Hall effect measurements and electronic structure calculations on ${\text{YbRh}}_2{\text{Si}}_2$ and its reference compounds ${\text{LuRh}}_2{\text{Si}}_2$ and ${\text{YbIr}}_2{\text{Si}}_2$

We report experimental and theoretical investigations of the Hall effect in ${\text{YbRh}}_2{\text{Si}}_2$ and its reference compounds ${\text{LuRh}}_2{\text{Si}}_2$ and ${\text{YbIr}}_2{\text{Si}}_2$. Based on band-structure calculations we identify two bands dominating the Hall coefficient in all these compounds. For the case of ${\text{LuRh}}_2{\text{Si}}_2$—the nonmagnetic reference compound of ${\text{YbRh}}_2{\text{Si}}_2$—the temperature dependence of the Hall coefficient is described quantitatively to arise from two holelike bands. For ${\text{YbIr}}_2{\text{Si}}_2$ and ${\text{YbRh}}_2{\text{Si}}_2$, renormalized band calculations yield two bands of opposite character. In ${\text{YbRh}}_2{\text{Si}}_2$ these two bands almost compensate each other. We present strong indications that sample dependences of the low-temperature Hall coefficient observed for ${\text{YbRh}}_2{\text{Si}}_2$ arise from slight variations in the relative scattering rates of the two bands. Minute changes in the composition appear to be the origin. The results of our band-structure calculations reveal that a transition of the $4f$ electrons from localized to itinerant leads to a decrease in the Hall coefficient.

Figure 1

${\text{YbRh}}_2{\text{Si}}_2$: electronic bands along symmetry lines with the Fermi energy $E_{\text{F}}=0$ chosen as reference energy. The $\text{Yb}4f$ electrons are treated as part of the ion core. We follow the notation of Ref. 38 using the labels Z (0,0,1), $\Gamma$ (0,0,0), X (1,1,0), P (1,1,1), and N $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ in units of $\left(\frac{\pi }{a},\frac{\pi }{a},\frac{\pi }{a}\right)$. The labels s, f, and u refer to $\left(\tilde{a},0,0\right)$, $\left(\tilde{b},0,2\right)$, and $\left(\tilde{b},\tilde{b},2\right)$, respectively, with $\tilde{a}=1+{\left(\frac{a}{c}\right)}^2$ and $\tilde{b}=1-{\left(\frac{a}{c}\right)}^2$.

Figure 2

(Color online) ${\text{YbRh}}_2{\text{Si}}_2$: comparison of the total DOS in the local-moment regime ($f$-core calculation, solid line) and in the heavy-Fermi-liquid regime (RBC, red shaded area). The reference energy is the Fermi energy $E_{\text{F}}=0$. The two bands in the low-energy part are derived from the $\text{Si}s$ states. The dominant features are the $\text{Rh}4d$ bands which hybridize with $\text{Si}p$ and $\text{Rh}s$ states near the bottom of the $d$ bands and with $\text{Si}d$ and $\text{Rh}p$ states near the top, respectively.

Figure 3

Dispersion of the renormalized bands along symmetry lines for ${\text{YbRh}}_2{\text{Si}}_2$ (upper panel) and ${\text{YbIr}}_2{\text{Si}}_2$ (lower panel). The anisotropy of the CEF ground state leads to highly anisotropic hybridization strength which affects the relative shifts and the widths of the bands. The topology of the Fermi surfaces is mainly determined by the steep conduction bands. The symmetry of the CEF ground state is reflected in effective-mass anisotropies. The coordinates of the symmetry points Z, $\Gamma$, X, P, and N are specified in the caption of Fig. 1

Figure 4

Quasiparticle DOS for ${\text{YbRh}}_2{\text{Si}}_2$ in the renormalized band-structure calculation. For a comparison with the DOS plotted in Fig. 1 consider the different scales.

Figure 5

Calculated Fermi surfaces of ${\text{YbRh}}_2{\text{Si}}_2$: major sheets of the Fermi surface in the $f$-core calculation representing the local-moment regime (top row) and the heavy-fermion regime (bottom row). In addition to the donut (left panel) and the jungle gym (right panel) there is a small electron surface (pill box) which is not displayed here. The topology of the Fermi surface agrees well with previous findings (Refs. 16, 19, 44, 45).

Figure 6

(Color online) (a) Temperature dependence of the linear-response Hall coefficient $R_{\text{H}}$ of ${\text{LuRh}}_2{\text{Si}}_2$. The inset displays the resistivity of ${\text{LuRh}}_2{\text{Si}}_2$ as a function of temperature. Solid lines represent the simulated data according to the two-band model described by Eqs. (10, 11, 12, 13, 14, 15), using the parameters specified in Table (see text). Dashed line in the inset denotes the electrical resistivity calculated on the basis of a measured phonon spectrum (Ref. 41). Adding the experimentally determined residual resistivity ${\rho }_{\text{R}}=1.2\mu \Omega \text{cm}$ in accordance with Eq. (14) yields a precise match with the measured data. (b) sketches the setup.

Figure 7

Initial-slope Hall coefficient $R_{\text{H}}$ of ${\text{YbIr}}_2{\text{Si}}_2$. The arrow marks the temperature below which LFL behavior was observed (Ref. 33). Inset displays the temperature dependence of the resistivity.

Figure 8

(Color online) Temperature dependence of the Hall coefficient for different samples of ${\text{YbRh}}_2{\text{Si}}_2$. See Table for legend. Results for samples of the same batch are shown in identical color. Arrow indicates the Néel temperature. Inset displays the resistivity of two selected crystals.