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Influence of the biquadratic exchange interaction in the classical ground state magnetic response of the antiferromagnetic icosahedron

The icosahedron has a ground state magnetization discontinuity in an external magnetic field when classical spins mounted on its vertices are coupled according to the antiferromagnetic Heisenberg model. This is so even if there is no magnetic anisotropy in the Hamiltonian. The discontinuity is a consequence of the frustrated nature of the interactions, which originates in the topology of the cluster. Here it is found that the addition of the next order isotropic spin exchange interaction term in the Hamiltonian, the biquadratic exchange interaction, significantly enriches the classical ground state magnetic response. For relatively weak biquadratic interaction new discontinuities emerge, while for even stronger the number of discontinuities for this small molecule can go up to seven, accompanied by a susceptibility discontinuity. These results demonstrate the possibility of using a small entity like the icosahedron as a magnetic unit whose ground state spin configuration and magnetization can be tuned between many different non-overlapping regimes with the application of an external field.