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

Abstract

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...