Dear Arina Levina yes, some anionic sulfate complexes of rare earth elements do exist. Please see this relevant article entitled "Ammonium neodymium(III) bis[sulfate(VI)] tetrahydrate" published by Polish authors. The title compound (NH4)[Nd(SO4)2(H2O)3]xH2O is apparently just one member of an entire family of closely related anionic rare-earth sulfato complexes. The article is Open Access and can be freely downloaded as full text:
Hi, on the website http://athena.unige.ch/athena/mineral/search.html you can find some hydrous rare sulphates with REE contents. In Article Minerals of the rhabdophane group and the alunite supergroup...
we have observed corkite and hinsdalite (sulphates) which were REE enriched but only to 10 wt. %.