Magnetic field tuning of valley population in the Weyl phase of ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$

The frustrated magnet ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where strong correlations together with spin-orbit coupling play a crucial role, is predicted to be a Weyl semimetal and to host topological pairs of bulk Dirac-like valleys. Here we use an external magnetic field to manipulate the localized rare-earth 4f moments coupled to the 5d electronic bands. Low-energy optical spectroscopy reveals that a field of only a few teslas suffices to create charge-compensating pockets of holes and electrons in different regions of momentum space, thus introducing a valley population shift that can be tuned with the field.

Figure 1

Optical conductivity data. (a) Real part of the optical conductivity ${\sigma }_1$ as function of energy for different magnetic fields at $T=6$ K. The main field effects are red shift of the spectra and the increase of the Drude component. (b) Same as (a) but for low energy. DC conductivity data are presented as solid circles. Vertical dashed lines [(a) and (b)] mark the energy below which the fits are extrapolated outside our measured data range. (c) Temperature evolution of the relative reflectivity at $H=7\text{T}$. $R_0$ is the zero-field reflectivity and $\delta R=R\left(H\right)-R_0$. Above $T\approx 13$ K we are not able to detect any change with field. (d) Fits to the reflectivity data at 0 T (black) and 7 T (red) with Drude part taken as constant with field (blue).

Figure 2

Drude spectral Weight at $T=6$ K. The free charge carrier density doubles from 0 to 7 tesla, supporting the creation of charge compensated pockets. Antiferromagnetic domain walls exist until 2–3 tesla, as known from [14]. Error bars correspond to $1\%$ error of the reflectivity.

Figure 3

Simulation data. (a) Ir average magnetic moments as function of field. Black squares represent Ir pseudospin along the (1,1,1) field direction, whereas red circles represent the other three Ir's. (b) Illustration of the 4-in-0-out and 3-in-1-out configurations of the Nd moments. The Nd atoms reside on the tetrahedron's corners. (c) The first Brillouin zone with high symmetry points marked. (d) Illustration of two pairs of Weyl points for $H=7$ T in the $\mathrm{\Gamma }{L}_1{L}_2$ plane. Orange plane represents the chemical potential. Small holes and electrons pockets are seen in the two nonequivalent points $L_1$ and $L_2$. (e)–(h) Band structure along $\mathrm{\Gamma }{L}_1$ line for various fields, where a transition from Weyl semimetal to Weyl metal is clearly observed.

Figure 4

Simulated optical conductivity for $\mathbf{U}=\mathbf{1}.\mathbf{365}$ eV, ${\mathbf{c}}_{\mathbf{1}}=\mathbf{0}.\mathbf{026}$ eV, and ${\mathbf{c}}_{\mathbf{2}}=-\mathbf{0}.\mathbf{039}$ eV. The appearance of Drude spectral weight and an overall red shift of the spectra qualitatively match the experimental data. In order to match quantitatively, one needs $t_0=0.26$ eV, suggesting a factor of four mass renormalization of the 5d bands.

Figure 5

Specific heat data as function of magnetic field. The lines are the fits to data with single type 1 domain.

Figure 6

Exchange potential at the Nd sites.