Ferroelectric phase transition of Li-doped KTa1-xNbxO3 single crystals with weak random fields: Inelastic light scattering study

Accepted Manuscript Ferroelectric phase transition of Li-doped KTa1-xNbxO3 single crystals with weak random fields: Inelastic light scattering study Md. Mijanur Rahaman, Tadayuki Imai, Tadashi Sakamoto, Md.Al Helal, Shinya Tsukada, Seiji Kojima PII:

S0925-8388(17)33785-4

DOI:

10.1016/j.jallcom.2017.11.039

Reference:

JALCOM 43732

To appear in:

Journal of Alloys and Compounds

Received Date: 31 March 2017 Revised Date:

22 October 2017

Accepted Date: 4 November 2017

Please cite this article as: M.M. Rahaman, T. Imai, T. Sakamoto, M.A. Helal, S. Tsukada, S. Kojima, Ferroelectric phase transition of Li-doped KTa1-xNbxO3 single crystals with weak random fields: Inelastic light scattering study, Journal of Alloys and Compounds (2017), doi: 10.1016/ j.jallcom.2017.11.039. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Ferroelectric phase transition of Li-doped KTa1-xNbxO3 single crystals with weak random fields: Inelastic light scattering study Md. Mijanur Rahamana,b*, Tadayuki Imaic, Tadashi Sakamotoc, Md. Al Helala,

a

Tsukadad,

and

Seiji

Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki

b

SC

305-8573, Japan

Department of Materials Science and Engineering, University of Rajshahi, Rajshahi 6205,

M AN U

Bangladesh c

Kojimaa*

RI PT

Shinya

NTT Device Innovation Center, Nippon Telegraph and Telephone Corporation, Atsugi,

Kanagawa 243-0198, Japan d

Faculty of Education, Shimane University, Matsue, Shimane 690-8504, Japan

TE D

Corresponding author: Md. Mijanur Rahaman and Seiji Kojima

Email address: [email protected]; [email protected]

AC C

Raman scattering

EP

Keywords: polar nano-regions; random fields; relaxor-like ferroelectrics; Brillouin scattering;

Abstract

The broadband gigahertz dynamics of a ferroelectric phase transition of the 2.5%Li-doped KTa1-xNbxO3 crystals with x = 0.38 (KLTN/2.5/38) was investigated by inelastic light scattering. Its phase transition was found to be slightly diffused type due to weak random fields (RFs) caused by disorder in B-site of perovskite structure. The microscopic origin of the central peak (CP) and the local symmetry of the polar nanoregions (PNRs) in the cubic phase were studied by Raman scattering. In Brillouin scattering, the remarkable elastic 1

ACCEPTED MANUSCRIPT anomaly of the longitudinal acoustic (LA) mode was observed near paraelectric cubic to ferroelectric tetragonal phase transition temperature, TC-T = 46 ˚C, which is attributed to the coupling between fluctuating local polarization in PNRs and the LA mode. The intermediate temperature, T* ~ 97 ˚C, at which a dynamic to static transition of PNRs occurs, was

RI PT

determined from the significant increase of damping and intensity of the LA mode and the CP upon cooling. In the vicinity of the TC-T, a slightly stretched slowing down of the relaxation time, τCP, a feature of order-disorder nature of the ferroelectric phase transition

SC

with weak RFs, was clearly observed.

M AN U

1. Introduction

In relaxor ferroelectrics, the understanding of the role of random fields (RFs) related to polar nanoregions (PNRs) is important, therefore, it becomes one of the active research fields. In the midst of oxide perovskite, the relaxor-like ferroelectric Li-doped KTa1-xNbxO3 (KTN)

TE D

with the random occupancy of homovalent B-site cations is suitable to study the role of PNRs for weak RFs, because of its structural simplicity of perovskite structure and Pb-free environmental friendly nature. The comparison with that for strong RFs in the Pb-based

EP

relaxor ferroelectrics with heterovalent B-site cations is also important. In addition, the Li-

AC C

doped KTN single crystals exhibit large quadratic electro-optic effect [1,2], excellent photorefractive effect [3], and good piezoelectric effect [4], which make them one of the potentials alternative of the Pb-based relaxor ferroelectrics for application to both optical and electromechanical devices.

The relaxor ferroelectrics are characterized by the RFs that induce the significant frequency dispersion and the diffusive temperature dependence of the dielectric susceptibility. The compositional disorder, i.e., the disorder in the arrangement of different

2

ACCEPTED MANUSCRIPT ions [e.g. Mg2+ and Nb5+ in Pb(Mg1/3Nb2/3)O3, PMN ] in a crystallographic equivalent site is a common origin of the RFs, which are the origin of PNRs and chemical order regions (CORs) [5,6]. The appearance of PNRs is a consequence of the cation off-centering at B-site that is a common property of the most perovskite ferroelectrics. All the off-centered ions are

RI PT

expected to switch relatively freely between their stable positions and the time average structure remains cubic in high temperature ranges [7]. However, their positions and motions become correlated upon cooling, giving rise to PNRs. It has been well accepted that the PNRs

SC

in a parelectric phase are characterized by the Burns temperature, TB [8], at which the dynamic PNRs begin to appear, and the intermediate temperature, T*, at which the dynamic

M AN U

PNRs start to transform into static PNRs [9,10]. However, the microscopic mechanism underlying their appearance, growth, dynamics, and how they affect ferroelectric properties are still remain unclear.

TE D

In KTN, Nb ions go off-center at the B-site, and its microscopic origin was predicted by the pseudo Jahn-Teller effect (PJTE) [11]. The off-centering of Nb ions in KTN was discussed using an inelastic light scattering by the eight site model in which Nb ions displace

EP

along the equivalent [111] directions [12]. By the X-ray absorption fine structure (XAFS)

AC C

measurement, the off-center displacements of Nb ions in the KTN were accurately determined by Hanske-Petitpierre et al. [13]. Therefore, in KTN, the PNRs can be induced by off-center displacements of Nb ions at the B-site [13]. Owing to the homovalency at B-site cations, the KTN has no COR that induces the diffusive phase transition, which occurs in a Pb-based relaxor ferroelectric with the heterovalent cations at the B-site [14]. Hence, the charge disorder at B-site of KTN are different from those of the Pb-based relaxor ferroelectrics. By the acoustic emission measurement of a high quality KTa0.68Nb0.32O3 (KTN/32) single crystal, the TB and the T* were observed at 347 ˚C and 37 ˚C, respectively

3

ACCEPTED MANUSCRIPT [15]. Moreover, the normal critical slowing down phenomenon related to PNRs was also observed by Brillouin scattering [9,16]. In addition, the existence of PNRs in the paraelectric cubic phase of KTN crystals was investigated by different types of experiments [16-21]. Nowadays, the Li-doping effect in KTaO3 is one of the interesting research topics in

RI PT

materials science. It was reported that the Li ions in K1-yLiyTaO3 (KLT) occupy one of six off-center positions along the [100] direction at the A-site [22,23], which can lead to the formation of RFs related to PNRs. However, a critical concentration in KLT was reported at

SC

around yC = 0.022 below which the KLT freezes into a dipole glass state at the glass transition temperature, Tg, and above which it undergoes a ferroelectric transition at TC-T [24].

M AN U

Such a drastic change in transition behavior of KLT across the yC attributed to the piezoelectric character of PNRs, which ultimately drives the structural transition with a critical level of local polarization [24]. Moreover, KLT/2.6 (y = 0.026) exhibited a broad phase transition under the moderate electric field along the [100] directions, while the

TE D

KLT/6.3 displayed relatively sharp one [25].

Thus, the Li-doped KTN is an interesting system to investigate the Li-doping effects on

EP

PNRs and the physical properties related to a ferroelectric phase transition. In Li-doped KTN,

AC C

not only the ions of B-site, Nb ions are displaced by 0.145 Å [13], but also the Li ions, the ions of A-site, is off-centered by 1.2 Å [22], which enhance the RFs and the appearance of PNRs. Recently, Rahaman et al. observed the 5%Li-doping effect on elastic anomaly that was broaden in comparison with the non-doped KTN/40 by the enhanced growth of PNRs [10]. By the 5%Li-doping, the transformation of A1(z) mode of PNRs of R3m symmetry in non-doped KTN [9] to the E(x,y) mode of PNRs of R3m symmetry was also observed by Raman scattering [26]. Most recently, the effects of electric fields and injected electrons in 5%Li-doped KTN crystals were observed by the creation of PNRs and lowering the value of

4

ACCEPTED MANUSCRIPT the critical end point (CEP) [27,28]. Therefore, it is very important to study the effect of Lidoping on precursor dynamics, especially local symmetry of PNRs, where the concentrations of Li ions near the yC. In the present study, the broadband Brillouin spectroscopy of a 2.5%Li-doped KTN (x = 0.38) single crystal was studied to provide new insights into the

RI PT

PNRs related to the elastic anomaly in the GHz range and their slightly stretched type slowing down mechanism. The local symmetry of PNRs, which was responsible for the central peak (CP) and the breaking of symmetry in the paraelectric cubic phase, was

2. Experiment 2.1. Brillouin scattering

M AN U

SC

discussed on the basis of the results of angular dependence of Raman scattering.

The K0.975Li0.025Ta0.62Nb0.38O3 (KLTN/2.5/38) single crystal grown by the top seeded solution growth (TSSG) method

at NTT Corporation was cut having the size of

TE D

4.37×3.15×1.00 mm3 with the largest faces oriented perpendicular to the [100] direction. The largest (100) faces were polished to optical grade to obtain inelastic light scattering spectra. The Brillouin scattering spectra were measured by a Sandercock-type 3+3 passes tandem

EP

Fabry-Perot interferometer at a back scattering geometry [29]. A diode-pumped solid state

AC C

laser (DPSS) with a wavelength of 532 nm and a power about 100 mW was used to excite the sample. The free spectral ranges (FSR) of 75 GHz and 300 GHz were used to observe acoustic modes and the broad CP, respectively. The temperature of the sample was controlled by a heating/cooling stage (Linkam, THMS600) with the temperature stability of ±0.1˚C over all temperatures.

2.2 Raman scattering

5

ACCEPTED MANUSCRIPT The temperature dependence of the ā(cc)a (VV) Raman scattering spectra were measured at a back scattering using a double monochromator (Horiba-JY, U-1000). For the angular dependence of Raman scattering, the VV and ā(bc)a (VH) Raman spectra were obtained using a polarization rotation device (Sigma Koki) equipped with a broadband half-waveplate

RI PT

(Kogakugiken) [30]. The Raman scattering was excited at 532 nm from a single frequency DPSS laser. The angular dependence of Raman spectra were collected at a back scattering geometry and analyzed by a single monochromator (Lucir) combined with the xyz mapping

SC

stage (Tokyo Instruments) installed in the microscope (Olympus) and a charge coupled

M AN U

device (CCD, Andor).

3. Results and discussion 3.1. Brillouin scattering 3.1.1. Elastic anomaly

TE D

To study the elastic anomaly in the vicinity of the cubic-tetragonal phase transition temperature, TC-T = 46 ˚C, the temperature dependence of the Brillouin scattering spectra was measured above and below TC-T as shown in Fig. 1. As can be seen in Fig. 1, each spectrum

EP

consists of two doublets and a CP at zero frequency shift. The high- and low-frequency

AC C

doublets correspond to the longitudinal acoustic (LA) the transverse acoustic (TA) modes, respectively. In a paraelectric cubic phase, the TA mode is forbidden at a back scattering geometry in accordance with the Brillouin selection rule [31]. Thus, the existence of the TA mode in the paraelectric phase may indicate the breaking of cubic symmetry. In cubic phase of the KTN and the Li-doped KTN crystals, the breaking of symmetry due to the existence of PNRs with the rhombohedral R3m symmetry was observed by Raman scattering [9,26].

6

ACCEPTED MANUSCRIPT The LA mode was fitted by the Lorentzian function to determine frequency shift and damping. The temperature dependence of frequency shift and damping of the LA mode is plotted in Fig. 2. Upon cooling, the LA frequency shift shows a remarkable softening in the vicinity of the TC-T = 46 ˚C due to the piezoelectric coupling between the LA mode and the

RI PT

local polarization fluctuations in PNRs [9,10,16]. In addition, the significant increase of the damping of the LA mode towards TC-T was observed upon cooling from a high temperature as shown in Fig. 2. Such a behavior of the frequency shift and damping of LA mode was

SC

extensively observed in various Pb-based perovskite relaxors, such as 0.70Pb(Sc1/2Nb1/2)O3– 0.30PbTiO3 (PSN-30PT), PMN- 35PT PZN-15PT etc. [32-34]. It is noticeable that the

M AN U

damping of the LA mode starts to deviate at around 97 ºC from the constant temperature dependence at high temperatures. This temperature of deviation was marked as the intermediate temperature (T*), at which the dynamic PNRs begin to transform into static PNRs [9,10,16]. The value of the T* is in good agreement with the value reported in Refs. 10

TE D

and 26.

3.1.2 Critical slowing down

EP

In order to have a better understanding of precursor dynamics of the KLTN/2.5/38

AC C

crystal, we investigated a broad CP, which is related to the polarization fluctuations of dynamic PNRs. The contour color map of the temperature dependent Brillouin spectra of a broad CP is shown in Fig. 3. It is significant that the CP developed on cooling and its intensity drastically increases towards TC-T below the T* (Fig. 3), reflecting the rapid growth of the volume fraction of PNRs [9,10,16]. The remarkable increase of the damping of the LA mode was observed from T* to TC-T (Fig. 2) owing to the scattering of the LA mode by growing PNRs.

7

ACCEPTED MANUSCRIPT To discuss the nature of the ferroelectric phase transition, the dielectric property of the KLTN/2.5/38 crystal was studied. The temperature dependence of the real part, εʹ of the dielectric constant at some selected frequencies is shown in Fig. 4(a). It is important to note that the frequency dispersion of the KLTN/2.5/38 crystal is very weak or almost negligible.

RI PT

The almost negligible frequency dispersion can be due to the weakness of RFs. The dielectric behaviors are similar to those observed in the KLTN/5/60 single crystal [2]. Therefore, to clarify the phase transition behavior, we also study the inverse of the real part of the

SC

dynamical susceptibility, χ'(0) determined from the CP intensity by the following relation [35], and compared with the inverse dielectric constant [Fig. 4(b)].

ICP

ω

 ∝ χ' (0) -1

M AN U

∝ 0

∞ χ'' (ω)

T

-1

.

(1)

The dynamical susceptibility is related to the dielectric susceptibility that may obey the extended Curie-Weiss law [34,36], which was used to explain the phase transition behavior of typical relaxor ferroelectrics.

= +

T-TC-T 

TE D

1

χ' (0)

1

χb

2δ2

γ

,

(2)

EP

where χb is the magnitude of the susceptibility peak. γ and δ are fitting parameters denoting the degree of the diffuseness of the phase transition. When γ = 1, Eq. (2) expresses the Curie-

AC C

Weiss behavior of the ferroelectrics, while for γ = 2 describes a typical relaxor property. Figure 4(b) shows the T/ICP (diamonds) as a function of temperature, and the best fitted results by Eq. (2) are shown as solid line. As can be seen in Fig. 4(b), the inverse of the susceptibility of the KLTN/2.5/38 crystals is well fitted by the Eq. (2) with the critical exponent γ = 1.12 ± 0.03, indicating relaxor-like behavior of the Li-doped KTN single crystals with weak RFs. Since Brillouin scattering measurements are in the gigahertz range, which is near the high-frequency end of the distribution of relaxation time. However, the dielectric constant of the kilohertz frequency range measured by the conventional impedance 8

ACCEPTED MANUSCRIPT analyzer is near the main frequency range of the distribution of relaxation time, therefore, the value of γ may increase. We studied also the inverse of the dielectric constant (circles) measured at 1 kHz frequency [Fig. 4(b)]. By the Eq. (2), a good consistency between the dielectric data and the fitting result was obtained with the exponent of γ = 1.19 ± 0.003,

RI PT

which can be the clear indication of a relaxor-like ferroelectric phase transition of the KLTN/2.5/38 crystal. It is significant that the magnitude of the ε'(T) maxima of the KLTN/2.5/38 appeared to be smaller than those of the KTN/40 in the vicinity of the TC-T [9],

SC

although there is a slight dimensional discrepancy between KTN/40 and KLTN/2.5/38 single crystals. As investigated by Shannon [37], the polarizability for Li ion is considerable lower

M AN U

than for K ion. As a result, the substitution of K ions by the Li ions leads to decrease of polarizability per volume, and hence the dielectric constant decreases by the Li doping in KTN [38]. By the Li-doping, the decrease of the dielectric constant of KTaO3 was also

TE D

reported in Ref. 39.

To discuss the dynamics of the CP, the mean relaxation time was estimated by assuming the following equation [40]:

EP

π × (FWHM of CP) × τCP = 1,

(3)

AC C

where τCP is the mean relaxation time of the CP. The temperature dependence of the inverse of the τCP is displayed in Fig. 5. As the dynamical susceptibility follows the extended CurieWeiss law [Fig. 4(b)], the generalized Lyddane Sachs Teller (LST) relation predicts that the inverse of the relaxation time can be followed by the stretched-type slowing in the vicinity of the TC-T. Such a stretched-type slowing down behavior of the relaxation time under the influence of RFs might be described by the following empirical relation. 1 τ

= +  τ τ 1

1

T-TC-T

0

1

TC-T

, β

(β ≥ 1) for T > TC-T ,

9

(4)

ACCEPTED MANUSCRIPT where β is the stretched index related to the RFs. β = 1.0 means the normal critical slowing down without RFs and it assumes values > 1.0 depending on the strength of the RFs. The τ1 and τ0 are the characteristic time and relaxation time attributed to defects, respectively [16,41]. The observed relaxation time in the temperature interval between TC-T and TC-T+50

RI PT

˚C is well fitted by the Eq. (4) with the critical exponent β = 1.1, implying the order-disorder nature of the ferroelectric phase transition with weak RFs. The observed values of τ0 and τ1 are 1.86 ps and 2.33 ps, respectively. It was seen that the inverse of the relaxation time in

SC

non-doped KTN/40 showed normal critical slowing down (Fig. 5), which was reported in Ref. 9. Thus, the observed value of the β slightly more than 1.0 can be attributed to the weak

M AN U

RFs, which is induced by the Li-doping.

It is worthy to compare the value of 0 for other typical relaxor crystals which exhibited

the order-disorder nature of the ferroelectric phase transition at the TC-T. The value of the 0 is

TE D

similar to that reported for PZN-15PT [42]. From these results one can conclude that an order-disorder mechanism contributes to the slowing down of the dynamics PNRs in a KLTN/2.5/38 single crystal. It is also significant to compare the value of the 0 = 1.86 ps of

EP

the KLTN/2.5/38 with the value of the 0 = 1.61 ps of the non-doped KTN/40 [9]. The value

AC C

of τ0 is increased by the Li-doping. The small amount of Li ions doping in KTN may induce additional polarizations due to the off-center displacements of Li ions at A-site. These extra polarizations are cooperative with the neighboring PNRs resulting in larger PNRs [10], which enhance the value of τ0.

3.2. Raman scattering 3.2.1. Temperature dependence of Raman scattering spectra

10

ACCEPTED MANUSCRIPT To avoid the effect of Bose-Einstein phonon population, the reduce intensity, Ir (ω) was calculated from the Stokes component from the observed Raman scattering intensity I(ω) by the following equation:

1

ħω exp  kB T

I(ω)

.

ω[nω +1]

(5)

RI PT

nω =

Ir ω =

is the Bose-Einstein population factor, in which ħ and kB are the Dirac and

Boltzmann constants, respectively. The temperature dependence of the reduced Raman

SC

spectra of the KLTN/2.5/38 single crystal is shown in Fig. 6. The presence of intense first order TO2 mode (Fano resonance) near 196 cm-1 at 65 ˚C reflects the local symmetry

M AN U

breaking from cubic Pm3 m symmetry. In KTN, the detailed assignment of optical modes was

reported in Refs. 43-45. According to the phase diagram of KTN [46,47], the expected value of TC-T of the non-doped KTN/38 crystal is at around 23 ˚C. However, the value of the TC-T of the KTN/38 increases by the Li-doping. The increase of the TC-T by the Li-doping indicates

TE D

the enhanced ferroelectric instability of the Li-doped KTN crystals. Prater et al. also observed the effect of Li-doping on the TC-T of the KTN crystals by Raman scattering [48]. We are concern about the microscopic origin of the TO2 mode in the cubic Pm3 m symmetry, which

EP

is Raman inactive according to the Raman selection rule. To investigate the symmetry of the TO2 mode, all spectra in the frequency range 165 ~ 250 cm-1 were fitted by the Fano function

AC C

with third order polynomial as follows [49]:  r ω = IB +

I0 q+ε 2 1+ε2 

,

(6)

where IB = Pω-ωTO2  + Qω-ωTO2  + Rω-ωTO2  + S . I0 and q are the intensity and 3

2

asymmetry parameter of the TO2 mode, respectively. ε = 2(ω-ωTO2 )ΓTO2 is the parameter, where ΓTO2 is the FWHM of the TO2 mode. The example of a fit using Eq. (6) is shown in Fig. 7(a) by the solid line.

11

ACCEPTED MANUSCRIPT It is important to note that the reduced mode intensity, I0 of the TO2 mode decreases rapidly in the vicinity of the TC-T upon heating. Above the TC-T, the reduced mode intensity of the TO2 mode decreases gradually and shows the anomaly at around T* ~ 97 ˚C, at which a dynamic-to-static transition of PNRs starts. The value of the characteristic temperature T* is

RI PT

in good agreement with the value observed by Brillouin scattering. It is also worth noting that the ΓTO2 shows noticeable changes associated with these precursors effects as shown in the lower part of the Fig. 7(b). Hence, the presence of the weak mode intensity of the TO2 mode

SC

in a cubic phase reflects the breaking of symmetry due to the presence of PNRs with R3m symmetry. In the cubic phase, the symmetry breaking owing to the existence of PNRs with

M AN U

R3m was also reported in some typical relaxors by Raman scattering [50,51].

3.2.2. Angular dependence of Raman scattering spectra

In order to clarify the microscopic origin of CP and symmetry breaking in the cubic

TE D

phase, we analyzed the angular dependence of both VV and VH Raman scattering spectra. The angular dependence of contour color map of the Raman scattering intensity observed in both VV and VH scattering in a paraelectric cubic phase of the KLTN/2.5/38 single crystal is

EP

shown in Figs. 8(a) and 8(b), respectively. It is clearly seen that the intensity of the map

AC C

changes periodically with the rotation of the plane of the polarization, and the change of the intensity is mutually opposite between the VV and VH spectra (Fig. 8). In the analysis of the angular dependence of Raman spectra, we are mainly concerned about the local symmetry of PNRs that are related to the existence of the CP and the TO2 mode at 196 cm-1 in the cubic phase. To investigate the angular dependence of the CP, all spectra were fitted in the frequency range 20 ~ 193 cm-1 by the combination of a Lorentzian CP and damped harmonic oscillator (DHO) model by the following equation [52]: ω =

2ACP π

ГCP 4ω2

+ Г2CP

+ nω +1 ∑i 12

Ai Гi ω2i ω

ω2 -ω2i  +ω2 Г2i 2

,

(7)

ACCEPTED MANUSCRIPT where, ACP and ΓCP are intensity and FWHM of the CP, respectively. ωi, Γi, and Ai are frequency, damping constant, and intensity of the ith Raman active optical mode, respectively. The example of a fit of Raman spectrum using Eq. (7) is shown in Fig. 9(a). The angular dependence of Raman spectra was analyzed on the basis of the Raman tensors

RI PT

calculation assuming local R3m symmetry of PNRs. In PMN, the symmetry of PNRs was reported as rhombohedral R3m symmetry according to the neutron pair distribution function analysis [53]. The rhombohedral R3m symmetry has A1(z) , E(-x), and E(y) Raman active

0 a 0

0 0 0 , E-x = -c b -d

-c -d c 0 0 , Ey = 0 0 0 0

M AN U

a A1 z = 0 0

SC

modes with the following Raman tensors [54].

0 -c d

0 d 0

(8)

Using these Raman tensors, the angular dependence was calculated by the following expression

1  = 0 where R 0

0 cosθ sinθ

(9)

TE D

 -1 ·A1 z or E-x or Ey C  ·R -1 ·C , R 0 -sinθ, cosθ

EP

 and θ are the transformation matrix corresponding to Raman tensors modification from C

AC C

rhombohedral to cubic coordinates and rotation angle with the experimental coordinates, respectively [54]. The angular dependence was calculated in the multi-domain states in which the contributions of all eight domains are summed up equally, because the local rombohedral regions are oriented randomly along the eight equivalent polarization directions. The angular dependence of the integrated intensity of the CP and the TO2 mode observed in both VV and VH spectra is shown in Figs. 9(b) and 9(c), respectively. It is important to note that the variation of the intensity of CP and TO2 mode with the rotation of the plane of polarization in the cubic phase of the KLTN/2.5/38 crystal is similar to the nature of PNRs with A1(z) mode 13

ACCEPTED MANUSCRIPT of R3m [54]. Hence, to discuss the angular dependence of Raman results of the KLTN/2.5/38 crystal, we excluded the consideration E(x,y) mode of PNRs. For the A1(z) mode of PNRs of R3m, after transforming the Raman tensor components using Eq. (9), one can obtain the

RI PT

values of the intensity of the cc (VV) the bc (VH) components as follows [55]:

IAcc! (z) ∝ 9 [4|a|2 + 4|a||b|cosφ + |b|2 + |a|2 - 2|a||b|cosφ + |b|2 sin2 2θ 8

IAbc1 (z) ∝ (|a|2 - 2|a||b|cosφ + |b|2 )cos2 2θ 9

(11)

SC

8

(10)

M AN U

For A1(z) mode of PNRs, here φ = argb - arg(a) stands for the phase difference of the two independent components of the Raman tensor.

As shown in Fig. 9(b), the change of the intensity of CP and TO2 mode with the rotation

TE D

angle shows the sinusoidal tendency, implying the anisotropy of Raman scattering of the KLTN/2.5/38 crystal. It is apparent from Figs. 9(b) and 9(c) that the variation of the intensity of CP and TO2 mode observed in both VV and VH spectra is well fitted by the theory via

EP

Eqs. (10) and (11), respectively. The fitted curves reproduce the change in intensity with the rotation of the plane of polarization rather well, indicating that the CP and the first order TO2

AC C

mode in the cubic phase of the KLTN/2.5/38 single crystal comes from the A1(z) mode of PNRs with a rhombohedral R3m symmetry. It is clear from Figs. 9(b) and 9(c) that the angular variation of the intensity of both the CP and the TO2 is similar and both belong to the same symmetry, therefore, the CP and the TO2 mode can be coupled resulting in a Fano like asymmetry peak at around 196 cm-1 in Li-doped KTN single crystal [26]. Recently, Rahaman et al. observed that the breaking of local symmetry in the cubic phase of the 5%Li-doped KTN caused by E(x,y) mode at 196 cm-1 of PNRs with a R3m symmetry [26], while nondoped KTN/40 crystal, the breaking of symmetry attributed to the A1(z) mode at 540 cm-1 of 14

ACCEPTED MANUSCRIPT PNRs with a R3m symmetry [9]. In KTN, the PNRs might be induced only by off-center displacements of Nb ions along [111] direction at the B-site corresponding to one set of atomic displacements related to 180˚ fluctuations i.e., longitudinal polarization fluctuations in PNRs [56], therefore the A1(z) mode at 196 cm-1 of PNRs is reasonable in the case of KTN

RI PT

crystals. In Li-doped KTN, it is believed that the off-center displacements of Li ions occur along the equivalent [100] directions at the A-site [22,23]. However, the local displacements along [100] direction are correlated in the medium range with the displacements along [111]

SC

direction [53]. Since the off-centering of Li ions at A-site is much larger than that of the offcentering of Nb ions at B-site, therefore, the Li ion has a relatively larger dipole in

M AN U

comparison with the Nb ion. As a result, at relatively high Li concentrations, it is expected that the correlation of displacements can be dominated along the equivalent [100] directions. In KLTN/2.5/38 crystal, the displacements are dominated by the Nb ions because of the relatively small concentration of Li ions, and on an average Li ions for the [100], [010], and

TE D

[001] displacements are along equivalent [111] directions [53], results in a A1(z) mode at 196 cm-1 of PNRs. However, in 5%Li-doped KTN, the correlations between Li-Nb become stronger due to the relatively high Li concentrations, therefore their displacements are

EP

dominated along [100], [010], and [001] directions. The switching among [100], [010], and [001] polarization directions may enhance the transverse polarization [56], giving rise to

AC C

E(x,y) mode at 196 cm-1 of PNRs in 5%Li-doped KTN. Toulouse et al. also observed the effective displacement of B-site cations along [100] directions in rhombohedral PNRs by restricted their displacements among four sites in a plane in the vicinity of the T* [52].

The another possibility is that the transformation of A1(z) mode to E(x,y) mode of PNRs of R3m symmetry in 5%Li-doped KTN may due to the occupancy of a few percentage of Li ions at B-site. The invariant of the local symmetry of PNRs of the KLTN/2.5/38 in

15

ACCEPTED MANUSCRIPT comparison with the non-doped KTN indicates that the Li ions occupy only at A-site up to 2.5%Li doping, results in a weak RFs because of the homovalent cations at both sites. Wakimoto et al. observed the Li+-Li+ dipolar pairs in Ca-doped KLT/5, which were reoriented with the reorientation of two nearest neighbor Li+ ions [57]. In 5% Li-doped KTN,

RI PT

We do believe that the dipolar pair may exist and the dipolar pair can be reoriented with the reorientation of the nearest neighbor Li+ ions. However, the strength of the dipole-dipole interaction depends on orientations, the size of both dipoles, and on their proximity. In

SC

general, the proximity effect enhances with the increase of the concentration of dopant. Hence, the strong repulsive interaction between dipolar pairs and neighboring Li+ ions in

M AN U

5%Li-doped KTN may persist due to proximity effect and their random orientations in the high temperatures above the T*, results in a few percentage of Li ions might have change to occupy at B-site through hopping from A-site. As a result, it is expected that there is a strong interactions between Li and Nb ions in a fluctuating PNRs corresponding to two sets of

TE D

atomic displacements result in the E(x,y) mode of PNRs in 5%Li-doped KTN crystals. The similar results were observed in a PMN single crystal, in which off-center displacements of

EP

cations occur at both A- and B-site whereas charge disorder exist at B-site [54].

AC C

Recently, Helal et al. observed the transformation of rhombohedral R3m symmetry of PNRs of the PMN single crystal [53], to tetragonal P4mm symmetry in Ti rich PMN-56PT single crystal by the angular dependence of Raman scattering [56]. Therefore, the angular dependence of Raman results of the KLTN/2.5/38 single crystal was also studied by the considering the tetragonal P4mm symmetry of PNRs. For tetragonal P4mm symmetry there are Raman active A1(z), E(x), E(y), B1, and B2 modes given by the following Raman tensors [56,58]

16

ACCEPTED MANUSCRIPT a z A1 = 0 0

0 a 0

0 B2 = e 0

0 0

e 0 0 0

0 0 , b

0 Ex = 0 c

0 0 0

c 0 , 0

0 Ey = 0 0

d 0 c , B1 =  0 0 0

0 0 c

0 -d 0

0 0 , 0

(12)

is suggested to be proportional to -1 ·D  -1 ·A1 z or Ex or Ey D  ·R , R

RI PT

Using these Raman tensors, the angular dependence of Raman intensity in a cubic coordinate

(13)

SC

 is the transformation matrix for the modification of the Raman tensor components where D from tetragonal to cubic coordinates [56]. After transforming Raman tensor components

M AN U

using Eq. (13), one can obtain the values of the intensity of the cc (VV) the bc (VH) components for A1(z) mode of PNRs of P4mm as follows [56]:

IAcc1 (z) ∝ -|a|2 - 2|a||b|cosφ + |b|2  sin2 2θ + 4|a|2 + 2|b|2

TE D

IAbc1 (z) ∝ |a|2 - 2|a||b|cosφ + |b|2 sin2 2θ

(14) (15)

EP

It is clear from Eq. (15) that A1(z) mode of PNRs with tetragonal P4mm symmetry implies zero Raman scattering intensity for the VH scattering geometry when the incident plane of

AC C

polarization is parallel (θ = 0˚) or perpendicular (θ = 90˚) to the polar axis. On the other hand we observed the strongest Raman signal at θ = 0˚ and 90˚ in the VH scattering geometry [Fig. 9(c)]. Hence, the observed experimental results cannot be well reproduced by the Eq. (15). Therefore, it is concluded that the symmetry of PNRs in KLTN/2.5/38 single crystal is rhombohedral R3m symmetry.

4. Conclusions

17

ACCEPTED MANUSCRIPT The ferroelectric phase transition of a 2.5%Li-doped KTN (x = 0.38) crystal with weak random fields was investigated by Brillouin and Raman scatterings. It was found that its paraelectric cubic to ferroelectric tetragonal phase transition at TC-T = 46 ˚C shows slightly diffusive nature. The significant softening of frequency and remarkable increase in damping

RI PT

of the LA mode were clearly observed in the vicinity of TC-T. Upon cooling in a paraelectric phase, the damping of the LA mode begins to increase below the intermediate temperature, T* ~ 97 ˚C, implying the start of rapid growth of the volume fractions of PNRs. The broad CP

SC

clearly appears in the paraelectric phase and its intensity shows the significant increase in the vicinity of TC-T, which can be the clear evidence of the growth of dynamic PNRs. According

M AN U

to the analysis of the angular dependence of Raman scattering spectra, it is concluded that the symmetry of the CP and the mode related to breaking of local symmetry in the paraelectric cubic phase were attributed to A1(z) mode of lower R3m symmetry of PNRs. Above TC-T, the relaxation time determined from the width of abroad CP shows the slightly stretched slowing

phase transition.

EP

Acknowledgments

TE D

down due to weak random fields, indicating the order-disorder nature of the ferroelectric

AC C

This research was supported in part by the JSPS KAKENHI grant numbers JP17K05030, 16K04931. The authors are thankful to Mr. M. Aftabuzzaman for experiments, and to Dr. Y. Fujii for his technical support on the angular dependence of Raman scattering system.

References [1]

Y. C. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, Opt. Lett. 38 (2013) 4574-4577. 18

ACCEPTED MANUSCRIPT [2]

Y. Li, J. Li, Z. Zhou, R. Guo, and A. Bhalla, Ferroelectrics 425 (2011) 82-89.

[3]

A. Agranat, R. Hofmeister, and A. Yariv, Opt. Lett. 17 (1992) 713-715.

[4]

Z. Zhou, J. Li, H. Tian, Z. Wang, Y. Li, and R. Zhang, J. Phys. D: Appl. Phys. 42 (2009) 125405. L. E. Cross, Ferroelectrics 76 (1987) 241-267.

[6]

A. A. Bokov and Z.-G. Ye, J. Mater. Sci. 41 (2006) 31-52.

[7]

S. Vakhrushev, S. Zhukov, G. Fetisov, and V. Chernyshov, J. Phys.: Condens. Matter 6 (1994)

SC

4021-4027.

RI PT

[5]

G. Burns and F. H. Dacol, Phys. Rev. B 28 (1987) 2527-2530.

[9]

M. M. Rahaman, T. Imai, J. Miyazu, J. Kobayashi, S. Tsukada, M. A. Helal, and S.

M AN U

[8]

Kojima, J. Appl. Phys. 116 (2014) 074110.

[10] M. M. Rahaman, T. Imai, J. Kobayashi, and S. Kojima, Jpn. J. Appl. Phys. 54 (2015) 10NB01.

TE D

[11] V. Polinger, Chem. Phys. 459 (2015) 72-80.

[12] J. P. Sokoloff, L. L. Chase, and L. A. Boatner, Phys. Rev. B 41 (1990) 2398-2408. [13] O. Hanske-Petitpierre, Y. Yakoby, J. Mustre De Leon, E. A. Stern, and J. J. Rehr, Phys.

EP

Rev. B 44 (1991) 6700-6707.

AC C

[14] J.-H. Ko, T. H. Kim, S. Kojima, X. Long, A. A. Bokov, and Z. G. Ye, J. Appl. Phys. 107 (2010) 054108.

[15] E. Dul’kin, S. Kojima, and M. Roth, Europhys. Lett. 97 (2014) 57004. [16] R. Ohta, J. Zushi, T. Ariizumi, and S. Kojima, Appl. Phys. Lett. 98 (2015) 092909. [17] O. Svitelskiy and J. Toulouse, J. Phys. Chem. Solids 64 (2003) 665-676. [18] J. Toulouse, P. DiAntonio, B. E. Vugmeister, X. M. Wang, and L. A. Knauss, Phys. Rev. Lett. 68 (1992) 232. [19] W. Kleemann, F. J. Schäfer, and D. Rytz, Phys. Rev. Lett. 54 (1985) 2038-2041.

19

ACCEPTED MANUSCRIPT [20] A. Pashkin, V. Železný, and J. Petzelt, J. Phys.: Condens. Matter 17 (2005) L265-L270. [21] L. A. Knauss, X. M. Wang, and J. Toulouse, Phys. Rev. B 52 (1995) 13261-13268. [22] G. Samara, J. Phys.: Condens. Matter 15 (2003) R367-R411. [23] R. Machado, M. Sepliarsky, and M. G. Stachiotti, Phys. Rev. B 86 (2012) 094118.

RI PT

[24] L. Cai, J. Toulouse, L. Harrier, R. G. Downing, and L. A. Boatner, Phys. Rev. B 91 (2015) 134106.

[25] H. Schremmer, W. Kleemann, and D. Rytz, Phys. Rev. Lett. 62 (1989) 1896-1899.

SC

[26] M. M. Rahaman, T. Imai, T. Sakamoto, S. Tsukada, and S. Kojima, Sci. Rep. 6 (2016) 23898.

M AN U

[27] M. M. Rahaman, T. Imai, T. Sakamoto, and S. Kojima, Integrated Ferroelectrics in press.

[28] M. M. Rahaman, T. Imai, T. Sakamoto, and S. Kojima, Appl. Phys. Lett. 111 (2017) 032904.

TE D

[29] S. Kojima, Jpn. J. Appl. Phys. 49 (2010) 07HA01.

[30] Y. Fujii, M. Noju, T. Shimizu, H. Taniguchi, M. Itoh, and I. Nishio, Ferroelectrics 462 (2014) 8-13.

EP

[31] R. Vacher and L. Boyer, Phys. Rev. B 6 (1972) 639-673.

AC C

[32] F. M. Jiang and S. Kojima, Phys. Rev. B 62 (2000) 8572-8575. [33] S. Kojima, and J.-H. Ko, Curr. Appl. Phys. 11, (2011) S22-S32. [34] S. Kojima, S. Tsukada, Y. Hidaka, A. A. Bokov, and Z.-G. Ye, J. Appl. Phys. 109 (2011) 084114.

[35] I. G. Siny, S. G. Lushinikov, R. Katiyar, and E. A. Rogacheva, Phys. Rev. B 56 (1997) 7962-7966. [36] Z.-Y. Cheng, R. S. Katiyar, X. Yao, and A. Guo, Phy. Rev. B 55 (1997) 8165-8174. [37] R. D. Shannon, J. Appl. Phys. 73(1) (1993) 348-366.

20

ACCEPTED MANUSCRIPT [38] M. M. Mao, X. C. Fan, and X. M. Chen, Int. J. Appl. Ceram. Technol., 7(S1) (2010) E156-E162. [39] H. Yokota and Y. Uesu, J. Phys. Soc. Jpn. 77 (2008) 023713. [40] S. Kojima and S. Tsukada, Ferroelectrics 405 (2010) 32-38.

RI PT

[41] A. Hushur, S. Gvasaliya, B. Roessli, S.Lushnikov, and S. Kojima, Phys. Rev. B 76 (2007) 064104.

[42] K. K. Mishra, V. Sivasubramanian, A. K. Arora, and D. Pradhan, J. Appl. Phys. 112 (2011)

SC

114109.

[43] S. K. Manlief and H. Y. Fan, Phys. Rev. B 5 (1972) 4046-4060.

M AN U

[44] G. E. Kugel, M. D. Fontana, and W. Kress, Phys. Rev. B 35 (1987) 813-820. [45] G. E. Kugel, H. Mesli, M. D. Fontana, and D. Rytz, Phys. Rev. B 37 (1988) 5619-5628. [46] S. Triebwasser, Phys. Rev. 114 (1959) 63-71.

[47] D. Rytz and H. J. Scheel, J. Cryst. Growth 59 (1982) 468-484.

TE D

[48] R. L. Prater, L. L. Chase, and L. A. Boatner, Solid State Commun. 40 (1981) 697-701. [49] Y. Yacoby, Z. Physik B 31 (1978) 275-282.

114106.

EP

[50] M. S. Islam, S. Tsukada, W. Chen, Z. G. Ye, and S. Kojima, J. Appl. Phys. 112 (2012)

AC C

[51] H. J. Trodahl, N. Klein, D. Damjanovic, N. Setter, B. Ludbrook, D. Rytz, and M. Kuball, Appl. Phys. Lett. 93 (2008) 262901. [52] J. Toulouse, F. Jiang, O. Svitelskiy, W. Chen, and Z.-G. Ye, Phys. Rev. B 72 (2005) 184106.

[53] I.-K. Jeong, T. W. Darling, J. K. Lee, T. h. Proffen, R. H. Heffner, J. S. Park, K. S. Hong, W. Dmowski, and T. Egami, Phys. Rev. Lett. 94 (2005) 147602. [54] H. Taniguchi, M. Itoh, and D. Fu, J. Raman spectrosc. 42 (2011) 706-716.

21

ACCEPTED MANUSCRIPT [55] M. M. Rahaman, T. Imai, T. Sakamoto, S. Tsukada, and S. Kojima, Ferroelectrics 503 (2016) 85-93. [56] M. A. Helal, M. Aftabuzzaman, S. Tsukada, and S. Kojima, Sci. Rep. 7 (2017) 44448.

Shirane, and S.-H. Lee, Phys. Rev. B 74 (2006) 054101.

RI PT

[57] S. Wakimoto, G. A. Samara, R. K. Grubbs, E. L. Venturini, L. A. Boatner, G. Xu, G.

[58] D. F. Edwards, Raman scattering in crystals, Lawrence Livermore National Laboratory,

M AN U

SC

University of California, California, 1988, pp. 21-22.

TE D

Figures caption

Fig. 1. The Brillouin scattering spectra of the KLTN/2.5/38 single crystal at some selected

EP

temperatures measured with the FSR = 75 GHz.

Fig. 2. The frequency shift and damping of the LA mode of the KLTN/2.5/38 single crystal

AC C

as a function of temperature. The solid line is guide to the eye.

Fig. 3. Contour color map of the Brillouin spectra of a broad CP of the KLTN/2.5/38 single crystal as a function of temperature. The intense elastic scattering was shut down by a shutter in the frequency range between -60 to 55 GHz.

Fig. 4. (a) The real part of the dielectric constant of the KLTN/2.5/38 crystal as a function of temperature at some selected frequencies. (b) The temperature dependence of the T/ICP 22

ACCEPTED MANUSCRIPT (diamonds) and the inverse dielectric constant (circles) measured at 1 kHz of the KLTN/2.5/38 single crystal. The solid lines are the best fitted curves by Eq. (2).

Fig. 5. The inverse of the relaxation time determined from the full width at half maximum

RI PT

(FWHM) of CP as a function of temperature, where the solid lines are result fitted by Eq. (4). The result of non-doped KTN/40 (Ref. 9) is also shown for the comparison with the Li-doped

SC

KLTN/2.5/38.

at some selected temperatures.

M AN U

Fig. 6. The reduced ā(cc)a (VV) Raman scattering spectra of the KLTN/2.5/38 single crystal

Fig. 7. The example of a fitted curve using Eq. (6) is shown in (a). (b) The reduced mode intensity, I0, line shape parameter, q, and FWHM, ΓTO2 of the TO2 mode observed in VV

TE D

scattering spectra of the KLTN/2.5/38 single crystal as a function of temperature.

Fig. 8. Contour color map of the angular dependence of (a) VV and (b) VH Raman scattering

EP

spectra of the KLTN/2.5/38 single crystal.

AC C

Fig. 9. (a) The example of a fit of Raman spectrum by the Eq. (7). The angular dependence of the integrated intensity of the CP (upper half) and the TO2 mode (lower half) observed in (b) VV and (c) VH spectra. The solid lines in (b) and (c) are the best fitted results obtained by the Eqs. (10) and (11), respectively.

23

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT Highlights

The diffusive nature of a ferroelectric phase transition was found.

•

The interaction between LA mode and PNRs caused the elastic anomaly.

•

The precursor dynamics in the paraelectric cubic phase was clearly observed.

•

The order-disorder nature of a ferroelectric phase transition was observed.

•

The symmetry breaking due to A1(z) mode of R3m symmetry of PNRs was confirmed.

AC C

EP

TE D

M AN U

SC

RI PT

•