[Paper Review] Interface control of emergent ferroic order in Ruddlesden-Popper Sr$_{n+1}$Ti$_n$O$_{3n+1}$

Turan Birol, Nicole A. Benedek+1 more|arXiv (Cornell University)|Oct 6, 2011

Ferroelectric and Piezoelectric Materials3 citations

TL;DR

This paper demonstrates that epitaxial strain in Ruddlesden-Popper Sr$_{n+1}$Ti$_n$O$_{3n+1}$ thin films controls the perpendicular coherence length of ferroic distortions rather than directly inducing ferroelectricity, enabling a nearly degenerate state between ferroelectricity and antiferroelectricity. First-principles calculations reveal that structural relaxations at SrO/SrTiO$_3$ interfaces break Ti-O-Ti chain coherence, suppressing in-plane polar instability in n=1 despite strain sufficient to induce ferroelectricity in bulk SrTiO$_3$, with ferroelectricity emerging only at higher n due to increased coherence length.

ABSTRACT

We have discovered from first-principles an unusual polar state in the low n Sr$_{n+1}$Ti$_n$O$_{3n+1}$ Ruddlesden-Popper (RP) layered perovskites in which ferroelectricity is nearly degenerate with antiferroelectricity, a relatively rare form of ferroic order. We show that epitaxial strain plays a key role in tuning the "perpendicular coherence length" of the ferroelectric mode, and does not induce ferroelectricity in these low dimensional RP materials as is well known to occur in SrTiO$_3$. These systems present an opportunity to manipulate the coherence length of a ferroic distortion in a controlled way, without disorder or a free surface.

Motivation & Objective

• To understand how epitaxial strain controls ferroic order in low-dimensional Ruddlesden-Popper oxides where conventional finite-size effects do not apply.
• To investigate why SrTiO$_3$-like ferroelectricity does not emerge in n=1 RP phases despite sufficient strain to stabilize it in bulk SrTiO$_3$.
• To explore the role of interfacial structural relaxations in disrupting the coherence of polar modes across perovskite slabs.
• To demonstrate that the perpendicular coherence length of the ferroelectric mode is tunable via strain, enabling access to a competition between ferroelectric and antiferroelectric states.
• To provide a design principle for engineering emergent ferroic order in oxide heterostructures through interface control of coherence length, avoiding disorder or free surfaces.

Proposed method

• Density-functional theory (DFT) calculations using the PBEsol functional and PAW pseudopotentials in VASP with a 500 eV plane-wave cutoff.
• Use of a Γ-centered 8×8×8 k-point mesh for Brillouin zone integration and a 0.5 meV/Å force convergence threshold for structural relaxations.
• Calculation of interplanar force constants (IPFCs) for supercells with varying numbers of SrTiO$_3$ layers to model the effective harmonic Hamiltonian.
• Construction of the IPFC matrix from atomic force constants, with symmetrization to ensure perfect symmetry and minimal error (<1%) in eigenvalues.
• Analysis of in-plane polar phonon frequencies as a function of n to extract the coherence length via exponential fitting.
• Estimation of ferroelectric transition temperatures from the energy gain of the ferroelectric state relative to the paraelectric state, using first-principles energy differences.

Experimental results

Research questions

• RQ1 Why does epitaxial strain fail to induce in-plane ferroelectricity in n=1 Sr$_{n+1}$Ti$_n$O$_{3n+1}$ despite inducing it in bulk SrTiO$_3$?
• RQ2 How do interfacial structural relaxations at SrO/SrTiO$_3$ interfaces affect the coherence of Ti-O-Ti chains and polar distortions?
• RQ3 To what extent can epitaxial strain tune the perpendicular coherence length of the ferroelectric mode in low-n RP phases?
• RQ4 What is the role of interlayer coupling and interface structure in stabilizing a nearly degenerate ferroelectric-antiferroelectric state?
• RQ5 Can the coherence length of ferroic order be controlled independently of the polarization direction, particularly in the in-plane direction where depolarization fields are screened?

Key findings

• In n=1 Sr$_{n+1}$Ti$_n$O$_{3n+1}$, epitaxial strain sufficient to induce ferroelectricity in bulk SrTiO$_3$ fails to trigger a polar instability due to broken Ti-O-Ti chain coherence at the interface.
• The in-plane polar phonon frequency decreases exponentially with increasing n, indicating a growing coherence length of the ferroelectric mode, well-fit by a single exponential decay.
• For n=1 under 1.7% strain, the energy gain of the ferroelectric state is ~0.4 meV/f.u., comparable to unstrained bulk SrTiO$_3$, suggesting quantum fluctuations suppress long-range order.
• At n=2 under 1.1% strain, the energy gain reaches ~0.4 meV/f.u., while for n≥4 under 1.1% strain or n≥2 under 1.7% strain, the energy gain exceeds 8 meV/f.u., comparable to bulk SrTiO$_3$’s 8 meV/f.u. and its room-temperature ferroelectricity.
• The transition temperature estimate suggests that n≥4 under 1.1% strain or n≥2 under 1.7% strain could exhibit ferroelectric transitions near room temperature.
• Interfacial structural relaxations disrupt the long-range coherence of the ferroelectric mode, making the system sensitive to strain tuning of the coherence length rather than direct polarization induction.