We present an extensive numerical study of a 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 $n=\frac{1}{2}$ and $\frac{2}{3}$. In particular, we show that an intriguing glassy magnetic state characterized by ordering wave vectors $\mathbf{q}=\left(\frac{1}{3},\frac{1}{3},1\right)$ gives a rather satisfactory description of the low-temperature phase recently observed in spinel ${\mathrm{GeFe}}_2{\mathrm{O}}_4$.

• Received 6 April 2018
• Revised 9 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.214423