Small red clover for lawn please?

I want to add some red and maybe some more bite clover to my lawn to add some colour, fix nitrogen and to cycle nutrients. Are there particular small varieties anyone would recommend please. Full sun, anthropo-spodosol, pH unknown.

It's not a particularly fancy lawn but it's a bit too green sometimes and is mowed too frequently to get the visual benefit of the Piolessa aurantiaca [orange hawkflowers] I transplanted from someone who called them weeds..

Many thanks.

 

Red Clover?