Reference prior specification for proportional odds model

Hi all, let’s say that one is interested in estimating a proportional odds ratio between a single binary exposure and an ordinal outcome with J categories using Bayesian inference: what is a standard form of a reference prior (i.e. a prior that is invariant to re-parametrisation for the proportional log-OR (if there is a known form) and/or is there a way to specify a reference prior for this proportional log-OR in existing software, say in Stan?

Thanks in advance!