"Reverse" Magnetostriction Effects in the [001] Shape Magnetostriction of ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}\mathrm{Sb}$ and ${\mathrm{Sm}}_x{\mathrm{La}}_{1-x}\mathrm{Sb}$ Single Crystals

Shape magnetostriction measurements along the [001] direction were carried out for all the magnetic rare-earth ions, $R$, in $R_x{\mathrm{La}}_{1-x}\mathrm{Sb}$. At low temperatures the magnetostriction of both Ce and Sm are "reversed" with respect to the high temperatures. A crystal-field model can explain this phenomenon by the sign reversal of the expectation value of the quadrupole operator $〈{{\hat{O}}_2}^0〉$. The data are consistent with a negative second-order magnetoelastic coupling constant, ${V_2}^3$, for all the rare-earth ions.