Symmetry breaking via hybridization with conduction electrons in frustrated Kondo lattices

In frustrated magnets when magnetic ordering is suppressed down to low temperature, the formation of a quantum spin liquid becomes a possibility. How such a spin liquid manifests in the presence of conduction electrons is a question with potentially rich physical consequences, particularly when both the localized spins and conduction electrons reside on frustrated lattices. We propose a mechanism for symmetry breaking in systems where conduction electrons hybridize with a quantum spin liquid through Kondo couplings. We apply this to the pyrochlore iridate ${\text{Pr}}_2$${\text{Ir}}_2$${\text{O}}_7$, which exhibits an anomalous Hall effect without clear indications of magnetic order. We show that hybridization between the localized Pr pseudospins and Ir conduction electrons breaks some of the spatial symmetries, in addition to time-reversal symmetry, regardless of the form of the coupling. These broken symmetries result in an anomalous Hall conductivity and induce small magnetic, quadrupolar, and charge orderings. Further experimental signatures are proposed.

Figure 1

(a) Crystal structure of ${\text{Pr}}_2$${\text{Ir}}_2$${\text{O}}_7$. (b) Illustration of flux pattern induced from the local basis rotation, with spin-dependent parts ignored for clarity.

Figure 2

Hybridization form factor ${(-1)}_{r,r^{\prime }}{\gamma }_{r{r}^{\prime }}^z$ for ${\Gamma }_{5u}$ and ${\Gamma }_{6u}$ intermediate states, where $+1$ is shown in blue and $-1$ in red. Explicit form factors for the hexagon in each $\left[111\right]$ plane are shown alongside, oriented so that the local $\widehat{x}$ axis at the central site is ${60}^{\circ }$ from the vertical.

Figure 3

(a) The band structure of the uniform Ansatz for $E=2\chi =0.1$. (b) The phase diagram considering triplet extensions to both the monopole and uniform Ansätze.

Figure 4

The AHE coefficient (a) and net magnetization (b) along the $\left[111\right]$ direction for several values of $E$ as functions of $V$, with $t_2/t_1$ fixed at $0.1$ and $\chi /E=0.5$. The pattern of local magnetic and quadrupolar moments on the Pr (c) and of local magnetic moments on the Ir (d).