Temperature and Field Dependence of the Order Parameter in the Antiferroquadrupolar Phase of CeB6 from μ+ Knight Shift Measurements

Abstract

The Fermi contact hyperfine contribution to the Knight shift of positive muons, implanted at the interstitial 3d sites in CeB6, is found to exhibit the same temperature dependence below T(Q) in phase II as the quadrupolar order parameter determined from resonant and nonresonant x-ray scattering. Furthermore, the contact coupling parameter is shown to be anisotropic and field dependent. These unanticipated features are interpreted to arise from the RKKY induced conduction electron spin polarization, which depends on the orientation and expectation value of the ordered 4f quadrupole moments.

Magnetic spin resonance inCeB6

“…However, the view on this problem in literature is contradictory. In the muon-spin-relaxation and neutron-diffraction experiments [25][26][27] ferromagnetic component in the phase II was not observed although ferromag-netic correlations were found in the phase III ͑antiferromagnetic phase͒. From the other hand, the analysis of transport ͑resistivity, magnetoresistance, Hall-effect, and thermoelectric power͒ and magnetic data have lead authors of Ref.…”

“…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.…”

“…It is worth noting that the exact magnetic structure in AF phase is still remains the subject of debates. [24][25][26][27][28] However, all modifications in the theoretical models suggested up to now for the description of the peculiar magnetic properties of this material assume that ͑i͒ magnetism of CeB 6 originate from the single source, namely, the LMMs of Ce 3+ somehow affected by Kondo screening and ͑ii͒ the ground state of Ce 3+ in crystal field is ⌫ 8 quartet rather than ⌫ 7 doublet as long as only this type of symmetry allows electric-quadrupolar effects.…”

Freezing out of a low-energy bulk spin exciton in SmB6

“…Thus, only modifications of the Zeeman split Γ 8 quartet are relevant in the low T regime. In CeB 6 , which does not develop a Kondo insulating gap, K i linearly scales with χ mol above 10 K. Hence it is unlikely that the µ + induces the Knight shift observed in SmB 6 below 20 K. We note that the loss of scaling between K i and χ mol in CeB 6 below 10 K is due to the development of antiferroquadrupolar ordering, 49 which does not occur in SmB 6 .…”

Spectral analysis of resonant x-ray scattering inCeB6under an external magnetic field

“…In CeB 6 , the antiferroquadrupolar ͑AFQ͒ order-ing phase is inferred from various indirect observations such as macroscopic measurements, resonance methods, neutron scattering, and so on. [16][17][18][19][20][21] The most direct evidence of the AFQ order is provided by the RXS experiment by Nakao et al 22 and Yakhou et al, 23 who have succeeded in detecting the RXS signal at the Ce L 3 edge at an AFQ Bragg spot G = ͑ 1 2 , 1 2 , 1 2 ͒. Later, another experimental support was given by Tanaka et al 24 from the non-resonant x-ray Thomson scattering ͑NRXTS͒ study which detected directly an evidence of the aspherical charge density.…”