Identification of Giant Mott Phase Transition of Single Electric

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Identification of Giant Mott Phase Transition of Single Electric Nanodomain in Manganite nanowall wire Azusa N. Hattori, Yasushi Fujiwara, Kohei Fujiwara, Anh T. V. Nguyen, Takuro Nakamura, Masayoshi Ichimiya, Masaaki Ashida, and Hidekazu Tanaka Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b00264 • Publication Date (Web): 26 May 2015 Downloaded from http://pubs.acs.org on June 7, 2015

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Identification of Giant Mott Phase Transition of Single Electric Nanodomain in Manganite nanowall wire Azusa N. Hattori1,*, Yasushi Fujiwara1, Kohei Fujiwara1, Thi Van Anh Nguyen1, Takuro Nakamura1, Masayoshi Ichimiya2,3, Masaaki Ashida2, and Hidekazu Tanaka1,** 1

Nanoscience and Nanotechnology Center, The Institute of Scientific and Industrial Research,

Osaka University, 8-1 Mihoga-oka, Ibaraki, Osaka 567-0047, Japan 2

Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho,

Toyonaka, Osaka 560-8531, Japan 3

School of Engineering, The University of Shiga Prefecture, 2500 Hassaka-cho, Hikone, Shiga

522-8533, Japan

KEYWORDS Electric nanodomain, Phase separation, Manganite nanowall wire, Insulator-metal transition, first-order transition

ACS Paragon Plus Environment

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ABSTRACT

In the scaling down of electronic devices, functional oxides with strongly correlated electron system provide advantages to conventional semiconductors, namely, huge switching owing to their phase transition and high carrier density, which guarantee their rich functionalities even at the 10 nm scale. However, understanding how their functionalities behave at a scale of 10 nm order is still a challenging issue. Here, we report the construction of the well-defined (La,Pr,Ca)MnO3 epitaxial oxide nanowall wire by combination of nanolithography and subsequent thin-film growth, which allows the direct investigation of its insulator-metal transition (IMT) at the single domain scale. We show that the width of a (La,Pr,Ca)MnO3 nanowall sample can be reduced to 50 nm, which is smaller than the observed 70-200 nm-size electronic domains, and that a single electronic nanodomain in (La,Pr,Ca)MnO3 exhibited an intrinsic first-order IMT with an unusually steep single-step change in its magnetoresistance and temperature-induced resistance due to the domains arrangement in series. A simple model of the first-order transition for single electric domains satisfactorily illustrates the IMT behavior from macroscale down to the nanoscale.


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Strongly correlated electrons in metal oxides generate a rich variety of electronic phases with unique properties including superconductivity in cuprates, colossal magnetoresistance (CMR) in manganites, and so on. These electronic phases are accompanied with a distinct phase transition upon the application of an external field. Thus, devices consisting of strongly correlated electron materials are expected to be a new generation of functional devices based on novel mechanisms, as reported in the “Emergent Research Device Materials” section in the International Technology Roadmap for Semiconductor Devices. The phenomena accompanying the electronic phase transition provide a variety of novel functions beyond those of conventional semiconductor devices (1), leading to the realization of “Mottronics”, such as Mott field-effect transistors (FETs). Moreover, such functional devices, in principle, have advantages in terms of device scaling because correlated oxides have essentially metallic electron densities (1022 to 1023 cm-3) even in their insulating phases. This should help ensure a sufficient number of carriers in a nanoscale device to avoid the limits of carrier density fluctuations, which are becoming increasingly important in conventional semiconductor devices at the 10 nm scale. To satisfy scientific curiosity and to evaluate the applicability of such nanoscale devices, the electronic conduction properties at the nanoscale in strongly correlated electron systems require urgent attention. Recently, the inhomogeneity of electronic phases in the form of nanoscale spatial electronic separation was discovered to occur in correlated electron materials (2-12) by observation using scanning probe microscopy (SPM), transmission electron microscopy, and so on. As a typical example, the coexistence of ferromagnetic metal (FM) and charge and orbital order insulator (COI) nanoscale phases in (La,Pr,Ca)MnO3 (2-4) has been reported, and the physical properties of the CMR in manganites are considered to be dominated by competing


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nanoscale electronic phases. To understand single-domain properties, the spatial confinement of these metal oxides to length scales smaller than the single electronic domain is an ultimate solution. The SPM can reveal the distribution of coexisting FM and COI domains, but it cannot be easily used to examine individual electronic domains and investigate their quantitative properties under multiple environments such as a high magnetic field and a wide range of temperatures. An alternative way is the nanofabrication of correlated oxides at a scale of 10 nm order, and there have been several reports on the production of confined manganite structures, typically using the lithography technique (13, 14). However, the previous reported structures, which had a size of 0.5-10 µm, were too large to achieve the nanoconfinement effect in a phaseseparated sample. Here, we make a three-dimensional (3D) well-defined epitaxial manganite nanowall wire using a unique nanofabrication technique combining of top-down nanolithography and bottom-up epitaxial thin-film growth, namely, 3D nanotemplate pulsed laser deposition (PLD) (15-18). The realization of NW samples of strongly correlated materials enables us to capture single electronic domains, when their size, i.e., the width of the NW, approaches a single electronic domain, and to identify their IMT characteristics. (La0.275Pr0.35Ca0.375)MnO3 (LPCMO) samples were fabricated by PLD (ArF excimer, λ=192 nm). For the growth of LPCMO nanowall wires 3D single-crystal MgO nanowalls (3D MgO) were used as a substrate (15, 18). The LPCMO NWs were deposited onto the side-surface of the 3D-MgO, as shown in Fig. 1(a), at 1070 K under PO2 = 1 Pa. After deposition, the unwanted LPCMO layers were removed by Ar ion milling, then postannealing treatment at 970 K under an O2 flow was performed to improve the crystal quality of the LPCMO NWs. 3D nanotemplate PLD technique takes advantage of the preparation of well-defined shape by a top-down nanoprocess and accurate width control with sub-nanometer-scale resolution based on oxide


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thin-film growth by a bottom-up nanoprocess. As a result, this technique can overcome the limitations in the nanofabrication of correlated oxides and produce (La,Pr,Ca)MnO3 nanowall wire (NW) structures at a scale down to 10 nm. The LPCMO samples were characterized by X-ray diffraction (Cu Kα, λ= 0.154 nm) as well as by RHEED to obtain the crystal structures. SEM and atomic-force microscopy observations were also performed to investigate the sample structures. The electrical resistances R of a single LPCMO nanowall and micrometer-size wires were investigated using a Physical Property Measurement System (Quantum Design). A pair of Pt/Au electrodes with a 2 µm gap was fabricated on a LPCMO sample by photolithography and electron beam deposition. Two-probe electrical measurements were carried out in the temperature range of 10-300 K under a magnetic field H of 0-9 T. The cathode luminescence (CL) measurement was performed using SEM-CL system (17, 19, 20) in the temperature range of 10-200 K under zero magnetic field. Then, 10 nm-thick rhodamine6G (R6G), typical luminescent coloring matter (21), was thermally deposited on the LPCMO film and 50 nm-width NW samples, and CL spectrum mapping were performed. The details of SEM-CL measurement is described in a supplemental information. Figure 1(b) shows a scanning electron microscopy (SEM) image of LPCMO NWs with 50 nm width on a MgO (001) single crystal substrate. Well-defined LPCMO NWs with homogeneous lateral interfaces between each NW and the side-surface of the 3D-MgO nanotemplate were realized. A typical reflection high-energy electron diffraction (RHEED) image (Fig. 1(c)) of the NW sample proves that the LPCMO NWs were grown epitaxially. A single LPCMO NW bridging two electrodes was fabricated as a two-probe device using photolithography as shown in Fig. 1(d).


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Figures 2(a)-(c) and (d)-(f) show the magnetic field dependences of the normalized resistance MR (=R/R9T) and differential resistance ∆MR/∆H, respectively, for wall widths ranging from 1000 µm (corresponding to conventional thin-film) to 50 nm (NW). We see that applying an external magnetic field of a few Tesla induces a decrease in the resistance of all samples, corresponding to the IMT of LPCMO, and that there is a the clear difference of the MR curve shape among the samples. The 50 nm-width LPCMO NW sample displayed a single very sharp drop in MR (Fig. 2(a)), whereas the thin-film sample showed a more gradual decrease of MR with increasing magnetic field (Fig. 2(c)). For the 50 nm-width LPCMO NW at 80 K, the MR suddenly dropped at 2.5 T, after which it remained almost constant. In more detail, the intermediate 250 nm-width NW sample showed a moderately large drop of resistance at 3.0 T and additional step changes in MR at magnetic fields of 3.5 T and 4.5 T (indicated by the thin arrows in Fig. 2(b)), namely, multiple-step changes in MR. The change in the MR of the NW sample can be expressed in terms of a discrete step change in its function. This tendency was more clearly seen in the differential MR shown in Figs. 2(d)-(e). Here, the maximum value of

∆MR/∆H is defined as ∆MRmax. The singular nature of the discrete step change in MR is strongly related to the sample size; the single-step change in MR was only observed for a wire width of smaller than 100 nm. With increasing sample size from 50 nm (Fig. 2(a)) to 1000 µm (Fig. 2(c)), the change in MR shifts from a step change to a gradual change. Additionally, we can see clear differences in residual resistance after transition from insulator to metal phase, namely quite flat in NW sample, but gradual decrease in film sample. After ∆MRmax, the MR value was almost constant with less than 10 % change in NW sample (Fig. 2(a)) while the film sample showed ~105 % MR change(Fig. 2(c)).


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Usually the IMT is understood by the collapse of an insulating charge-ordered state (electron crystal) to a metallic ferromagnetic state (electron liquid) without considering the spatial domain distribution. However, to understand this nanostructuring effect, it is essential to introduce the nanoconfinement effect on the dispersed electronic domains with their unusually sharp IMT nature in addition to considering results of observing in bulk/film samples. Conceptually, it is required that single electronic domains show a discrete step-like IMT, that is, they exhibit a very high resistive state under a low magnetic field, which abruptly changes to a very low resistive state when magnetic field exceeds a threshold value HC. Here, HC can be defined the critical magnetic field for the IMT for a single domain. In a NW sample whose width is narrower than a single electronic domain, a domain can be confined into one dimension, resulting in a series domain network. In a series network composed of two types of resistors, i.e., metal and insulator domains, the change in MR induced by the single-domain IMT have a huge effect on the observed signal because the final robust insulating domain becomes a bottleneck in the current path, causing its phase transition from an insulator to a metal, which governs the conductivity of the sample, to appear as a discrete single-step change in MR. On the other hand, a 2D film can be defined as a large network consisting of a mixture of parallel and series resistors. Even though a bottleneck current path exists in 2D network, the total resistance of the path via the insulating domains will be lower due to large number of current paths; thus, the total resistance can be measured as the average resistance of all domains. For LPCMO systems, the average singledomain size has been reported to be 10-100 nm order (2-4). Thus, we can conclude that the single-step change in MR with the largest variation observed for the 50 nm NW sample (Fig. 2(a)) was caused by the nanoconfinement, which allowed us to observe the effect of the IMT of single domains in a series chain of 1D domains. The multiple-step changes in MR in Fig. 2(b)


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are thought to be caused by broadly defined domain confinement effects (13, 14), where the sample size of µm order or less was still larger than the domain size. These results suggest the possibility of controlling the variation in MR via the size of the nanostructures. As further analysis, we estimate the IMT property of a single electronic domain as a function of the external magnetic field. Based on the above discussion, the IMT of a single electric domain must have a discrete step change across a threshold value HC. Assuming the simplest first-order IMT, the resistance of a single domain ρs at a given temperature T1 is described as a function of the magnetic field as () = {

( ) − ( < ) ( ) − ( ≥ )

--(1),

where, ( ) ≫ ( ) . HC is the critical magnetic field, and ρins and ρmet are the resistances in the insulating and metallic phases under a magnetic field of 0 T, respectively. α and β are coefficients representing the proportional decrease in resistance with increasing magnetic field (22). The MR curve for a single domain following Eq. (1) is shown in Fig. 3(a). Here, we construct a simple but effective model to describe the change in the domain population of a manganite. The main idea is to define the critical magnetic field for the IMT for each domain (indexed by i) as HCi (HC1, HC2,···,HCN), where each domain has a volume fraction of vi = v(HCi) [%] (23). Thus, the total resistance of a 1D nanowire composed of N domains can be defined as () = ∑ ∙ ( , ) = ∑ ( ) ∙ ( , )

--(2),


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where ρs(HCi, H) denotes the resistance for an individual domain with a critical magnetic field of HCi. By taking suitable values of HCi and v(HCi) (as shown in Fig. 3(b)), the observed MR curve can be well fitted to the curve representing the IMT for the 1D nanowire. Figure 3(b) shows the v(HCi) used to reproduce the experimental MR curve. In the 1D series network, the system resistance abruptly drops when the final insulating domain becomes metallic. Eventually the 1D nanowire becomes completely metallic and its discrete IMT mainly reflects the very sharp IMT of the final nanodomain with the highest critical magnetic filed of HCN (Fig. 3(c)). This model explains not only the nanoconfinement effect of MR in a manganite but also the unusual shape of the first-order IMT of a single electronic nanodomain. The excellent agreement between the experimental and calculated results supports the validity of our model, in which the MR of a 1D nanowire consists of a series of first-order IMTs. This model is also applicable to 2D films, which can be considered as an ensemble of many domains in combination with a random resistor network model (24-29), and the simulated results for a 2D film are also well fitted to the experimentally observed gradual change in MR (see Fig. S-1). Equation (2) strongly indicates that the change in resistance through the IMT in a sample with a single-domain size would be more drastic than that in a sample with a larger volume. The phase-separated domain structure (Fig. 4(a)): the metal and insulator single domains arranged in a series chain in the 50 nm-width NW was successfully observed. Figure 4(b) shows an integral CL intensity image from 450 nm to 520 nm in wavelength. Since the luminescence intensity difference originates from the different luminescent efficiency of R6G on metal/insulator (Fig. S-3) due to the interface energy transfer effect (30, 31), this image show the arrangement of metal and insulator domains in a 50 nm-NW. The red area with higher intensity and the blue area with lower intensity in Fig. 4(b) correspond to insulator and metal domains,


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respectively. Conversely, in the CL intensity image from 680 nm to 705 nm in wave length (Fig. 4(c)) the red area with high intensity shows metal domains and blue region with lower intensity reflects insulator domains. The exact opposite relation between Fig. 4(b) and Fig. 4(c) shows reliability of our nanoelectric domain observation. Thus, we can conclude the single domain size in LPCMO was 70-200 nm, which is consistent with the reported domain size for (La,Pr,Ca)MnO3 samples (2-4). A noteworthy fact is that single domains made series configuration in the 50 nm-width NW. This result can prove our designed model (Fig. 3 and Eq. (2)) to explain the step-MR change, and the quite flat residual resistance change in the NW sample (Fig. 2(a)), due to the formation of bottleneck in the current path in 1D domain arrangement. If this sharp IMT is an intrinsic feature of manganites, it is expected that the 50 nm-width NW sample with 1D series domain arrangement would also show steep single-step IMT behavior induced by a change in temperature. Figure 5(a) shows the temperature dependence of the resistance (RT) in the 50 nm-width NW sample. The RT curve for the NW sample exhibited a sharp drop, i.e., a step change, in contrast to the gradual change in that of the 2D film sample (Fig. 5(b)). Under a magnetic field of 1.5 T, the RT curve showed a single-step change at 35 K in the cooling process. This RT curve also reminds us of the first-order transition; the resistance behavior drastically changed from insulating to metallic at the critical temperature of 35 K. The RT curves for the NW sample showed similar features under magnetic fields of 2.0 T and 2.5 T. In the same way as for the magnetic field, we can also consider the simplest first-order IMT, namely, at the transition temperature TC the resistivity of a single domain ρs(T) drastically switches from a high-resistivity state: ρins(T) to a low-resistivity state: ρmet(T).


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Judging from the observed RT curves, we can adopt the following function for ρs(T) as the simplest form to describe the observed results quantitatively: ( ) =

( ) = !"# $

%&

'( ) ;

* ( > : -!./0123405/! 6!7/12)

( ) = 8 + : + < = ( ≤ : .!5?@@/0 6!7/12)

--(3),

where A, B, and C are coefficients, ρ0 is the residual resistance in the metallic phase, Eg is the activation energy in the insulating (semiconducting-like) phase (24, 25, 28), and kB is the Boltzmann constant. Using Eq. (3), we confirmed that the RT curves not only for the 1D NW but also for the 2D film can be reproduced as a statistical ensemble of ρs(T), as shown in Figs. 5(a) and (b), respectively, even though there is much difference between the 1D NW and 2D film samples. The good agreement between the observed data and the fitting for both NW sample with a step discontinuous change and the film sample with a gradual continuous change indicates validity of our model. We finally show the distribution of insulating and metallic domains to describe the IMT behavior in more detail. At a low magnetic field of less than HC1, all the domains are insulating, and at a high magnetic field of above HCN, all are metallic. At intermediate fields (HC1 ≤ H ≤ HCN), insulator and metal domains coexist with various volume fractions, and at higher fields, all the domains are insulating. The temperature dependence of spatial domain distribution was estimated from the observed MR curves of the 50 nm-width LPCMO NW sample (Fig. 6(a)) by fitting using ( ) as parameters. All the MR curves observed in the temperature range of 50 K

to 150 K displayed single-step changes. The distribution of ( ) indicates the volume for each domain, corresponding to the size and number of domains. The normalized total volume fraction of metallic domain, ABCD (), at magnetic field of H is expressed as


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ABCD () = ∑ ( )/ ∑ ( ) -- (4), Figure 6(b) shows ABCD () evaluated for various magnetic fields and temperatures. With

increasing magnetic field H, ABCD () systematically increases, finally reaching a value of 1,

corresponding to the completion of IMT. Although the function representing the IMT for a single domain is a simple function based on Eq. (1), this model can explain the MR behavior over a wide temperature range. However, the origin of the HC and distributions for each domain is still unknown. The existence of quenched disorder states caused by fluctuations of the dopant density, the strain field, or the intrinsic instability in electronic phases resulting from strong electron-electron correlation (32-35), might be possible origins. In this paper, we firstly elucidated the nature of the discrete single-step change in the MR and RT of a nanoscale single electric domain, and proposed new nano-material and devices design concept based on the results. Equations (1) and (3) represent the simplest resistance behaviors for the magnetic field and temperature, respectively, based on the observed quite sharp first order IMT. To describe characteristics of domains in more detail, we introduced HCi, TCi, v(HCi), and v(TCi), which are currently fitting parameters in Eqs. (2) and (4). To determine v(HCi) and v(TCi) corresponding to domain size, more direct measurement for the nano dot samples with a few tens nm diameter by SPM observation and conductivity measurements with nanogap-electrodes is one of the solutions, which can be used to extend our model. In summary, for the (La0.275Pr0.35Ca0.375)MnO3 system, we constructed a well-defined epitaxial nanowall wire with a width down to 50 nm using a 3D nanotemplated PLD technique. The 50 nm-width NW exhibited an unusually sharp IMT, corresponding to the series configuration of single domains. We experimentally elucidated the true nature of the first-order transition with a discrete single-step change in the MR of a nanoscale single electric domain, as well as its field-


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and temperature-dependent behavior. Electronic phase transitions are very interesting and useful phenomena in many correlated electron systems including not only manganites with colossal magnetoresistance but also high-TC cuprates, the Mott insulator vanadium oxide, and so on. Our work demonstrates the power of 3D nanofabrication for elucidating and manipulating intrinsic and giant physical properties in correlated oxides, providing a way of realizing next-generation oxide nanoelectronics.

Corresponding Authors *[email protected], **[email protected]


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ASSOCIATED CONTENT Supporting Information. The comparison between the experimentally observed MR and the simulated results for a 2D film, and a description of nanodomain imaging using SEM-CL and the CL spectrum for metallic and insulating LPCMO are provided in support of the results presented above. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENT The authors are grateful to M. Sakuma, A. Iwaki, and the staff in the Comprehensive Analysis Center (CAC) in ISIR, Osaka University, for their helpful assistance. This study was partially supported by Grants-in-Aid for Young Scientists S (No. 21676001) and Young Scientists B (No. 25800178) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Part of this work was also supported by “Nanotechnology Platform Project (Nanotechnology Open Facilities in Osaka University)” of MEXT, Japan [Nos. S-12-OS-0002 and F-12-OS-0005]. One of the authors (ANH) was supported in part by Shiseido Female Research Science Grant.


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(16) Kushizaki, T.; Fujiwara, K.; Hattori, A. N.; Kanki, T.; Tanaka, H. Nanotechnology 2012, 23, 485308. DOI: 10.1088/0957-4484/23/48/485308. (17) Hattori, A. N.; Ichimiya, M.; Ashida, M.; Tanaka, H. Appl. Phys. Express 2012, 5, 125203. DOI: 10.1143/APEX.5.125203 (18) Hattori, A. N.; Fujiwara, Y.; Fujiwara, K.; Murakami, Y.; Shindo, D.; Tanaka, H. Appl. Phys. Express 2014, 7, 045201. DOI: 10.7567/APEX.7.045201 (19) M. Ichimiya, T. Horii, T. Hirai, Y. Sawada, M. Minamiguchi, N. Ohno, M. Ashida, and T. Itoh: J. Phys.: Condens. Matter 2006, 18, 1967. (20) Ichimiya, M; Sawada, Y; Ashida, M; Itoh, T. Phys. stat. sol. (c) {\bf 3} (2006) 1189. (21) Zhang, B.; Chandrasekhar, M.; Chandrasekhar, H. M.; Appl. Opt. 1985, 24, 2779. (22) Abramovich, A. I.; Gorbenko, O. Y.; Kaul’, A. R.; Koroleva, L. I. Michurin, A. V. J. Exp. Theor. Phys. 2004, 99, 820. DOI: 10.1134/1.1826175 (23) The volume fraction v(HCi) [%] is defined as ∑ ( ) = 100 [%]. The summation of vn

(=∑ ) gives the population of metallic domains at a magnetic field of HCn.

(24) Li, G.; Zhou, H.-D.; Feng, S. J.; Fan, X.-J.; Li, X.-G.; Wang, Z. D. J. Appl. Phys. 2006, 92, 1406.


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DOI: 10.1063/1.1490153 (25) Joshi, L.; Keshri, S.; Phase Transitions 2010, 83, 263. DOI:10.1080/01411591003665758 (26) Rao, G. H.; Sun, J. R.; Sun, Y. Z.; Zhang, Y. L.; Liang, J. K. J. Phys.: Condens. Matter 1996, 8, 5393. (27) Mayr, M.; Moreo, A.; Vergés, J. A.; Arispe, J.; Feiguin, A.; Dagotto, E. Phys. Rev. Lett. 2000, 86, 135. DOI: http://dx.doi.org/10.1103/PhysRevLett.86.135 (28) Egilmez, M.; Chow, K. H.; Jung, J. Appl. Phys. Lett. 2008, 92, 162515. DOI: 10.1063/1.2908931 (29) Zhao, G.; Smolyaninova, V.; Prellier, W.; Keller, H. Phys. Rev. Lett. 2000, 84, 6086. DOI: 10.1103/PhysRevLett.84.6086 (30) Chance, R. R.; Prock, A; Silbey, R; J. Chem. Phys. 1975, 62, 2245. (31) Becker, H; Burns, S. E.; Friend, R. H.; Phys. Rev. B 1997, 56, 1893. (32) Chen, C. H.; Cheong, S.-W. Phys. Rev. Lett. 1996, 76, 4042. DOI: 10.1103/PhysRevLett.76.4042 (33) Tomioka, Y; Asamitsu, A; Kuwahara, H.; Moritomo, Y.; Tokura Y. Phys. Rev. B 1996, 53, R1689.


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DOI: 10.1103/PhysRevB.53.R1689 (34) Hervieu, M.; Van Tendeloo, G.; Caignaert, V. V.; Maignan, A.; Raveau, B. Phys. Rev. B 1996, 53, 14274. DOI: 10.1103/PhysRevB.53.14274 (35) Cao, G.; Zhang, J.; Cao, S.; Jing, C.; Shen, X. Phys. Rev. B 2005, 71, 174414 (2005). DOI: 10.1103/PhysRevB.71.174414 (36) The model was defined on an M×N lattice (M = 100 and N = 40), where a single domain can dominate the transport as shown in Fig. 5(a). A unit (uij: u11, u12,···, uMN) corresponds to a single electric domain. At each link in this effective lattice, either a metallic or insulating resistance is randomly selected with a population of metallic domains of Pmetal(H). Considering the network flow in the system by Kirchhoff’s law, the currents and voltages are related by K = ∑ 7L (M − ML ), where Ii and Vi denote the current and voltage at node i, respectively, and gij is the conductance of link ij, with the sum running over all links ij. The net resistivity of the system was solved by the cycle current method using the circuit resistance matrix R to obtain, i = Ht×[(H×R)×Ht]-1×H×s. No interaction among the domains is considered. (37) Nguyen, T. V. A.; Hattori, A. N.; Fujiwara, Y.; Ueda, S.; Tanaka, H.; Appl. Phys. Lett. 2013, 103, 223105.


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Figures

Figure 1: (a) Concept of an original nanofabrication technique, 3D-nanotemplate PLD, where LPCMO is deposited onto the side-surface of 3D MgO using inclined PLD. (b) Bird’s-eye view SEM image and (c) RHEED pattern of the LPCMO NWs with 50 nm width and 150 nm height. SEM image and RHEED pattern ([100]MgO incidence, 30 kV) were taken at 300 K. (d) Top-view SEM image of an LPCMO NW structure bridging electrodes with a 2 µm-gap.


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Figure 2: MR(R/R9T) curves at 80 K for LPCMO samples with widths of (a) 50 nm (NW), (b) 250 nm (NW), and (c) 1000 µm (film), and (d)-(f) corresponding ∆MR/∆H curves. The diagonal arrows in (b) highlight multiple-step changes in MR.


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Figure 3: Conceptual representation of Eqs. (1) and (2). (a) MR property for single domain ρs(Hci, H) described as a first-order change (Eq. (1)) with various critical magnetic fields Hci (Eq. (2)). (b) Volume ratio for the domain with critical magnetic field Hci, namely vi=v(Hci), in Eq. (2). (c) Comparison between MR curve observed for LPCMO NW wire sample at 60 K (red squares) and calculated MR curve (open black squares). In this model, the system MR is modeled by an ensemble of first-order changes ρs(Hci, H) in domain i with volume fraction vi. The parameters in Eq. (1) for the fitting were α = 1.27×106 Ω/T and β = 0.301 Ω /T.


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Figure 4: (a) Schematic image of metal and insulator domain arrangement in LPCMO NW sample at 150 K. CL intensity mapping for 10 nm-R6G deposited LPCMO NW sample with 50 nm-width. The images show the integrated sum of CL intensities (b) from 450 nm to 520 nm, and (c) from 680 nm to 705 nm in wave length at 150 K (see Fig. S-3). The integrated intensity was normalized by total CL intensity (380 – 880 nm).


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Figure 5: RT curves (cooling process) for (a) LPCMO NW sample and (b) LPCMO film sample under various magnetic fields. The open black squares show the calculated RT curves with volume ratio for the domain with critical magnetic field Tci as shown in insets. The parameters in Eq. (3) for the fitting of NW were A = 4.55 Ω/K, Β = 9.29 Ω/K2, C = 2.43×10-4 Ω/K5, Eg = 104.5 meV, and ρ0 = 3.47×103 Ω, and those for the fitting of film were A = 0.379 Ω/K , Β = 9.69×10-3 Ω/K2, C = 2.99×10-7 Ω/K5, Eg = 89.5 meV, and ρ0=167.0 Ω.


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Figure 6: (a) MR(R/R9T) curves for an LPCMO NW wire sample at various temperatures. (b) Schematic phase diagram showing the phase boundaries between the metal, coexisting, and insulator phases. The metal ratio, calculated by the summation of IMT probabilities vi, is expressed as a color. The black dots represent metal ratios obtained from the experimental MR curves in (a), using Eq. (3).


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Identification of Giant Mott Phase Transition of Single Electric

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