Magnetic Structure and Quadrupolar Order Parameter Driven by Geometrical Frustration Effect in NdB₄

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Neutron diffraction experiments have been carried out to characterize the magnetic structures and order parameters in an intermediate phase of NdB4 showing the successive phase transitions at T0 = 17.2 K, TN1 = 7.0 K, and TN2 = 4.8 K. We have revealed the antiferromagnetic ordering with the propagation vectors \(\textbf{q}_{0} = (0,0,0)\), q0 and \(\textbf{q}_{\text{s}1} = (\delta ,\delta ,0.4)\) (δ ∼ 0.14), and q0 and \(\textbf{q}_{\text{s}2} = (0.2,0,0.4)\) in phase II (TN1 < T < T0), phase III (TN2 < T < TN1), and phase IV (T < TN2), respectively. The observed patterns in phase II are successfully explained by postulating a coplanar structure with static magnetic moments in the tetragonal ab-plane. We have found that the magnetic structure in phase II can be uniquely determined to be a linear combination of antiferromagnetic “all-in/all-out”-type (Γ4) and “vortex”-type (Γ2) structures, consisting of a Γ4 main component (77%) with a small amplitude of Γ2 (23%). We propose that the quadrupolar interactio...

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