New Type of the Domain-Redistribution at Low Magnetic Fields in Phase II of CeB6

We performed the detailed investigation of the magnetization ($M$) of CeB 6 at low magnetic fields in the $O_{xy}$-type antiferro-quadrupole (AFQ) ordered phase II to clarify the mechanism of the domain redistribution by magnetic field. Although $M$ in phase II is isotropic above ${\sim}1$ kOe, it is anisotropic at lower magnetic fields and the magnetic field of the domain redistribution ($H_{\text{c}}^{\text{IIA{\mbox{--}}IIB}}$) is highly anisotropic. $M^{[001]}H_{\text{c}}^{\text{IIA{\mbox{--}}IIB[111]}}$. Here, $M^{[001]}$ and $H_{\text{c}}^{\text{IIA{\mbox{--}}IIB[001]}}$ are $M$ and $H_{\text{c}}^{\text{IIA{\mbox{--}}IIB}}$ for $H\parallel[001]$, etc. respectively. Although there exist three domains of $O_{xy}$-, $O_{yz}$-, and $O_{zx}$-AFQ ordered states at $H=0$ as in a usual AF magnet, these domains are coupled in magnetic fields and the single domain state is formed by the linear combination of $O_{xy}$, $O_{yz}$, and $O_{zx}$ quadrupole moments above $H_{\text{c}}^{\text{IIA{\mbox{--}}IIB}}$ through the magnetic field induced higher order $T_{xyz}$-antiferro-octupole (AFO) interaction. The domain redistribution takes place due to the competition between the small tetragonal lattice distortion stabilized by the $O_{xy}$-type AFQ order at $H=0$ and the Zeeman interaction. For $H\parallel[001]$, $M$ is smallest and $H_{\text{c}}^{\text{IIA{\mbox{--}}IIB}}$ is highest because only the $O_{xy}$-domain couples with the $T_{xyz}$-AFO moment inducing the effective ferromagnetic interaction but the two domains of $O_{yz}$ and $O_{zx}$ are not. For $H\parallel[111]$, $M$ is largest below ${\sim}1$ kOe and $H_{\text{c}}^{\text{IIA{\mbox{--}}IIB}}$ is lowest because the $T_{xyz}$-AFO moment is induced in all the three domains and each of $O_{xy}$, $O_{yz}$, and $O_{zx}$ domain changes continuously to the $(O_{yz}+O_{zx}+O_{xy})/\sqrt{3}$ single domain with increasing magnetic field. The coefficients of the linear combination of three domains gradually changes with magnetic field through the magnetic field induced $T_{xyz}$-AFO moment. This type of the continuous domain redistribution is different from that in the usual antiferro-magnet, where there does not exist the coupling among the different domains.