Magnetic Rare-Earth Ion Doping Effect on Phase IV of CexLa1-xB6
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Recently, the importance of the orbital degrees of freedom (the multipole moment) has been clarified in the f-electron systems. In particular, the multipole ordering that the multipole moment orders spontaneously have been intensively studied because of the appearance of the unusual behaviors which have not known.
Recently, many compounds showing the multipolar ordering have been discovered. CeB6 is one of the most famous compound which has been studied since 40 years ago. CeB6 is the first example in which the octupole interaction is verified to play an essential role in the unusual antiferro-quadrupole (AFQ) ordered phase. CeB6 shows the AFQ order at TQ=3.3 K, the antiferro (AF) magnetic order at TN = 2.3 K. These two phases are called as phases II and III, respectively. The paramagnetic phase is called as phase I. The unusual behaviors of this compound originate from the coexistence and competition of the different kinds of the interactions, i.e., Oxy-type AFQ, Txyz-AF octupolar (AFO), and AF magnetic interactions. Recently, a possibility of the pure octupolar ordering was pointed out in NpO2. The physics of the octupolar ordering is the exciting theme in the f-electron systems.
In the course of the study of CexLa1-xB6, a new phase called as phase IV was discovered. Phase IV exhibits the following unusual features. The magnetic susceptibility exhibits a peak at the IV-I transition temperature, TIV-I. The elastic constant of the C44 mode exhibits a large softening in phase IV The magnetoresistance in phase IV is very small. Although the intensive studies by the neutron diffraction, NMR and μSR are performed, the evidence of the magnetic ordering could not be obtained. However, the recent resonant X-ray diffraction indicated that the long-range order(LRO) with Q = (1/2 1/2 1/2) is realized in phase IV. Soon after their discovery of the LRO in phase IV, Kusunose and Kuramoto were able to explain their results by assuming the Γ5u-type AFO order. Thus, the Γ5u-type AFO ordering is said to be a strong candidate for the LRO in phase IV.
Although the Γ5u-type AFO ordering is the most plausible candidate for the LRO in phase IV, there exist the difficulties which remain to be explained by the Γ5u-type AFO ordering. Thus, the order parameter of phase IV is still controversial and further studies are necessary to clarify its nature.
In order to obtain the information on the order parameter of phase IV, we have studied CexRyLa1-x-yB6 (x = 0.7, 0.65, 0.6, 0.5 and 0.4) with R = Pr and Nd up to y = 0.1. Although for x > 0.6 TIV-I shows a small y dependence, TIV-I for x < 0.5 shows a drastic enhancement by Pr and Nd doping. The results for x < 0.5 indicate that the order parameter in phase IV for x < 0.5 is coupled with the magnetic dipole moment of Pr and Nd ions. The ground state of the Γ5u-type AFO ordered phase which is the nonmagnetic singlet cannot be coupled with the magnetic dipole moment of R ions. Thus, the present results strongly suggest that phase IV is different from the Γ5u-type AFO ordering at least for x < 0.5.
We have also carried out the mean field calculation for the two-sublattice model in which the Oxy-AFQ, Txyz-AFO, Γ5u-type AFO, and AF exchange interactions are taken into account and discussed the effect of the above three interactions on the Γ5u-type order. The magnetic phase diagram obtained by the calculation seems to reproduce those of CexLa1-xB6. However, a peak of the magnetic susceptibility which is one of the most characteristic properties in phase IV disappears easily by introducing the Oxy-AFQ interaction as a result that which is because the Oxy-FQ order accompanied with the Γ5u-AFO order is easily suppressed by the Oxy-AFQ interaction. Thus, it seems to be difficult to explain the overall properties in this system with phase IV by Γ5u-AFO model.
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