Is using "iff" appropriate?

The abbreviation iff is generally understood in several fields outside logic, and in my experience it is well understood by physicists, but the golden rule is to define every abbreviation at its first use and/or provide a list of abbreviations. In this way, even those not familiar with an abbreviation will be able to understand the text.

However, in general, abbreviations may make a text less readable and therefore should be used judiciously. Thus, ask yourself if you will have to use the expression if and only if so frequently to warrant an abbreviation, sparing you just a bunch of characters, and think whether to limit its use to e.g. theorem statements.

You can sort this sort of thing out by looking at papers in journals. Google speeds this along. I searched as follows:

"iff" journal die reine und angewandte mathematik

and

"iff" "Physical review"

to confirm that there are plenty of papers in physics and math that use "iff" without explanation. The one paper I saw that defined this was in Physical Review Letters. You might want to search similarly in one of your target journals.

However: Do think about your target audience. An experimental physicist might be confused by this abbreviation.

A nice trick is to write things with nice large figures and few abbreviations and see how long the paper is. If you are over the page limits for a journal by just a little, you start shrinking images, tightening the prose, and using the more common abbreviations. Many physics papers have way too many abbreviations so do try to not use every abbreviation possible.

Another reason to use an abbreviation or a symbol (like \Leftrightarrow) is to make a multiline-equation a single-line equation, or to make a two-column equation fit in one column. This can greatly improve the look and readability of a paper.

The use of iff outside of formal logic is shorthand, and so is only appropriate in contexts where shorthand is appropriate.

For example, it's probably fine in a piece of maths homework, may or may not be a good choice in lecture notes (depending on their style), and not suitable for a research paper (at least in pure maths).