Phase Competition in the Double-Exchange Model on the Frustrated Pyrochlore Lattice

Competition between the ferromagnetic double-exchange interaction and the superexchange antiferromagnetic interaction is theoretically studied in the presence of geometrical frustration. As the superexchange interaction increases, the ferromagnetic metal becomes unstable and is taken over by a cooperative paramagnetic metal, in sharp contrast to a discontinuous transition to the antiferromagnetic insulator in the absence of frustration. In the critical region, the system exhibits a peculiar temperature-independent behavior with highly incoherent transport, suggesting a large residual entropy at low temperatures. We discuss the relevance of the results to the pressure-induced behaviors in Mo pyrochlore oxides [S. Iguchi et al., Phys. Rev. Lett. 102, 136407 (2009)].

Figure 1

Phase diagram of the pyrochlore double-exchange model at quarter filling. FM, PS, PM, and CPM represent ferromagnetic metal, phase separation, paramagnetic metal, and cooperative paramagnetic metal, respectively. Closed symbols represent the phase transition boundaries, while open ones indicate the magnitude of Curie-Weiss temperature. The lines are guides for the eye. The inset shows the cubic unit cell of the pyrochlore lattice. The dotted bond shows an example of the 1D chain for the calculations of the spin correlation in Fig. 3.

Figure 2

Temperature dependences of (a) the squared magnetic moment and (b) the inverse of the uniform magnetic susceptibility. (c) Curie-Weiss temperature estimated from the fitting of $\chi$ for various system sizes $N_s$. (d) Temperature dependence of the uniform magnetic susceptibility for large $J_{\mathrm{AF}}$. In (a), (b), and (d), circles and crosses are the data for $N_s=128$ and 64, respectively.

Figure 3

Spin correlation $⟨{\mathbf{S}}_i·{\mathbf{S}}_j⟩$ along the 1D chains in the pyrochlore structure (see the inset of Fig. 1) as a function of distance (measured in unit of the nearest-neighbor bond length). The data are for $N_s=128$.

Figure 4

(a)–(c) Density of states and (d)–(f) optical conductivity. The data are for $N_s=128$.

Figure 5

Temperature dependences of (a) the internal energy, (b) the kinetic energy, and (c) the SE energy per site. Circles and crosses represent the data for $N_s=128$ and 64, respectively. In (a), arrows indicate inflection points which correspond to the transition to FM state (see text).