Anomalous temperature dependence of the magnetic field induced antiferromagnetic moment in the antiferroquadrupolar ordered state of CeB6

Revealing the Nature of Antiferroquadrupolar Ordering in Cerium Hexaboride: CeB_{6}

The cerium hexaboride (CeB_{6}) f-electron compound displays a rich array of low-temperature magnetic phenomena, including a "magnetically hidden" order, identified as multipolar in origin via advanced x-ray scattering. From first-principles electronic-structure results, we find that the antiferroquadrupolar (AFQ) ordering in CeB_{6} arises from crystal-field splitting and yields a band structure in agreement with experiments. With interactions of p electrons between Ce and B_{6} being small, the electronic state of CeB_{6} is suitably described as Ce(4f^{1})^{3+}(e^{-})(B_{6})^{2-}. The AFQ state of orbital spins is caused by an exchange interaction induced through spin-orbit interaction, which also splits the J=5/2 state into a Γ_{8} ground state and a Γ_{7} excited state. Within the smallest antiferromagnetic (AFM) (111) configuration, an orbital-ordered AFQ state appears during charge self-consistency, and it supports the appearance of a "hidden" order. Hydrostatic pressure (either applied or chemically induced) stabilizes the AFM (AFQ) states over a ferromagnetic one, as observed at low temperatures.

Multipolar phases and magnetically hidden order: review of the heavy-fermion compound Ce1-x La x B6

Cerium hexaboride is a cubic f-electron heavy-fermion compound that displays a rich array of low-temperature magnetic ordering phenomena which have been the subject of investigation for more than 50 years. Its complex behaviour is the result of competing interactions, with both itinerant and local electrons playing important roles. Investigating this material has proven to be a substantial challenge, in particular because of the appearance of a 'magnetically hidden order' phase, which remained elusive to neutron-scattering investigations for many years. It was not until the development of modern x-ray scattering techniques that the long suspected multipolar origin of this phase was confirmed. Doping with non-magnetic lanthanum dilutes the magnetic cerium sublattice and reduces the f-electron count, bringing about substantial changes to the ground state with the emergence of new phases and quantum critical phenomena. To this day, Ce1-x La x B6 and its related compounds remain a subject of intense interest. Despite the substantial progress in understanding their behaviour, they continue to reveal new and unexplained physical phenomena. Here we present a review of the accumulated body of knowledge on this family of materials in order to provide a firm standpoint for future investigations.

Nesting-driven multipolar order in CeB6 from photoemission tomography

Some heavy fermion materials show so-called hidden-order phases which are invisible to many characterization techniques and whose microscopic origin remained controversial for decades. Among such hidden-order compounds, CeB₆ is of model character due to its simple electronic configuration and crystal structure. Apart from more conventional antiferromagnetism, it shows an elusive phase at low temperatures, which is commonly associated with multipolar order. Here we show that this phase roots in a Fermi surface instability. This conclusion is based on a full 3D tomographic sampling of the electronic structure by angle-resolved photoemission and comparison with inelastic neutron scattering data. The hidden order is mediated by itinerant electrons. Our measurements will serve as a paradigm for the investigation of hidden-order phases in f-electron systems, but also generally for situations where the itinerant electrons drive orbital or spin order.

In compounds containing 4f and 5f elements, hidden-order phases exist which are undetectable by many methods, the origins of which are debated. Here, the authors use photoemission and neutron scattering methods to show how such a multipolar-ordered phase emerges due to Fermi surface instability in CeB₆.

Magnetic field induced orbital polarization in cubic YbInNi4: determining the quartet ground state using x-ray linear dichroism

We have been able to induce a linear dichroic signal in the Yb M(5) x-ray absorption white line of cubic YbInNi(4) by the application of a magnetic field. The nonzero integrated intensity of the magnetic field induced dichroic spectrum indicates a net noncubic 4f orbital polarization. A quantitative analysis of the temperature and field strength dependence establishes that the crystal-field ground state is a Γ(8) quartet. The results demonstrate the potential of magnetic field induced linear dichroism as a new powerful approach for the investigation of the degeneracy and orbital degrees of freedom of cubic heavy-fermion and Kondo systems.

Temperature and field dependence of the order parameter in the antiferroquadrupolar phase of CeB6 from mu+ Knight shift measurements

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.

Field-induced magnetization distribution and antiferroquadrupolar order in CeB(6)

The anisotropic Knight shift of implanted positive muons (micro(+)) in CeB(6) has been studied between 2.2 and 200 K in a field of 0.6 T. The results imply that the field-induced magnetization distribution is not only found at the Ce sites but also in other regions of the unit cell (e.g., near or inside the B6 molecule, as proposed by Saitoh et al. [J. Phys. Soc. Jpn. Suppl. 71, 106-108 (2002)]). While above the antiferroquadrupolar ordering temperature T(Q) approximately 3.55 K this additional magnetization appears to be antiparallel to the Ce moments, a drastic change is observed below T(Q), and the additional magnetization is eventually aligned parallel to the Ce moments.