Symmetry analysis of antiferroquadrupolar order and accompanying atomic displacements in CeB6

Magnetic spin resonance inCeB6

“…It is established that T I-II ͑B͒ increases with magnetic field whereas T II-III ͑B͒ decreases; for B =0 T I-II ͑0͒ = 3.2 K and T II-III ͑0͒ = 2.3 K. [8][9][10][11][12][13][14] Conventional explanation of this magnetic phase diagram is based on the models, which account interplay between spin and orbital degrees of freedom and imply scenario with the orbitalordering temperature T Q higher than the spin-ordering temperature T N . [15][16][17][18][19][20][21][22][23][24][25][26][27][28] Therefore the transition phase I → phase II͑P → AFQ͒ is usually interpreted as an f-orbital-ordering phenomenon at T Q ͑B͒ = T I-II ͑B͒ and no change in the spin structure at this phase boundary is expected in theory. As an experimental ground for this interpretation the observation of the magnetic field-induced antiferromagnetic vector k = ͑1 / 2,1/ 2,1/ 2͒ corresponding to the doubling of the lattice period 8,9,28 is considered.…”

“…As an experimental ground for this interpretation the observation of the magnetic field-induced antiferromagnetic vector k = ͑1 / 2,1/ 2,1/ 2͒ corresponding to the doubling of the lattice period 8,9,28 is considered. Indeed, in absence of the noticeable atomic displacements in phase II as compared to the P phase, 8,9,27 it looks natural to explain this phenomenon in terms of orbital ordering of the f shells of the Ce 3+ ions leading to the three-dimensional alternating structure of the electric quadrupoles of the opposite sign 8,[18][19][20][21][22][23] thus motivating the application of the aforementioned term "antiferroquadrupole phase." The other transition phase II → phase III͑AFQ→ AF͒ is supposed to correspond to T N ͑B͒ = T II-III ͑B͒ and leads to a complicated Neel-type ordering of the Ce 3+ LMMs.…”

Group theory for magnetic structure determination: Recent developments and quadrupolar ordering analysis

“…The compound is isostructural with CeB 6 and it crystallizes in the structure described by Pm-3m space group. Contrary to the quadrupolar ordering of CeB 6 , which is found to be anti-ferroquadrupolar, with k = (1/2, 1/2, 1/2) [10,11], the experimental data in HoB 6 indicate a ferroquadrupolar ordering below 6.1K [12]. It means, that the symmetry analysis for this transition should be done for k = (0, 0, 0).…”

“…For k = (0, 0, 0) the structure is the same in all elementary cells, while for k = (1/2, 1/2, 1/2) it forms a sequence of alternating signs along the k vector direction. As a result the possible models of quadrupolar structure -mainly the shapes of QMT matrices and the relations of their main axes to the crystallographic ones -calculated for HoB 6 are the same as the ones calculated for CeB 6 [11]. However, as mentioned above, the sensitivity of experimental data to the quadrupolar ordering in HoB 6 is rather small therefore it difficult to confront directly the calculated models with experiment.…”

Symmetry analysis of hydrogen related structural transformations in Laves phase intermetallic compounds

“…The method introduced at first by E.F. Bertaut and developed intensively recently [1], [2] works under the assumption that the symmetry change in phase transition preserves the group-subgroup relation (it means it is the continuous or "semicontinuous" phase transition) and that the "property" under consideration is localised on some sets of equivalent positions in the crystal initial phase.…”