This paper reveals soliton solutions to magneto-optic waveguides that maintain parabolic-nonlocal law of refractive index. The unified Riccati equation expansion together with extended auxiliary equation approach together reveal bright, dark, singular as well as straddled optical solitons. These soliton solutions are obtained through a limiting process when the modulus of ellipticity approaches unity. Finally, the conservation laws are also listed. (C) 2020 Elsevier B.V. All rights reserved.