We study quadrupole orders in heavy-fermion compound ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$ under magnetic fields on the basis of the Landau theory. Assuming $E_g$ electric quadrupolar orders in the cubic symmetry with the ordering wave number at the L points in the face-centered-cubic lattice Brillouin zone as observed experimentally, we construct a Landau free energy and analyze the resulting free energy. We find that the unidentified high-temperature ordered phase under the magnetic field $\mathit{H}\parallel \left[001\right]$ reported earlier arises from the rotation of the quadrupole moments of $f$ electrons on the Pr site. We also discuss the phase diagram for other magnetic-field directions and possible double-$\mathit{q}$ quadrupolar orders in this system.

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• Landau theory
• Multipole order
• Orbital order
• Phase diagrams
• Phase transitions
• Heavy-fermion systems