Figure 1.

a) Frustrated magnetism in ITLAFM. It is impossible to place the three spins such that they all point in the opposite direction with respect to their neighbors. b) Triangle of Ising‐like electric dipoles realizing an equivalent frustration problem. The electric dipoles pointing toward c and toward ‐ c are colored in orange and blue, respectively and the displacement of the Al(5) ion is exaggerated for the clarity of the figure. c) View from the b ^* direction of the unit cell of the hexagonal crystal structure of EuAl₁₂O₁₉ at T = 35 K. The bipyramid AlO₅ carrying electric dipoles are highlighted in green. d) View from the c axis of a selected part of the unit cell showing the triangular lattice of electric dipoles. e) Single crystal of EuAl₁₂O₁₉ on a millimeter‐paper. f) Examples of various electric dipole configurations at the minimum of energy of the ITLAFE. They are characterized by all the triangles harboring one or two dipoles pointing up, i.e., there is no triangle with three dipoles pointing in the same direction. Disordered configurations with zero polarization are favored at finite temperature by the minimization of the free energy. The stripe order and the up‐up‐down order are expected to be selected when the degeneracy is lifted by second nearest neighbor dipolar interactions and by external electric field, respectively.^{[ 14} , ¹⁵ , ^{16 ]} g) Calculated phonon dispersion curves for EuAl₁₂O₁₉ with the Al(5) ion sitting at the centre of the AlO₅ bipyramid. Only phonons below 8 THz are shown to focus on the low energy branches. Imaginary frequencies are represented by negative values.