Electrostatic tuning of Kondo effect in a rare-earth-doped wide-band-gap oxide

As a long-lived theme in solid-state physics, the Kondo effect reflects the many-body physics involving the short-range Coulomb interactions between itinerant electrons and localized spins in metallic materials. Here we show that the Kondo effect is present in ZnO, a prototypical wide-band-gap oxide, doped with a rare-earth element (Gd). The localized 4$f$ electrons of Gd ions do not produce remanent magnetism, but interact strongly with the host electrons, giving rise to a saturating resistance upturn and negative magnetoresistance at low temperatures. Furthermore, the Kondo temperature and resistance can be electrostatically modulated using electric-double-layer gating with liquid ionic electrolyte. Our experiments provide the experimental evidence of tunable Kondo effect in ZnO, underscoring the magnetic interactions between localized and itinerant electrons and the emergent transport behaviors in such doped wide-band-gap oxides.

Figure 1

(a) XRD patterns of the pure and the Gd-doped ZnO thin films, indicating that the Gd-doped ZnO films have the single wurtzite structure with a (002) preferential orientation, and no impurity phase was observed for all samples. (b) Enlarged view of the ZnO (002) diffraction peaks. A shift of the diffraction peaks to low diffraction angles indicates that the $c$-axis lattice constant increases with the Gd concentration. (c) Gd-concentration dependence of the out-of-plane strain obtained from both the XRD data and the first-principles calculation. The tensile strain in the $c$ axis increases with the Gd concentration as a result of the larger atom radius of Gd.

Figure 2

Electric double-layer transistor (EDLT) with the undoped and the Gd-doped ZnO thin films as channels. (a) Schematic diagram of the EDLT with a drop of ionic liquid electrolyte, DEME-TFSI, covering the channel and the gate electrodes. As the channel, ZnO thin films were grown on $a$-plane sapphire substrates and patterned into Hall bars. (b) Schematic illustrating the charge accumulation at the interface between the liquid electrolyte and the oxide channel. The field-induced drift and distribution of cations, (CH${}_3$CH${}_2$)${}_2$(CH${}_2$CH${}_2$OCH${}_3$)CH${}_3$N${}^{+}$ (DEME), and anions, (CF${}_3$SO${}_2$)${}_2$N${}^{-}$ (TFSI), accomplish the electrostatic gating. (c),(d) Temperature dependence of channel resistances measured under various gate voltages ($V_{\mathrm{G}}$) for pure ZnO and 1.8 at. $\%$ Gd-doped ZnO, respectively. In the measurement sequence, increasing positive $V_{\mathrm{G}}$ was applied, and after the maximum $V_{\mathrm{G}}$ the R-T curve at $V_{\mathrm{G}}=0$ (circles) was remeasured; the almost complete overlap of the second zero-gate curve with the pristine one suggests negligible electrochemical reaction at the channel/electrolyte interface.

Figure 3

Transport and Kondo effect in the Gd-doped ZnO channel. (a) Temperature dependence of channel resistance at $V_{\mathrm{G}}=0$. Fitting to Eq. (1) (solid curve) gives parameters $R_0=17.07$ Ω, $q=1.01\times {10}^{-5}$ Ω/K${}^2$, $p=1.04\times {10}^{-11}$ Ω/K${}^5$, $R_{\mathrm{K}}$(0 K) $=$ 0.055 Ω, and $T_{\mathrm{K}}=22.01$ K. (b) Universal Kondo behavior of the normalized resistivity [$R$($T$)−$R_0$–$q{T}^2-p{T}^5$]/$R$(0) versus $T$/$T_{\mathrm{K}}$ measured at various $V_{\mathrm{G}}$. The red line illustrates the universal Kondo curve from the numerical renormalization-group calculation. (c) Temperature dependence of the channel resistance at $H=0$, 4, and 8 T. The magnetic field suppresses the Kondo resistance upturn at low temperatures. The inset shows the temperature-dependent data of the resistance modulation, i.e., $R$($T$)$-R$(10 K). (d) Negative magnetoresistance observed at $T=5$, 10, and 15 K.

Figure 4

Magnetic properties of Gd-doped ZnO. (a) Temperature dependence of magnetization of the 1.8 at. $\%$ Gd-doped ZnO thin film measured by SQUID under both the zero-field-cooled (ZFC) and field-cooled (FC) conditions. The solid curve shows the fitting to the Cure-Weiss law, indicating a paramagnetic behavior. The inset shows the M-H curve at 5 K. (b) XMCD data measured at 300 K shows no hysteresis, and it is consistent with the paramagnetic nature of the Gd-doped ZnO. The upper-left and bottom-right insets show the polarized x-ray-absorption spectra and the XMCD signals at the Gd $M_{4,5}$ edge ($H=4$ T), respectively. (c) Spin-resolved density of states calculated for the Gd${}_2$Zn${}_{34}$O${}_{36}$ system. The upper and lower panels show the total and partial density of states, respectively. The Fermi level lies in the conduction band and close to the Gd-$f$ level, indicating the energetic proximity between the conduction electrons and the local magnetic moments of Gd-$f$ orbital.

Figure 5

Gate-modulated Kondo effect in Gd-doped ZnO. (a) Temperature dependence of the normalized channel resistance, $R$($T$)−$R$(4 K), measured while applying various gate voltages. (b) Gate tuning of the Kondo temperature $T_{\mathrm{K}}$ and the upturn resistance $R$(4 K)−$R_{\min }$.

Figure 6

Temperature dependence of the conductivity of the 1.8 $\%$ Gd-doped ZnO. The red solid curve is the best fitting to Eq. (3). The fitting parameters are $F_{\sigma }=0.51$, $l=0.34$ nm, and $D=2.61\times {10}^{-8}$ m${}^2$/s. It is clear that the EEI does not dominate the transport character in Gd-doped ZnO.

Figure 7

Temperature and gate dependence of (a) the sheet carrier density $n_{\mathrm{sheet}}=-1/R_{\mathrm{H}}e$ and (b) the mobility μ, respectively.