  The equiatomic quaternary Heusler alloy CoFeCrAl is a candidate material for
spin-gapless semiconductors (SGSs). However, to date, there have been no
experimental attempts at fabricating a junction device. This paper reports a
fully epitaxial (001)-oriented MgO barrier magnetic tunnel junction (MTJ) with
CoFeCrAl electrodes grown on a Cr buffer. X-ray and electron diffraction
measurements show that the (001) CoFeCrAl electrode films with atomically flat
surfaces have a $B2$-ordered phase. The saturation magnetization is 380
emu/cm$^3$, almost the same as the value given by the Slater--Pauling--like
rule, and the maximum tunnel magnetoresistance ratios at 300 K and 10 K are 87%
and 165%, respectively. Cross-sectional electron diffraction analysis shows
that the MTJs have MgO interfaces with fewer dislocations. The temperature- and
bias-voltage-dependence of the transport measurements indicates magnon-induced
inelastic electron tunneling overlapping with the coherent electron tunneling.
X-ray magnetic circular dichroism (XMCD) measurements show a ferromagnetic
arrangement of the Co and Fe magnetic moments of $B2$-ordered CoFeCrAl, in
contrast to the ferrimagnetic arrangement predicted for the $Y$-ordered state
possessing SGS characteristics. Ab-initio calculations taking account of the
Cr-Fe swap disorder qualitatively explain the XMCD results. Finally, the effect
of the Cr-Fe swap disorder on the ability for electronic states to allow
coherent electron tunneling is discussed.
