Impact of Mn doping

Journal of Asian Ceramic Societies 3 (2015) 426–431

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Journal of Asian Ceramic Societies journal homepage: www.elsevier.com/locate/jascer

Electrical conduction mechanism in BiFeO3 -based ferroelectric thin-film capacitors: Impact of Mn doping Hiroki Matsuo a,∗ , Yuuki Kitanaka b , Yuji Noguchi b , Masaru Miyayama b a b

Department of Advanced Interdisciplinary Studies, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

a r t i c l e

i n f o

Article history: Received 11 August 2015 Received in revised form 17 September 2015 Accepted 3 October 2015 Available online 21 October 2015 Keywords: BiFeO3 Pulsed-laser deposition Mn doping Electrical conduction Ferroelectric Switchable diode effect

a b s t r a c t Electrical conduction properties of SrRuO3 (SRO)/BiFeO3 (BFO)/SRO and SRO/10% Mn-doped BFO(BFMO)/SRO ferroelectric thin-film capacitors are investigated. The BFO capacitors exhibit a switchable diode effect accompanied by a conduction change from ohmic to space-charge-limited current with increasing external field. In contrast, the BFMO capacitors show only an ohmic conduction, arising from a considerable reduction in depletion layer width at the SRO/BFMO interfaces. These results suggest that the diode property can be tuned by Mn content in the BFO film. Our study opens the possibility of controlling the diode effect in BFO-based devices by a dilute Mn doping. © 2015 The Ceramic Society of Japan and the Korean Ceramic Society. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction Resistive switching in metal oxides has attracted much attention because the phenomena can be applicable for a new-type of non-volatile memory, the so-called resistive random access memory (ReRAM) [1,2]. The mechanism of the resistive switching has been reported to be related to a filamentary conducting path [3–6] or a conducting layer in the vicinity of electrode/metal oxide interfaces [7–9]. However, the reliability and thermal stability of data retention are critical issues to be addressed, because the driving mechanism is accompanied by a chemical reaction of the metal oxides [10,11] such as a thermal redox reaction caused by Joule heating and/or an oxygen-vacancy migration [12,13]. Ferroelectrics with a reversible spontaneous polarization (Ps ) are regarded as one of the promising candidates for ReRAMs, because ferroelectric capacitors having the metal–ferroelectric–metal structure exhibit resistive switching phenomena, where chemical reactions play a minor or almost no role. For the ferroelectric capacitors, the mechanism of the resistive

∗ Corresponding author. E-mail address: [email protected] (H. Matsuo). Peer review under responsibility of The Ceramic Society of Japan and the Korean Ceramic Society.

switching is classified into the following two types. One is a tunneling electroresistance effect observed for ultra-thin ferroelectric films, where its tunneling barrier height can be changed by a polarization reversal [14–18]. The other is a switchable diode effect that dominates the electrical properties of the capacitors with a thicker ferroelectric layer. These capacitors show a diode-like behavior and the diode polarity can be switched by a Ps reversal [19–22]. The switchable diode effect has been reported for several ferroelectrics such as PbTiO3 [23], Pb(Zr1−x ,Tix )O3 [24,25], and BiFeO3 [26–28]. The diode effect in BiFeO3 (BFO) has been intensively studied because BFO has a large Ps up to 100 ␮C/cm2 [29–31] and a relatively narrow band gap (Eg = 2.7 eV) [32]. In addition to the resistive switching phenomena, these fascinating properties enable us to uncover a novel function resulting from a coupling between the diode effect and the photovoltaic effect in the BFO capacitors [20,33,34]. However, the detailed mechanism of the switchable diode effect is still under intense debate, because the electrical conduction in the BFO capacitors is not sufficiently clarified. The present study investigates the electrical conduction properties of epitaxial BFO and Mn-doped BFO (BFMO) ferroelectric capacitors deposited by a pulsed-laser deposition (PLD) method. We reveal that the BFO capacitors present the space-charge-limited current (SCLC) conduction whereas the BFMO capacitors show an ohmic current–voltage behavior. In addition, the switchable diode effect is seen only for the BFO capacitors while both the BFO and BFMO films exhibit a comparable remanent polarization. We

http://dx.doi.org/10.1016/j.jascer.2015.10.001 2187-0764 © 2015 The Ceramic Society of Japan and the Korean Ceramic Society. Production and hosting by Elsevier B.V. All rights reserved.

H. Matsuo et al. / Journal of Asian Ceramic Societies 3 (2015) 426–431

address the possibility of controlling the diode property by Mn content in the ferroelectric film of the BFO-based devices. 2. Experiment BiFeO3 (BFO) and 10% Mn-doped BFO (BiFe0.9 Mn0.1 O3 , BFMO) ferroelectric thin films were deposited on (0 0 1) STO single-crystal substrates by a pulsed-laser deposition (PLD) method. We used SrRuO3 (SRO) as top and bottom electrodes. The bottom SRO electrode with a thickness of 100 nm was fabricated at a substrate temperature (Tsub ) of 700 ◦ C under 15 mTorr O2 atmosphere with a laser repetition rate of 1 Hz. Ferroelectric BFO and BFMO layers with a thickness of 250 nm were deposited at Tsub = 690 ◦ C under 20 mTorr O2 , and the laser repetition rate was set as 7 Hz. For the fabrication of the top SRO electrode (50 nm), the Tsub during the deposition was lowered to 650 ◦ C and the other parameters were set to the same values as those of the bottom SRO electrode. After the deposition process, the capacitors were annealed in air at 350 ◦ C for 1 h. In this paper, we take the upward polarization and applied electric field as positive (+P and +E) and the downward ones as negative (−P and −E). For the BFO capacitors, we performed an ‘electrical training’ before the measurements of polarization–electric field (P–E) and current–voltage (I–V) properties. This treatment was performed to diffuse oxygen vacancies accumulated at the bottom SRO/BFO interface, because our previous studies have indicated that the oxygen vacancy accumulation in the as-annealed BFO capacitors leads to a highly asymmetric P–E hysteresis loop [35]. The electrical training was performed by the following procedure: first, a negative voltage of 12 V at 5 kHz, which corresponds to an electric field of −480 kV/cm, was repeatedly applied to the samples to realize the −P state. Then, the samples in the −P state were heated at 200 ◦ C for 30 min in air. The detailed process and the effects of the electrical training will be discussed elsewhere. Unlike the BFO capacitors, their as-annealed BFMO capacitors show a typical (symmetric) P–E hysteresis loop, and therefore the electrical training was not performed for the BFMO ones. The P–E and I–V properties were measured at 25 ◦ C by using a ferroelectric testing system (Toyo Corporation; Model 6252 Rev. B). Before the I–V measurements, poling treatments were performed for the samples by applying a positive or negative voltage of 12 V at 5 kHz to achieve the initial polarization state of +P or −P. Current density (J) obtained from I was shown throughout, while electric field (E) or V was used properly based on the underlying basis. To investigate the conduction mechanism, we applied several conduction models for the J–V data obtained. 3. Results and discussion 3.1. P–E and J–E properties Fig. 1(a) shows a reciprocal space map in the q110 –q001 plane observed for the BFMO capacitors. The BFMO film is confirmed to be epitaxially grown on the (1 0 0) STO substrate. In addition to the fundamental reflections, superlattice reflections, such as 1/2 1/2 3/2, can be observed as indicated in the inset of Fig. 1(a). The measurements of the –2 scan (not shown) lead to a d001 of 0.401 nm for the BFMO film, which is longer than that of bulk BFMO (d001 = 0.395 nm). In addition, the q110 value of BFMO is close to that of the STO substrate [see, Fig. 1(a)]. These results indicate that the BFMO film is under compressive strain owing to the epitaxial growth from the STO substrate. Fig. 1(b) and (c) shows the P–E properties after the annealing at 350 ◦ C for 1 h. The capacitors exhibit typical P–E hysteresis loops and the values of Pr are estimated to be 82 ␮C/cm2 for the BFO film

427

and 84 ␮C/cm2 for the BFMO one. This result demonstrates that the Mn doping up to 10% does not have a significant influence on Ps as reported in Ref. [36]. Fig. 2(a) and (b) shows the J–E properties of the BFO capacitors in +P and −P states with |V| ≤ 1.2 V, where an asymmetry is marked. The J–E data of the BFMO capacitors in +P and −P states are also plotted in Fig. 2(c) and (d). For the BFO capacitors in +P [Fig. 2(a)], a high J was observed under a positive field (+E) whereas the J values are suppressed under a negative field (−E). In the −P state [Fig. 2(b)], a high J is seen under −E while the J data are decreased under +E. These characteristic J–E properties indicate that the BFO capacitors show a ‘diode’ effect and that the diode polarity can be switched by the reversal of Ps . The BFO capacitors are in forward bias with E parallel to the net polarization while in reverse bias with E opposite to it. In contrast, as shown in Fig. 2(c) and (d), the J–E curves of the BFMO capacitors are affected neither by the polarization state nor the direction of E. These results demonstrate that the switchable diode effect can be observed only for the BFO capacitors whereas it disappeared in the BFMO ones. 3.2. Leakage current models The models of leakage current in ferroelectric materials with a relatively large thickness can be classified into the following three types: the thermionic emission, the Poole–Frenkel emission, and the space-charge limited current (SCLC). The thermionic emission is due to an interface-limited conduction while the Poole–Frenkel emission and the SCLC are categorized into a bulk-limited conduction. For the thermionic emission model, the J–V characteristic under forward bias is expressed by J ∝ exp(qV/kT), where T is the temperature, k is the Boltzmann constant, q is the charge of carrier, and is the ideality factor. The value of can be obtained from the slope of the ln J vs. V plot. should be in the range of 1–2 for typical metal–semiconductor contacts dominated by the thermionic emission. The Poole–Frenkel emission is a conduction governed by an intersite hopping of charge carriers between the traps with localized states [37]. The conductivity () obeys the following equation:

J EI 1 = = Cexp − + E kT kT

q3 E ε0 εop

0.5

,

(1)

where C is a constant, EI is the trap ionization energy, ε0 is the permittivity of vacuum, and εop is the optical dielectric constant. The Poole–Frenkel emission provides the relation of ln() ∝ E0.5 and the slope of ln() vs. E0.5 leads to εop of the material. For ferroelectrics with deep traps, the SCLC model provides the J–V relation with an ohmic behavior, J ∝ V, at low voltages. In this ohmic region, thermally generated carriers are predominant over the injected charge carriers from the electrode. In the middle V region, the traps begin to be filled with the injected carriers. In this trap-filled-limited (TFL) region, a relationship of J ∝ Vn (n > 2) is often seen. With further increasing V, the injected carriers exceed the thermally generated carriers, and then the current density rises sharply. Theoretically, a critical voltage (Vcr ) where J begins to show the J ∝ Vn (n > 2) relation is approximately expressed by Vcr ≈

2 ent,0 wm , 2ε0 εst

(2)

where nt,0 denotes unoccupied trap concentration; wm , the material thickness, and εst , static dielectric constant [38]. Typically, under a sufficiently high E where the traps are completely filled with the injected carriers, the current density

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Fig. 1. (a) Wide-range reciprocal space map of the BFMO capacitors and polarization properties of the (b) BFO and (c) BFMO films. Data of (b) and (c) have reported in Ref. [36].

obeys Child’s law (J ∝ V2 ) and the carriers behave as if they were in a trap-free state. The current density in the Child’s-law region is expressed by J=

9ε0 εst V 2 3 8wm

,

(3)

where denotes the mobility of the charge carriers and V, the external voltage. It has been reported that a relation of J ∝ V3 can be sometimes observed in a high V region instead of typical Child’s-law (J ∝ V2 )[39,40]. The details will be discussed later. 3.3. Leakage currents in the BFO capacitors First, we verify the thermionic emission model. The ln J vs. V plots in the (+P, +E) [Fig. 3(a)] and (−P, −E) (not shown) states yield values of 4.9 and 4.8, respectively. Considering that should be in the range of 1–2 for typical metal–semiconductor contacts, we

-1.5

-0.5

Voltage (V) 0 0.5

1

1.5

10 −2

(a) BFO, +P state

10 −3 10 −4 10 −5 10 −6

−E

10 −7 10 −8 10 −9 -60

-1.5

-40

-1

+E

-20 0 20 40 Electric Field (kV/cm) -0.5

Voltage (V) 0 0.5

-1.5

Current Density (A/cm2)


10 −2

-1

think that this interface-limited thermionic emission model is not appropriate for our BFO capacitors. Secondly, we examine the Poole–Frenkel (PF) emission model from the ln(J/E) vs. E0.5 relation. The PF plot in the (+P, +E) state yields a strong nonlinearity, as shown in Fig. 3(b). Regardless of the polarization and bias states, we confirm that the linear ln(J/E) vs. E0.5 relation is not satisfied. These results force us to consider that the PF emission model is not suitable for the BFO capacitors. Thirdly, we investigate the SCLC conduction. In Fig. 4(a)–(d) we display the SCLC plots, i.e., log |J| vs. log |V|, for the BFO capacitors in various polarization and bias states. In the all states, we obtain a slope (n) of approximately one in the low V region where the ohmic conduction is dominant. In the forward bias, as shown in Fig. 4(a) [(+P, +E)] and (d) [(−P, −E)], we found n = 5.2 and 4.1 in the middle-V region, respectively. In this middle-V region with such a high n, the traps inside the material begin to be filled with the injected carriers. Then, a region with n ∼ 3 emerges at much higher

1

10

-6

1.5

-20 0 20 40 Electric Field (kV/cm)

60

10 −6 10 −7 10 −8

1.5

-1.5

-1

-0.5

Voltage (V) 0 0.5

1

1.5


60

10 -1



10

1

10 −5

-40

10 -3

-5

Voltage (V) 0 0.5

10 −4

10 −9 -60

10 -2

10

-0.5

(b) BFO, −P state

10 −3

60

10 -1

-4

-1

(c) BFMO, +P state

10 -7 -60

-40


60

10 -2 10 -3 10 -4 10 -5 10 -6

(d) BFMO, −P state

10 -7 -60

-40

Fig. 2. J–E properties of the BFO and BFMO capacitors: (a) BFO in the +P state and (b) in the −P state; (c) BFMO in the +P state and (d) in the −P state.


the ohmic region and the following nonlinear character observed in the reverse bias can also be explained by the SCLC conduction. As described above, the thermionic emission and the PF emission models do not provide a rational explanation for the observed J–V data. In both the forward and reverse biases, the ohmic conduction does appear in the low-V region. In addition, the nonlinear J–V relations observed in the high-V regions can be reasonably explained only by the SCLC conduction. These results lead to the conclusion that the SCLC conduction model is most appropriate for the BFO capacitors. It is noteworthy that Vcr where J begins to show a steep increase is depending on the bias state. The value of Vcr in the forward bias [(+P, +E) and (−P, −E)] is calculated to be ∼0.3 V while that in the reverse bias [(+P, −E) and (−P, +E)] is much higher (∼0.7 V). Because of the difference in Vcr , leakage currents in the forward bias are much high compared with that in the reverse bias at |V| > 0.3 V even though comparable leakage currents were found in the ohmic region of |V| < 0.3 V. Based on these results, we conclude that the feature of Vcr depending on the polarization and bias states results in the diode effect observed in the BFO capacitors.

10

ln (J / Am−2)

(a) +P, +E 5 0

η = 4.9

-5 -10 0

2

4 V (V)

6

8

-5

ln (J/E / Sm−1)

(b) +P, +E -10 -15 -20 -25 0

2000 4000 E 0.5 (V/m) 0.5

Fig. 3. (a) ln(J) vs. V plot and (b) ln(J/E) vs. E

3.4. Leakage currents in the BFMO capacitors

6000

plot for the BFO capacitors in +P, +E.

n = 3.1

(a) +P, +E

Vcr ≈ 0.3 V

n = 5.2

n = 1.2

-2

-1.5

Fig. 5(a) and (b) represents the SCLC plots for the BFMO capacitors in (+P, +E) and (+P, −E), which correspond to the measurement conditions in the forward and reverse biases for the BFO capacitors, respectively. Unlike the BFO capacitors, n remains one throughout the entire V region in both (+P, +E) and (+P, −E). The similar conduction behavior of n ∼ 1 was observed in the −P state for the BFMO capacitors regardless of the direction of E. These results show that the BFMO capacitors have the ohmic conduction even under a high V irrespective of the polarization and bias states. In our previous works for the BFO capacitors with SRO electrodes, it has been suggested that the Schottky contact is formed at the SRO/BFO interfaces. The width of a depletion layer and a Schottky barrier height can be modulated by surface charge derived from ferroelectric polarization [22,42]. For the SCLC conduction in capacitors with the Schottky contacts, the conduction behavior is considered to be governed by the depletion layer adjacent to the

log (J / Acm−2)

log (J /Acm−2)

fields. The n = 3 region can be explained by an SCLC transport taking account of the effects of carrier diffusion [39], a finite life-time of injected charge carriers [40], and/or double injection [41]. All of the leakage properties observed in the forward bias can be reasonably explained by the SCLC conduction. In the reverse bias, as plotted in Fig. 4(b) [(+P, −E)] and (c) [(−P, +E)], the ohmic conduction (n ≈ 1) is clearly seen, as in the forward bias. In addition, a nonlinear J–V relation with n > 1 was also found at higher electric fields. In the reverse bias, we cannot evaluate leakage currents in the higher V region, because the polarization states are destroyed by applying electric fields. The existence of 0 -1 -2 -3 -4 -5 -6 -7 -8 -9

-1

-0.5

0

0.5

0 -1 -2 -3 -4 -5 -6 -7 -8 -9

1

(b) +P, −E

Vcr ≈ 0.7 V

-2

log (J /Acm−2)

log (J / Acm−2)

(c) –P, +E

Vcr ≈ 0.7 V n = 1.2

-2

-1.5

-1

n = 2.1

-0.5

log (V / V)

0

0.5

1

n = 1.9

n = 1.1

-1.5

log (V / V) 0 -1 -2 -3 -4 -5 -6 -7 -8 -9

429

0 -1 -2 -3 -4 -5 -6 -7 -8 -9

-1

-0.5

log (|V| / V)

(d) –P, −E

0

0.5

1

n = 3.1

Vcr ≈ 0.3 V

n = 4.1

n = 1.2 -2

-1.5

-1

-0.5

0

0.5

1

log (|V| / V)

Fig. 4. Log J vs. log V plots for the BFO capacitors annealed in air at 350 ◦ C for 1 h: (a) +P, +E; (b) +P, −E; (c) −P, +E; (d) −P, −E.

430


For the electronic structures of BFMO, our density functional theory (DFT) calculations suggest that the half-occupied gap states constructed by the Mn-3d orbital are formed in the band gap of BFO and that the gap states are located at about 0.8 eV from the valence band maximum. This result indicates that the gap states formed by the Mn doping can act as deep acceptors. In metal–semiconductor junctions, the depletion layer width w can be expressed by

0

(a) +P, +E log (J / Acm−2)

-1

n = 1.0

-2 -3

-4

w=

-5 -2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

log (V / V)

log (J / Acm−2)

0

(b) +P, −E

-1

n = 1.0

-2 -3 -4 -5 -2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

log (|V| / V) Fig. 5. Log J vs. log V plots for the BFMO capacitors annealed in air at 350 ◦ C for 1 h: (a) +P, +E and (b) +P, −E.

metal–semiconductor interface, because a carrier concentration in the depletion layer is much lower than that in the other bulk region [43]. In this case, the value of wm in Eq. (2) should be replaced by the depletion layer width (w). Since our BFO films have p-type conduction owing to Bi vacancy as reported in Ref. [35], the top SRO/BFO interface in +P has a band bending, as depicted in Fig. 6(a). In the BFO capacitors in +P, w of the top SRO/BFO interface extends because of the positive ferroelectric polarization charge whereas that of the bottom interface is markedly reduced by the negative ferroelectric polarization charge. The overall conduction properties are dominated by the depletion layer formed in the top interface. Since w of the top SRO/BFO interface is reduced under +E, Vcr shifts to a lower voltage according to Eq. (2). On the other hand, under −E, Vcr is increased because the application of −E widens the top depletion layer. As a result, Vcr varies depending on the direction of E (+E or −E). In the −P state, the polarity of the diode effect is switched by the reversal of Ps .

2ε0 εst (V + Vbi ) , qNA

(4)

where εst denotes static dielectric constant; Vbi , built-in potential; NA , concentration of acceptor. For the factors affecting Vbi in metal–ferroelectric junctions, the polarization charge derived from Ps in addition to a difference in work functions should be included. Since the doping of acceptor with a higher concentration leads to a reduction of w as indicated in Eq. (4), the doping of Mn with 10% on the Fe site in BFO markedly reduces w in the vicinity of the SRO/BFO interfaces. We note that a decrease in work function of BFO by the Mn-doping can also contribute to the reduction of w. The schematic of the expected band bending in the BFMO capacitors is displayed in Fig. 6(b). The detailed electronic structure of BFMO will be discussed elsewhere. We think that the concentration of the traps in BFMO is several orders of magnitude higher than that in BFO. The w value in the BFMO capacitors therefore remains sufficiently small even when V or Vbi is relatively high. The abundant deep acceptor traps originating from the Mn-d gap states leads to the ohmic contact at the SRO/BFMO interface, and then the ohmic conduction is dominant throughout our experimental condition irrespective of the polarization states. In contrast, the BFO capacitors showing the SCLC conduction present the switchable diode effect as a result of the Vcr shift. These results indicate that the shift of Vcr arising from the polarization reversal is responsible for the switchable diode effect in the BFO capacitors. These results suggest that a control of the acceptor concentration in a low Mn-content region enables us to vary the depletion layer width and therefore tune the Vcr value. There is a possibility that designing the diode property of the BFO-based ReRAMs can be realized through a dilute Mn doping. Since the concentration of the traps in BFO is not easy to be determined and is sensitive to preparation conditions, a precise control of Mn content in the BFO film is required for realizing the tuning of the diode property in BFO-based devices, which will be studied in near future.

4. Summary

Fig. 6. Schematics of the band bending in the top interface of the capacitors in +P state: (a) SRO/BFO and (b) SRO/BFMO.

The electrical conduction properties of the BFO and BFMO thinfilm capacitors are investigated. The detailed analysis of the J–V data reveals that the SCLC mechanism dominates the conduction properties of the BFO capacitors whereas the BFMO capacitors exhibit only an ohmic behavior even under high electric fields. We found that the switchable diode effect observed for the BFO capacitors originates from a shift of critical voltage (Vcr ). This Vcr shift can be explained by an asymmetric band modulation in the depletion layer adjacent to the SRO/BFO interface caused by the ferroelectric polarization. The Mn doping is revealed to decrease the depletion layer width as a result of the formation of acceptor levels in the band gap of BFO. These results imply that a dilute Mn doping can control the diode property in the BFO thin-film capacitors. Controlling the diode property by the dilute Mn doping is expected to be applicable to the development of ReRAMs using BFO-based devices.


Acknowledgement This research is supported by Japan Society for the Promotion of Science (JSPS) through Grant-in-Aid for JSPS Fellows (26-4693) and partly through the Funding Program for Next Generation World-Leading Researchers (NEXT Program, GR026), initiated by the Council for Science and Technology Policy (CSTP). References [1] F. Pan, S. Gao, C. Chen, C. Song and F. Zeng, Mater. Sci. Eng. R Rep., 83, 1–59 (2014). [2] D.S. Jeong, R. Thomas, R.S. Katiyar, J.F. Scott, H. Kohlstedt, A. Petraru and C.S. Hwang, Rep. Prog. Phys., 75, 076502 (2012). [3] D.-H. Kwon, K.M. Kim, J.H. Jang, J.M. Jeon, M.H. Lee, G.H. Kim, X.-S. Li, G.-S. Park, B. Lee, S. Han, M. Kim and C.S. Hwang, Nat. Nanotechnol., 5, 148–153 (2010). [4] K.M. Kim, B.J. Choi and C.S. Hwang, Appl. Phys. Lett., 90, 242906 (2007). [5] M.-J. Lee, C.B. Lee, D. Lee, S.R. Lee, M. Chang, J.H. Hur, Y.-B. Kim, C.-J. Kim, D.H. Seo, S. Seo, U.-I. Chung, I.-K. Yoo and K. Kim, Nat. Mater., 10, 625–630 (2011). [6] J.J. Yang, M.-X. Zhang, J.P. Strachan, F. Miao, M.D. Pickett, R.D. Kelley, G. Medeiros-Ribeiro and R.S. Williams, Appl. Phys. Lett., 97, 232102 (2010). [7] A. Sawa, Mater. Today, 11, 28–36 (2008). [8] Z.L. Liao, Z.Z. Wang, Y. Meng, Z.Y. Liu, P. Gao, J.L. Gang, H.W. Zhao, X.J. Liang, X.D. Bai and D.M. Chen, Appl. Phys. Lett., 94, 253503 (2009). [9] S. Tsui, A. Baikalov, J. Cmaidalka, Y.Y. Sun, Y.Q. Wang, Y.Y. Xue, C.W. Chu, L.A. Chen and J. Jacobson, Appl. Phys. Lett., 85, 317–319 (2004). [10] K. Kinoshita, T. Tamura, M. Aoki, Y. Sugiyama and H. Tanaka, Appl. Phys. Lett., 89, 103509 (2006). [11] T. Ninomiya, S. Muraoka, Z. Wei, R. Yasuhara, K. Katayama and T. Takagi, IEEE Electron. Dev. Lett., 34, 762–764 (2013). [12] A. Baikalov, Y.Q. Wang, B. Shen, B. Lorenz, S. Tsui, Y.Y. Sun, Y.Y. Xue and C.W. Chu, Appl. Phys. Lett., 83, 957–959 (2003). [13] S.H. Jeon, B.H. Park, J. Lee, B. Lee and S. Han, Appl. Phys. Lett., 89, 9–12 (2006). [14] P. Maksymovych, S. Jesse, P. Yu, R. Ramesh, A.P.S. Baddorf and V. Kalinin, Science, 324, 1421–1425 (2009). [15] V. Garcia, S. Fusil, K. Bouzehouane, S. Enouz-Vedrenne, N.D. Mathur, A. Barthélémy and M. Bibes, Nature, 460, 81–84 (2009). [16] E.Y. Tsymbal and A. Gruverman, Nat. Mater., 12, 602–604 (2013). [17] A. Chanthbouala, V. Garcia, R.O. Cherifi, K. Bouzehouane, S. Fusil, X. Moya, S. Xavier, H. Yamada, C. Deranlot, N.D. Mathur, M. Bibes, A. Barthélémy and J. Grollier, Nat. Mater., 11, 860–864 (2012). [18] M. Zhuravlev, R. Sabirianov, S. Jaswal and E. Tsymbal, Phys. Rev. Lett., 94, 246802 (2005).

431

[19] A. Tsurumaki, H. Yamada and A. Sawa, Adv. Funct. Mater., 22, 1040–1047 (2012). [20] H.T. Yi, T. Choi, S.G. Choi, Y.S. Oh and S.-W. Cheong, Adv. Mater., 23, 3403–3407 (2011). [21] Y. Guo, B. Guo, W. Dong, H. Li and H. Liu, Nanotechnology, 24, 275201 (2013). [22] L. Pintilie and M. Alexe, J. Appl. Phys., 98, 124103 (2005). [23] P.W.M. Blom, R.M. Wolf, J.F.M. Cillessen and M.P.C.M. Krijn, Phys. Rev. Lett., 73, 2107–2110 (1994). [24] K. Gotoh, H. Tamura, H. Takauchi and A. Yoshida, Jpn. J. Appl. Phys., 35, 39–43 (1996). [25] Z.X. Li, X.L. Liu, W.J. Chen, X.Y. Zhang, Y. Wang, W.M. Xiong and Y. Zheng, AIP Adv., 4, 127111 (2014). [26] D. Lee, S.H. Baek, T.H. Kim, J.-G. Yoon, C.M. Folkman, C.B. Eom and T.W. Noh, Phys. Rev. B, 84, 125305 (2011). [27] T. Choi, S. Lee, Y.J. Choi, V. Kiryukhin and S.-W. Cheong, Science, 324, 63–66 (2009). [28] Y. Yao, B. Zhang, L. Chen, Y. Yang, Z. Wang, H.N. Alshareef and X.X. Zhang, J. Phys. D. Appl. Phys., 46, 055304 (2013). [29] J. Wang, Science, 299, 1719–1722 (2003). [30] D. Lebeugle, D. Colson, A. Forget and M. Viret, Appl. Phys. Lett., 91, 022907 (2007). [31] J. Li, J. Wang, M. Wuttig, R. Ramesh, N. Wang, B.A. Ruette, P. Pyatakov, A.K. Zvezdin and D. Viehland, Appl. Phys. Lett., 84, 5261 (2004). [32] S.R. Basu, L.W. Martin, Y.H. Chu, M. Gajek, R. Ramesh, R.C. Rai, X. Xu and J.L. Musfeldt, Appl. Phys. Lett., 92, 091905 (2008). [33] S.Y. Yang, L.W. Martin, S.J. Byrnes, T.E. Conry, S.R. Basu, D. Paran, L. Reichertz, J. Ihlefeld, C. Adamo, A. Melville, Y.-H. Chu, C.-H. Yang, J.L. Musfeldt, D.G. Schlom, J.W. Ager and R. Ramesh, Appl. Phys. Lett., 95, 062909 (2009). [34] Y. Ukai, S. Yamazaki, T. Kawae and A. Morimoto, Jpn. J. Appl. Phys., 51, 09LE10 (2012). [35] H. Matsuo, Y. Kitanaka, R. Inoue, Y. Noguchi and M. Miyayama, J. Appl. Phys., 118, 114101 (2015). [36] H. Matsuo, Y. Kitanaka, R. Inoue, Y. Noguchi and M. Miyayama, Jpn. J. Appl. Phys., 54, 10NA03 (2015). [37] G.W. Pabst, L.W. Martin, Y.-H. Chu and R. Ramesh, Appl. Phys. Lett., 90, 072902 (2007). [38] M.A. Lampert and P. Mark, Current Injection in Solids, Academic Press (1970). [39] F. Neumann, Y.A. Genenko, R. Schmechel and H. Von Seggern, Synth. Met., 150, 291–296 (2005). [40] M.A. Lampert and A. Rose, Phys. Rev., 121, 26–37 (1961). [41] R. Baron, Phys. Rev., 137, A272–A285 (1965). [42] L. Pintilie, I. Boerasu, M.J.M. Gomes, T. Zhao, R. Ramesh and M. Alexe, J. Appl. Phys., 98, 124104 (2005). [43] H.P. Hall, M.A. Awaah and K. Das, Phys. Stat. Sol., 201, 522–528 (2004).