If I'm not mistaken, the taxonomy of archaea falls under the International Code of Nomenclature of Prokaryotes, together with bacteria. As a bacterial taxonomist, I use the LPSN database as a reference (link below). Taxonomy is a turbulent field, where literature can get outdated pretty quickly. Up-to-date curated databases are a good source for current taxonomy and nomenclature and can be cited in scientific literature.

I recommend reading a bit about how the taxonomy and nomenclature of prokaryotes actually work. You can check out the Nomenclature and FAQ pages on the LPSN website.

On the website linked below, you can find the names of archaeal phyla, including many with Candidatus status. The database also links to many useful resources, such as the effective publication of the taxon you're currently viewing, synonyms, and other notes.

Actually, the two domains and seven kingdoms of prokaryotes were officially included in the code one month ago (link to publication below), before that, domains and kingdoms were not included in the code at all. The same happened with Phyla a couple of years ago, before that, we only had species, genera, families, orders and classes. I guess the linked paper on its own would answer your question, but I think the database comes in handy when you want to browse the ranks.

https://lpsn.dsmz.de/domain/archaea

Article Valid publication of names of two domains and seven kingdoms...