Welcome to the forum. Firstly, a D visa only gets you into Switzerland for more than 90 days. It's the permit itself that gives you the right to live/work here. I assume as a PhD, you'll get a B permit and your spouse will get the same. As far as I'm aware since a PhD is considered work, your spouse would also be able to look for a job and wouldn't come under the non-EU hiring rules. He doesn't apply for a work permit, his residence permit would include that if he finds a job. He'd just need to take his employment contract to the gemeinde to let them know he'd found a job.

However, be aware that as his permit is dependent on yours, if you do lose/finish your PhD and lose your permit then he can't switch to being the main permit holder and would have to give up his employment as well.