I hesitated to answer because it really comes down to the chosen definition for refugium.
Some folks would go so far as to say you don't have refugium unless you have an deep sand bed or mud bed for anaerobic bacteria to complete the nitrate cycle. They expect the detritus to collect, degrade and off gas nitrogen.
http://www.advancedaquarist.com/2014/5/chemistry
Note: This essentially took the Jaubert's Method, aka 'Monaco System, from the display and put it in the sump.
Others consider any place in your system (sump chamber, hang-on box, etc) where zooplankton (amphipods, copepods, mysis shrimp, miscellaneous worms, ect) can be cultured free of predators....
a place that provides shelter
And then there are a bunch of in-between versions,
ATS, mangrove, sponge, etc, but today it looks most common to have a sump chamber with some live rock rubble and grow macro algae....and lots of zooplankton
Mine only has live rock rubble...
Seachem Matrix for denitrafication and a place for zooplankton to avoid predators. To address the detritus collection, I have the rubble/matrix in a mesh vegetable bag that lets me easily lift the rubble out of the way and siphon it out during water changes. For completeness, I do run a SantaMonica drop-in ATS is in the first sump chamber with the skimmer.