What makes John Donne a metaphysical poet? Refer to "The Sun Rising" and "A Valediction: Forbidding Mourning" for evidence.

Samuel Johnson, who coined the term "metaphysical" to describe seventeenth-century poets like John Donne, wrote that they "yoke" unlikely comparisons (metaphors) together. They like to startle us with their ingenious ideas and images. Not for them are the standard Renaissance metaphors comparing a beloved to a beautiful red rose.
In "A Valediction: Forbidding Mourning," Donne startles us with an unusual metaphor to describe two lovers. He compares them to a drawing compass, a tool that enables people to draw perfect circles by holding one "foot" or rod steady in the center of the page while the other foot, attached to a pencil, travels around it. He says the two lovers are like the two feet of the compass: no matter how far apart they might be physically, they are always connected by a spiritual center. This is a startling way to describe love, one that had not been used before.
In "The Sun Rising," Donne turns the tables on the sun. The bed the lovers lie in becomes the sun. This is a startling idea. His speaker addresses the sun, saying,

This bed thy center is, these walls, thy sphere

Metaphysical poets also liked to use hyperbole (exaggeration), and Donne does so in this poem, stating of his lover and himself that they are greater than all states and princes. This is startling but expresses how lovers often feel, that there is nothing in the world but each other:

She's all states, and all princes, I,
Nothing else is.
Princes do but play us; compared to this,
All honor's mimic, all wealth alchemy.