Magnetic and quadrupole coupling emerging in NdB4 with geometrically frustrated orthogonal antiferromagnetic dimer...

Unusual successive order in NdB4 with the frustrated Shastry-Sutherland lattice was investigated by means of inelastic neutron scattering. We found that the pseudoquartet with |±5/2⟩ and |±7/2⟩ in the paramagnetic state splits into four levels in the magnetically ordered states. The observed spectra are in good agreement with the 𝑓-electron states obtained from the on-site Hamiltonian with the magnetic interaction ⟨𝐽𝑥⟩⁢𝐽𝑥, the coupling of 𝐽𝑥 with quadrupole 𝑂𝑧⁢𝑥, and the crystalline electric field potential. The 𝑓-electron states reproduce the temperature dependences of the in-plane moment 𝑚⊥=⟨𝐽𝑥⟩, which is the primary order parameter, and a weakly induced 𝑚𝑐=⟨𝐽𝑧⟩ as the secondary order parameter. The magnetic-quadrupole coupling emerges and plays an essential role under the geometrical frustration, where the Heisenberg interactions are canceled out.