Competition between helimagnetic and ferroquadrupolar ordering in a monoaxial chiral magnetDyNi3Ga9studied by resonant x-ray diffraction

Abstract

Successive phase transitions in a rare-earth monoaxial chiral magnet ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ have been investigated by resonant x-ray diffraction. Magnetic dipole and electric quadrupole degrees of freedom arising from the large angular moment of $J=15/2$, in combination with the symmetric and antisymmetric exchange interactions and the crystal field anisotropy, give rise to competing ordered phases. We show that the antiferromagnetically coupled Dy moments in the $ab$ plane form an incommensurate helimagnetic order with $\mathbit{q}\ensuremath{\sim}(0,0,0.43)$ just below ${T}_{\text{N}}=10$ K, which further exhibits successive first-order transitions to the commensurate helimagnetic order with $\mathbit{q}=(0,0,0.5)$ at ${T}_{\text{N}}^{\ensuremath{'}}=9.0$ K, and to the canted antiferromagnetic order with $\mathbit{q}=(0,0,0)$ at ${T}_{\text{N}}^{\ensuremath{''}}=8.5$ K, both with large coexistence regions. The relation of the magnetic helicity and the crystal chirality in ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ is also uniquely determined. Splitting of the (6,0,0) Bragg peak is observed below ${T}_{\text{N}}^{\ensuremath{''}}$, reflecting the lattice distortion due to the ferroquadrupole order. In the canted antiferromagnetic phase, a spin-flop transition takes place at 5 K when the temperature is swept in a weak magnetic field. We discuss these transitions from the viewpoint of the competing energies described above.