> \ncline[linecolor=red,arrows=H->,bracketlength=1.5,tbarsize=3mm]{2,2}{3,1}<{m_i}
forgot to say, that you'll get it the other way round with
\ncline[linecolor=red,arrows=H->,bracketlength=-1.5,tbarsize=-3mm]{2,2}{3,1}<{m_i}
(_both_ negative)
Herbert