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Mapping Analysis for a Spin Dimer

To gain insight into the meaning of the symmetric (or Heisenberg) spin exchange interaction, we consider a spin dimer consisting of two equivalent spin-1/2 spin sites, I and 2, with one electron at each spin site (24.7) [1,26]. The energy of the spin [Pg.745]

In principle, the spin at site (= 1,2) of the spin dimer can have either up-spin a or down-spin p state. For a single spin S= V2 and = 1/2 so that, in terms of the S, Sz) notations, these states are given by [Pg.746]

The eigenstates of Hspin allowed for the spin dimer are the singlet state S) and triplet state IT), [Pg.746]

Note that the broken-symmetry (or Neel) states, ot( 1) (2) and (l)a(2), interact through Hspin (see equation 24.17) to give the symmetry-adapted states S) and T). [Pg.746]

We evaluate the ener gies of T) and S), spin(7) and Espin(S), respectively, by using equation 24.17 to find spin(7) = —J/4 and spjn(S) = 3J/4. Thus the energy difference between the two states is given by [Pg.746]


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