The magnetic properties of $({\mathrm{La}}_{1\ensuremath{-}x}{R}_{x}{)}_{4}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{2}{\mathrm{O}}_{10}$ were studied for $R=\mathrm{Nd},\mathrm{Sm},\mathrm{Gd},\mathrm{and}\mathrm{Eu},$ of which the end material, ${\mathrm{La}}_{4}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{2}{\mathrm{O}}_{10},$ is known as a rather exceptional ferromagnet among the known copper-oxide insulators. It was found that the average ionic radius of the elements at the La site r determines the solubility limit of R elements. When r is larger than $\ensuremath{\sim}1.11\mathrm{\AA{}}\mathrm{},$ the compound has the ${\mathrm{La}}_{4}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{2}{\mathrm{O}}_{10}$-type structure, while for smaller r, the ${\mathrm{Y}}_{2}{\mathrm{BaCuO}}_{5}$ type structure is formed. The magnetic behavior of the compounds depended on the R element; even a rather small amount of Nd altered the ferromagnetic ground state to an antiferromagnetic one, with a possible spin-glass state in between. For $R=\mathrm{Sm}$ and Gd, the experimental results suggest a similar change of ferromagnetism to antiferromagnetism, but a ferrimagnetlike behavior was observed for intermediate compositions. On the other hand, ferromagnetism resided up to the solubility limit for $R=\mathrm{Eu}.$ The application of high pressure up to 8.0 GPa hardly affected the magnetism of ${\mathrm{La}}_{4}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{2}{\mathrm{O}}_{10}.$ This result, as well as the results of Rietveld analyses of R-substituted ${\mathrm{La}}_{4}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{2}{\mathrm{O}}_{10},$ indicate that the reduction of ferromagnetism with the increase in x is not attributable to the structural change induced by the substitution, the chemical pressure effect.
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