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 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 Ni2+–Cu2+–Ni2+ trimer with realistic Hamiltonian. The calculated spin values 〈SNi〉 = 0.9 and 〈SCu〉 = 0.3 are within 10% accuracy in agreement with the experiment, providing a strong complementary argument in favor of a multi-arm magnetic structure.