Abstract
Neutron polarization analysis has been carried out in order to clarify the magnetic structures of multiple order parameter f-electron system NdB4. We confirmed the noncollinear “all-in all-out” structure (Γ4) of the in-plane moment, which is in good agreement with our previous neutron powder diffraction study. We found that the magnetic moment along the c-axis mc showed diagonally antiferromagnetic structure (Γ10), inconsistent with previously reported “vortex” structure (Γ2). The microscopic mixture of these two structures with →q0=(0,0,0) appears in phase II and remains stable in phases III and IV, where an incommensurate modulation coexists. The unusual magnetic ordering is phenomenologically understood via Landau theory with the primary order parameter Γ4 coupled with higher-order secondary order parameter Γ10. The magnetic moments were estimated to be 1.8±0.2 and 0.2±0.05μB at T=7.5K for Γ4 and Γ10, respectively. We also found a long-period incommensurate modulation of the →q1=(0,0,1/2) antiferromagnetic structure of mc with the propagation →qs1=(0.14,0.14,0.1) and →qs2=(0.2,0,0.1) in phase III and IV, respectively. The amplitude of sinusoidal modulation was about mc=1.0±0.2μB at T=1.5 K. The local (0,0,1/2) structure consists of in-plane ferromagnetic and out-of-plane antiferromagnetic coupling of mc, opposite to the coexisting Γ10. The mc of Γ10 is significantly enhanced up to 0.6μB at T=1.5 K, which is accompanied by the incommensurate modulations. The Landau phenomenological approach indicates that the higher-order magnetic and/or multipole interactions based on the pseudoquartet f-electron state play important roles.
