Glassy spin density wave states and frustrated Kondo chains on the pyrochlore lattice

We investigate the spin density wave (SDW) states in frustrated pyrochlore lattice with degenerate orbitals. The directional nature of $t_{2g}$ orbitals leads to a highly anisotropic electron conduction. In the leading order approximation, the pyrochlore magnet can be viewed as a cross-linking network of Kondo or double-exchange chains. In contrast to models based on Mott insulators, this itinerant magnetism approach provides a natural explanation for several spin and orbital superstructures observed in pyrochlore lattice. Here we show that a novel commensurate multiple-$\mathbf q$ SDW order characterized by Bragg peaks at $\langle \frac{1}{3},\frac{1}{3}, 1\rangle$ wavevectors is stabilized at low temperatures when the $t_{2g}$ band is $1/3$ or $2/3$ filled. Interestingly, the SDW phase exhibits a large number of quasi-degenerate meta-stable states. Through extensive Monte Carlo simulations, we provide strong evidence for the glassy nature of this SDW state. Finally, our results successfully describes the recent experimental observations on spinel GeFe$_2$O$_4$. \footnote{T. Zhou {\em et al.} APS March Meeting 2016, Abstract K5.00009}