I like the sound of the change from a minor chord to a major chord one semitone lower and just wanted to ask if there was a particular name for this type of chord movement? For example, I have the chord Am and then move to an Ab major.
In Neo-Riemannian Theory, this is known as a Slide (or S) transformation.
In an S transformation, a consonant triad (major or minor) moves to a consonant triad of opposite mode by keeping the third and "sliding" the perfect fifth up or down a half step.
In your example, the third of Am, C, stays constant, while the fifth A–E slides down by half step.
Note that this transformation is an involution, which simply means applying S to the resulting triad will return you to the original triad of Am.