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The magnetic properties of 50 nm Ni80Fe20 deposited on Cu underlayers with different thicknesses by obliquely sputtering were studied. It was found that the in-plane uniaxial magnetic anisotropy (IPUMA) of the Ni80Fe20 film can be induced by the obliquely sputtered Cu underlayer deposited under the NiFe layer. The IPUMA field of NiFe film varies between 20 Oe and 40 Oe when the thickness of Cu underlayer varies from 5 nm to 50 nm. The permeability spectrum results show that the damping factor increases with increasing Cu underlayer thickness. This indicates that changing the thickness of the Cu underlayer of obliquely sputtering is an effective method to adjust the damping factor in the dynamic magnetization process of Ni80Fe20 thin films. [ABSTRACT FROM AUTHOR]