  The mixed valence Cr compound NaCr$_2$O$_4$, synthesized using a
high-pressure technique, offers a unique playground for investigating
unconventional physical properties in condensed matter. In the present study,
muon spin rotation/relaxation ($\mu^+$SR) and high-resolution neutron powder
diffraction (NPD) measurements were carried out to clarify the true magnetic
ground state of this interesting compound. Our detailed study brings new
insight, allowing us to confirm the existence of a commensurate
antiferromagnetic order (C-AFM) and to extract its ordered Cr moment $\mu^{\rm
C}_{\rm Cr}=(4.30\pm0.01)\mu_B$. Such a value of the ordered moment is in fact
compatible with the existence of high-spin Cr sites. Further, the value of the
canting angle of the Cr spin axial vector is refined as $\theta_{\rm
c}=(8.8\pm0.5)^{\circ}$. Employing high-quality samples in combination with
time-of-flight NPD, a novel magnetic supercell was also revealed. Such
supercell display an incommensurate (IC)-AFM propagation vector
(0~0~${\textstyle \frac{1}{2}-}\delta$), having an ordered moment $\mu^{\rm
IC}_{\rm Cr}=(2.20\pm0.03)\mu_B$. It is suggested that the C-AFM and IC-AFM
modulations are due to itinerant and localized contributions to the magnetic
moment, respectively. Finally, the direct measurement of the magnetic order
parameter provided a value of the critical exponent $\beta = 0.245 \approx
\frac{1}{4}$, suggesting a non conventional critical behavior for the magnetic
phase transition in NaCr$_2$O$_4$.
