There are some weak stones available that crumble/split when subjected to the stresses created by thermal cycling, using an uncoupling layer under these may reduce the probability of them failing. If I was still tiling then I would pass on the advise that an uncoupling membrane is recommended by the stone fed for fixing (all) stone tiles over a heated floor. Personally if tiling onto a concrete floor then I can't see that it is necessary with slate as I've fixed hundreds of m2 in the past and have not had any fails however as it is an anhydrite screed then I would recommend using one as described above (stuck down with an anhydrite compatible adhesive onto the sanded, vacuumed floor with primer as recommended by the adhesive manufacturer; and then a
cement based adhesive over the top to fix the slate) because then there can be no contact between the
cement and anhydrite screed (so the membrane will have two purposes).
I have seen slate fixed over ditra crack but that was because no movement joints used where they were needed! I have also seen porcelain tiles crack when fixed directly over anhydrite (primer barrier then
cement based addy) this because the water temp being passed through the screed was not correctly regulated and far too hot (not even raised slowly in temp after fixing the tiles). So make sure movement joints are used if needed, check the water temp regulated correctly and raise it's temp slowly up to the user temp when the floor fixing is finished and adhesive cured (I can't remember how long to leave it and how many degrees per day are recommended).
