Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

Abstract

We investigate antiferro quadrupole orders in a diamond lattice under magnetic fields by Monte Carlo simulations for two types of classical effective models. One is an XY model with Z3 anisotropy, and the other is a two-component φ 4 model with a third-order anisotropy. We confirm that the universality class of the zero-field transition is that for the three-dimensional XY model. Magnetic field corresponds to a Z3 field in the effective model, and under this field, we find that collinear and canted antiferro-quadrupole orders compete. Each phase is characterized by symmetry breaking in the sector of (sublattice Z2)⊗(reflection Z2 for the order parameter). When Z3 anisotropy and magnetic field vary, it turns out that this system is a good playground for various multicritical points; bicritical and tetracritical points emerge in a finite field. Another important finding is about the scaling of parasitic ferro quadrupole order at the zero-field critical point. This is the secondary order parameter induced by the primary antiferro order, and its critical exponent β ′ =0.815 clearly differs from the expected value that is twice the value for the primary order parameter. The corresponding correlation length exponent is also different, ν ′ =0.597(12). We also discuss relation of the present effective quadrupole models with the 3-state Potts model as well as implication to undertanding of orbital orders in Pr-based 1-2-20 compounds.

Landau theory of multipolar orders in Pr(Y)2X20 Kondo materials ( Y=Ti , V, Rh, Ir; Lee1, Trebst2, Kim3 et al. 2018Phys. Rev. B470420View full textAdd to dashboardCite

“…For FQ order, we find that the Landau theory permits a cubic anisotropy term, which was previously pointed out within a microscopic theory and classical Monte Carlo study of a lattice model. 39,40 This selects an FQ ordered state which is consistent with experimental results on PrTi 2 Al 20 . 35 On the other hand, AFQ order is generally accompanied by a "parasitic" FQ order due to a cubic term which couples them.…”

Anisotropic B–T Phase Diagram of Non-Kramers System PrRh2Zn20

“…In fact, it has been reported that a thermal fluctuation drives the reentrant behavior of the AFQ phase without any interactions of field-induced moments. 40) On the other hand, the anisotropy of B Q,C can be explained by that of the energy splitting of the non-Kramers doublet for each field direction. The magnitude of the splitting δ is estimated by the second-order perturbation to be δ [100] > δ [110] .…”

Octupolar order in d -orbital Mott insulators

“…In certain pyrochlore magnets, all-in all-out magnetic order has been proposed to lead to "effective octupoles" on tetrahedra [7]. Ongoing experimental [8-10] and theoretical investigations [11][12][13][14] of PrTi 2 Al 20 and PrV 2 Al 20 have also uncovered quadrupolar and ferro-octupolar orders.Recently, unconventional multipolar orders have also been proposed in d-orbital metals to occur as Pomeranchuk instabilities of spin-orbit coupled Fermi surfaces [15]. Specifically, metallic oxides which have d-orbital ions with large SOC, such as LiOsO 3 and Cd 2 Re 2 O 7 , have been proposed as potential candidates to realize this physics [15].…”