Once you have a mixed rare earth liquor, you still do not have gadolinium. You have a soup that often includes Sm-Eu-Gd-Tb-Dy plus lighter REEs, and the elements behave annoyingly similarly.
Solvent extraction is the workhorse, and it's stage-heavy
Solvent extraction is widely described as the main industrial technology for separating individual rare earths, and flowsheets can require up to hundreds of mixer-settler stages depending on targets and configuration.
For gadolinium, the pain point is the middle-REE neighborhood. Cleanly splitting Gd from adjacent lanthanides is exactly the type of tight separation that turns into long SX trains, high reagent use, and lots of recycles.
Alternative/assisted methods show why "middle REE" is hard
Research on separating Sm/Eu/Gd mixtures shows how processes may combine more specialized techniques (for example, reduction steps targeting Eu chemistry paired with chromatographic separation of Sm and Gd). The value here is not "this exact method is your flowsheet," but the message: Sm-Eu-Gd separations are intrinsically tight, and plants need real know-how to hit purity.
Translation: The middle-REE neighborhood where gadolinium lives is where separation becomes expensive, time-consuming, and capacity-constrained.