Is it ethical to ask a graduate student to help me with my paid external research?
Before anything else, you need to be certain about the legal ground on which you stand:
- Is the external work that you are doing bound by any sort of non-disclosure agreement or other agreement to which your interactions with the student would be subject?
- Do the university's terms of employment for the student state anything that whether a student can work externally and under what conditions?
If it's clear from both sides, then if the student will be doing a non-trivial amount of consulting work, they should get paid just like you are getting paid. Almost certainly, they should get paid by the company you are paid by, and not by you (unless you are doing your own work as an LLC or some such entity). A good litmus test is: would I be doing this work for free? Clearly, you aren't.
If it were five minutes of work, that might be different. But if it's complex enough that you are struggling with it, it's likely to take hours, maybe many hours, and could impact your students progress in classes or other research projects. In that case, pay is clearly deserved.
I may sound a little strict about this, but when a guy does partly the job you are paid to do, he should get paid for it. Period. It does not matter if he is a graduate student or he thinks he must owe you a favour in exchange for a future reference letter. Slavery has been abolished (at least in civilized countries). You must pay him for his effort's worth. Where this money comes from (your pocket or your outside employer) is for you to decide.