Strain-induced polarization enhancement in $\mathrm{BaTi}{\mathrm{O}}_{3}$ core-shell nanoparticles

Strain-induced polarization enhancement in $BaTi O_{3}$ core-shell nanoparticles

Eugene A. Eliseev, Anna N. Morozovska, Sergei V. Kalinin, and Dean R. Evans

Phys. Rev. B 109, 014104 – Published 18 January 2024

Abstract

Despite fascinating experimental results, the influence of defects and elastic strains on the physical state of nanosized ferroelectrics is still poorly explored theoretically. One of the unresolved theoretical problems is the analytical description of the strongly enhanced spontaneous polarization, piezoelectric response, and dielectric properties of ferroelectric oxide thin films and core-shell nanoparticles induced by elastic strains and stresses. In particular, the 10-nm quasi-spherical $BaTi O_{3}$ core-shell nanoparticles reveal a giant spontaneous polarization up to $130 µ C / c m^{2}$ , where the physical origin is a large Ti off-centering. The available theoretical description cannot explain the giant spontaneous polarization observed in these spherical nanoparticles. This work analyzes polar properties of $BaTi O_{3}$ core-shell spherical nanoparticles using the Landau-Ginzburg-Devonshire approach, which considers the nonlinear electrostriction coupling and large Vegard strains in the shell. We reveal that a spontaneous polarization greater than $50 µ C / c m^{2}$ can be stable in a (10–100)-nm $BaTi O_{3}$ core at room temperature, where a 5-nm paraelectric shell is stretched by (3–6)% due to Vegard strains, which contribute to the elastic mismatch at the core-shell interface. The polarization value $50 µ C / c m^{2}$ corresponds to high tetragonality ratios (1.02–1.04), which is further increased up to $100 µ C / c m^{2}$ by higher Vegard strains and/or intrinsic surface stresses leading to unphysically high tetragonality ratios (1.08–1.16). The nonlinear electrostriction coupling and the elastic mismatch at the core-shell interface are key physical factors of the spontaneous polarization enhancement in the core. Doping with the highly polarized core-shell nanoparticles can be useful in optoelectronics and nonlinear optics to increase beam coupling efficiency, electric field enhancement, reduced switching voltages, ionic contamination elimination, catalysis, and electrocaloric nanocoolers.

Received 30 August 2023
Revised 6 November 2023
Accepted 2 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.014104

Physics Subject Headings (PhySH)

Ferroelectricity Pyroelectricity

Core-shell nanoparticles

Landau-Ginzburg-Devonshire theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Eugene A. Eliseev ¹, Anna N. Morozovska ^2,*, Sergei V. Kalinin^3,†, and Dean R. Evans^4,‡

¹Frantsevich Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Omeliana Pritsaka 3, 03142 Kyiv, Ukraine
²Institute of Physics, National Academy of Sciences of Ukraine, 46, pr. Nauky, 03028 Kyiv, Ukraine
³Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
⁴Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Ohio 45433, USA

^*Corresponding author: anna.n.morozovska@gmail.com
^†Corresponding author: sergei2@utk.edu
^‡Corresponding author: dean.evans@afrl.af.mil

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 109, Iss. 1 — 1 January 2024

Reuse & Permissions

Access Options

Article part of CHORUS

Accepted manuscript will be available starting 17 January 2025.

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) A spherical core-shell nanoparticle: a ferroelectric core of radius $R_{c}$ is covered with a paraelectric shell of thickness $Δ R$ , which is full of elastic defects and free charges. The nanoparticle is placed in an isotropic dielectric medium; $ɛ_{b}$ , $ɛ_{s}$ , and $ɛ_{e}$ are the core background, shell, and surrounding media dielectric permittivities. (b),(c) Block scheme of the main assumptions (b) and their implications (c).
Reuse & Permissions
Figure 2
The spontaneous polarization $P_{s}$ of a single-domain $BaTi O_{3}$ core-shell nanoparticle with radius $R_{c} = 5$ nm (a), (e), 10 nm (b), (f), 25 nm (c), (g), and 50 nm (d), (h) calculated as a function of temperature $T$ and Vegard strain $w_{s}$ using the 2–4–6 (a)–(d) and 2–4–6–8 (e)–(h) LGD free energy without nonlinear electrostriction coupling, $λ = 0.5$ nm, $Δ R = 5$ nm, and $ɛ_{s} = 500$ . Color coding in the diagrams is the absolute value of $P_{s}$ in the deepest potential well of the LGD free energy. The color scale shows the $P_{s}$ in $µ C / c m^{2}$ . The abbreviations “PE” and “FE” refer to the paraelectric and ferroelectric phases, respectively.
Reuse & Permissions
Figure 3
The spontaneous polarization $P_{s}$ of a single-domain $BaTi O_{3}$ core-shell nanoparticle with radius $R_{c} = 5$ nm (a), (e), 10 nm (b), (f), 25 nm (c), (g), and 50 nm (d), (h) calculated as a function of temperature $T$ and Vegard strain $w_{s}$ using optimal nonlinear electrostriction values. For 2–4–6 LGD free energy, $W_{c} = 0$ and $Z_{c} = 0.27 m^{8} / C^{4}$ (a)–(d); and 2–4–6–8 LGD free energy, $W_{c} = 1.2 \times 10^{- 12} m^{4} / (Pa C^{2})$ and $Z_{c} = 0.44 m^{8} / C^{4}$ (e)–(h). Other parameters and designations are the same as in Fig. 2.
Reuse & Permissions
Figure 4
The strain components $u_{1}^{c}$ (a), (b) and $u_{3}^{c}$ (c), (d), and the tetragonality ratio $c / a$ (e), (f) of the single-domain $BaTi O_{3}$ core with radius $R_{c} = 5$ nm (a), (c), (e) and 50 nm (b), (d), (f) calculated as a function of temperature $T$ and Vegard strain $w_{s}$ using the 2–4–6–8 LGD free energy; $W_{c} = 1.2 \times 10^{- 12} m^{4} / (Pa C^{2})$ and $Z_{c} = 0.44 m^{8} / C^{4}$ . Other parameters are the same as in Fig. 2.
Reuse & Permissions
Figure 5
The spontaneous polarization $P_{s}$ (a)–(c) and the electrocaloric temperature change $Δ T_{E C}$ (d)–(f) of a single-domain $BaTi O_{3}$ core-shell nanoparticle calculated as a function of core radius $R_{c}$ and Vegard strain $w_{s}$ using the 2–4–6–8 LGD free energy, $W_{c} = 1.2 \times 10^{- 12} m^{4} / (Pa C^{2})$ and $Z_{c} = 0.44 C^{- 4} m^{8}$ , and temperatures $T = 298$ K (a), (d), 338 K (b), (e), and 388 K (c), (f). Color scale corresponds to $P_{s}$ in $µ C / c m^{2}$ and $Δ T_{E C}$ in K. Other parameters are the same as in Fig. 2.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Strain-induced polarization enhancement in $BaTi O_{3}$ core-shell nanoparticles

Eugene A. Eliseev, Anna N. Morozovska, Sergei V. Kalinin, and Dean R. Evans

Phys. Rev. B 109, 014104 – Published 18 January 2024

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Strain-induced polarization enhancement in BaTiO3 core-shell nanoparticles

Eugene A. Eliseev, Anna N. Morozovska, Sergei V. Kalinin, and Dean R. Evans

Phys. Rev. B 109, 014104 – Published 18 January 2024

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Strain-induced polarization enhancement in $BaTi O_{3}$ core-shell nanoparticles