Theoretical Analyses of Spin Exchange Interactions in Extended Magnetic Solids Containing Several Unpaired Spins per Spi
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Theoretical Analyses of Spin Exchange Interactions in Extended Magnetic Solids Containing Several Unpaired Spins per Spin Site D. Dai, H.-J. Koo and M.-H. Whangbo* Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204 ABSTRACT For extended magnetic solids containing several unpaired spins per spin site, we reviewed briefly recent progress in quantitative and qualitative methods of describing their spin exchange interactions on the basis of electronic structure calculations for their spin dimers. INTRODUCTION In a magnetic field up to magnetic saturation, the magnetic energy states allowed for an extended magnetic solid may not have a gap (Fig. 1a) or may have a gap between the singlet ground state and the first excited state (i.e., a spin gap) (Fig. 1b) [1,2]. It is also possible that a magnetic solid has a spin gap as well as another gap in the middle of the excited states (Fig. 1c) (i.e., “mid-spin gap”) [3]. A spin gap causes the magnetic susceptibility to vanish below a certain low temperature, while either a spin gap or a midspin gap causes a plateau in the magnetization vs. magnetic field curve (i.e., magnetization plateau). For a Heisenberg chain of L spin sites per unit cell and spin S per spin site, a magnetization plateau is predicted to occur when the magnetization m per spin site satisfies the condition L(S - m) = integer [4]. In recent years magnetic solids with spin gaps and magnetic plateaus have received much attention.
Figure 1. Schematic diagrams showing the allowed magnetic energy states of an extended magnetic solid in a magnetic field up to magnetic saturation for the cases of (a) no forbidden energy gap, (b) a spin gap, and (c) a spin gap and a mid-spin gap.
GG5.3.1
Allowed magnetic states of a magnetic solid are described in terms of a spinHamiltonian written as a sum of pair-wise spin exchange interactions − J ij Sˆ i ⋅ Sˆ j between adjacent spin sites i and j. ( Sˆ and Sˆ are the spin operators at the sites i and j, i
j
respectively, and Jij is the spin exchange parameter associated with the spin exchange interaction between the two sites.) Thus a spin-Hamiltonian expresses low-energy excitation energies of a magnetic solid in terms of spin exchange parameters Jij. Experimentally these excitations are probed typically by measuring magnetic susceptibility as a function of temperature or neutron inelastic scattering at a very low temperature (e.g., ~10 K). When the temperature-dependent magnetic susceptibility or angle-resolved inelastic neutron scattering data are analyzed in terms of a spinHamiltonian, the Jij parameters act as numerical fitting parameters needed to reproduce the experimental data. What set of Jij parameters to employ in this fitting process depends on our perception of what spin exchange pathways are important for the magnetic solid under investigation. In principle, therefore, experimental data can be fitted equally well with more than one set of Jij parameters especially for magnetic solids of complex crystal structure. To rela
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