We report on the structure, magnetization, magnetic anisotropy, and domain morphology of ultrathin yttrium iron garnet (YIG)/Pt films with thickness ranging from 3 to 90 nm. We find that the saturation magnetization is close to the bulk value in the thickest films and decreases towards low thickness with a strong reduction below 10 nm. We characterize the magnetic anisotropy by measuring the transverse spin Hall magnetoresistance as a function of applied field. Our results reveal strong easy plane anisotropy fields of the order of 50-100 mT, which add to the demagnetizing field, as well as weaker in-plane uniaxial anisotropy ranging from 10 to 100 $mu$T. The in-plane easy axis direction changes with thickness, but presents also significant fluctuations among samples with the same thickness grown on the same substrate. X-ray photoelectron emission microscopy reveals the formation of zigzag magnetic domains in YIG films thicker than 10 nm, which have dimensions larger than several 100 $mu$m and are separated by achiral N{e}el-type domain walls. Smaller domains characterized by interspersed elongated features are found in YIG films thinner than 10 nm.
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