# Successive ferroelectric orders and magnetoelectric coupling without long-
range magnetic order in highly frustrated pyrochlore compounds: Sm2Ti2-xVxO7

S. Mukherjee1 O. Ivashko2 S. Majumdar1 A. Kumar3 S. Giri1 Corresponding
author<EMAIL_ADDRESS>1School of Physical Sciences, Indian Association
for the Cultivation of Science, Jadavpur, Kolkata 700032, India  2Deutsches
Elektronen-Synchrotron DESYNotkestr. 85, 22607 Hamburg, Germany  3Solid State
Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India and Homi
Bhabha National Institute, Anushaktinagar, Mumbai 400094, India

###### Abstract

Sm2Ti2O7, a member of rare-earth titanate pyrochlores, exhibits dipolar-
octupolar antiferromagnetism below $T_{N}$ = 0.35 K. We observed two
ferroelectric transitions at 182 ($T_{FE1}$) and 52 K ($T_{FE2}$),
significantly higher than $T_{N}$ for Sm2Ti2-xVxO7 ($x$ = 0, 0.1). Although
the ferroelectric transition temperatures remain unchanged, the polarization
value decreases considerably with V doping. A structural transition to a polar
$R3m$ rhombohedral phase from the cubic $Fd\bar{3}m$ structure occurs at
$T_{FE1}$, involving a distortion in the pyochlore lattice. Remarkably,
significant linear magnetoelectric coupling is observed in both compounds,
with further enhancement of magnetoelectric coupling due to magnetic V doping.
The existence of magnetoelectric coupling without long-range magnetic order in
a frustrated pyrochlore system could enable the tailoring of magnetoelectric
coupling properties, which can be further fine-tuned through V doping. The
emergence of ferroelectricity in a frustrated magnetic system introduces an
intriguing aspect to these compounds and paves the way for developing
ferroelectric order driven by the alleviation of magnetic frustration in
pyrochlore systems.

##  I Introduction

The frustrated pyrochlore structure, manifesting in compounds with the
chemical formula $R_{2}$B2O7 [1] ($R$ = Rare earth elements; M=Zr, Hf, Ti, Sn,
Pb), stands as a captivating archetype in the realm of condensed matter
physics and materials science. This structure, defined by a lattice of corner-
sharing tetrahedra formed by $R$ cations interconnected by oxygen ions,
embodies a symphony of competing interactions and geometric frustrations. The
delicate interplay between the magnetic frustration inherent in the pyrochlore
lattice and the magnetic exchange interactions often gives rise to a plethora
of exotic physical phenomena, spanning from unconventional magnetic ground
states to intriguing electronic behaviors. Within the domain of magnetism,
frustrated pyrochlores have garnered significant attention due to their
propensity to host intriguing magnetic phases such as spin liquids [2, 3],
spin ice [4, 5, 6], and spin glasses [7, 8].

The pyrochlore family, represented by the chemical formula $R_{2}$Ti2O7 (where
$R$ ranges from Gd to Yb), is renowned for being exemplary three-dimensional
geometrically frustrated systems [9]. This recognition stems from their
intriguing and unconventional magnetic characteristics. Within these
insulating pyrochlore structure, a variety of rich characteristic features
have been witnessed. These include suppressed moment in Gd2Ti2O7 [10, 11],
single-ion anisotropy of Tb3+ within the collective paramagnetic-spin liquid
state in Gd2Ti2O7 [12, 13], and the realization of quantum order by disorder
and accidental soft mode in Er2Ti2O7 [14, 15]. On the other hand, intriguing
magnetic behavior from spin ice state to supercooled spin liquid state has
been observed in Dy2Ti2O7 [16, 17], the emergence of magneic monopoles has
been noted in Gd2Ti2O7 [18, 19, 20], and evidence of quantum spin-liquid
behavior has been found in Yb2Ti2O7 [21, 22].

Figure 1: (a) Equidistant pyrochlore structure of STO formed by Sm atoms and
(b) formation of an equidistant hexagonal structure by Ti atoms, with Sm atoms
sitting at the center.

Magnetism of our focal compound, Sm2Ti2O7, as a member of pyrochlore
$R_{2}$Ti2O7 family, has been relatively underexplored at the microscopic
level, particularly through neutron scattering. This is due to the fact that
149Sm is a strong neutron absorber. Nevertheless, recent neutron scattering,
facilitated by enriching the 154Sm isotope, and muon relaxation studies have
revealed that the compound exhibits the all-in, all-out magnetic structure
with an ordered moment of 0.44(7)$\mu_{B}$ below $T_{N}$ = 0.35 K. This
observation aligns with expectations for antiferromagnetically coupled Ising
spins on the pyrochlore lattice [23, 24]. Consistent with this findings, bulk
magnetization studies do not indicate long range magnetic order down to 0.5 K.
This absence was attributed to weak exchange (Curie-Weiss temperature $\sim$
-0.26 K) and dipolar interactions ($\mu_{eff}\sim$ 0.15 $mu_{B}$) between the
Sm3+ spins within this pyrochlore structure [25].

Recent developments suggest the potential occurrence of ferroelectric (FE)
order in the pyrochlore $R_{2}$Ti2O7 family, where $R$ = La, Ce, Pr, and Nd,
based on first-principles studies utilizing density functional theory [27].
While the search for FE order has rarely been attempted in polycrystalline
materials [28, 29] and films [30, 31], we are motivated to explore FE order as
well as magnetoelectric coupling in Sm2Ti2-xVxO7 ($x$ = 0, 0.1), members of
this pyrochlore family. In line with previous findings, Fig. 1(a) depicts the
characteristic pyrochlore structure of Sm2Ti2O7, wherein all vertices of a
regular tetrahedron are equidistant from each other, measuring a length of
3.6082 $\AA$ at 300 K, as obtained from Rietveld refinement (Fig. 2(a)).
Figure 1(b) illustrates the formation of an equidistant (3.6082 $\AA$)
hexagonal structure by Ti atoms, with magnetic Sm3+ occupying the center.
Notably, Ti atoms form Edge-sharing equilateral triangles, with the Sm atom
positioned at the common vertices. Now, if we replace the Ti4+ ion with
magnetic V4+, the magnetic V4+ ions, arranged in an equilateral triangle,
influence frustrated magnetism due to the pyrochlore structure formed by Sm3+
ions and act as a perturbation to the frustrated magnetism of Sm2Ti2O7.

In this article, we present findings on FE order accompanied by a structural
transition to a polar $R3m$ structure from the cubic $Fd\bar{3}m$ structure.
Of particular significance is the observation of magnetoelectric (ME) coupling
in the absence of long-range magnetic order, a phenomenon further amplified by
V doping. We discuss the influence of structural distortion and potential
short-range effects driven by V doping on the ME coupling.

##  II Experimental details

Figure 2:  Rietveld refined XRD patterns at 300 K of (a) STO and (b) STVO. (c)
XPS spectrum of STVO. Inset shows deconvolution of (solid curve) of 2$p_{1/2}$
and 2$p_{3/2}$ spectrum of V4+ for STVO.

Polycrystalline Sm2Ti2O7 (STO) and Sm2Ti1.9V0.1O7 (STVO) were synthesized
using a standard solid-state reaction technique. Stoichiometric amounts of
Sm2O3 and TiO2 and V2O5 (for STVO) were finely ground and thoroughly mixed for
several hours. This mixture was first preheated at 500∘C for 5 hours.
Subsequently, the mixtures were ground and thoroughly mixed before undergoing
a final heat treatment at 1300∘C for 24 hours after being pressed into pellets
[32].

The single-phase chemical compositions were verified using standard X-ray
diffraction (XRD) studies at 300 K using a PANalytical X-ray diffractometer
(Model: X’ Pert PRO) with Cu-K$\alpha$ radiation. Low-temperature synchrotron
X-ray diffraction studies were carried out in the range of 10-300 K using a
wavelength, $\lambda$ = 0.1123 $\AA$ at P21.1 beam line at DESY, Hamburg,
Germany. The diffraction patterns were analyzed using the Rietveld refinement
with a commercially available open-source software MAUD (Material Analysis
Using Diffraction). Properly prepared pelletized samples were used for the
pyroelectric measurements, electrical contacts made using silver paint.
Pyroelectric current ($I_{p}$) was recorded in constant temperature sweep and
magnetic field sweep rates using an electrometer (Keithley, model 6517B)
connected to a commercial PPMS-II, EverCool system of Quantum Design. Poling
electric fields were applied during the cooling process, and at the lowest
temperature, the pellet was properly short-circuited before measuring $I_{p}$
during the heating process. Similarly, dielectric measurements were performed
using an Agilent E4890A LCR meter connected with the same PPMS-II.
Magnetization was measured using a commercial magnetometer of Quantum Design
(MPMS, EverCool). X-ray photoemission spectroscopy (XPS) was recorded with a
spectrometer of Omicron Nanotechnology.

##  III Experimental results and discussions

The XRD patterns at 300 K of STO and STVO are depicted in Figs. 2(a) and 2(b),
respectively. These compounds crystallize in $Fd\bar{3}m$ space group, and
Rietveld calculated XRD patterns are represented by the continuous curves in
the figures. The goodness of fits for STO and STVO is satisfactory, confirming
the absence of any impurity phase, as indicated by the difference plotted
below. The Wyckoff positions for STO are as follows: Sm(0.5000, 0.5000,
0.5000), Ti(0, 0, 0), O1(0.3270(6), 0.1250, 0.1250), O2(0.3750, 0.3750,
0.3750), with a lattice constant, $a$ = 10.2815(3) $\AA$. The reliability
parameters are $R_{w}$(%) $\sim$ 3.47, $R_{exp}$(%) $\sim$ 1.41,
$\chi^{2}\sim$ 1.56. The lattice constant at 300 K is close to the reported
value for STO [26]. Here, all the Wyckoff positions are fixed except for $x$
for O1. The refined $x$ coordinate for STVO is 0.3272(6). For STVO, the
refined lattice constant is $a$ = 10.2785(6) $\AA$, with reliability
parameters $R_{w}$(%) $\sim$ 3.04, $R_{exp}$(%) $\sim$ 1.78, $\chi^{2}\sim$
1.71. In line with the smaller crystal radius of six-coordinated V4+ compared
to Ti4+, the lattice constant contracts upon V doping. To identify the
oxidation state of V, XPS was recorded for STVO, as shown in Fig. 2(c).
Satisfactory fits of the peaks are demonstrated by the continuous curves in
the figure. The two peaks located at $524$ and $516$ eV indicate $V^{4+}$
states of $2p_{1/2}$ and $2p_{3/2}$, respectively, consistent with a previous
report [35], confirming the presence of V4+ replacing Ti4+.

Figure 3: (a) Thermal ($T$) variations of magnetization ($M$) recorded with
1000 Oe for (a) STO and (c) STVO. $T$ variations of $dM/dT$ for (b) STO and
(d) STVO. Inset of (c) highlights an anomaly, as indicated by an arrow. Figure
4: (a) Isothermal magnetization of STVO at selected $T$. Inset of (a), and (b)
show linear dependence of magnetic field ($H$) in the high-$H$ regions at 2
and 150 K, respectively. Figure 5: $T$ variations of real part of dielectric
constant ($\epsilon^{\prime}$) at $H$ = 0 and 50 kOe, and dielectric loss
($\tan\delta$) at $H$ = 0 for (a) STO and (b) STVO, respectively. Figure 6:
$T$ variations of $I_{DC}$ for (a) STO and (e) STVO, $I_{P}$ for different
thermal sweep rates for (b) STO and (f) STVO, polarization ($P$) for different
thermal sweep rates for (c) STO and (g) STVO, $P$ at different electric fields
for (d) STO and (h) STVO, respectively. Insets of (b) and (f) show $I_{P}$ for
-5kV/cm poling field. Inset of (h) highlights saturating $P$-value below
$T_{FE2}$ for STVO.

Temperature-dependent magnetization ($M$) recorded in zero-field-cooled (ZFC)
mode for STO and STVO is illustrated in Figs. 3(a) and 3(c), respectively. In
the ZFC mode, samples were cooled in zero-field, and magnetization was
recorded in the warming mode with $H$ = 1 kOe. Broad maxima in $M(T)$ are
observed around 150 K for both samples, with a sharp rise observed below
$\sim$ 35 K, consistent with a previous report on STO [25]. The broad maximum
in STO was attributed to the crystal field effect of Sm3+ [25]. For STVO, a
new broadened anomaly appears around 270 K, as highlighted in the inset of
Fig. 3(c), which emerges due to 5% V doping. Plots of $dM/dT$ with $T$ are
depicted in Figs. 3(b) and 3(d), respectively, highlighting prominent
characteristic features by the arrows for STO and STVO. The change of slope in
$dM/dT(T)$ around 180 K and an anomaly around 52 K for both STVO and STO, are
significant. Because these signatures coincide with the ferroelectric
transitions at 52 and 180 K, as discussed elsewhere, indicating
magnetoelectric coupling. Additionally, a sharp minimum is observed at 272 K
for STVO, likely due to short-range magnetic order attributed to the 5 % V
doping. The probable short-range ordering in STVO requires further
confirmation using other experimental methods. The isothermal magnetization
curves of STVO are depicted in Fig. 4(a) at selected $T$. Unlike the linear
behavior of the magnetization curves for STO [25], non-linearity in the
magnetization curves is evident at low $H$ for STVO, as highlighted in the
inset of Fig. 4(a) at 2 K and 4(b) at 150 K. Arrows in the figures indicate
magnetic field, beyond which linearity of the magnetization curves is
observed, decrease with increasing $T$. This non-linearity may correlate with
the emergence of a short-range magnetic order below 270 K for STVO.

The dielectric permittivity ($\epsilon$) of STO and STVO were recorded from 2
K to 300 K, for example, at a frequency, $f$= 2007 Hz, under zero-field and
with $H$ = 50 kOe. Thermal variations of the real component
($\epsilon^{\prime}$) and the dielectric loss ($\tan\delta$) are depicted for
STO and STVO in Figs. 5(a) and 5(b), respectively. The $\epsilon^{\prime}(T)$
and $\tan\delta(T)$ show anomalies at 180 ($T_{FE1}$) and 52 K ($T_{FE2}$) for
both the compounds. Observing anomalies in $\epsilon^{\prime}(T)$ and
$\tan\delta(T)$ at the same temperature primarily indicates the onset of
spontaneous polar order[37, 38]. In the presence of a 50 kOe magnetic field,
$\epsilon^{\prime}(T)$ decrease for both compounds, indicating magneto-
dielectric (MD) response. The percentages of MD responses, defined as
$\epsilon^{\prime}(H)/\epsilon^{\prime}(H=0)-1$ at 2 K are $2.1$ % and $2.4$ %
for STO and STVO, respectively and are consistent with the previous reports
[34, 37].

Figure 7: $T$ variations of magnified polarization ($P$) under different
magnetic fields ($H$) below $T_{FE2}$ for (a) STO and (e) STVO, and below
$T_{FE1}$ for (b) STO and (f) STVO, respectively. $H$ variations of $\Delta
P/P$ at $2$ and 150 K for (c) STO and (g) STVO, respectively. Time ($t$)
dependent oscillations in $H$ and corresponding $I_{P}$ at 150 K for (d) STO
and (h) STVO, respectively.

The confirmation of polar order was achieved through various techniques. Upon
cooling the sample to its lowest temperature in zero electric field, the bias
electric current ($I_{DC}$) was recorded in the presence of a bias electric
field of 5 kV/cm, at a rate of 5 K/min in the warming mode [33]. As depicted
in Figs. 6(a) and 6(e), anomalies are evident at 52 and 180 K, indicating the
onset of long-range polar order for STO and STVO, respectively, consistent
with previous reports [34, 33, 36]. Further, The pyroelectric current
($I_{P}$) was recorded under different conditions, such as varied temperature-
sweeping rates and different poling electric fields ($E$), including $E$
reversal, as depicted in Figs. 6(b-d) and 6(f-h). The peak positions at $52$ K
and $180$ K remain unchanged in these measurements, indicating genuine polar
orderings for both the compounds. We observe a reduction in the $I_{P}$-value
with a decrease in temperature-sweeping rate, as depicted in Figs. 6(b) and
6(f) for STO and STVO, respectively. The insets of these figures illustrate
$I_{P}(T)$ at a sweep rate of 5 K/min for a negative poling field of -5 kV/cm.
Reversing of $I_{P}(T)$ confirms ferroelectric order. Integratiing $I_{P}(T)$
over time yields electric polarization ($P$) using the equation
$P=\int{I_{P}dt}$. The $P(T)$ curves for STO and STVO are shown in Figs. 6 (c)
and (g) respectively, for different sweep rates. No significant deviation in
$P(T)$ is observed accross different sweep rates, indicating the absence of
extrinsic contributions from thermally stimulated depolarization current
(TSDC) [36]. Additionally, we measured $P(T)$ at different poling fields of 5,
3, and 1 kV/cm, as shown in Figs. 6(d) and 6(h). The saturating $P$-values for
STO and STVO are $\sim$ 108 and $\sim$ 75 $\mu C/m^{2}$ respectively,
comparable to values for promising multiferroics. [39, 37, 40]. While the
transition temperatures $T_{FE1}$ and $T_{FE2}$ remain unchanged, a decrease
in $P(T)$ is observed with V doping in STVO, consistent with prior findings
regarding the effects of doping [41, 42]. The changes in $P(T)$ at $T_{FE1}$
smears out due to V doping for STVO. In contrast to the behavior observed
around $T_{FE1}$, the increase in $P(T)$ at $T_{FE2}$ is more pronounced and
abrupt for STVO compared to STO. Although a slight upward trend in $P(T)$ is
observed below $T_{FE2}$ down to the lowest recorded temperature for STO,
$P(T)$ stabilizes and remains almost constant below $\sim$ 20 K for STVO, as
shown in the inset of Fig. 6(h).

Figure 8: (a) Selected diffraction peaks at different $T$ around $T_{FE1}$.
(b) $T$ variation of the integrated intensity of (111) peak. (c) Rietveld
refinement of synchrotron diffraction pattern at 175 K. The (111) peak is
highlighted by a circle. (d) Connecting Sm-polyhedra and Ti-octahedra below
$T_{FE1}$. $T$ variations of lattice parameters (e) $a$ and $c$, and (f) unit
cell volume ($V/Z$) for STO, where $Z$ is the number of formula unit within
the unit cell.

To investigate the manifestation of ME coupling, the polarization was recorded
under various applied magnetic field conditions. The $P(T)$ values at selected
$H$ are highlighted for STO and STVO in Figs. 7(a) and 7(e), respectively in
the low-$T$ region below $T_{FE2}$, with a poling field of 5 kV/cm.
Correspondingly, Figs. 7(b) and 7(f) illustrate the same for the high-
temperature range below $T_{FE1}$. The percentage changes in polarization
($\Delta P/P$), calculated as $[P(H)-P(H=0)]/P(H=0)\times$ 100, are plotted
against $H$ at 2 K (representative temperature below $T_{FE2}$) and 150 K
(representative temperature below $T_{FE1}$) in Figs. 7(c) and 7(g) for STO
and STVO, respectively. It is observed that the decrease in $\Delta P/P$ at 2
K surpasses that at 150 K, indicating stronger ME coupling below $T_{FE2}$ for
both the cases. A linear decrease of the $P-H$ curves is noted in the high-$H$
region for both STO and STVO. The curve remains linear at 150 K and extends
into linearity for STO above above 10 kOe. Similarly, for STVO, the $P-H$
curve exhibits linearity above $\sim$ 12 kOe at 150 K and $\sim$ 25 kOe 2 K.
Since the initial observation of the linear ME effect in Cr2O3 in the 1960s
[43, 44], the pursuit of single-phase ME materials demonstrating linear ME
coupling has been highly sought after. Recently, linear ME coupling has been
identified in LiFePO4 and LiNi0.8Fe0.2P4 [45], Na2Co2TeO6 [34], Co3V2O8 [37],
and Gd2MnFeO6 [46]. Additionally, it is noted that the values of $\Delta P/P$
are $\sim$ 1.5% and $\sim$ 2% under 60 kOe and at 2 K for STO and STVO,
respectively. An enhancement of ME is observed due to V doping, albeit with a
considerable reduction in the P-value.

Figure 9: (a) Sm2$-$Sm2 and Sm1$-$Sm2 distances with $T$ below $T_{FE1}$.
Schematic representations of distortion of pyrochlore structure below (b)
$T_{FE1}$ and (c) $T_{FE2}$.

The time-dependent behavior of ME was additionally monitored at 150 K for both
STO and STVO. In this measurement, sample was initially polarized with an
electric field of 5 kV/cm down to 2 K. Subsequently, the electric field was
withdrawn, and the sample was properly short-circuited. The sample temperature
was then raised to 150 K. The magnetic field was varied between $\pm$ 10 kOe
with a sweep rate of 100 Oe/s, while simultaneously recording the $I_{P}$ over
time ($t$), as depicted in Figs. 7(d) and 7(h). For STO, the $I_{P}(t)$
oscillates approximately between $\pm$ 5 fA, exhibiting a phase shift compared
to the oscillation of the magnetic field. The value of $I_{P}(t)$ is small,
but it is reproducible and beyond the current measurement resolution of the
electrometer. Conversely, the nature of $I_{P}(t)$ for STVO differs from that
of STO. Unlike the regular oscillation $I_{P}(t)$ for STO, the positive cycle
of $I_{P}(t)$ remains nearly flat and extends over a longer time period
compared to sharp change in the negative cycle of $I_{P}(t)$.

The low-temperature synchrotron diffraction experiments were conducted within
the temperature range of 10-300 K for STO. In Figure 8(a), a narrow 2$\theta$
region of the diffraction pattern is highlighted around $T_{FE1}$ at selected
$T$, with a 4 K interval. While changes in the intensity of the prominent peak
are not readily discernible, subtle variations in the intensity of the smaller
peak, indicated by an arrow, are faintly observed, with a notable increase in
peak height around $T_{FE1}$ at 180 K. The integrated intensity of the (111)
peak, highlighted in Fig. 8(c), is shown in Fig. 8(b). The plot indicates a
consistent intensity from higher temperatures until $T_{FE1}$, below which it
begins to rise quite sharply, reaching a peak around 75 K before declining
below $T_{FE2}$. The observed changes in integrated intensity around $T_{FE1}$
resemble those observed in multiferroics, suggesting potential structural
transitions, including isostructural changes [47, 48] and transitions to the
lower symmetries [49, 50, 39, 37]. No additional diffraction peaks were
detected below $T_{FE1}$. However, refinement of the diffraction pattern below
$T_{FE1}$ using the room temperature $Fd\bar{3}m$ space group yielded
unsatisfactory results, implying a probable structural transition.

We utilize the open-source web software ISODISTORT [52] to discern potential
structures at low temperatures. Our analysis reveals that $R3m$ (no. 227)
represents a polar structure, exhibiting the highest symmetry among the
various structures considered. This finding aligns with the rhombohedral
distortion-driven structural transition to $R3m$ structure from $Fd\bar{3}m$,
which was associated with the observed FE order in ZnFe2O4 [51]. A
satisfactory Rietveld refinement of the diffraction pattern at 175 K,
employing the $R3m$ space group, is presented in Fig. 8(c). The various
Wyckoff positions are as follows: Sm1(0,0,0), Sm2 (0.50,0,0), Ti1(0,0,0),
Ti2(0.833333,0.166667,0.166667), O1(0, 0, 0.625), O2(0, 0, 0.375),
O2-1(0.532000, 0.468000, 0.141000), O2-2(0.801330, 0.198670, 0.275670),
O2-3(0.134670, 0.865330, 0.192330), O2-4(0.865330, 0.134670, 0.057670). This
refinement identifies two Sm, two Ti, and six oxygen atoms within the
structure. The connectivity of Sm-polyhedra and Ti-octahedra formed by oxygen
atoms is illustrated in Fig. 8(d). The thermal variations of lattice
parameters, $a$ and $c$, and unit cell volume ($V/Z$), as obtained from the
refinement, are depicted in Figs. 8(e) and 8(f), respectively, where $Z$ is
the number of formula unit within the unit cell. Besides the structural
changes at $T_{FE1}$, the lattice parameters and the volume show another iso-
structural transition near TFE2.

The pyrochlore structure in the $R3m$ phase comprises two Sm atoms, denoted as
Sm1 and Sm2. Figure 9(a) shows temperature variations of the Sm2$-$Sm2 and
Sm1$-$Sm2 distances below $T_{FE1}$. As temperature decreases, the Sm2$-$Sm2
distance increases, while the Sm1$-$Sm2 distance decreases. Figure 9(b)
demonstrates that the direct distance between Sm1 and Sm2 is smaller than the
Sm2$-$Sm2 distance, indicating a distortion in the pyrochlore structure. It is
significant to note that the equidistant pyrochlore structure formed by Sm
atoms at high temperatures, exhibiting the $Fd\bar{3}m$ structure as depicted
in Fig. 1, leads to significant magnetic frustration, which becomes distorted
following the structural transition at $T_{FE1}$. We propose that the release
of magnetic frustration is a consequence of the structural transition and
highlights its pivotal role in the occurrence of ferroelectric order. Evidence
supporting the release of magnetic frustration has been observed through an
iso-structural transition in the widely studied CaBaCo4O7 [53, 54], resulting
in the ferroelectric order. Additionally, in ZnFe2O4, a structural transition
from a cubic structure to a lower symmetry of $R3m$ structure is observed to
release magnetic frustration and facilitates the occurrence of ferroelectric
order. The release of geometric magnetic frustration, attributed to the
antiferromagnetic exchange-coupled pyrochlore structure, strongly correlates
with this structural transition [51]. Furthermore, it is noteworthy that the
structural change at $T_{FE1}$ in STO bears a resemblance to the well-studied
multiferroic BiFeO3, where the $R3m$ structure induces a rhombohedral
distortion of the cubic high-temperature perovskite structure formed by the Bi
atoms. This structural distortion is closely associated with the emergence of
ferroelectric order in BiFeO3 [55, 56]. The emergence of ferroelectric order
in the presence of magnetic frustration adds a compelling layer of complexity
to these materials, rendering them highly intriguing subjects for further
scientific exploration. In Fig. 9(a), the significant changes in slope of
Sm$-$Sm distances are observed below $T_{FE2}$, indicating another distortion
in the pyrochlore structure. Figure 9(c) shows nature of further distortion in
the pyrochlore structure below $T_{FE2}$. These results demonstrate successive
distortions in the pyrochlore structure, corresponding to the successive
ferroelectric transitions.

Our comprehensive investigation into the structural and ferroelectric
characteristics of frustrated pyrochlore compounds, particularly focusing on
both the pristine and V-doped STO, has provided rich insights into the
interplay between magnetic frustration and ferroelectric order. We have
uncovered distinct ferroelectric phases in both compounds, manifesting around
temperatures of $\sim$ 182 K ($T_{FE1}$) and $\sim$ 52 K ($T_{FE2}$).
Remarkably, these ferroelectric transitions occur in the absence of long-range
magnetic ordering, suggesting that the emergence of ferroelectricity is
primarily driven by factors beyond conventional magnetic interactions. The
introduction of V dopants has revealed intriguing effects on the ferroelectric
properties, as evidenced by the observed reduction in polarization values.
This reduction may be correlated with the structural disorder in STVO caused
by V doping. Additionally, the identification of a novel short-range magnetic
ordering around 272 K exclusively in the V-doped compound underscores the
intricate interplay between magnetic dopants and frustrated pyrochlore
structure of the system. As highlighted in Fig. 1, the direct Sm$-$Sm distance
in the pyrochlore structure and the V/Ti$-$Sm distance are exactly the same in
the $Fd\bar{3}m$ structure, indicating comparable exchange coupling due to V
doping. Therefore, V doping introduces a significant perturbation to the
frustrated pyrochlore systems, strongly influencing the ME coupling as well as
the polarization value. The occurrence of ME coupling without long-range
magnetic order promising for developing ME materials, which can be further
enhanced by doping with magnetic elements. Looking ahead, future research
endeavors could delve deeper into elucidating the underlying mechanisms
governing ME coupling in frustrated pyrochlore compounds, especially without
long-range magnetic order.

To conclude, two ferroelectric orders are revealed well above the dipolar-
octupolar antiferromagnetic ordering for STO. A structural transition around
182 K to a polar $R3m$ phase from the high-temperature $Fd\bar{3}m$ space
group is associated with the occurrence of higher-temperature ferroelectric
ordering. The frustrated pyrochlore structure formed by the Sm atoms is
correlated with the ferroelectric order, where the release of magnetic
frustration drives a distortion in the pyrochlore structure within the $R3m$
space group, suggesting a correlation with the emergence of ferroelectric
order. The replacement of non-magnetic Ti by magnetic $V^{4+}$ strongly
influences the ferroelectric polarization as well as the ME coupling in STVO.
The value of ferroelectric polarization decreases, while the ME coupling is
enhanced due to V doping in STO. The emergence of ME coupling without the
involvement of long-range magnetic order is unusual and is further enhanced by
V doping. This observation indicates a new pathway for tuning ME coupling.

Acknowledgment
S.G. would like to thank BRNS, India (No. 58/14/09/2023/11737), SERB, India,
for the CRG project (No. CRG/2022/000718), and the Department of Science and
Technology, India, for the financial support (Proposal No. ID-IB-2021-07), and
Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India for
facilitating the experiments at the beamline P21.1, DESY Synchrotron Facility,
Hamburg, Germany. S.G. also would like to acknowledge UGC-DAE Consortium for
the instrumental support of scientific research (No. CRS/2022-23/01/685).

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