Emerging single-phase state in small manganite nanodisks

Significance

Electronic phase separation (EPS) is a common phenomenon in complex oxides systems. However, little is known regarding how EPS responds when the size of the system is smaller than the characteristic size of EPS. This issue is not only important for understanding the physical origin of EPS but also for oxides device applications in which oxides have to be fabricated into small-sized structures. Our work on manganites shows a surprising transition from the EPS state to a single phase state when the spatial size of the system is smaller than the characteristic length scale of EPS. This observation paves a way to manipulate EPS, which is potentially useful for oxides electronic and spintronic device applications.

Abstract

In complex oxides systems such as manganites, electronic phase separation (EPS), a consequence of strong electronic correlations, dictates the exotic electrical and magnetic properties of these materials. A fundamental yet unresolved issue is how EPS responds to spatial confinement; will EPS just scale with size of an object, or will the one of the phases be pinned? Understanding this behavior is critical for future oxides electronics and spintronics because scaling down of the system is unavoidable for these applications. In this work, we use La_0.325Pr_0.3Ca_0.375MnO₃ (LPCMO) single crystalline disks to study the effect of spatial confinement on EPS. The EPS state featuring coexistence of ferromagnetic metallic and charge order insulating phases appears to be the low-temperature ground state in bulk, thin films, and large disks, a previously unidentified ground state (i.e., a single ferromagnetic phase state emerges in smaller disks). The critical size is between 500 nm and 800 nm, which is similar to the characteristic length scale of EPS in the LPCMO system. The ability to create a pure ferromagnetic phase in manganite nanodisks is highly desirable for spintronic applications.

Owing to strong coupling between spin, charge, orbital, and lattice (1, 2), different electronic phases often coexist spatially in strongly correlated materials known as electronic phase separation (EPS) (3, 4). For colossal magnetoresistance (CMR) manganites, EPS has been observed to have strong influence on the global magnetic and transport properties (5, 6). Regarding the physical origin of EPS, it has been shown theoretically that quenched disorder can lead to inhomogeneous states in manganites (1, 3, 7). Once long-range effects such as coulombic forces (8), cooperative oxygen octahedral distortions (9), or strain effects (10) are included, calculations show infinitesimal disorder (8, 11) or even no explicit disorder (10) may lead to EPS. Within a phenomenological Ginzburg–Landau theory, it has been shown that EPS is intrinsic in complex systems as a thermodynamic equilibrium state (12).

Although the details of the origin of the EPS remain as a matter of dispute, its very existence as a new form of electronic state has been well accepted. The length scale of the EPS has been observed to vary widely from nanometers to micrometers depending on many parameters that can affect the competition between different electronic phases (13–20). It is thus of great interest to examine whether the EPS state still exists as the system is scaled down, especially when the spatial dimension of the system is smaller than the length scale of the EPS domains.

In this work, we use La_0.325Pr_0.3Ca_0.375MnO₃ (LPCMO) as a prototype system to show a spatial confinement-induced transition from the EPS state to a single ferromagnetic phase state. The LPCMO system is chosen because of its well-known large length scale of EPS domains (approximately a micrometer) (21), which allows us to conveniently fabricate LPCMO epitaxial thin films into disks with diameters that are smaller than the EPS domain size. In LPCMO bulk (21) and thin films (6, 22), the EPS state was observed to be the low-temperature ground state. Using magnetic force microscope, we observe that the EPS state remains to be the ground state in disks with the size of 800 nm in diameter or larger but vanishes in the 500-nm-diameter disks whose size is distinctly smaller than the characteristic length scale of the EPS domains. In the 500-nm disks, only the ferromagnetic phase can be observed at all temperatures below Curie temperature T_c, indicating that the system is in a single-phase state rather than a EPS state. Our results further indicate that the large length scale EPS in the LPCMO system does not cost extra Coulomb energy, which otherwise should lead to a scaling down of EPS with decreasing size of the LPCMO disks (23, 24).

LPCMO films with 60-nm thickness were epitaxially grown on SrTiO₃(001) substrates by pulsed-laser deposition. The substrates were kept at 780 °C in oxygen atmosphere of 5 × 10⁻³ millibars during growth. Unit cell by unit cell growth was achieved as indicated by oscillations of intensity of reflection high-energy electron diffraction (RHEED). The films were postannealed to 950 °C for 3 h in flowing oxygen to reduce oxygen vacancy and make sure that the films have the same magnetic properties as the bulk. The LPCMO disks with diameters from 500 nm to 20 μm were fabricated from the epitaxial thin films by electron beam lithography with a negative tone resist (for details, see the sample fabrication method and Fig. S1 in the Supporting Information). Magnetic properties of the LPCMO disk arrays were carried out using superconducting quantum interference device (SQUID) and magnetic force microscope (MFM) measurements.

Fig. S1.

(A and B) Schematics of LPCMO disks samples for magnetic property measurement (A) and MFM mapping (B). (C) Optical microscopic image of LPCMO disk array with specific diameter. (D) SEM image of LPCMO disk sample for MFM imaging.

A distinct signature of the EPS state in the LPCMO system is the thermal hysteresis for temperature-dependent magnetic and transport properties. Fig. 1 A–D shows temperature dependent magnetic properties of LPCMO disks with different diameters. To enhance the measuring signal for SQUID, we fabricate disk arrays for each selected diameter (the optical microscopic image shown in Fig. 1B, Inset for the 1-μm disk array). Fig. 1 A–D shows temperature-dependent magnetization measured under 1,000 Oe in-plane field for 7-μm, 1-μm, 800-nm, and 500-nm disk arrays, respectively. Thermal hysteresis can be observed for disk arrays with size down to 800 nm, reflecting the fact that ferromagnetic metallic (FMM) and charge order insulating (COI) phases coexist during the first-order phase transition (7, 25). For the 500-nm disk array, however, no thermal hysteresis can be observed. This observation implies that the EPS state may no longer exist in the system (7, 26).

Fig. 1.

Temperature dependence of magnetization (black lines for cooling and red lines for warming) under 1,000 Oe (A–D) and initial magnetization (red lines) and hysteresis loop (black lines) (E–H) at 5 K of arrays of LPCMO disks with sizes of 7 μm (A and E), 1 μm (B and F), 800 nm (C and G), and 500 nm (D and H) in diameter and an area of 3 mm × 3 mm. (B, Inset) The optical microscopic image of d = 1 μm array. (C and D, Insets) Zoomed-in M vs. T loop around the thermal hysteresis region.

The lack of EPS state in the 500-nm disk array is supported by the field-dependent magnetization measurements. Fig. 1 E–H shows in-plane initial magnetization curves and magnetic hysteresis loops (M-H loops) for the disk arrays measured at 5 K after zero-field cooling. For 800-nm or larger disk arrays, there is a clear difference between the initial magnetization curves and the corresponding M-H loops due to the coexistence of FMM and COI phases. When the magnetic field is applied from the initial state, the magnetization of the FMM phase first quickly aligns along the field direction, leading to the low field fast rise of the initial magnetization curve. With increasing field, the COI phase is melted and transits into the FMM phase. Once transited, the FMM phase will mostly stay even if the field is reduced, giving rise to the difference between initial magnetization curve and the M-H loop. The difference, however, becomes smaller with decreasing size. For the 500-nm disk array, the initial magnetization curve and the M-H loop virtually superimpose each other, indicating no melting of COI phase occurs. Both the temperature- and field-dependent magnetization measurements show a transition from the EPS state to a single FMM state with decreasing size of the disk, and the critical size should be between 500 nm and 800 nm.

The transition from the EPS state to a single FMM state can be seen in MFM images shown in Fig. 2 (for MFM imaging details, see micromagnetic mapping method in Supporting Information). Fig. 2A shows morphological appearance of LPCMO disks with different sizes acquired by atomic force microscope (AFM). Fig. 2 B–D shows the corresponding MFM images of the LPCMO disks acquired at different temperatures under a perpendicular magnetic field of 1T. Here, the perpendicular magnetic field is applied to yield some perpendicular magnetization components for MFM imaging because the easy magnetization axis is in the plane. In the present color scale, the contrast below zero (red or black) represents FMM phase, whereas the contrast above zero (green or blue) represents nonferromagnetic phase [i.e., COI phase based on previous knowledge of the LPCMO system (21, 22)]. Apparently, except the 500-nm disk, all other disks show distinct features of the EPS state (i.e., the coexistence of the FMM and COI phases). Although the portion of FMM phase increases noticeably with decreasing temperature, the system stays in the EPS state even at 10 K. The typical length scale of the EPS domains is around a micrometer, which is consistent with previous reports (21, 27).

Fig. 2.

(A) AFM images of LPCMO disks with sizes of 500 nm, 1 μm, 2 μm, 3.8 μm, 5 μm, and 7 μm in diameter. (B–D) The MFM images of LPCMO disks under 1T field (external magnetic field direction is pointing perpendicularly to the sample surface plane) taken at 10 K (B), 100 K (C), and 180 K (D). The sizes of disks in MFM images are adjusted and corrected to have same scales for each size with the help of scanning electron microscope (SEM) images (shown in Fig. S2) and dash lines show the approximate physical boundary of disks. The negative value in MFM image indicates attractive force and positive value indicates repulsive force.

In stark contrast to the larger disks, the 500-nm disk does not exhibit any features of EPS in Fig. 2. Instead, the whole disk is in a ferromagnetic phase with a magnetization profile peaking in the center. To ensure that the EPS state is not diminished by the magnetic field applied during MFM imaging, we took MFM images of the 500-nm disk at 10 K under different perpendicular magnetic fields from 0T to 1T, as shown in Fig. 3A. At 0T, signals with opposite sign can only be seen on two sides of the disk along the marked line (MFM images of 4 disks shown in Fig. S3). This pattern is a typical MFM image for an in-plane ferromagnetic single domain, because only the two ends of an in-plane magnetic dipole yield perpendicular field gradient (with opposite signs) for the MFM tip to detect. Once a perpendicular field of 0.15T is applied, the in-plane magnetization is driven out of plane, leading to a center peaked MFM contour. The MFM signal increases with increasing field, as shown in Fig. 3B by the marked line profiles extracted from Fig. 3A.

Fig. 3.

(A) MFM images of 500-nm disks at 10 K under different magnetic field. The lines show the path the line profile extracted. (B) Line profiles extracted from MFM images partly shown in Fig. 3A. (C) Simulated results corresponding to line-profiles in B. (D and E) The simulated Z-component of stray field 100 nm above sample disks and magnetic structure of 500-nm disks under a different magnetic field. In E, the direction and size of arrows show the direction and relative value of in-plane component of magnetization, and the color of disk indicates the value of Z-component of magnetization presented by ratio of Z-component to total magnetization, as shown in the color bar.

Fig. S3.

MFM images of 500-nm disks taken at 10 K under zero field after zero-field cooling.

The field-dependent behavior of the MFM contrast of the 500-nm disk is in qualitative agreement with micromagnetic simulations. Based on the MFM observation, the 500-nm disk is in an in-plane, single-domain state. Using this model as input, we performed micromagnetic simulation and obtained the Z-component of magnetic stray field distribution at 100 nm above sample surface (Fig. 3D; for details, see the micromagnetic simulation method in the Supporting Information), which is virtually the signal detected by MFM tip. The corresponding magnetic structures under different magnetic fields are shown in Fig. 3E. The marked line profiles extracted from simulation (Fig. 3D) are shown in Fig. 3C alongside with the experimental MFM line profiles (Fig. 3B). The subtle differences between Fig. 3B and Fig. 3C are likely caused by the fact that experimental MFM images are convoluted from signals of both the LPCMO disks and the MFM tips (∼100 nm in size). The consistency of MFM images and simulation confirms that the 500-nm disk is in a ferromagnetic single-domain state with an in-plane easy magnetization axis.

Finally, we show that the 500-nm disk is in a single FMM state at all temperatures. Fig. 4 shows MFM images of the 500-nm disk acquired every 20 K, from 20 K to 200 K under 1,000 Oe. Other than the center-peaked FMM phase, no traces of COI phase can be observed. The MFM signal decreases with increasing temperature, which is consistent with the behavior of the temperature-dependent magnetization shown in Fig. 1. Considering the fact that we have never observed pure COI phase in the 500-nm disks, we believe this phenomenon may be caused by the existence of the ferromagnetic metallic edge state in the LPCMO system (22), which assists the 500-nm disk to be in pure ferromagnetic state when a single state is energetically preferred in the 500-nm disk.

Fig. 4.

MFM images of 500-nm disks taken every 20 K, from 20 K to 200 K.

In summary, we discovered a spatial confinement-induced transition from a EPS state featuring coexistence of FMM and COI phases to a single FMM state in the LPCMO system. The critical size for the transition is between 500 nm and 800 nm, which is similar to the characteristic length scale of the EPS state in the LPCMO system. Combining the MFM data and the micromagnetic simulation, we conclude that the 500-nm LPCMO disk is in a single-domain ferromagnetic state at all temperatures below T_c. A similar conclusion can be reached for 300-nm LPCMO disks (shown in Fig. S4), although it needs to be studied further whether a new state would emerge if the disk size becomes a few tens of nanometers or smaller. Our work opens a way to control EPS without external field or introducing strain and disorder, which is potentially useful to design electronic and spintronic devices in complex oxides systems.

Fig. S4.

MFM images of 300-nm disks taken at different temperatures and magnetic fields.

Note 1: Sample Fabrication Method

Sixty-nanometer LPCMO films (60 nm) were grown on SrTiO₃ substrates by pulsed laser deposition and annealed at 950 °C for 3 h in flowing oxygen atmosphere. Magnetic properties of films were measured to ensure the sample quality. Two kinds of samples are designed, one with LPCMO disk array with specific diameter shown for magnetic measurement in Fig. S1 A and C, the other with a collection of LPCMO disks with different diameters for MFM mapping shown in Fig. S2 B and D. Electron beam lithography (Zeiss SIGMA SEM and Raith Elphy Plus pattern processor) was applied to fabricate LPCMO disks with AR-N 7520 as resist, which is a negative e-beam resist with a good sensitivity and very high resolution (<30 nm). The resist was spin-coated (3,000 revolutions per minute for 40 s, Raurell MODEL WS-650MZ-23NPP) to the film surface and prebaked at 90 °C for 90 s, and then the films were transferred to an SEM chamber and should avoid light exposure because the resist is also sensitive to photons. With the help of the pattern processor, SEM could write any patterns we draw in pattern processor controlling software, and SEM parameters were set to be most effective values (electron high voltage: 20 kV; beam current: 35 pA; dose: 80 μC/cm²; writing field: 200 μm × 200 μm, with a matrix repeat the disk area is 3 mm × 3 mm). After SEM writing, samples were dipped in developing liquid (RZX 3038: H₂O = 1:4) for 45 s and baked for 90 s at 120 °C. Ion beam etching was used to fabricate sample from resist pattern, the ion beam current, accelerate voltage, and etching time were set to be 80 mA, 300 V, and 8 min, respectively. The last step is to remove residual resist using reactive-ion etching with oxygen plasma. After all these procedures, LPCMO disks are well prepared for magnetic property measurements.

Fig. S2.

SEM images of disks with different sizes. (Scale bars: 250 nm, 500 nm, 1 μm, 2 μm, 2.5 μm, and 3.5 μm, respectively.)

Note 2: Micromagnetic Mapping Method

A commercial AFM/MFM (Atto AFM/MFM Ixs; Attocube Systems) was used to map the topography and magnetic image under the preset conditions. During the measurement, the MFM image was performed in the dual pass mode to remove the morphology contribution from MFM signals. In the first pass, the system takes a tipping AFM mode to get the line profile of the topography. In the second pass, the tip lifts up 100 nm and scans again following the first line profile loop to record the phase shift signal, which reflects the magnetic force provided by the magnetic domains of the sample. The magnetic information was extracted from the detected phase shift at a constant frequency. Thus, the patterns with negative phase shift (caused by attractive force) show ferromagnetic domains.

Note 3: Micromagnetic Simulation Method

The micromagnetic simulation is performed in COMSOL. Multiphysics using the finite elements method where the Landau–Lifshitz–Gilbert (LLG) equation is transformed into weak form and solved in a 3D environment. To simulate the dipole–dipole interaction precisely, the Maxwell equation is coupled with the LLG equation, and they are solved simultaneously. The radius of the sample disk is 250 nm, and the height is 60 nm. The disk is in-plane magnetized at initial time. An external field is applied on the disk along the out-of-plane axis. Data are extracted from the location 100 nm above the surface. The saturated magnetization Ms = 2.64 × 10⁵ A/m, exchange stiffness A = 0.328 × 10⁻¹⁰ A⋅m, out-of-plane hard axis anisotropy K = −2 × 10⁵ A/m, gyromagnetic ratio gamma = 2.21 × 10⁵ Hz/(A/m), and Gilbert damping α = 0.2.

Note 4: SEM Images of LPCMO Disks

SEM images of LPCMO disks shown in Fig. S2 are used for MFM image correction.

Note 5: MFM Images of 500-nm LPCMO Disks at 10 K Under Zero Field After Zero-Field Cooling

MFM images of four 500-nm disks at 10 K under zero field after zero-field cooling are shown in Fig. S3. The fact that the dipole-like signals of these four disks point to random directions is consistent with our inference of magnetic structure of 500-nm LPCMO disks.

Note 6: MFM Images of 300-nm LPCMO Disks at Different Temperature and Magnetic Field

MFM images of 300-nm LPCMO disks at 10 K and 100 K under 1T and 5T are shown, respectively, in Fig. S4. The images also show the same center-peaked MFM contours as that of the 500-nm disks, indicating single FMM domain behavior.