The proceeding magical beings are the ones most commonly used in the cores of magic wands. However should you choose to continue your studies in wand lore, you will learn about other beings used less often when crafting wands:

Brownies - Brownies are very loyal household spirits that love to help the members of the family that they serve. However, brownies become angry and destructive if not respected and properly fed. Brownie wands include brownie hair, which has the elemental Earth ...