I made a Lanthanide based nanoparticle coated with PVP, and there is no paper showed that pvp has a distinct layer over our core, but they said that if we see the core of nanoparticle burned by TEM beam, so there is PVP.
You can try both Infrared (IR) spectroscopy and thermogravimetric analysis (TGA) in air. By IR you'll see specific vibration bands of PVP (CH, CN, CO, etc). Perform IR of lanthanide NPs alone, PVP, alone, and then lanthanide NPs coated with PVP. IR of lanthanide NPs coated with PVP should be similar to PVP alone.
The same by TGA. Lanthanide NPs alone should lose only water, PVP alone has a profile specific to organic molecules (loss of water, CO2, nitrous oxides). So, your lanthanide NPs coated with PVP should have several weight loss steps specific to PVP.