${\mathrm{KCo}}_2{\mathrm{As}}_2$: A new portal for the physics of high-purity metals

High-quality single crystals of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ with the body-centered tetragonal ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$ structure were grown using KAs self flux. Structural, magnetic, thermal, and electrical transport properties were investigated. No clear evidence for any phase transitions was found in the temperature range 2–300 K. The in-plane electrical resistivity $\rho$ versus temperature $T$ is highly unusual, showing a $T^4$ behavior below 30 K and an anomalous positive curvature up to 300 K, which is different from the linear behavior expected from the Bloch-Grüneisen theory for electron scattering by acoustic phonons. This positive curvature has been previously observed in the in-plane resistivity of high-conductivity layered delafossites such as ${\mathrm{PdCoO}}_2$ and ${\mathrm{PtCoO}}_2$. The in-plane $\rho (T\to 0)=0.36\mu \mathrm{\Omega }$ cm of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ is exceptionally small for this class of compounds. The material also exhibits a magnetoresistance at low $T$ which attains a value of about 40% at $T=2$ K and magnetic field $H=80$ kOe. The magnetic susceptibility $\chi$ of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ is isotropic and about an order of magnitude smaller than the values for the related compounds ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ and ${\mathrm{BaCo}}_2{\mathrm{As}}_2$. The $\chi$ increases above 100 K, which is found from our first-principles calculations to arise from a sharp peak in the electronic density of states just above the Fermi energy $E_{\mathrm{F}}$. Heat capacity $C_{\mathrm{p}}\left(T\right)$ data at low $T$ yield an electronic density of states $N\left(E_{\mathrm{F}}\right)$ that is about 36% larger than predicted by the first-principles theory. The $C_{\mathrm{p}}\left(T\right)$ data near room temperature suggest the presence of excited optic vibration modes, which may also be the source of the positive curvature in $\rho \left(T\right)$. Angle-resolved photoemission spectroscopy measurements are compared with the theoretical predictions of the band structure and Fermi surfaces. Our results show that ${\mathrm{KCo}}_2{\mathrm{As}}_2$ provides a new avenue for investigating the physics of high-purity metals.

Figure 1

(a) Basal $ab$-plane electrical resistivity ${\rho }_{ab}$ of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ vs temperature $T$ from 2 to 300 K (red data). Also shown is the best fit of the data by the Bloch-Grüneisen (BG) model (black data). The residual-resistivity ratio (RRR) is $\rho$(300 K)/$\rho (T\to 0)$. The $\rho (T\to 0)$ was obtained from panel (b). The large RRR indicates high purity of the crystal measured. (b) Expanded plot of the data below 30 K (filled red circles), together with the fit by Eq. (1). The data below 30 K approximately follow a $T^4$ dependence as shown, instead of the $T^5$ dependence expected from the BG model.

Figure 2

(a) Natural logarithm of ${\rho }_{ab}\left(T\right)-{\rho }_0$ vs the natural logarithm of $T$ from 2 to 300 K [${\rho }_0$ is the residual resistivity at $T=0$ K from Fig. 1]. The nonlinear behavior shows that the temperature dependence $T^n$ does not have a $T$-independent exponent $n$ over this $T$ range. (b) The $T$ dependence of $n$ obtained from the data in (a) using Eq. (2) and also from a sliding derivative. The value $n\sim 4$ at 22 K, averaging over the scatter in the sliding derivative, agrees with the value of the exponent in the equation in Fig. 1; the source of the clear anomaly at 78 K in these data is unclear as yet.

Figure 3

(a) Basal $ab$-plane electrical resistivity ${\rho }_{ab}$ vs temperature $T$ of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ measured in two different magnetic fields $H=0$ and 8 T applied along the crystallographic $c$ axis. Inset: The ${\rho }_{ab}\left(T\right)$ at $H=0$ and 8 T for $T\le 50$ K. (b) Magnetoresistance ${(\mathrm{\Delta }\rho /\rho )}_{ab}$ vs $T$, where $\mathrm{\Delta }{\rho }_{ab}$ is the change in resistivity induced by an external 8 T magnetic field. The solid curve is a guide to the eye (c) ${(\mathrm{\Delta }\rho /\rho )}_{ab}$ vs $H$ measured at two different temperatures, $T=2$ and 25 K.

Figure 4

(a) Heat capacity $C_{\mathrm{p}}$ vs temperature $T$ of a single crystal of ${\mathrm{KCo}}_2{\mathrm{As}}_2$. (b) $C_{\mathrm{p}}/T$ vs $T$ (open circles), along with a fit of these data by Eq. (3) (black curve). The fitted parameters are listed. (c) The lattice contribution $C_{\mathrm{lattice}}$ vs $T$, obtained by subtracting the electronic $\gamma T$ contribution from the data in (a). The black curve a best fit of the data by the Debye model.

Figure 5

Magnetization divided by magnetic field $M/H$ vs temperature $T$ of a crystal of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ with the applied field $H=30$ kOe aligned in the $ab$ plane (open red circles) and along the $c$ axis (open blue squares). The data are seen to be nearly isotropic. A very good fit to the $M_{ab}/H$ vs $T$ data is obtained using Eq. (7) and is shown as the black curve. The parameters of the fit are given in the text.

Figure 6

Isothermal magnetization $M$ vs $H$ ($\parallel c$ axis) measured at six different temperatures. The data with decreasing temperatures are offset successively upwards by 1 G ${\mathrm{cm}}^3$/mol for clarity. The linear fits for $T=50$–300 K and $H=0$ to 55 kOe are shown as the straight lines, whereas the linear fits to the data for 5 and 10 K between 40 and 55 kOe are shown as the dashed lines with extrapolations to $H=0$. The linear fit parameters are given in Table 1.

Figure 7

Total density of states $N\left(E\right)$/f.u. versus energy $E$ (black line) in units of states/eV f.u. for both spin directions. The zero of energy is the Fermi energy. Also shown is the contribution from the Co $3d$ states (blue line).

Figure 8

Band Structure of ${\mathrm{KCo}}_2{\mathrm{As}}_2$. The points in the Brillouin zone are defined in Fig. 9. The top panel shows an overall view and the bottom panel shows an expanded plot below the Fermi energy.

Figure 9

Brillouin zone for the bct structure of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ with points in the Brillouin zone marked.

Figure 10

Fermi surfaces of ${\mathrm{KCo}}_2{\mathrm{As}}_2$, shown in perspective view, with $\mathrm{\Gamma }$ at the center and the zone edges indicated by white lines. The lower band is in the top panel and the upper band is in the lower panel. The shading is by velocity, ${\nabla }_{\mathbf{k}}E\left(\mathbf{k}\right)/\hslash$, where blue is lower velocity and green is higher velocity. The Fermi surfaces are electron-like. The lower band has an occupancy of 0.316 of the zone, while the upper band has an occupancy of 0.184 of the zone.

Figure 11

Transport function of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ versus temperature for electronic conduction (a) in the $ab$ plane and (b) along the $c$ axis.

Figure 12

Temperature dependence of the density of states at the Fermi level of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ in units of states/eV f.u. for both spin directions.

Figure 13

Calculated temperature dependence of the anisotropic Seebeck coefficient of ${\mathrm{KCo}}_2{\mathrm{As}}_2$ for heat transport along the $ab$ plane and along the $c$ axis as indicated.

Figure 14

Angle-resolved photoemission spectroscopy (ARPES) data on a ${\mathrm{KCo}}_2{\mathrm{As}}_2$ single crystal. (a) Intensity at the $E_{\mathrm{F}}$ integrated within 10 meV at $T=40$ K. (b) Same as in the panel (a) but measured at $T=100$ K. (c) Intensity along a momentum cut shown as the red dashed line in panel (a) measured at $T=40$ K. (d) Same as in panel (c), but measured at $T=100$ K. The arrows in panel (d) indicate energy locations of the band extrema of the three bands centered at $\mathrm{\Gamma }$.