Single-ion anisotropy, crystal-field effects, spin reorientation transitions, and spin waves inR2CuO4(R=Nd, Pr, and Sm)

We report a detailed study of single-ion anisotropy and crystal-field effects in rare-earth cuprates $R_2$CuO${}_4$ $(R$=Nd, Pr, and Sm). It is found that most of the magnetic properties are mainly due to the coupling between the copper and rare-earth magnetic subsystem which exhibits a large single-ion anisotropy. This anisotropy prefers ordering of rare-earth moments along [100] for $R$=Pr and Nd and along [001] for $R$=Sm. Combined with a pseudodipolar interaction arising from the anisotropy of the $R$-Cu exchange, we can explain the magnetic structures of these materials. The spin reorientation transitions in Nd${}_2$CuO${}_4$ can be explained in terms of a competition between various interplanar interactions which arises because of the rapid temperature dependence of the Nd moment below about 100 K. Finally we introduce a simple two-dimensional model for the Nd spin-wave spectrum. For zero wave vector, this model gives two optical modes involving Cu spins whose temperature-dependent energies agree with experimental results and an acoustic mode whose energy is predicted to be of order $\sqrt{{2k}_4\Delta }\approx 5\mu \mathrm{eV}$, where $k_4$ is the fourfold in-plane anisotropy constant and $\Delta$ is the Nd doublet splitting.