Magnetic Field Effects in Charge-Ordered Mixed-Valence Trimeric Clusters

Abstract

PACS: 71.70.EjThe influence of the external magnetic field on the phase states of a crystal consisting of trimeric mixed-valence clusters is examined. The initial model takes into account the intracluster Heisenberg exchange, electron transfer, as well as the Zeeman and intercluster dipole-dipole interactions. The conditions are elucidated under which the external magnetic field facilitates or suppresses the charge-ordered state. The behaviour of the system in the magnetic field is shown to give information about the key parameters of charge-ordered crystals.

Electric‐Field Effects on Trimeric Mixed‐Valence Clusters

“…The main effects of an external electric field on isolated dinuclear clusters36,37 can be observed for field directions that coincide with the axis along which the cluster ions are connected. The expected effects are quite similar to those obtained in the theory of charge and structural ordering15–29 with the following differences: (1) For charge ordering, the dipole moment of the crystal vanishes at the phase‐transition temperature, whereas the mean dipole moment for an isolated MV cluster in an external electric field tends gradually and diffusely to zero as a function of temperature. (2) For a single cluster, the low‐temperature limits of the dipole and magnetic moments as well as the temperature dependence of these moments can be changed with the aid of external electric fields, whereas these characteristics in a crystal that demonstrates charge ordering are determined by the intrinsic parameters and show a unique dependence.…”

“…For trimeric systems, the effects of charge ordering and those of the external electric field are completely different. In charge‐ordered crystals, the dipole moments can only be aligned in three directions defined by the angles ϕ 1 = π/2, ϕ 2 = (7π)/6, and ϕ 3 = (11π)/6, which provide the minimum of the crystal free energy,28,29 whereas, for an isolated cluster placed in an external electric field, a nonvanishing polarizability can appear for different field directions. The examined MV clusters can be referred to as type II multiferroics for which the magnetic (electric) moment can be changed by an electric (magnetic) field.…”

“…The possibility to manipulate directly the magnetic properties with the aid of the electric ones can also be provided by mixed‐valence (MV) clusters. The idea that MV clusters (ions with different oxidation degrees joint in a molecular system) can be considered as multiferroic originates from experimental studies10–15 and theoretical modeling15–29 of the charge and structural ordering in crystals containing these clusters as structural units. The essence of the phenomenon of charge ordering consists of the following.…”

“…As the energy E dip is determined by the crystal structure,16,19 that is, by the distance between the ions in the MV cluster and the mutual arrangement of the clusters in the crystal, the probability to find MV cluster‐based crystals for which the above‐mentioned inequality holds is not very high. The conditions for the observation of charge ordering in compounds containing trimeric clusters are less trivial 28,29. However, like in the dimeric systems, the charge‐ordered phase in these systems appears when the electron tunneling is suppressed by dipole–dipole interactions, the strength of which is also limited by the crystal structure.…”