Full propagation-vector star antiferromagnetic order in quantum spin trimer system Ca₃CuNi₂(PO₄)₄

Abstract

We show that the antiferromagnetic structure in the quantum spin trimer system Ca3CuNi2(PO4)4 is based on both arms of propagation vector k star {[, 0]} of the paramagnetic space group C2/c. The structure is generated by a symmetric direction of the order parameter of two dimensional irreducible representation of C2/c with one active magnetic mode and corresponds to the Shubnikov magnetic space group Ca2/c. We reveal the relation between representation analysis in the propagation vector formalism and Shubnikov symmetry. These types of multi-k structures are extremely rarely observed experimentally. To further prove the specific magnetic structure we have performed the calculations of the spin expectation values in the isolated Ni 2+ -Cu 2+ -Ni 2+ trimer with realistic Hamiltonian. The calculated spin values SNi = 0.9 and SCu = 0.3 are in 10% accuracy in agreement with the experiment, providing strong complimentary argument in favour of multi-arm magnetic structure.

Field-induced magnetic phase transitions and metastable states in Tb3Ni

“…It should be emphasized that the observed propagation vectors k 1 , k 2 , k 3 and k 4 apparently are not the arms of the single k-star since they are not related by the symmetry elements of the space group P nma. Thus the low temperature magnetic structure of Tb 3 Ni is not consistent with the multi-k scenario observed in numerous magnetic systems [38,40]. However, some of the observed propagation vectors still may be coupled and describe complicated magnetic structure with enlarged magnetic unit cell.…”