  In the nematic state of iron-based superconductors, twin formation often
obscures the intrinsic, anisotropic, in-plane physical properties.Relatively
high in-plane external magnetic fields $H_{\rm ext}$ greater than the typical
lab-scale magnetic fields 10--15 T are usually required to completely detwin a
sample. However, recently a very small in-plane $H_{\rm ext} \sim$ 0.1 T was
found to be sufficient for detwinning the nematic domains in EuFe$_2$As$_2$. To
explain this behavior, a microscopic theory based on biquadratic magnetic
interactions between the Eu and Fe spins has been proposed. Here, using
$^{153}$Eu nuclear magnetic resonance (NMR) measurements below the Eu$^{2+}$
ordering temperature, we show experimental evidence of the detwinning under
small in-plane $H_{\rm ext}$. Our NMR study also reveals the evolution of the
angles between the Eu and Fe spins during the detwinning process, which
provides the first experimental evidence for the existence of biquadratic
coupling in the system.
