If $\bar { z }$ denotes the conjugate of $z$, what is the non-zero complex number $z$ that satisfies the equation $z ^ { 2 } = \bar { z }$ and whose argument is between $\frac { \pi } { 2 }$ and $\pi$?\\
A) $\frac { - 1 } { 2 } + ( \sqrt { 3 } ) \mathrm { i }$\\
B) $\frac { - 1 } { 2 } + \left( \frac { \sqrt { 3 } } { 2 } \right) \mathrm { i }$\\
C) $\frac { - \sqrt { 2 } } { 2 } + \left( \frac { 1 } { 2 } \right) \mathrm { i }$\\
D) $\frac { - \sqrt { 2 } } { 2 } + \left( \frac { \sqrt { 2 } } { 2 } \right) i$\\
E) $\frac { - \sqrt { 3 } } { 2 } + \left( \frac { 1 } { 2 } \right) \mathrm { i }$