Frustrated Kondo chains and glassy magnetic phases on the pyrochlore lattice

We present an extensive numerical study of a new type of frustrated itinerant magnetism on the pyrochlore lattice. In this theory, the pyrochlore magnet can be viewed as a cross-linking network of Kondo or double-exchange chains. Contrary to models based on Mott insulators, this itinerant magnetism approach provides a natural explanation for several spin and orbital superstructures observed on the pyrochlore lattice. Through extensive Monte Carlo simulations, we obtain the phase diagrams at two representative electron filling fractions $n = 1/2$ and 2/3. In particular, we show that an intriguing glassy magnetic state characterized by ordering wavevectors $\mathbf q = \left( \frac{1}{3},\frac{1}{3}, 1\right)$ gives a rather satisfactory description of the low temperature phase recently observed in spinel GeFe$_2$O$_4$.