It is good idea to mention which nano-matrix you would like to prepare. Preparation method varies with metal of interest.

The most widely used preparation techniques of core–shell nanostructures, such as microemulsion method, epitaxial growth, microwave synthesis, electrochemical dealloying and multi-step reduction method, are limited by the complicated procedures, high costs, or difficulties to extend to large scales1

https://www.nature.com/articles/s41598-017-10630-5

Synthesis of core-shell nanoparticles metal oxide metal depends on many factors. Therefore, it is better to talk about the specific synthesis of a particular structure. For example, copper-copper oxide, iron-iron oxide can be obtained first by synthesizing metal nanoparticles, and then oxidized in air or other oxidizing agents (wet or dry oxidation). To obtain some oxide on the surface of gold nanoparticles, other methods are needed. For acquaintance with synthesis I recommend to get acquainted with the works

https://www.bnl.gov/isd/documents/41042.pdf

Using silane coupling agent such as Trimethoxy silylpropyl methacrylate (TMSPM) silane coupling agent.

The Stöber method for the core shell and then the APTMS (aminosilanization).

I published a method for Y2O3 and Gd2O3 nanoparticles, it´s an open access article.

Chávez D., Juárez-Moreno K., Hirata G. (2016) Aminosilane functionalization and cytotoxicity effects of upconversion nanoparticles Y2O3 and Gd2O3 Co-doped with Yb3+ and Er3+. Nanobiomedicine, 3, 1-7. doi: 10.5772/62252.

Md. Aminul Islam initially I will try to go for iron@iron oxide or Co@iron oxide

Kumail Abbas

We achieve Au@iron oxide by forming in situ gold on preformed seeds made out of iron oxide ultrasmall (USM) nanoparticles. More details here:

http://rsfs.royalsocietypublishing.org/content/6/6/20160058

By using silane coat to nano particles

Please try Electrochemical method it is a very good and reliable method for growth of magnetic core shell nanoparticles.@Kumail Abbas