Weak Kondo effect in the monocrystalline transition metal dichalcogenide $\mathrm{Zr}{\mathrm{Te}}_2$

Zr-Te compounds are an ideal platform to investigate novel electrical transport properties. Here we report the Kondo effect in single-crystalline ${\mathrm{ZrTe}}_2$. When $T<8$ K, ${\mathrm{ZrTe}}_2$ exhibits a $\log T$ dependence of resistivity, which may derive from three different mechanisms, including electron-electron interaction, weak localization, and Kondo effect. By measuring transport properties with magnetic field along different directions, the former two mechanisms were excluded. Isotropic negative magnetoresistance was extracted by subtracting different quadratic background signals caused by Lorentz force, which reveals the existence of a weak Kondo effect in this material.

Figure 1

(a) Side view and (b) top view of ${\mathrm{ZrTe}}_2$ crystal structure. (c) XRD pattern of ${\mathrm{ZrTe}}_2$ single crystal. The inset shows the photograph of a ${\mathrm{ZrTe}}_2$ single crystal on 1 $\times$ 1 mm grids.

Figure 2

(a) Temperature dependence of resistivity for ${\mathrm{ZrTe}}_2$. The red solid line indicates the fitting curve from 8 to 300 K using the Bloch-Grüneisen model. The inset shows the evolution of temperature derivative of the resistivity at low temperature in $\ln T$ scale. The red solid line represents a linear fit. (b) The enlarged part of resistivity with temperature from 2 to 12 K. The red and blue solid lines represent fittings using Hamann [Eq. (2)] and modified Hamann expressions [Eq. (3)], respectively. The inset shows enlarged parts of fitting curves in $T^2$ scale. The black dashed line is a guide for the eyes to show $T^2$ dependence. (c)–(e) Schematic drawing of the electrodes and relative directions between electric current and magnetic field. (f)–(h) Temperature dependence of resistivity from 2 to 20 K with magnetic field along different directions, as indicated in Figs. 2–2, respectively.

Figure 3

(a)–(c) Anisotropic magnetoresistance with magnetic field along different directions corresponding to Figs. 2–2, respectively. The inset of 3(a) shows the enlarged part of experimental data from $-3$ T to 3 T. (d)–(e) Anisotropic field dependence of magnetoresistance at 2 and 15 K, respectively. The solid lines represent quadratic fittings to experimental data from 6 to 9 T. (f) The comparison of magnetoresistance at 2 K (solid lines) and 15 K (dashed lines) with magnetic field along different directions.

Figure 4

(a) The enlarged part of ${\rho }_{xx}$ vs $B$ curves from −4 to 4 T. The solid lines are quadratic fittings. (b) Magnetic field dependence of resistivity after subtracting the residual resistivity and the quadratic part from Lorentz force. The remaining parts with magnetic field along different directions almost overlap with each other. The solid line represents quadratic fit. (c) The enlarged part of ${\rho }_{xx}$ vs $B$ curves from −4 to 4 T. The solid lines represent fittings using formula describing WL in 3D systems. (d) Magnetic field dependence of magnetoconductivity at 2 K. The solid lines are fittings by using the HLN formula. (e) The contributions from Kondo effect to MR at different temperatures. The solid lines represent quadratic fittings to experimental data from −1.5 to 1.5 T. (f) Temperature dependence of $S$ (left ordinate) and $S^{-1/2}$ (right ordinate) obtained from fittings of $\left|\mathrm{\Delta }MR\%\right|$ at low-field region. The solid lines are inversely quadratic (black) and linear (blue) fits, respectively.

Figure 5

(a)–(c) Magnetic field dependence of the square root of $\left|\mathrm{\Delta }MR\%\right|$ at 2, 2.5, and 3 K, respectively. The solid lines represent Brillouin fittings with different $S$ values. (d) Square root of $\left|\mathrm{\Delta }MR\%\right|$ as a function of $B/T$. The solid lines are Brillouin fittings with $S$ = 1/2, 1, and 3/2, respectively.

Figure 6

Angle dependence of resistivity at different magnetic fields, the directions of which rotate (a) out of plane and (b) in $ab$ plane. The solid lines are fitting curves using $\rho$ = $A$ ${\cos }^2\alpha$.