We present the results of the high-temperature neutron and x-ray diffraction experiments on the Ca3–xSrxTi2O7 (x = 0.5, 0.8, 0.85, 0.9) compounds. The ferro- to paraelectric transition in these hybrid improper ferroelectric materials arises from the so-called trilinear coupling. Depending on the strontium content, various structures and phase transitions, different from theoretical predictions, emerge. The in situ x-ray powder diffraction indicates a direct ferro- to paraelectric transition between the orthorhombic A21am and the tetragonal undistorted I4/mmm phase for x ≤ 0.6. We identified a reduction in the trilinear coupling robustness by increasing the Sr-doping level to lead to the emergence of the intermediate tetragonal P42/mnm phase and the gradual suppression of the orthorhombic phase. The observed character of the structure transitions and the Ca3–xSrxTi2O7 phase diagram are discussed in the framework of theoretical models of other related hybrid improper ferroelectric systems.

Proper ferroelectrics (FEs) are characterized by polarization which is the primary order parameter originating from zone-center polar lattice instability. On the other hand, in hybrid improper ferroelectrics (HIF), polarization is part of a more complex lattice distortion arising from a combination of two nonpolar lattice modes with different symmetries, the so-called trilinear coupling.1,2 In perovskites, these modes correspond to oxygen polyhedral distortions, commonly rotations or tilts, which can, in addition, induce magnetoelectricity and weak ferromagnetism. Such an electric-field-controllable mechanism can be extremely attractive for device applications if operated at room temperature and hereby attracts enormous attention.3 Moreover, it has been shown for Ca3–xSrxTi2O7 crystals recently that there is a unique domain topology associated with various types of oxygen octahedral distortions having a direct impact on ferroelectric properties.4,5,6

The family of HIF compounds reveals an amazingly rich set of structure transitions, as was demonstrated on Ca3–xSrxTi2O7,4 Sr3Zr2O7,7 and Ca3Mn2O7,8 recently. These materials belong to the Ruddlesden-Popper phases described by the general formula An+1BnO3n+1 (n = 2). The structure consists of perovskite ABO3 building blocks stacked along the [001]-axis with a rocksalt AO layer interspersing every two perovskite unit cells. In the ferroelectric (FE) state, A3B2O7 forms the orthorhombic polar space group A21am, which corresponds to the distorted tetragonal I4/mmm structure where the paraelectric (PE) phase is eventually established upon heating. How the orthorhombic structure transforms into the distortion-free aristotype phase upon heating has been the subject of many theoretical works.1,2,9 Experimentally, it has been demonstrated that each of these compounds exhibits its own unique route (summarized in Table I).

TABLE I.

The temperature evolution of the crystal structures with corresponding irreducible representations in various HIF systems.4,7,8

T increases →
Ca3–xSrxTi2O7 X2+X3 X3 
I4/mmm 
A21am P42/mnm 
Sr3Zr2O7 X2+X3 X1X3 X3 … 
A21am Pnab Amam I4/mmm 
Ca3Mn2O7 X2+X3 X1 
I4/mmm 
A21am Acaa 
T increases →
Ca3–xSrxTi2O7 X2+X3 X3 
I4/mmm 
A21am P42/mnm 
Sr3Zr2O7 X2+X3 X1X3 X3 … 
A21am Pnab Amam I4/mmm 
Ca3Mn2O7 X2+X3 X1 
I4/mmm 
A21am Acaa 

Improper hybrid ferroelectricity has been experimentally demonstrated for the first time in the orthorhombic Sr-doped Ca3Ti2O7.3 This distortion includes the rotation of the BO6 octahedra around the [001]-axis described by the in-phase rotation mode X2+ and the diagonal (with respect to the tetragonal-like basal plane) tilting mode X3 around the [110]-axis, which are simultaneously coupled to the Γ5 polar zone-center mode, thereby creating the trilinear coupling.1 By introducing the Sr-substitution, one can tune the robustness of distortions as the paraelectric Sr3Ti2O7 phase crystallizes in the I4/mmm space group. Theoretical works predicted the existence of an intermediate phase, either Amam or Acam;1,9 however, the combined study of Ca3–xSrxTi2O7 provided a different picture4 by discovering the intermediate paraelectric P42/mnm phase in Ca2SrTi2O7 characterized by the X3 [100] tilting mode oriented along the tetragonal-like directions. The impact of the discovered structure on physical properties has been studied experimentally10 and also theoretically by a first-principles study recently.11 The A21am-P42/mnm transition corresponds to the relaxation of the in-phase rotation X2+.4 Crossing the P42/mnm-I4/mmm border is related to the relaxation of the X3 tilting mode.

Sr3Zr2O7 undergoes a first-order FE-PE transition, where the paraelectric polymorph competes with the polar phase and emerges from a trilinear coupling of rotation and tilt modes interacting with an antipolar mode.7 The structure transforms from A21am to I4/mmm via two intermediate paraelectric phases upon heating: first, the X1 rotation mode is lost in the second-order Pnab → Amam transition and then the tilting mode X3 is lost in the second-order Amam → I4/mmm transition. The A21am → Pnab structure transition reveals hysteresis corresponding to a first-order transition linked to the competition of the X1 out-of-phase and the X2+ in-phase rotations.

In Ca3Mn2O7, the high-temperature I4/mmm structure undergoes a transition to an intermediate PE orthorhombic Acaa structure upon cooling and then changes to A21am.12 As the temperature is further lowered, an antiferromagnetic order sets in at 115 K. The Acaa symmetry is generated by the out-of-phase rotation X1; thus, the transition pathway from Acaa to A21am results in the competition of the X1 out-of-phase and X2+ in-phase rotations, thereby related to peculiar physical phenomena.8 It is worth noting that the Mn substitution on the Ti-site of Ca3Ti2O7 has also been studied both experimentally13,14 and theoretically;15 for the Ti-rich side, I4/mmm goes directly to polar A21am symmetry upon cooling while the structural transition processes via the Acaa symmetry for the Mn-rich side.13 

In this work, we present the temperature evolution of structure phase transitions revealed by varying the strontium concentration in Ca3–xSrxTi2O7 (0.5 ≤ x ≤ 0.9) using in situ high-temperature x-ray diffraction. We show that on the Ca-rich side the structure transition processes directly from I4/mmm to polar A21am (x < 0.8), while the intermediate phase P42/mnm is preferred in the transition pathway for the Sr-rich compositions. The structure-Sr concentration phase diagram is constructed and discussed within the framework of related HIF compounds.

The polycrystalline Ca3–xSrxTi2O7 samples (x = 0.5, 0.8, 0.9) were prepared using a solid-state reaction method as described in Ref. 4. The Ca2.15Sr0.85Ti2O7 single crystals were grown by an optical floating zone method.3 The samples with x = 0.5, 0.8, and 0.9 were characterized using the high-resolution x-ray diffractometer (Bruker XRD D8 Discover with Cu Kα source) equipped with the high-temperature chamber HTK 1200 N. Additionally, the sample with x = 0.5 was measured on the high-resolution synchrotron powder diffraction beamline I11 at Diamond Light Source using the multianalyzer crystal detector stages and 15 keV x-rays calibrated against NIST SRM 640c silicon powder. Samples were loaded in quartz capillaries and variable temperature heating provided by a cyberstar hot air blower.16 The neutron diffraction of pulverized single crystals with x = 0.85 was measured on the D2B high-resolution powder diffractometer (ILL). The single-crystal diffraction on the x = 0.85 sample from a different batch was measured using the hot neutron four-circle D9 diffractometer (ILL) equipped with a four-cycle furnace. The sets of D2B and D9 data can be found in Ref. 17. The diffraction data were analyzed using FullProf18 software. The differential scanning calorimetry (DSC) was measured using SETSYS Evolution 24 instrument (SETARAM) in the He atmosphere. The heating/cooling rate was 10 K/min and the transition temperatures were determined by the onset of the observed peaks.

Powder neutron diffraction study of a sample with x = 0.85 revealed the decay of the (237) and (033) reflections at ∼550 °C upon increasing temperature as shown in Figs. 1(a) and 1(b). The single-crystal neutron diffraction of a sample from a different batch observed the decay of the (033) Bragg peak at slightly higher temperature ∼580 °C, which might be caused by a negligible variation of the strontium concentration.

FIG. 1.

The temperature evolution of the powder neutron diffraction pattern of Ca2.15Sr0.85TiO7 showing the detail of the decay of (a) the (237) reflection and of (b) the (033) reflection. The arrows mark the position of the decaying reflections. The data are shifted vertically for clarity. The simulated I(033) intensity for the octahedral rotations ωR and ωT corresponding to various strontium concentrations (c).

FIG. 1.

The temperature evolution of the powder neutron diffraction pattern of Ca2.15Sr0.85TiO7 showing the detail of the decay of (a) the (237) reflection and of (b) the (033) reflection. The arrows mark the position of the decaying reflections. The data are shifted vertically for clarity. The simulated I(033) intensity for the octahedral rotations ωR and ωT corresponding to various strontium concentrations (c).

Close modal

As the (237) reflection has a lower intensity and higher 2θ in the x-ray diffraction data compared to the (033) reflection, the latter was chosen to identify transitions across various structure phases. The integrated intensities I(033) of the superlattice peaks are expected to scale as the square of the order parameter Q for these phase transitions, where Q is given by the rotation and tilting angles ωR and ωT of the oxygen octahedra, respectively. The angles are given by the strontium concentration as was shown by the synchrotron x-ray diffraction experiment.4 Simulation of the (033) reflection integrated intensity for different octahedral rotations (tilts) which corresponds to the increasing strontium concentration is shown in Fig. 1(c). It clearly shows the decrease of intensity by ∼15% for the sample with x = 0.8 and ∼18% for sample with x = 0.9 from the undoped Ca3Ti2O7. The values of I(033) were obtained by fitting of the peak profile using the Lorentz function. The (033) reflection of the x = 0.8, 0.85, and 0.9 samples was scanned in the 2θ region from 51.1° to 53.1° upon cooling using the Bruker diffractometer. In the case of x = 0.5 sample, the reflection was tracked in the 2θ region from 16.0° to 16.5° upon warming using the I11 instrument. The resulting scans upon decreasing temperature are summarized in Fig. 2. In all four compounds, a gradual decrease of the (033) intensity with increasing temperature is revealed. The free energy of the HIF superlattice system in terms of Ginzburg-Landau (GL) theory19,20 is given by

G=A1(TTC)ω2+A2ω4+A3ω6+C3PωRωT+C4P2PE,
(1)

where ω=(12ωR,12ωR,ωT), E is the external electric field, and P is the electrical polarization of Ca3Ti2O7. The quadratic term and the biquadratic terms coupling the rotations and polarization stated in Eq. (1)20 are omitted with respect to the trilinear term for temperatures close to TC. Assuming the first-order nature of the phase transition and the collaborative trilinear interaction, the coefficients A1, A3, and C4 are expected to be positive while A2 and C3 negative, respectively. The equilibrium solution providing non-negative ω2 obtained by minimizing the free energy is

ω2=16A3(2A2+(4A2212A3[A1(TTC)+C3P])12),
(2)

where the term C3 is defined analogically to Ref. 4, providing a first-order transition for A2 < 0, tricritical transition for A2 = 0, and a continuous transition for A2 > 0. With respect to the I(033)(T) error bars, qualitative results, i.e., the signs are given for the fitting coefficients except the transition temperatures.

FIG. 2.

The temperature dependence of the (033) reflection intensity of (a) Ca2.5Sr0.5Ti2O7, (b) Ca2.2Sr0.8Ti2O7, (c) Ca2.15Sr0.85Ti2O7, and (d) Ca2.1Sr0.9Ti2O7. The red dashed line is the GL fit. The aspects of the fitting procedure and the fitting parameters are discussed in the main text. The insets show temperature-intensity contour plots from the in situ x-ray diffraction measured at I11 (a) and measured using the Bruker diffractometer [(b)–(d)]. The data were collected while warming, except the data in (c), which were measured both upon cooling and warming.

FIG. 2.

The temperature dependence of the (033) reflection intensity of (a) Ca2.5Sr0.5Ti2O7, (b) Ca2.2Sr0.8Ti2O7, (c) Ca2.15Sr0.85Ti2O7, and (d) Ca2.1Sr0.9Ti2O7. The red dashed line is the GL fit. The aspects of the fitting procedure and the fitting parameters are discussed in the main text. The insets show temperature-intensity contour plots from the in situ x-ray diffraction measured at I11 (a) and measured using the Bruker diffractometer [(b)–(d)]. The data were collected while warming, except the data in (c), which were measured both upon cooling and warming.

Close modal

In the case of Ca2.5Sr0.5Ti2O7, the intensity decreases monotonically down to background values at TC using data combined from the I11 and Bruker measurements as shown in Fig. 2(a). The structure of the room-temperature phase corresponds to the A21am space group, while the phase above TC can be described by the I4/mmm space group. The fit of the data for the Ca2.5Sr0.5Ti2O7 sample offer TC = 605(15) °C, positive A1 and A3 parameters, negative C3 coefficient in line with the trilinear coupling, and the A2 coefficient approaching zero values within the large error bars proposing the composition with xSr = 0.5 is very close to the tricritical point.

In Figs. 2(b) and 2(c), we observe a different situation. Upon cooling, the temperature dependence of the (033) reflection intensity is characterized by a steplike structure emerging at TC1 = 360(25) °C in Ca2.2Sr0.8Ti2O7 and TC1 = 280(30) °C in Ca2.15Sr0.85Ti2O7. This remarkable change of slope signifies a transition from the room-temperature A21am space group to the tetragonal phase described by the P42/mnm symmetry. The corresponding coefficients A1 and A3 are positive, while C3 and A2 are negative for both systems, pointing to the first-order nature of the A21am-P42/mnm structural transition as expected from the group-subgroup relations. The (033) intensity decays completely at TC2 = 480(15) °C in Ca2.2Sr0.8Ti2O7 (TC2 = 550(18) °C in Ca2.15Sr0.85Ti2O7) when the high-temperature I4/mmm structure is established. The fitting parameter A2 is clearly positive for Ca2.2Sr0.8Ti2O7 and Ca2.15Sr0.85Ti2O7, respectively, revealing a continuous P42/mnm-I4/mmm transition in agreement with the Landau theory. To verify the order of the transitions obtained by the fits, we have measured the Ca2.15Sr0.85Ti2O7 sample both upon cooling and warming. A clear declination from the warming curve signifying hysteretic behavior and hence a discontinuous transition is observed below ∼350 °C, although lower temperatures could not be measured due to the gradual degradation of the sample in the furnace.

The intensity evolution in Ca2.1Sr0.9Ti2O7 is different from the previous two samples, as shown in Fig. 2(d). Here, the smooth decay of the (033) intensity suggests a second-order, single structure transition between the two tetragonal phases P42/mnm and I4/mmm at TC2 = 510(10) °C with the positive A2 parameter.

We further note that the DSC experiment on Ca2.15Sr0.85Ti2O7 does not show any anomaly up to 1300 °C [see Fig. 3(b)], which might be caused by the structure disorder increasing for higher strontium concentration, smearing out the discontinuous character of the transition at TC1 ∼ 280 °C. On the other hand, the heating and cooling curves obtained on Ca3Ti2O7 [inset of Fig. 3(b)] still show a transition at TC ∼ 760 °C with hysteresis ΔT ∼ 10 °C, which agrees well with the DSC data presented in Ref. 21.

FIG. 3.

(a) The temperature-Sr concentration phase diagram of the Ca3–xSrxTi2O7 system. The squares mark the O → T′ transition and the red triangles mark the O/T′ → T transition from the x-ray diffraction. The other triangles mark the O → T transition from DSC (this work and Refs. 10 and 21). The circles represent data (x < 0.9) from the ex situ observation of twin-change under POM. The data point for x = 0.9 marked by the circle was obtained from in situ TEM and the error bar is within the symbol. The solid lines are guides to the eye. (b) DSC curves of Ca2.15Sr0.85Ti2O7 measured up to 1300 °C. The inset shows the detailed view of Ca3Ti2O7 with the transition temperature ∼760 °C marked by vertical lines. The solid and dotted lines represent the heating and cooling processes, respectively.

FIG. 3.

(a) The temperature-Sr concentration phase diagram of the Ca3–xSrxTi2O7 system. The squares mark the O → T′ transition and the red triangles mark the O/T′ → T transition from the x-ray diffraction. The other triangles mark the O → T transition from DSC (this work and Refs. 10 and 21). The circles represent data (x < 0.9) from the ex situ observation of twin-change under POM. The data point for x = 0.9 marked by the circle was obtained from in situ TEM and the error bar is within the symbol. The solid lines are guides to the eye. (b) DSC curves of Ca2.15Sr0.85Ti2O7 measured up to 1300 °C. The inset shows the detailed view of Ca3Ti2O7 with the transition temperature ∼760 °C marked by vertical lines. The solid and dotted lines represent the heating and cooling processes, respectively.

Close modal

The data are summarized in the temperature-concentration phase diagram shown in Fig. 3(a). It can be separated into three regions O, T′, and T defined by the A21am, P42/mnm, and I4/mmm space groups. Clearly, the Ca-rich side reveals a direct transition from the orthorhombic to the undistorted tetragonal structure, while a narrow region of the intermediate phase opens in the Sr concentration range 0.6 < x < 0.8 and broadens with increasing x. According to Ref. 4, the undistorted I4/mmm phase is finally stabilized for x > 1. The phase diagram includes data obtained from the in situ x-ray diffraction, ex situ observation of twin-change under polarized optical microscopy (POM) after various heat treatments, in situ transmission electron microscopy (TEM) of Ca2.1Sr0.9Ti2O7,4 and DSC (this work and Ref. 10).

Turning our attention to the character of the structure transitions in HIF, we observe an agreement between our and previously published data: a first-order phase transition has been observed on the DSC curves in Ca3Ti2O721 and Ca3–xSrxTi2O7 for x < 0.5,10 corresponding to the O → T crossover in line with the group-subgroup relations. Similarly, a discontinuous change of the tilting order parameter when crossing the O → T′ boundary was reported in the Sr-rich composition with x = 0.9.4,5 The character of the transitions can be revealed also by the domain topology which has been heavily discussed recently.4,5,6 The formation of Z2xZ2 domains with Z4 vortices is associated with a second-order transition in the Sr-rich compounds. On the other hand, the phases with x < 0.95 form the Z4xZ2 domains with Z3 vortices which are related to discontinuous transitions.5 Our data show a discontinuous transition in the case of the A21am-P42/mnm paths when the trilinear term in the GL fit is considered, while a second-order transition for the P42/mnm-I4/mmm crossover is observed in all measured compositions. Interestingly, the GL fit of the A21am-I4/mmm transition in Ca2.5Sr0.5Ti2O7 suggests that this concentration might be on the verge of the tricritical point as indicated in the phase diagram.

In a loose analogy with the mean-field calculations using a simple microscopic Hamiltonian applied on the Aurivillius compounds, we can find a close resemblance with the Ca3–xSrxTi2O7 phase diagram shown in Fig. 2,22 and the order of the structure transitions. The temperature evolution of the order parameters ϕ1 and ϕ3 [Fig. 1(b),22] corresponds very well to the temperature evolution of the (033) intensity in Ca2.15Sr0.85Ti2O7 and Ca2.2Sr0.8Ti2O7. Depending on the coupling strength γ (strontium concentration in our case), the character of the O → T′ and T′ → T transitions can be either second- or first-order. Increasing γ leads to a single first-order transition [Fig. 1(c) 22] which, in this simplified view, corresponds to the Ca2.5Sr0.5Ti2O7 data. In further analogy with these schemes, we should expect the T′ → T transition to reveal a second-order character in Ca2.1Sr0.9Ti2O7, and both types of transitions can emerge in the intermediate compositions. Such a scenario implies the existence of a tricritical point, where a first-order transition changes into a second-order one. It has been suggested that the density of domain walls is expected to be smaller for a tricritical phase transition, compared to a second-order one.23 The tricritical behavior near the xSr = 0.5 concentration demands experiments focused on the region of the O, T′, and T phase coexistence investigating a variety of strontium compositions.

Using in situ high-temperature x-ray diffraction and other techniques, we have studied the structural transitions in the Ca3–xSrxTi2O7 HIF compounds tuning the trilinear coupling strength by varying the Sr-doping level. Consistent with previous studies, the Ca-rich compositions reveal a single direct transition from the orthorhombic ferroelectric A21am phase to the tetragonal paraelectric I4/mmm phase. For x ≥ 0.8, an intermediate paraelectric P42/mnm phase emerges wedged in between the room-temperature and the high-temperature phase as revealed by two successive transitions. Above x ∼ 0.9, we observe a single phase transition from P42/mnm to I4/mmm at high temperatures. The temperature dependence of the I(033) intensities and the phase diagram corresponds qualitatively very well to the calculated diagrams of the Aurivillius phases. Using the GL fit with the trilinear term included, we show that the A21am-P42/mnm structural transition across the series is first-order-like, while the P42/mnm-I4/mmm crossover reveals a continuous character, consistently with previous experiments. Moreover, the data suggest the presence of the tricritical behavior for the xSr = 0.5 concentration. We have also shown that the simple x-ray diffraction method can be used to identify the order of the transitions using the modified GL fit for the HIF systems. To clarify the related domain configuration and the properties of the domain walls in the vicinity of the critical point where the three phases merge, the next step is to prepare high-quality samples from the concentration range 0.6 < x < 0.8 and explore this part of the Ca3–xSrxTi2O7 phase diagram by further x-ray and neutron diffraction experiments.

This work was supported by the Institute for Basic Science (IBS) in Korea (No. IBS-R009-G1). We acknowledge the Institute Laue-Langevin (ILL), Grenoble, France, for the allocation of time on D2B and D9 diffractometers. The work was supported within the program of Large Infrastructures for Research, Experimental Development and Innovation (Project Nos. LM2015050 and LTT17019) financed by the Ministry of Education, Youth and Sports, Czech Republic. We acknowledge the support and beam time under Award No. “EE16074” at Diamond Light Source in providing synchrotron research facilities used in this work. The DSC experiments were performed in MGML (https://mgml.eu/) through the program of Czech Research Infrastructures (No. LM2011025). The work at Rutgers University was supported by the DOE under Grant No. DOE: DE-FG02-07ER46382.

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