Competition of magnetic and quadrupolar order parameters in HoB4

Daisuke Okuyama, Takeshi Matsumura, Takuya Mouri, Naoko Ishikawa, Kenji Ohoyama, Haruhiro Hiraka, Hironori Nakao, Kazuaki Iwasa, Youichi Murakami

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18 Citations (Scopus)


The successive magnetic phase transitions of HoB4 with T N1 = 7.1 K and TN2 = 5.7 K have been investigated in detail by neutron and X-ray diffraction. Since Ho ions in the c-plane form a Shastry-Sutherland lattice, geometrical frustration has been expected in this compound. Below TN1, HoB4 exhibits an incommensurate antiferromagnetic order with q = (δ, δ, δ′) (δ = 0.022, δ′ = 0.43), followed by a first-order transition at T N2 into a commensurate order with q = (0, 0, 0), where four magnetic moments are antiferromagnetically coupled in a unit cell. After determining the magnetic structures of the two phases by neutron powder diffraction, we pay particular attention to diffuse scatterings responsible for the critical behavior. Very broad diffuse scatterings, extending almost to the zone boundary, are observed already in the paramagnetic phase at around q = (0, 0, 0) and (0, 0, 1/2) with magnetic correlation lengths of ξ < 10 Å. Below T N1, a strong diffuse scattering develops in a more concentrated region at around q = (0, 0, δ′) with ξ ∼ 30 Å, followed by the appearance of a Bragg peak at (δ, δ, δ′). Simultaneously, a sharp Bragg peak corresponding to q = (0, 0, 0) also develops at (1, 0, 1) upon diffuse scattering. This complex critical behavior is discussed from the viewpoint of competing order parameters of magnetic and quadrupolar origins. The striking resemblance of the critical behavior to that of HoB2C2 with a square lattice of Ho is interpreted as a manifestation of a universality for a three-dimensional system with competing magnetic and quadrupolar order parameters and a long-ranged RKKY interaction. It is considered that the microscopic difference in interionic interaction due to the difference in crystal structure becomes less prominent in the critical behavior as the correlation length becomes much larger than the lattice constant. On the other hand, the strong diffuse scattering in HoB4, which is hardly detected in HoB2C2, might be ascribed to geometrical frustration. The softening of the elastic constant in HoB 4 and HoB2C2 is also discussed.

Original languageEnglish
Article number044709
Journaljournal of the physical society of japan
Issue number4
Publication statusPublished - 2008 Apr


  • Critical phenomenon
  • Geometrical frustration
  • HoB
  • HoBC
  • Magnetic structure
  • Neutron diffraction
  • Quadrupolar interaction
  • Short range order
  • X-ray diffraction

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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