A general procedure to evaluate many-body spin operator amplitudes from periodic calculations: application to cuprates

Ibério de P R Moreira, Carmen J Calzado, Jean-Paul Malrieu, Francesc Illas
2007 New Journal of Physics  
A general procedure is presented which permits the form of an extended spin Hamiltonian to be established for a given magnetic solid and the magnitude of its terms to be evaluated from spin polarized, Hartree-Fock or density functional calculations carried out for periodic models. The computational strategy makes use of a general mapping between the energy of pertinent broken-symmetry solutions and the diagonal terms of the spin Hamiltonian in a local representation. From this mapping it is
more » ... s mapping it is possible to determine not only the amplitude of the well-known two-body magnetic coupling constants between near-neighbor sites, but also the amplitudes of four-body cyclic exchange terms. A scrutiny of the on-site spin densities provides additional information and control of the many broken-symmetry solutions which can be found. The procedure is applied to the La 2 CuO 4 , Sr 2 CuO 2 F 2 , Sr 2 CuO 2 Cl 2 and Ca 2 CuO 2 Cl 2 square lattices and the SrCu 2 O 3 ladder compound. It is shown that a proper description of the magnetic structure of these compounds requires that two-and four-body terms are explicitly included in the spin Hamiltonian. The implications for the interpretation of recent experiments are discussed. Phase Energy expression Values in SrCu 2 O 3 AFM9 J l /6 + J r /6 − 3J d /2 − 0.05J ring 44.98 (57.15) [10.79] AFM8 J l /4 − J d /4 + J i /8 31.92 (48.85) [6.86] AFM7 J l /2 − J d /2 + J i /4 67.38 (96.23) [14.23] AFM6 J l /2 − J d /2 − J i /4 83.78 (114.37) [18.53] AFM5 J l /4 + J r /8 − J d /4 − J i /8 − 0.075J ring 57.68 (75.75) [13.35] AFM4 J r /4 − J d /2 38.87 (50.22) [8.14] AFM3 J l /4 + J r /8 − J d /4 − 0.075J ring 53.43 (70.73) [12.24] AFM2 J r /8 − J d /4 16.20 (20.41) [4.07] AFM1 J l /8 + J r /16 − J d /8 − 0.0375J ring 26.68 (35.39) [6.15] AFM gs 0 0.0 (0.0) [0.0] Table 4. Numerical values (in meV) for the two-and four-body exchange amplitudes in SrCu 2 O 3 ladder compound obtained using the Fock-35, (B3LYP), and [UHF] potentials. Available experimental data are discussed in sections 1 and 4. System J l J r J d J i J ring J ring /J r
doi:10.1088/1367-2630/9/10/369 fatcat:na2idno4srd2rg2w4aoukxr3nq