Possible multipolar density wave in NdFe$_2$Ga$_8$

We study the magnetism in NdFe$_2$Ga$_8$ by the neutron-diffraction and thermal-expansion techniques. Thermodynamical measurements have demonstrated that there are two magnetic transitions at 10 and 14.5 K, respectively. Neutron-diffraction measurements confirm that the lower one is an antiferromagnetic transition with a commensurate magnetic structure. Both the commensurate and incommensurate magnetic peaks are found below the higher transition but their intensities only gradually increases with decreasing temperature. Below 10 K, the commensurate peak intensity increases quickly with decreasing temperature, signaling the antiferromagnetic transition, while the incommensurate peak intensity disappears below 5 K. We attribute the high-temperature magnetic transition as a multipolar order, which induces incommensurate magnetic peaks. The multipolar ordering is suppressed by field at about 7 T, where the linear {Gruneisen} parameter along $c$-axis diverges with decreasing temperature as $T^{-1}$. Our results suggest that NdFe$_2$Ga$_8$ exhibits a multipolar density wave that is analogous to the spin density wave for the dipole moment.