Group theory and octupolar order inURu2Si2

Abstract

Recent experiments on URu 2 Si 2 show that the low-pressure hidden order is non-magnetic but it breaks time reversal invariance. Restricting our attention to local order parameters of 5f 2 shells, we find that the best candidate for hidden order is staggered order of either T β z or T xyz octupoles.Group theoretical arguments for the effect of symmetry-lowering perturbations (magnetic field, mechanical stress) predict behavior in good overall agreement with observations. We illustrate our general arguments on the example of a five-state crystal field model which differs in several details from models discussed in the literature. The general appearance of the mean field phase diagram agrees with the experimental results. In particular, we find that a) at zero magnetic field, there is a first-order phase boundary between octupolar order and large-moment antiferromagnetism with increasing hydrostatic pressure; b) arbitrarily weak uniaxial pressure induces staggered magnetic moments in the octupolar phase; and c) a new phase with different symmetry appears at large magnetic fields.

Competition between hidden order and antiferromagnetism inURu2Si2under uniaxial stress studied by neutron scattering

“…The present experiments do not exclude the possibility that the low-pressure magnetism is induced by an order parameter that breaks time reversal invariance but is nearly non-magnetic, such as an octupole moment. 44 …”

Γ3-Type Lattice Instability and the Hidden Order of URu2Si2

“…1,17) The whole feature of the electrical resistivity is similar to the typical Kondo-lattice behavior, whereas the large reduction of the c-axis magnetic susceptibility at low temperature seems to be unconventional, suggesting the influence of crystalline-electric-field (CEF) effects and/or large antiferromagnetic correlations. 7,11,12,18) However, there is no consensus of the mechanism behind the formation of the low-temperature heavy-electron state of this system, even on the CEF 5f level schemes assumed in the local limit.On the other hand, when applying a magnetic field over 35 T along c-axis, three-successive transitions have been observed in resistivity, specific-heat, magnetization, and longitudinal-ultrasonic-velocity measurements. 17,[19][20][21][22] These cascade transitions occur in the vicinity of the upper phase boundary of the HO phase and are associated with meta-magnetic-like increases in the c-axis magnetization.…”

“…1,17) The whole feature of the electrical resistivity is similar to the typical Kondo-lattice behavior, whereas the large reduction of the c-axis magnetic susceptibility at low temperature seems to be unconventional, suggesting the influence of crystalline-electric-field (CEF) effects and/or large antiferromagnetic correlations. 7,11,12,18) However, there is no consensus of the mechanism behind the formation of the low-temperature heavy-electron state of this system, even on the CEF 5f level schemes assumed in the local limit.…”

“…Since 29 Si-NMR and zero-magnetic-field SR measurements have detected little ( 1 G) or no significant internal-magnetic field in the HO phase, [4][5][6] non-dipolar-type order parameters, e.g., electric quadrupole (rank 2), hexadecapole (rank 4), À 3 -type magnetic octupole (rank 3), or dotriacontapole (rank 5) order parameters, are recently attracting attention. [7][8][9][10][11][12][13] Thus far, none of the characteristic signatures of the electric-quadrupole or magnetic-octupole order has been identified in resonant X-ray scattering (under magnetic fields) and neutron scattering under uniaxial stress. 14,15) On the other hand, a nematicity of the electron state in the HO is pointed out, since an in-plane rotational four-fold symmetry breaking is observed in the HO by the magnetic-torque measurement by use of cantilever technique.…”

Local suppression of the hidden-order phase by impurities in URu2Si2

“…Since few impurities are added to the sample, NMR is a particularly useful bulk probe sensitive to the local atomic environment to reveal what happens to the HO state at the impurity site. Recently the 29 Si NMR spectrum has been reported in U(Ru 1−x Rh x ) 2 Si 2 as a function of temperature and Rh concentration 18 . The experiment showed local suppression of the HO state and the emergence of satellite NMR peaks, indicating the onset of local antiferromagnetic droplets near each Rh impurity.…”