The automorphism group of the free group of rank two is a CAT(0) group
  We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above. 
Adam Piggott, Kim Ruane and Genevieve S. Walsh