Magnetic cluster excitations

Abstract

Magnetic clusters, i.e., assemblies of a finite number (between two or three and several hundred) of interacting spin centers which are magnetically decoupled from their environment, can be found in many materials ranging from inorganic compounds, magnetic molecules, artificial metal structures formed on surfaces to metalloproteins. The magnetic excitation spectra in them are determined by the nature of the spin centers, the nature of the magnetic interactions, and the particular arrangement of the mutual interaction paths between the spin centers. Small clusters of up to four magnetic ions are ideal model systems to examine the fundamental magnetic interactions which are usually dominated by Heisenberg exchange, but often complemented by anisotropic and/or higher-order interactions. In large magnetic clusters which may potentially deal with a dozen or more spin centers, the possibility of novel many-body quantum states and quantum phenomena are in focus. In this review the necessary theoretical concepts and experimental techniques to study the magnetic cluster excitations and the resulting characteristic magnetic properties are introduced, followed by examples of small clusters demonstrating the enormous amount of detailed physical information which can be retrieved. The current understanding of the excitations and their physical interpretation in the molecular nanomagnets which represent large magnetic clusters is then presented, with an own section devoted to the subclass of the singlemolecule magnets which are distinguished by displaying quantum tunneling of the magnetization. Finally, some quantum many-body states are summarized which evolve in magnetic insulators characterized by built-in or field-induced magnetic clusters. The review concludes addressing future perspectives in the field of magnetic cluster excitations.

Magnetic properties of a classical XY spin dimer in a “planar” magnetic field

“…Starting with a dimer system also makes sense since such a system represents an important building block for more complicated spin dimerized structures. Dimer systems under a variety of conditions ranging from classical to quantum regimes have always drawn great interest with the majority of studies treating the spin variables as 3D vectors [13][14][15][16][17] . However, recent progress in nano-fabrication techniques has made possible the fabrication of ultra-small spin systems where the spin motion is further confined to a two-dimensional (2D) space.…”

Combined use of translational and spin-rotational invariance for spin systems

“…The knowledge of exact quantum numbers such as S, M , and k provides such benefits for instance in spectroscopic experiments as, for instance, inelastic neutron scattering (INS), where selection rules can be inferred. [66][67][68] The method also complements other existing exact methods, in particular Bethe ansatz methods. These work for isotropic nearest-neighbor interactions of arbitrary spin s, [69][70][71][72][73] but only for certain linear combinations of powers of s ∼ i · s ∼ i+1 .…”

The Lagrange variety approach applied to frustrated classical wheels

“…Ring-shaped magnetic molecules play an important role due to possible realization of single molecule magnets or molecular qubits [1][2][3][4][5][6]. Moreover, these, with an odd number of spins and dominant antiferromagnetic couplings, are interesting subjects in the study of the spin frustration [7][8][9][10][11][12][13][14].…”