Quantum memory is the core device for the construction of large-scale quantum networks. For scalable and convenient practical applications, integrated optical memories, especially on-chip optical memories, are crucial requirements because they can be easily integrated with other on-chip devices. Here, we report the coherent optical memory based on a type-IV waveguide fabricated on the surface of a rare-earth ion-doped crystal (i.e. $mathrm{Eu^{3+}}$:$mathrm{Y_2SiO_5}$). The properties of the optical transition ($mathrm{{^7}F{_0}rightarrow{^5}D{_0}}$) of the $mathrm{Eu^{3+}}$ ions inside the surface waveguide are well preserved compared to those of the bulk crystal. Spin-wave atomic frequency comb storage is demonstrated inside the type-IV waveguide. The reliability of this device is confirmed by the high interference visibility of ${97pm 1%}$ between the retrieval pulse and the reference pulse. The developed on-chip optical memory paves the way towards integrated quantum nodes.
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