Exchange interactions and magnetic anisotropy in the ‘Ni₄’ magnetic molecule

Abstract

The magnetic properties of the tetrahedral 'Ni 4 ' molecule are discussed in terms of the Heisenberg model, with magnetic anisotropy terms included, and on the basis of first-principle calculations within the density functional theory. It is shown that the isotropic Heisenberg model does not provide an adequate description of magnetization at low temperatures, and the inclusion of single-site anisotropy terms does not help to improve the situation. We assume that the magnetostriction of the molecule and, hence, the dependence of the interatomic coupling parameters on the magnetization may be important for an adequate description of the magnetic properties. The first-principle calculations confirm the system's general preference for antiferromagnetic coupling, as well as the failure of the isotropic Heisenberg model. A conjugated-gradient search for the relaxed structure of the 'Ni 4 ' molecule in ferromagnetic and antiferromagnetic configurations did not show any clear tendency to diversification of the interatomic distances. These calculations, however, have not yet included the spin-orbit coupling, which can be essential for analysing the effects of magnetostriction.

Observation of field-dependent magnetic parameters in the magnetic molecule{Ni4Mo12}

“…These excitations take place in both majority and minority channels according to recent DFT calculations. 33 The features above 3 eV are assigned as O p to Ni d charge transfer excitations. The energy range of our magneto-optical investigation is also shown in Fig.…”

Determination of spin Hamiltonian in the Ni4magnetic molecule

“…Distances between Ni 2+ ions within a cluster are 6.69, 6.70, 6.62, and 6.60Å, whereas the shortest distance between Ni 2+ ions that belong to different clusters is 7.15Å. Previous bulk property measurements using bulk susceptibility, high field magnetization, electron paramagnetic resonance, optical conductivity, and magneto-optical response [8][9][10] showed that the dominant interaction in the system is antiferromagnetic, which is due to the superexchange interaction through the Ni-O-Mo-ONi bonds. 9 The most interesting property of the Ni 4 nanaomagnet is an adiabatic change with non-equidistant steps observed in the magnetization measurements as a function of external magnetic field.…”

“…Previous bulk property measurements using bulk susceptibility, high field magnetization, electron paramagnetic resonance, optical conductivity, and magneto-optical response [8][9][10] showed that the dominant interaction in the system is antiferromagnetic, which is due to the superexchange interaction through the Ni-O-Mo-ONi bonds. 9 The most interesting property of the Ni 4 nanaomagnet is an adiabatic change with non-equidistant steps observed in the magnetization measurements as a function of external magnetic field. [9][10][11] This was explained by a model Hamiltonian that consists of a field-dependent exchange parameters, a single-ion anisotropy, and a biquadratic interaction.…”

“…9 The most interesting property of the Ni 4 nanaomagnet is an adiabatic change with non-equidistant steps observed in the magnetization measurements as a function of external magnetic field. [9][10][11] This was explained by a model Hamiltonian that consists of a field-dependent exchange parameters, a single-ion anisotropy, and a biquadratic interaction. 10 The spin Hamiltonian should be determined by a more direct tool than the bulk property measurements to check its validity.…”

“…In the calculation of χ balk , the geometrical factor was taken to be g = 2.22. [8][9][10][11] The background due to isolated Ni 2+ ions was estimated by the Curie law and added to the calculated χ bulk . The existence of the biquadratic terms in H indicates a spin-lattice coupling in this system.…”