Dark matter models with uniquely spin-dependent detection possibilities

With much higher sensitivities due to coherence effects, it is often assumed that the first evidence for direct dark matter detection will come from experiments probing spin-independent interactions. We explore models that would be invisible in such experiments, but detectable via spin-dependent interactions. The existence of much larger (or even only) spin-dependent tree-level interactions is not sufficient, due to potential spin-independent subdominant or loop-induced interactions. We find that, in such a way, most models with detectable spin-dependent interactions would also generate detectable spin-independent interactions. Models in which a light pseudoscalar acts as the mediator seem to uniquely evade this conclusion. We present a particular viable dark matter model generating such an interaction.