Carrier-mediated Kondo effect and Hall mobility by electrolyte gating

PHYSICAL REVIEW B 90, 205107 (2014)

Carrier-mediated Kondo effect and Hall mobility by electrolyte gating in slightly doped anatase TiO2 films Yin-Long Han,* Zhong-Zhong Luo,* Cheng-Jian Li, Sheng-Chun Shen, Guo-Liang Qu, Chang-Min Xiong, Rui-Fen Dou, Lin He, and Jia-Cai Nie† Department of Physics, Beijing Normal University, Beijing 100875, People’s Republic of China (Received 27 May 2014; revised manuscript received 26 September 2014; published 4 November 2014) Carrier density (ns ) is a crucial parameter that governs the properties of correlated oxides, so the field-effect approach is an ideal tool to investigate the novel physics of the system. Here, the carrier-mediated transport of slightly doped anatase TiO2 epitaxial films were studied by electric double layer transistor (EDLT) gating. The ns has been increased hugely, and concomitantly, the channels of anatase TiO2 films undergo an insulator-metal transition with a decrease in resistivity by almost three orders of magnitude. More fascinating, the Kondo effect depends very strongly on ns , and the Hall mobility could be enhanced about one order of magnitude with increasing ns . This study shows that EDLT gating is a powerful method to stimulate and mediate novel phenomena of correlated oxides. DOI: 10.1103/PhysRevB.90.205107

PACS number(s): 72.20.−i

I. INTRODUCTION

Modulating the properties and functionalities of materials has been a long-term theme for both fundamental study and device design. Carrier density (ns ) is a key parameter of the electronic state of condensed matter. Modulation of ns not only changes the conductivity, but also can greatly modify the fundamental electronic properties of materials [1,2]. The most common method to modulate the ns is chemical doping, which is successful but always introduces much disorder. Another alternative is electrostatic doping through a field-effect transistor (FET) structure. Especially, the electric double layer transistor (EDLT) [3,4], utilizing a liquid electrolyte instead of a conventional solid gate insulator, has been developed as a powerful device structure allowing accumulation of sufficiently high charge density (> 1014 cm−2 ) to stimulate a novel exotic phase which is difficult for a conventional FET [4–6]. Transition-metal oxides, which have been regarded as one of the most promising materials for next-generation electronics devices, exhibit many novel physics and intriguing functionalities as a function of ns , especially at higher ns (> 1014 cm−2 ), which could be easily achieved by using an EDLT rather than a conventional FET [6]. For example, SrTiO3 (STO) could undergo transitions from band insulator to semiconductor and further to metal as ns increases, more attractively, Kondo effect [7,8], superconductivity [3], ferromagnetism [9,10], and anomalous Hall effect [11] could emerge in STO by EDLT gating. Anatase TiO2 is a band insulator with almost the same band gap of ∼ 3.2 eV and a similar electric structure to that of STO. The electrical properties of both TiO2 and STO are mainly determined by their degenerate 3d orbitals of Ti induced by the crystalline field of the Ti-O octahedron. Therefore, abundant fascinating physics induced by EDLT gating as STO does may be expected in anatase TiO2 . However, studies on anatase TiO2 using the EDLT method have been limited in number [12].

* †

These authors contributed equally to this paper. [email protected]

1098-0121/2014/90(20)/205107(6)

In this study, the ns of slightly doped anatase TiO2 epitaxial films have been modulated hugely from ∼ 5.0 × 1013 to ∼ 1.5 × 1015 cm−2 by EDLT gating. Concomitantly, the channels of anatase TiO2 films undergo a transition from a lowconductivity semiconductor to a high-conductivity metal with a decrease in resistivity by almost three orders of magnitude. More fascinatingly, the Kondo effect exhibits very strong dependence on ns indicating the widely tunable coupling of conduction electrons to local magnetic moments in anatase TiO2 , and the Hall mobility could be enhanced about one order of magnitude.

II. EXPERIMENT

Pure anatase TiO2 is an insulator, and it is very hard to carry out the field-effect gating measurement. Therefore, slight doping in the anatase TiO2 could provide some carriers to develop the conductivity which is helpful for the field-effect gating measurement. In our sets of experiments, the films of anatase TiO2 are slightly doped by Nb (Nb:TiO2 ) or fabricated in a little lower oxygen pressure in order to get slightly oxygen-deficient TiO2−δ . Epitaxial films of anatase Nb:TiO2 were fabricated on a STO (001) substrate in 2 × 10−5 Torr of O2 by pulsed laser deposition, whereas the anatase TiO2−δ samples were fabricated in 5 × 10−6 Torr of O2 . The substrate temperature was held at 700 °C. The laser pulses were supplied by a KrF excimer source (λ = 248 nm) with an energy density of 1.5 J/cm2 and a frequency of 2 Hz. X-ray diffraction patterns indicated that all the films were epitaxial with single phase anatase character and (00l) orientation (data not shown). Nominal thickness of the films was about 50 nm, which was determined by an atomic force microscope and the calibrated growth rate. The same preparation method of anatase TiO2 films had been reported in our other paper [13]. And all the reagents were used in ultrahigh purity with an impurity content of less than 0.01%; the extrinsic magnetic pollution in our samples can be excluded. In our EDLT gating experiments, both the 0.3 at. % Nb-doped TiO2 (Nb0.003 Ti0.997 O2 ) films and the slightly oxygen-deficient TiO2−δ films were used to as the channels

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©2014 American Physical Society

HAN, LUO, LI, SHEN, QU, XIONG, DOU, HE, AND NIE

PHYSICAL REVIEW B 90, 205107 (2014) III. RESULTS AND DISCUSSION

FIG. 1. (Color online) (a) Diagram of our EDLT with a drop of ionic liquid electrolyte DEME-TFSI only contacting the TiO2 channel and the gate electrode. The other Au electrodes and the STO substrate were separated from the ionic liquid electrolyte by a layer of hardbaked photoresist. (b) Optical micrograph of a typical device without the ionic liquid electrolyte. (c) Schematic molecular structures of the DEME-TFSI (right) and the cross section of DEME-TFSI/TiO2 EDLT (left) illustrating the charge accumulation at the interface between the ionic liquid electrolyte and the oxide channel.

in EDLT devices. Figures 1(a) and 1(b) show a schematic and a photograph of the EDLT devices. The Hall bar, 500 μm in length and 60 μm in width, was patterned by standard photolithography and reactive-ion etching. Electrodes of Au (∼ 70-nm thick)/Ti (∼ 10-nm thick) were deposited by electron-beam evaporation. Finally, we patterned a 3-μm-thick film of hard-baked photoresist as a separator so that the electrolyte only contacted the gate electrode and channel. The electrolyte used in this study is an ionic liquid N,N -diethyl-N-(2-methoxyethyl)- N -methylammoniumbis(trifluoromethylsulfonyl)-imide (DEME-TFSI) as shown in Fig. 1(c), which has previously been widely employed in oxide-based EDLT, e.g., Co-doped TiO2 [12], ZnO [4,14], and STO [11]. The transport characteristics at different gate voltages (Vg ) were measured in a physical properties measurement system. The Vg was set at 300 K maintaining at least 20 min for the EDLT to arrive at equilibrium to accumulate the carriers in the channel [Fig. 1(c)]. First, the sample was cooled down to about 7 K, then the measurements were performed, and the data of both resistance vs temperature (R-T) and Hall effect were acquired during the subsequent warming and cooling procedures from ∼ 7 to 200 K. DEME-TFSI becomes a glasslike solid below 200 K where the ionic mobility falls to zero, but above 200 K, the ion can move and the field effect would be partly lost [4,11,14]. So the measurement at each Vg was stopped at 200 K. During the measurements, the leakage current through the gate was less than 1 nA. Before switching to another Vg , the sample was warmed up to 300 K.

Figure 2(a) shows the data of the Hall resistance vs magnetic field (μ0 H ) at 100 K with different Vg in a representative Nb0.003 Ti0.997 O2 EDLT device. The data at other temperatures are not shown. The slope of the lines decreases obviously with an increase in Vg from 0 to 4.0 V, which indicates the increase in ns . The ns data obtained from the Hall-effect measurements for each Vg at different temperatures are shown in Fig. 2(b). It is clear that the ns increases from ∼ 5.0 × 1013 cm−2 at Vg = 0 V to ∼ 1.5 × 1015 cm−2 at Vg = 4.0 V and is almost temperature independent for each Vg . The ns of TiO2−δ EDLT devices also increases by similar amplitudes (from ∼ 1.4 × 1013 to ∼ 1.42 × 1015 cm−2 , data not shown) as Vg increases from 0 to 4.8 V and is unchanged with temperature for each Vg . The temperature (T ) dependence of resistivity (ρ) as shown in Fig. 2(c) clearly illustrates that the resistivity of the Nb0.003 Ti0.997 O2 channel decreases by almost three orders of magnitude from ∼ 10−1 cm (Vg = 0 V) to ∼ 10−4 cm (Vg = 4.0 V). The TiO2−δ EDLT devices show similar results as illustrated in Fig. 2(d). What should be noted that, for Vg < 3.0 V, the devices can recover, but for higher Vg , they cannot recover totally, for example, the purple lines in Figs. 2(c) and 2(d) showing the results without gate voltage after the Vg = 4.0 and 4.8 V gating experiments, respectively. Therefore, for higher Vg , excepting the electrostatic effects, some electrochemical processes, such as the migrations of oxygen from the oxide films into the ionic liquid also may occur in this system, which were observed in similar EDLT gating experiments by others [15–18]. However, in this paper, we focused on the carrier density dependence of transport properties of anatase TiO2 , and so the origin of the added carrier density due to both electrostatic effects and some electrochemical processes had a negligible impact on our conclusions. Now, we carry out a more detailed analysis of the ρ-T data of anatase Nb0.003 Ti0.997 O2 EDLT devices. For each Vg between 0 and 3.0 V, there is a temperature (Tmin ) at which the resistivity has a minimum [Fig. 2(c)]. It is clearer to see the enlarged views as shown in Fig. 3(a) (for Vg = 0 and 3.0 V, other Vg ’s are not shown). The resistivity rises when the temperature increases or decreases away from Tmin , i.e., around Tmin , dρ/dT > 0 at T > Tmin and dρ/dT < 0 at T < Tmin . It means that there is a transition from insulator to metal for each Vg . The Tmin decreases monotonically from 150 K (Vg = 0 V) to 36 K (Vg = 3.0 V) as shown in Fig. 3(b). For Vg = 3.5 and 4.0 V, the Tmin disappears in the temperature range of our measurements, which proves that the TiO2 channel has completely become a good metal. Furthermore, we focus again on the data sets of the Vg from 0 to 3.0 V, for each Vg , it is found that the resistance upturns below Tmin with ln T behavior and then deviates from the ln T behavior presenting a saturation tendency when the temperature is further reduced [Fig. 3(a)]. Such a resistance upturn suggests that this behavior is dominated the by Kondo effect [19,20] caused by the enhanced spin scattering between the carriers and the local magnetic moments rather than two-dimensional weak localization [7,8,13,14,21,22]. Evidence for a Kondo effect in anatase TiO2 has also been reported in both our other study [13] and Ref. [21]. The ρ-T curve in the temperature

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CARRIER-MEDIATED KONDO EFFECT AND HALL . . .


FIG. 2. (Color online) (a) The Hall resistance vs magnetic field (μ0 H ) at 100 K with different Vg in the representative Nb0.003 Ti0.997 O2 EDLT device. The line of 3.5 V is almost under the one of 4.0 V. (b) The sheet carrier density (ns ) vs temperature (T ) for various Vg ’s in the Nb0.003 Ti0.997 O2 EDLT device. (c) and (d) The temperature (T ) dependence of resistivity (ρ) under various gate voltages (Vg ) for the Nb0.003 Ti0.997 O2 and TiO2−δ EDLT devices, respectively. The purple lines marked by dashed circles show the results of the devices without gate voltage after the Vg = 4.0 and Vg = 4.8 V gating experiments, respectively.

range around Tmin can be well described by a simple Kondo model [7,13,14], ρ(T ) = ρ0 + aT 2 + bT 5 + ρK (T /TK ),

(1)

where ρ0 is the residual resistivity due to sample disorder and the T 2 and T 5 terms represent the contributions of electronelectron and electron-phonon scatterings, respectively. We used an empirical form for the last term [7,14,23], s TK2 ρK (T /TK ) = ρK,0 K , (2) T 2 + TK2 where TK = TK /(21/s − 1)1/2 , TK is the Kondo temperature, and s = 0.225 according to the result of the numerical renormalization-group (NRG) theory [23,24]. The ρ-T curves were fitted by using Eqs. (1) and (2) yielding a series of fitting parameters for each Vg . The fitting curves of Vg = 0 and Vg = 3.0 V are shown in Fig. 3(a). Table I shows the values of the fitting parameters for different Vg ’s. Using the fitting parameters, we can scale the ρ(T ) curves at different Vg in comparison with the universal Kondo behavior [23,24]. Figure 3(c) shows the normalized Kondo resistivity [ρ(T ) − ρ0 − aT 2 − bT 5 ]/ρK,0 K vs T /TK at each Vg and the universal Kondo behavior from the NRG [24]. From Fig. 3(c) we can find that all the experimental curves fall on one universal curve of the NRG, proving that the resistance upturns in our experiments are indeed due to the Kondo effect [8,14,22]. TK is a key parameter for the Kondo effect. The ns dependence of TK as shown in Fig. 3(b) illustrates that TK increases almost monotonically from ∼ 75 to ∼ 207 K with an increase in ns from ∼ 5.0 × 1013 to ∼6.35 × 1014 cm−2 . This indicates that the Kondo effect on our anatase Nb0.003 Ti0.997 O2 EDLT devices has been successfully modulated by ns . The qualitative explanation for the TK increase with ns proposed

in Ref. [14] may also work here: TK has the relationship with the density of states at the Fermi level D(E), i.e., kB TK ∼ e−1/[J D(E)] , where kB is the Boltzmann constant and J > 0 is the antiferromagnetic coupling constant; accordingly, the gate-induced electron accumulation enhances D(E), and then TK increases. The high value of TK of our sample is acceptable because TK is generally high for oxides, e.g., TK = 120 K for Co:TiO2 reported by Ref. [25]. The resistance upturn of Vg = 0 V is much more significant than that of Vg = 3.0 V as clearly shown in Fig. 3(a). In other words, the resistance upturn becomes weaker with increasing ns and finally disappears, and only a flat or a little downward terrace of resistance is left for Vg = 3.5 and 4.0 V [Fig. 2(c)]. We propose a possible explanation below: when T TK , the Kondo singlet state [26] emerges, i.e., the magnetic scattering centers are screened by carriers to become nonmagnetic centers, so the resistance upturn would weaken and the saturation appears lastly; in our case, TK is very high and increases with ns , so the Kondo singlet state would emerge at a higher temperature; when TK is high enough for a certain ns , the Kondo singlet state would dominate for all the low-temperature ranges of our measurements, so the magnetic centers would be completely screened, then the resistance upturn would disappear. Although, the above analyses and conclusions are based on Nb0.003 Ti0.997 O2 EDLT devices, they are actually also suitable for the TiO2−δ EDLT devices, considering that the ρ-T results of the TiO2−δ EDLT devices [Fig. 2(d)] are very similar to those of Nb0.003 Ti0.997 O2 EDLT devices [Fig. 2(c)]. The possible origins of the magnetic scattering centers resulting in the Kondo effect are (I) the presence of extrinsic magnetic impurities or (II) intrinsic localized Ti3+ states that can be induced by Nb doping, by vacancies of oxygen or by EDLT gating. All the reagents were used in ultrahigh purity

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FIG. 3. (Color online) Carrier-mediated Kondo effect in the Nb0.003 Ti0.997 O2 EDLT device. (a) The enlarged views of ρ-T curves of Vg = 0 and Vg = 3.0 V of Fig. 2(c). Red curves are the fits using Eqs. (1) and (2). The blue lines are linear guides. (b) The dependences of Tmin and TK on ns . The purple points surrounded by dashed circle show the results without gate voltage after the Vg = 4.0 V gating experiments. The dashed lines are guides for the eye. (c) Normalized Kondo resistivity vs temperature for the data from Vg = 0 to Vg = 3.0 V. The blue solid line describing the universal Kondo behavior was obtained from the numerical renormalizationgroup calculations. The color code here is the same as that in Fig. 2(c).

with the impurity content of less than 0.01%, and there are no signals of other extrinsic elements in the x-ray photoelectron spectroscopy measurements of the films (data not shown).

Both above can exclude the origin (I). In addition, we notice that the observed decrease in both Tmin and magnitude of resistance upturn with ns and the increases in TK with ns are very similar to those of (001) LaAlO3 /SrTiO3 interfaces (as shown in Fig. 1(a) of Ref. [27]) in which system the magnetic centers are attributed to the intrinsic localized Ti3+ states by many studies [27–30]. Our other study [13] also proves that Ti3+ mainly provides the local magnetic moment in anatase TiO2 films which are fabricated by the same procedures here. Therefore, the latter explanation of the origin of the magnetic scattering centers is more plausible. In addition, we also investigated the transport characteristics of chemical doping anatase TiO2 with different doping concentrations (0.5, 1.0, 2.0, and 3.0 at. % Nb doped), which were used to make a comparison with the results of the EDLT gating experiments. Figure 4(a) shows the temperature dependence of the ns of anatase TiO2 with different doping concentrations of Nb. ns increases from ∼ 5.0 × 1013 cm−2 (0.3%) to ∼ 2.3 × 1015 cm−2 (3%) and is almost temperature independent for each doping level. The ρ-T results [Fig. 4(b)] are similar to those of EDLT gating experiments. The Kondo effect is also observed, and the ns dependence of Tmin and TK are shown in Fig. 4(c). Apparently, with the increase in ns , Tmin decreases monotonically from 150 to 27 K, whereas TK also increases monotonically from ∼ 75 to ∼ 285 K. All these results are in line with those observed in the EDLT experiments above. To sum up, the Kondo effect depends very strongly on ns indicating the widely tunable coupling of conduction electrons to local magnetic moments in anatase TiO2 films. The temperature dependence of the Hall mobility (μH ) of the Nb0.003 Ti0.997 O2 EDLT device was shown in Fig. 5(a). It is clear that the amplitude of μH is enlarged by more than one order of magnitude as Vg increases from 0 to 4.0 V. To clarify the mechanism of such an enlargement of μH , the sheet carrier density dependence of μH was also plotted in Fig. 5(b). As shown in both Figs. 5(a) and 5(b), the obvious enlargement of μH takes place from ∼ 5.85 × 1013 cm−3 (Vg = 0.5 V) to ∼ 1.04 × 1014 cm−3 (Vg = 1.5 V). This obvious enlargement should be due to a transition of a dominant conduction mechanism from a lower mobility donor band to a higher mobility conduction band which had been observed in anatase TiO2 films by Tang et al. [31]. This transition was confirmed by the ρ-T curves [Fig. 2(c)] which exhibit mainly insulator behavior at Vg < 1.5 V and metal behavior at Vg 1.5 V. In addition, the characteristics of the μH -T curves [Fig. 5(a)] exhibit two different kinds of behaviors also supporting the existence of the transition: For

TABLE I. The values of the fitting parameters for different Vg ’s. Regression analysis was carried out to determine the parameters with the use of the software named ORIGIN. Vg (V) 0.0 0.5 1.0 1.5 2.0 2.5 3.0

ρ0 ( cm)

A ( cm K−2 )

B ( cm K−5 )

ρK,0 K ( cm)

TK (K)

2.28 × 10−2 1.28 × 10−2 7.74 × 10−3 3.25 × 10−3 2.51 × 10−3 1.54 × 10−3 3.08 × 10−4

1.66 × 10−8 8.35 × 10−8 3.18 × 10−8 3.35 × 10−8 1.48 × 10−8 2.18 × 10−8 7.61 × 10−9

3.41 × 10−14 3.01 × 10−14 8.24 × 10−15 6.08 × 10−15 8.78 × 10−15 3.02 × 10−15 9.70 × 10−16

8.64 × 10−2 9.69 × 10−2 1.05 × 10−2 1.23 × 10−3 5.64 × 10−4 3.04 × 10−4 1.36 × 10−4

75.01 70.11 79.41 85.21 101.97 110.05 207.63

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FIG. 4. (Color online) (a) The temperature (T ) dependence of the sheet carrier density (ns ) for Nb-doped anatase TiO2 films with different doping levels. (b) ρ-T dependences for different doping levels. (c) The ns dependence of Tmin and TK . The color codes in (b) and (c) are the same as those in (a).The dashed lines are guides for the eye.

Vg < 1.5 V as the temperature decreases, the μH increases first and then decreases at low temperatures, which can be qualitatively described by a temperature-activated grain boundaries limited mobility model (for details of the model, see Eq. (8) of Ref. [32]) corresponding to the region of lower mobility of the donor band. For Vg 1.5 V, with decreasing in T , the μH increases first too, whereas almost maintaining a

saturation for low temperatures, which can be well described by a metal-like mobility model (for details of the model, see Eq. (7) of Ref. [32]) corresponding to the region of higher mobility of the conduction band. After completely falling into the higher mobility region (Vg 2.5 V), the mobility is almost independent of ns [Fig. 5(b)]. Gating experiments of TiO2−δ EDLT devices have similar behaviors of μH -T and μH -ns (data not shown). What is more, for comparison, the μH -T of different levels of Nb-doping anatase TiO2 films are shown in Fig. 5(c). These films also illustrate two similar kinds of μH -T as EDLT devices do. However, their μH [Fig. 5(c)] are much smaller than those of the EDLT gating experiments [Fig. 5(a)], clearly demonstrating that many more disorders have been introduced by different levels of Nb doping than EDLT gating. In a word, for anatase TiO2 films here, there is a transition of a dominant conduction mechanism from a lower mobility donor band to a higher mobility conduction band as the carrier density increases. The Hall mobility could be enhanced by about one order of magnitude by EDLT gating which chemical doping cannot achieve here. It may provide new thoughts for the design of new electronic devices of oxides based on the modulation of the carrier mobility. IV. CONCLUSIONS

FIG. 5. (Color online) (a) The temperature (T ) dependence of Hall mobility (μH ) for each Vg of the Nb0.003 Ti0.997 O2 EDLT device. (b) The sheet carrier density dependence of μH . The black dashed arrow shows there is an obvious enlargement of μH . The color code is the same as that in (a). (c) The μH -T curves of different levels of Nb-doping anatase TiO2 films.

To summarize, by electrolyte gating, the ns of anatase TiO2 epitaxial films have been modulated hugely from ∼ 5.0 × 1013 to ∼ 1.5 × 1015 cm−3 , accompanied with a transition of the anatase TiO2 films from a low-conductivity semiconductor to a high-conductivity metal and a decrease in resistivity by almost three orders of magnitude. More fascinatingly, the Kondo effect depends very strongly on ns , indicating the widely tunable coupling of conduction electrons to local magnetic moments in anatase TiO2 , and the Hall mobility could be enhanced by about one order of magnitude. This study shows EDLT gating is a powerful method to stimulate and mediate novel phenomena of correlated oxides. The ns -dependent Hall mobility and Kondo effect strongly imply that the scattering of carriers with the local magnetic moments should be taken into account in terms of Hall mobility in the Kondo system, which calls for further theoretical and experimental investigations. ACKNOWLEDGMENTS

This work was supported by the Ministry of Science and Technology of China (Grants No. 2013CB921701,

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No. 2013CBA01603, and No. 2014CB920903), the National Natural Science Foundation of China (Grants No. 10974019, No. 51172029, No. 91121012, No. 11004010, No. 61125403, and No. 11374035), the program for New

Century Excellent Talents in the University of the Ministry of Education of China (Grant No. NCET-13-0054), and the Beijing Higher Education Young Elite Teacher Project (Grant No. YETP0238).

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