A microscopic solution to the magnetic detwinning mystery in EuFe$_2$As$_2$

One of the greatest recent advances in studying nematic phenomena in Fe-based superconductors was the mechanical detwinning of the 122-family compounds. Unfortunately, these techniques generate considerable stress in the investigated samples, which contaminates the results. Recently, we observed that a minuscule magnetic field of the order of 0.1 T irreversibly and persistently detwins EuFe$_2$As$_2$, opening an entirely new avenue for addressing nematicity\footnote{PRL 113,227001 (2014)}. However, further development was hindered by the absence of a microscopic theory explaining this magnetic detwinning. In fact, Eu$^{2+}$ has zero orbital moment and does not couple to the lattice, and its exchange coupling with the Fe sublattice cancels by symmetry. Moreover, further increase of the field to $\sim$ 1 T leads to a reorientation of Fe domains, while even larger fields $\sim$10 T reorient the domains once again. We will present a new microscopic model, based on a sizable biquadratic coupling between the Fe 3$d$ and Eu 4$f$ moments. This model quantitatively explains our old and new magnetization and neutron diffraction data, thus removing the veil of mystery and finally opening the door to full-scale research into magnetic detwinning and nematicity in Fe-based superconductors.