"Slave collars, evidence for the brutal force necessary for maintenance of a slave society, increased in popularity in post-Constantinian times, and many slave collars bear Christian iconography, such as the alpha and the omega or the chi-rho figure. So discomfiting are these objects that nineteenth-century scholars described them as dog collars rather than acknowledge that ancient Christians regularly bound other persons in a crude manner.“
Glancey “Slavery and the Rise of Christianity,” Camb. World Hist. of Slavery 1, 477f.
Any hard data on the "increase in popularity"?
Yes, there is evidence that slave collars increased in popularity in post-Constantinian times. Specifically, about forty-five items that can be securely identified as belonging to slave collars have ever been found (some are now lost again). Some of these cannot be dated reliably, but for the remainder, evidence either is definite to during/after the reign of Constantine or at least suggests a late date. In addition to the iconography mentioned in the Cambridge quote above, in several cases, inscriptions give the slave-owner ranks/titles that only came into use in Late Antiquity; in others, the slave-owner has a title from Christian church hierarchy, indicating a formal, institutionalized church and thus suggesting that they date from after the edicts of toleration.
(It is fairly common for the collar to pay more attention to the identity of the owner than to describing the slave, who of course anybody reading the collar would have had right in front of them; and particularly we should probably expect that those with high rank and titles would have advertised them; Saint Augustine remarked that landowners who found runaway slaves questioned them about their former owner and, in case of a low-ranking or less powerful owner, would feel less nervous about keeping the slave for themselves)
So, all of the Roman slave collars to which we can assign a date, and presumably some or all of those to which we can't, are from during or after Constantine's reign. Most scholars believe that earlier, tattooing was the favored method of putting a prominent, visible, and difficult to hide sign on a slave, and that the rising popularity of collars with inscriptions or tags in Late Antiquity corresponds to tattooing becoming somewhat less popular.
If you have the Cambridge volume on ancient slavery, you have access to its extensive bibliography already, but ancient slavery is a hot topic and there have been more publications since Cambridge. Relevant among these is Jennifer Trimble, The Zoninus Collar and the Archaeology of Roman Slavery.
https://www.jstor.org/stable/10.3764/aja.120.3.0447?seq=1#page_scan_tab_contents