO. Our symmetry analysis proves the absence of collinear $\text{Fe-}R$ Heisenberg interactions in $R\text{FeAsO}$. A strong Fe-Ce coupling due to non-Heisenberg anisotropic exchange is found in CeFeAsO which results in a large staggered Ce magnetization induced by the magnetically ordered Fe sublattice far above ${T}_{N}^{\text{Ce}}$. Finally, we argue that the magnetic $R\text{-Fe}$ interaction is probably not crucial for the observed enhanced superconductivity in $R{\text{FeAsO}}_{1\ensuremath{-}x}{\text{F}}_{x}$ with a magnetic $R$ ion.