  We have succeeded for the first time in synthesizing single crystals of
nanolaminated borides (Fe$_{1-x}$Mn$_{x}$)$_2$AlB$_2$ in the entire Fe-Mn
composition range using the Al self-flux method, and have established $T$-$x$,
$H$-$T$ and three-dimensional $H$-$T$-$x$ magnetic phase diagrams from the
results of magnetization measurements. The ferromagnetic correlation of
Fe$_2$AlB$_2$ is weakened with the Mn substitution, whereas the
antiferromagnetic correlation of Mn$_2$AlB$_2$ is enhanced with the Fe up to
$x=0.65$. The spin direction in the magnetic ordered states changes from the
$a$ to the $b$ axis with increasing Mn concentration and temperature. At $x$ =
0.31-0.46, there are three magnetic phases; ferromagnetic, antiferromganetic,
and intermediate phases in between. At $x$ = 0.65 and 0.74, a spin-flop-like
metamagnetic transition was observed at a finite field parallel to the spin
direction. These observations indicate that in (Fe$_{1-x}$Mn$_{x}$)$_2$AlB$_2$
the ferromagnetic and antiferromagnetic correlations coexist and the uniaxial
magnetic anisotropy competes between the $a$ and $b$ axes.
