Really I think it's over the top to associate "master race" ideology with Sparta. Sure, Spartans fought their share of wars, as all the Greek city states did. But I've never heard of them setting out to genocide another race in total.
The Nazis did a lot of things besides genocide.
The specific Nazi practices I was thinking of with regard to the Spartans were state-controlled eugenics and enslavement of entire peoples for the enrichment of the master race.
While slavery in Greek societies was widespread, only Sparta enslaved entire cities and regions, then controlled them by declaring war on them each year so that they could be killed with religious impunity.
The Spartans also invented the idea of the "secret police" brought to its peak by the Gestapo. However, since this is a hallmark of all totalitarian states, there's nothing specifically Nazi about it.