"slice within gibbs sampling"?

Hello,

I’m currently trying to calibrate a model compiled in cython, with the black-box method.
I’m using the slice sampling method since the NUTS method seems excessively long.
After looking into the code it seems to be a “slice-within-gibbs sampling” ?
I would like to know if there is a scientific reference (as it seems that Neal 2003 does not mention the “slice-within-Gibbs sampling”) and figure out what are the advantages compared to Metropolis-Hastings or Metropolis-within-gibbs.

Cordially,

Actually, it is clearly said in Neal 2003 that “it can be used to sample from a multivariate distribution by updating each variable in turn” I guess we can call that a “slice-within-gibbs sampling”.