Molecular platinum fluorides PtFn, n=1–6, are prepared by two different routes, photo‐initiated fluorine elimination from PtF6 embedded in solid noble‐gas matrices, and the reaction of elemental fluorine with laser‐ablated platinum atoms. IR spectra of the reaction products isolated in rare‐gas matrices under cryogenic conditions provide, for the first time, experimental vibrational frequencies of molecular PtF3, PtF4 and PtF5. Photolysis of PtF6 enabled a highly efficient and almost quantitative formation of molecular PtF4, whereas both PtF5 and PtF3 were formed simultaneously by subsequent UV irradiation of PtF4. The vibrational spectra of these molecular platinum fluorides were assigned with the help of one‐ and two‐component quasirelativistic DFT computation to account for scalar relativistic and spin–orbit coupling effects. Competing Jahn‐Teller and spin–orbit coupling effects result in a magnetic bistability of PtF4, for which a spin‐triplet (3B2g, D2h) coexists with an electronic singlet state (1A1g, D4h) in solid neon matrices.