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Yang Zhang, Yudai Hasegawa, Shingo Kitano, [Lihong Liu](https://orcid.org/0000-0002-8964-5512), [Tohru S. Suzuki](https://orcid.org/0000-0001-9458-6863), [Wei Yi](https://orcid.org/0000-0001-5040-8416), Hirofumi Akamatsu, Koji Fujita

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[Large magnetodielectric coupling in layered perovskite <math>  <mrow>    <msub>      <mi>Eu</mi>      <mn>2</mn>    </msub>    <mi>Ti</mi>    <msub>      <mi>O</mi>      <mn>4</mn>    </msub>  </mrow></math>](https://mdr.nims.go.jp/datasets/a7e3bbfd-4823-4e9f-ae9e-a68459ec7733)

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*fujita.koji.5w@kyoto-u.ac.jp      1 Large magnetodielectric coupling in layered perovskite Eu2TiO4  Yang Zhang,1 Yudai Hasegawa,1 Shingo Kitano,1 Lihong Liu,3 Tohru S. Suzuki,3 Wei Yi,1 Hirofumi Akamatsu,2 and Koji Fujita1*  1Department of Material Chemistry, Graduate School of Engineering, Kyoto University, Katsura Nishikyo-ku, Kyoto 615-8510, Japan 2Department of Applied Chemistry, School of Engineering, Kyushu University, Motooka, Fukuoka 812-0053, Japan 3Optical Ceramics Group, Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0047 Japan  Perovskite-type EuTiO3, which is quantum paraelectric and G-type antiferromagnetic (AFM) in the bulk form, has attracted great attention due to its strong spin-lattice coupling and strain-induced multiferroic in thin film form. In this study, significant magnetodielectric (MD) coupling is demonstrated in K2NiF4-type ferromagnetic (FM) layered perovskite Eu2TiO4, which features alternating rock-salt (Rs)-type EuO layers and perovskite (Pv)-type EuTiO3 layers. We find a dielectric anomaly as a local minimum of permittivity near the ferromagnetic transition temperature (TC = 9.5 K) in the temperature-dependent permittivity under zero magnetic field. Remarkably, an applied magnetic field induces a substantial increase in permittivity at TC (approximately 22% at 3 T), which is three times larger than that observed in bulk EuTiO3. Our experimental and first-principles studies reveal that the insertion of EuO layers in Eu2TiO4 enhances the Eu-f/Ti-d orbitals hybridization through pseudo-strain in the EuTiO3 layers, as well as modifies the magnetic exchange paths that favor ferromagnetism over antiferromagnetism. The enhanced hybridization highlights the role in the large MD coupling played by AFM superexchange interactions via the Ti 3d state, which competes with indirect FM interactions via the Eu 5d state. Our findings demonstrate the potential of layered structure to control MD coupling, paving the way for new strategies in designing MD materials.  I. INTRODUCTION The coupling between static electrical and magnetic properties is an interesting effect from the perspective of both fundamental physics and potential applications [1]. This coupling is exemplified by multiferroic materials where two or more primary ferroic orders — such as ferroelectrics, (anti)ferromagnetics, and ferroelastics — coexist. The interaction between these order parameters leads to many interesting effects [2–4]. Moreover, the growing interest in novel dielectric devices has spurred the exploration of the magnetodielectric (MD) coupling, wherein the dielectric properties are tunable by application of magnetic field [5]. This effect has been observed in various materials including Gd2CuO4, [6] YMnO3, [7] EuTiO3, [8] BiMnO3 [9] Pb2MnO4 [10], and TbMnO3 [55]. Among materials exhibiting MD coupling, perovskite oxides EuMO3 (M = Ti, Zr, Hf) containing Eu2+ with 4f7 spins (S = 7/2) have attracted significant attention due to their manipulable magnetic properties and strong spin-lattice coupling [11–14]. For example, bulk EuTiO3 exhibits a G-type antiferromagnetic (AFM) ordering below the Néel temperature (TN = 5.3 K) [15,16], quantum paraelectric (PE) behavior, and a 7% change in permittivity at 2 K under a magnetic field of 1.5 T [8]. Subsequent theoretical and experimental studies have demonstrated switchable ground states between AFM-PE and ferromagnetic-ferroelectric (FM-FE) phases through strain engineering in epitaxial EuTiO3 films. For instance, FM behavior can be induced by the one-dimensional (1D) out-of-plane elongation, while the FM-FE phase arises from 2D biaxial tension (e.g., due to a DyScO3 substrate) or from three-dimensional (3D) tension caused by negative pressure (e.g., due to the embedded MgO cylinders) [17–21]. Additionally, recent studies on bulk (Eu,A)ZrO3 solid solutions (A = Ca, Sr, Ba) have demonstrated that the 3D lattice expansion generated by chemical substitution at the A-site can alter magnetic properties, inducing a transition from AFM to FM states [22].  Regarding the AFM-to-FM switching behavior of EuMO3, Akamatsu et al. reported comprehensive computational studies, revealing the key role played by the hybridization between the Eu 4f orbitals and M nd orbitals. In EuTiO3, the G-type AFM state consists of antiparallel spin alignments between the two-interpenetrating face-centered cubic (FCC) sublattices of Eu ions. The magnetic interactions are primarily governed by nearest-neighbor (NN) AFM interactions (J1 < 0) and the next-nearest-neighbor (NNN) FM interactions (J2 > 0). The transition from AFM to FM ordering is linked to changes in lattice structure, such as 1D lattice expansion, 2D biaxial strain, or 3D strain-induced negative pressure as mentioned above. These mailto:*fujita.koji.5w@kyoto-u.ac.jp2  structural changes modify the balance between FM indirect exchange through Eu 5d states (Eu-Eu) and AFM superexchange via Ti 3d states (Eu-Ti-Eu), which leads to a reversal in the sign of J1 from negative to positive that is favored by the FM state.  The hybridization of Eu-4f/Ti-3d states is also considered the dominant source of MD effects in EuTiO3. The microscopic origin of MD effects has been discussed both theoretically and experimentally in terms of the spin-phonon coupling [23,24]. The soft phonon mode, which involves the vibration of Ti4+ ions against the O2− octahedra, contributes the most to permittivity and thus dominates MD coupling. The spin alignments of Eu2+ ions can significantly impact permittivity through the Eu-Ti-Eu superexchange interactions [25]. In EuTiO3 thin films with 3D tensile strain, the MD coupling (~0.1% at 1.5 T) has been observed with a 3% lattice expansion [19], and the magnitude of the coupling is approximately 70 times weaker than that in bulk EuTiO3 (~7% at 1.5 T). This reduction can be attributed to the volume expansion, which weakens the Eu-Ti-Eu interactions and suppresses the MD coupling. The strong dependence of spin-phonon coupling on the energy levels of empty d states of B-site cations explains why strong spin-lattice coupling has not been observed in other related perovskite oxides, such as EuZrO3 (~0.3% at 5 T)  [14,25,26]. Eu2TiO4, a Ruddlesden-Popper (RP) perovskite oxide, (space group I4/mmm), features alternately stacked monolayers of perovskite (Pv) EuTiO3 and rock-salt (RS) EuO, as shown in Fig. 1. The insertion of the RS layers introduces additional exchange bridges between Eu2+ ions, enhancing the hybridization between Eu 4f and 5d orbitals. This facilitates indirect FM exchange interactions between neighboring Eu2+ ions [15]. The Pv units in Eu2TiO4, separated by RS layers, form a tetragonal unit cell. Compared to cubic EuTiO3 in bulk form (lattice parameter a = b = c = 3.905 Å), the Pv units in Eu2TiO4 are compressed by approximately 0.5% and 6.5% in the in-plane and out-of-plane directions, respectively. This compression can be interpreted as a pseudo-uniaxial strain resulting from the intrinsic chemical nature of the layered perovskite structure. Such pseudo strain is expected to enhance the overlap of Eu 4f and Ti 3d orbitals in the Pv layers and thus to strengthen the spin-lattice coupling. In this respect, we focus on the potential MD effect in Eu2TiO4.  In this study, we demonstrate substantial MD coupling (~22% at 3T) near TC in the layered perovskite Eu2TiO4. A combined study of structure analysis and first-principles calculations suggest that the enhanced Eu-4f/Ti-3d orbital hybridization in the Pv layers may be the origin of the large MD coupling. This strong spin-lattice coupling arises from the interplay between RS and Pv layers, allowing for the coexistence of FM interactions and strong MD coupling—a combination that is not achievable in the simple perovskite oxide EuTiO3. The layered structure plays a unique role in integrating the magnetic and dielectric properties within this system.   FIG. 1. Crystal structure of Eu2TiO4 with RS-type EuO and Pv-type EuTiO3 layers. The NN interactions J1m (m = 1, 2, 3) and NNN interactions J2n (n = 1, 2) are shown with different color lines.  II. METHOD The polycrystalline samples of Eu2TiO4 were prepared by the solid-state reaction method. Reagent-grade Eu2O3 and TiO2 (both 99.9% pure, sourced from Kojundo Chemical Laboratory Co, Ltd) were used as starting materials. Prior to use, Eu2O3 was preheated at 900°C for 12 h to remove water and carbon dioxide. The solid-state synthesis was carried out in two steps. First, EuO precursors were prepared by the reduction of Eu2O3 using graphite carbon (C): Eu2O3 and C were mixed at a mole ratio of 1:1.2, pelletized, and heated at 1400℃ under flowing of Ar gas for 6 h. Next, EuO and TiO2 were mixed, pelletized, and heated at 1350℃ under flowing Ar gas for 6 h to get Eu2TiO4. We also prepared high-density ceramic samples (> 98% density) by spark plasma sintering (SPS). First, Eu2TiO4 powder was loosely placed into a graphite die with a diameter of 10 mm. Then, the SPS treatment was carried out in a vacuum condition at a heating rate of 100℃/min under a uniaxial pressure of 90 MPa using a SPS machine (SPS1050, Fuji Electronic Industrial Co., Ltd, Japan). Finally, the sintering was conducted at 1450℃ with a dwelling time of 1 min.  The phase purity of the final products, including SPS specimens, was checked by x-ray diffraction (XRD) using Smart-Lab diffractometer (Rigaku) with 3  Cu Kα radiation. (λ = 1.5418 Å). High-resolution synchrotron x-ray diffraction (SXRD) was performed at room temperature using the large Debye−Scherrer cameras with MYTHEN solid-state detectors installed at the beamlines BL02B2 (SPring-8). The incident beam was monochromatized to λ = 0.774702 Å. Finely ground powder samples were sieved through a 32μm mesh sieve and put into a Pyrex capillary with 0.1 mm inner diameter. The sealed capillary was rotated during measurements to reduce the effect of preferential orientation. The SXRD data collected were analyzed by the Rietveld method [27] using a Jana program [28]. Magnetization measurements were carried out with a superconducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design). Temperature dependence of magnetic susceptibilities was measured in a range 2–300 K at an external magnetic field of 0.01 T. The field dependence of magnetization was recorded at 2 and 9.5 K in magnetic fields up to 5 T. Dielectric properties were measured with an LCR meter (Agilent E4980) in the temperature range 2–300 K in the magnetic field of 0–5 T utilizing a home-made dielectric measurements probe coupled with the physical property measurement system (PPMS, Quantum Design). 50 nm/20 nm Au/Ti electrodes were deposited on the top and bottom surface of an Eu2TiO4 pallet (6 mm diameter) using electron beam evaporation (HITACHI, Japan). First-principles density functional theory (DFT) calculations were carried out for Eu2TiO4 (space group: I4/mmm) and EuTiO3 (space group: 𝑃𝑚3̅𝑚) using the projector augmented-wave (PAW) method [29,30] as implemented in the VASP code [31–36]. To reduce the computational costs, the generalized gradient approximation-PBEsol (GGA-PBEsol) [37–39] and HSE06 hybrid functional [40–42] were used for structural optimizations and electronic structure calculations, respectively.  The PAW datasets with radial cutoffs of 1.5, 1.3, and 0.8 Å were used with a plane-wave cutoff energy of 550 eV.  The following states were described as valence electrons: 4f7, 5s2, 5p6, 6s2 for Eu; 3d2, 4s2 for Ti; and 2s2, 2p4 for O. FM spin configurations were considered for Eu2TiO4 and EuTiO3.  The lattice constants and internal coordinates were optimized until the residual stress and forces converged to 0.2 GPa and 1 meV/Å, respectively.  A phonon band structure was calculated for Eu2TiO4 using the PHONOPY code [43].  The crystal orbital Hamilton population (COHP) between Eu and Ti atoms was calculated using the LOBSTER code [44,45]. The VESTA code was used to visualize crystal structures [46].    III. RESULTS According to laboratory XRD data, the main phase of the synthesized products was identified as Eu2TiO4 with an n = 1 RP (K2NiF4)-type structure. The 151Eu Mössbauer spectrum shows that almost all the europium ions exist as Eu2+ (see Fig. S1 and Table S1 in the Supplemental Material (SM) [51]). Figure 2 shows the SXRD pattern at room temperature. The main reflections can be indexed by a tetragonal unit cell with lattice parameters of 𝑎 = 𝑏 = 3.88619(1) Å, and 𝑐 = 12.54039(4) Å. The observed reflection conditions indicate the tetragonal symmetry (space group I4/mmm), in agreement with previous observation on Eu2TiO4 [15]. A negligibly small amount of EuO impurities (less than 1 wt%) is detected. Rietveld refinement with the I4/mmm structure model converges to a good reliability index Rwp (weighted profile R factor) of 6.65%. Separate occupancy refinement reveals no deviation from the ideal composition. Detailed structural parameters obtained from the refinement are summarized in Table S2 in SM [51].  FIG. 2. SXRD pattern (λ = 0.774702 Å) of n = 1 RP-type Eu2TiO4 at 300 K and fitting curve obtained by Rietveld refinement with the I4/mmm structure model. Black circles and red solid curves represent the observed and the calculated intensities, respectively. The blue solid line at the bottom indicates the difference between the experimental and calculated patterns. Purple and green ticks show the peak positions of Eu2TiO4 and EuO, respectively. The inset shows a schematic diagram for the movement of atoms in the Eu(TO1) mode in Eu2TiO4.  The crystal structure of n = 1 RP-type Eu2TiO4 can be interpreted as alternating layers of TiO2 and EuO planes stacked along the c-axis, as illustrated in Fig. 1. The stacking sequence follows a TiO2-EuO-EuO pattern, with the second EuO layer being shifted by 1/2a along the [110] direction relative to the first EuO layer. From the structural refinement, the EuTiO3 unit in the Pv layer shows lattice parameters of aPv = bPv = 3.88619(1) Å, cPv = 3.65819(1) Å, indicating a compressed c-axis compared to its in-plane dimensions.  4  Before presenting the dielectric properties and MD coupling of Eu2TiO4, it is crucial to first examine the magnetic characteristic of our Eu2TiO4 samples. Temperature dependence of magnetic susceptibility (χ−T) exhibits an FM transition around TC = 9.5 K [see Fig. 3(a)].  A Curie-Weiss analysis in the temperature range 15 K ≤ T ≤ 300 K yields effective magnetic moment μeff = 7.84(1)μB, consistent with the expected 7.8 μB for Eu2+ ions in a 4f7 (J = S = 7/2) configuration. The analysis also reveals a Weiss temperature 𝜃W = 10.05(2) K, indicating that FM interactions are dominant. These values of μeff and 𝜃W are in good agreement with those reported previously for polycrystalline Eu2TiO4 samples [47].  Temperature-dependent dielectric permittivity ε(T) under zero magnetic field at 1 MHz is displayed in Fig. 3(b). Below 30 K, we observed a negligible dependence of permittivity on frequency between 1 kHz and 1 MHz, along with a relatively low dielectric loss (tanδ < 0.3). The permittivity decreases with decreasing the temperature, indicating that Eu2TiO4 behaves distinctly from quantum paraelectric EuTiO3. As the temperature further decreases, a local minimum of permittivity is observed near 9.5 K, corresponding to the TC. This anomaly of permittivity is smeared out when the magnetic field of 5 T is applied, suggesting the presence of MD coupling in this system.  The magnetic field dependence of magnetization (M−H) and permittivity (ε−H) at 2 and 9.5 K is comparatively shown in Figs. 3(c) and 3(d), respectively. At 2 K [see Fig. 3(c)], the magnetization increases with the magnetic field increasing and reaches its saturation around 1.2 T. The saturation magnetization is 6.7 μB/Eu2+, which is close to the full moment of free Eu2+ (7 μB/Eu2+). Meanwhile, the permittivity is independent of the magnetic field and slightly decreases beyond 1.2 T. The slight decrease in the permittivity under high fields can be attributed to magnetostriction [54], similar to what was observed in the strain-induced FM EuTiO3 thin films [19]. The field-independent permittivity at low magnetic fields could result from the cancellation of positive contribution from magnetic structure changes and negative contribution from magnetostriction (see Fig. S5). Remarkably, at T = 9.5 K [see Fig. 3(d)], both magnetization and permittivity increase simultaneously when the magnetic field is applied up to 3 T. This is indicative of significant MD coupling, and the permittivity enhancement is about 22% at 3 T, which is three times larger than that observed in EuTiO3 (7% at 1.5 T) [8]. Note that the resistivity in our samples exceeds 106 Ω·cm below 30 K. In addition, a high frequency (1 MHz) was employed for the dielectric measurements in this study to mitigate the influence of charge carriers. Therefore, the contribution from the magnetoresistance could be negligible.  FIG. 3. (a) Temperature dependence of magnetic susceptibility χ (=M/H) of Eu2TiO4 collected at 0.01 T. The inset shows the inverse susceptibility 1/χ with Curie-Weiss fitting (pink line). (b) The permittivity of Eu2TiO4 as a function of temperature (2 K ≤ T ≤ 30 K) measured at 0 and 5 T under a frequency of 1 MHz. (c) and (d) Variation of magnetization and ε(H)/ε(H=0) of Eu2TiO4 with magnetic field at (c) 2 K and (d) 9.5 K. (e) and (f) Temperature dependence of (e) [(ε(H)−ε(H=0)] / ε(H=0) % and (f) Δ<Si·Sj> obtained by subtracting <Si·Sj> data at 0 T from those at 0.1, 0.5, 1, 3, and 5 T.  In bulk EuTiO3, permittivity as a function of temperature and magnetic field can be represented using the following equation [8]: 𝜀(𝑇, 𝐻)  =  𝜀(𝑇, 0) (1 +  𝛼 < 𝑺𝑖 · 𝑺𝑗 >) ,   (1) where ε(T, 0) is the permittivity at zero magnetic field. <Si·Sj> is the spin pair correlation between nearest-neighboring Eu2+, and α is the coupling constant between spin correlation and permittivity [8]. To estimate <Si·Sj> in Eu2TiO4, molecular-field calculations were conducted based on a Heisenberg model under an assumption that the 4f spins of Eu2+ (S = 7/2) are located on a tetragonal lattice with FM ordering. The Heisenberg Hamiltonian of the spin system is given by:      𝐻𝑚𝑒 = ∑ 𝐽𝑖𝑗 · 𝑺𝑖 · 𝑺𝑗𝑖𝑗  ,         (2) 5  where Jij represents the exchange constants between spins Si and Sj, with a restriction on considering only the NN and NNN interactions. This approach helps us evaluate the magnetic exchange interactions and their impact on the dielectric properties of Eu2TiO4. We used the exchange interaction parameters obtained with the previous first-principles calculations [48] (see Fig. 1, and Fig. S2, and Table S3 in the SM [51]): J11/kB = 0.2 K, J12/kB = 0.08 K and J13/kB = 0.0 K for NN interactions, J21/kB = 0.08 K and J22/kB = 0.04 K for NNN interactions, where kB is the Boltzmann constant. In the molecular-field calculation, <Si·Sj> is obtained as the product of <S> on two sublattices. To further analyze the impact of a magnetic field on the dielectric properties, we calculated the change in spin pair correlation: Δ〈𝑺𝑖 · 𝑺𝑗〉  =  〈𝑺𝑖 · 𝑺𝑗〉𝐻 − 〈𝑺𝑖 · 𝑺𝑗〉0 ,   (3) where <Si·Sj>H and <Si·Sj>0 are the spin pair correlations under finite and zero magnetic field, respectively. Figure 3(e) illustrates the relative permittivity change:   [(𝜀(𝐻)−𝜀(0)]  𝜀(0)× 100% ,      (4) in comparison with Δ<Si·Sj> [Fig. 3(f)]. The calculated results show remarkable agreement with the experimental findings, indicating that the MD effect in Eu2TiO4 is primarily governed by the pair correlation of the Eu2+ spins. The magnetodielectric coupling constant is α = 2.4 × 10–2, which obtained by Eq. (1) for Eu2TiO4, is the largest among perovskite-type oxides with Eu2+ occupying the A-sites, e.g., EuZrO3 (α = 1.1 ×10–4) [14] and EuTiO3 (α = 2.74 × 10–3) [8], highlighting the unique magnetodielectric properties of Eu2TiO4. IV. DISCUSSION A. Magnetic properties of Eu2TiO4 We start with a brief survey of the magnetic properties of Eu2TiO4. For perovskite and related oxides with Eu2+ occupying the A-sites, both AFM and FM interactions coexist between the nearest-neighboring (NN) Eu2+−Eu2+ pairs. Hence, the magnetism of these oxides alters depending on the relative strength of the competing magnetic interactions, i.e., the sign of J1. In bulk EuTiO3, Eu2+ ions have six nearest neighbors within the cubic lattice, where the indirect FM exchange via the Eu 5d states and the AFM superexchange via the Ti 3d states coexist. The G-type AFM state of bulk EuTiO3 appears due to the AFM superexchange via the Ti 3d states. Moreover, it was also suggested that the third nearest neighbor magnetic exchange (J3) may play a crucial role in the MD coupling in EuTiO3 [49]. In the case of J3, the exchange occurs between Eu ions at opposite corners of a cube through the central Ti ion, forming a 180° Eu-Ti-Eu superexchange pathway, further highlighting the significance of Eu-Ti-Eu superexchange interactions. In contrast, the layered structure in Eu2TiO4 introduces significant changes in the magnetic exchange paths: the number of NN Eu2+−Eu2+ pairs increases from 6 in EuTiO3 to 9 in Eu2TiO4. Specifically, the insertion of an RS layers between the Pv units introduces four additional Eu2+-Eu2+ pairs along the <11√2> direction (exchange constant J11), maintaining four Eu2+-Eu2+ interactions along the <100> and <010> directions (exchange constant J12), while it eliminates one of two Eu2+-Eu2+ pairs along the <001> direction (exchange constant J13 for the remaining pair); (see Table. S3 in the SM [51]). The absence of Ti atoms in the RS-type EuO layers results in the exclusive presence of FM indirect exchange (positive J11). Namely, the additional magnetic exchange pathways in Eu2TiO4 leads to the FM ground state.  Previous first-principles studies of Eu2TiO4 have suggested competition between FM and AFM exchanges within the Pv layers (near zero J13) and in the RS-Pv interlayers (slightly positive J12) [48]. To compare such competition in Eu2TiO4 with those in EuTiO3, we checked the refined structure data: in Eu2TiO4, the Pv layers, sandwiched by the RS layers, have a tetragonal unit cell (aPv = bPv = 3.88619(1) Å, cPv = 3.65819(1) Å), which is compressed by approximately 0.5% and  6.5% in the in-plane and out-of-plane directions, respectively, relative to the cubic unit cell of bulk EuTiO3 (lattice parameter a = b = c = 3.905 Å). This uniaxial compression effectively reduces the Eu-Ti distance in Eu2TiO4 (3.301 Å) compared to that in bulk EuTiO3 (3.382 Å). This pseudo-strain along the c-axis caused by the insertion of the RS layers works to enhance the overlap between Eu 4f and Ti 3d orbitals in the Pv layers, potentially strengthening the spin-lattice coupling.   B. Magnetodielectric effect of Eu2TiO4 The observation of large MD coupling constant in the Eu2TiO4 raises two questions: What is the origin of MD coupling in FM Eu2TiO4? Additionally, why is the magnitude of MD coupling even larger than bulk EuTiO3?  According to Lyddane-Sachs-Teller (LST) relation, the permittivity is connected to the optical phonon frequency:       𝜀0𝜀∞=𝜔LO2𝜔TO2  ,            (5) where ε0 is the static permittivity, which includes the lattice contribution, ε∞ is the electronic contribution, 6  and ωLO and ωTO are the zone-center longitudinal and transverse optical (LO and TO) phonon frequencies, respectively. The ε0 of a material is primarily influenced by the lowest-energy TO phonon mode. Although Eu2TiO4 is a multi-mode system, Eq. (5) is used here for a qualitative discussion based on a simplified single-mode approximation. Our first-principles calculations on Eu2TiO4 (see Table. S4 in SM [51]) identify this as the Eu(TO1) mode, which involves Ti4+ and Eu2+ ions vibrating against the O2− octahedra within the a-b plane (see the inset of Fig. 2), analogous to the behavior observed in n = 1 RP-type Sr2TiO4 [50]. This finding suggests that the Eu(TO1) mode plays a crucial role in the dielectric properties of Eu2TiO4. Specifically, the application of an external magnetic field near TC can align the Eu spins in the field direction, which may soften the Eu(TO1) mode and increase permittivity. Note that the in-plane movement of the Eu(TO1) mode in the Pv layers of Eu2TiO4 closely resembles the T1u mode in EuTiO3 [24], where changes in Eu spin configuration under a magnetic field alter the phonon frequency through modified hybridization between the Eu 4f and Ti 3d orbitals [25]. More detailed analyses of the phonon modes in Eu2TiO4 using infrared and Raman spectroscopy [56] should be performed in future work to reveal its phonon nature. To estimate the Eu/Ti orbital hybridization in Eu2TiO4, we calculated the electronic state by site-projected partial density of states (PDOS). The valence band mainly consists of O 2p states, while the conduction band chiefly has Ti 3d and Eu 5d characters. The occupied Eu 4f bands lying between these bands are narrow, indicating their localized nature [see Fig. 4(a)]. The enlarged view of the PDOS in the energy region near the Eu 4f band is shown in Figs. 4(b) and 4(c) for Eu2TiO4 and EuTiO3, respectively. The Eu 4f states, which possess the localized spins near the Fermi level, are hybridized with the Ti 3d and O 2p states [see Fig. 4(b)]. Compared to EuTiO3 [Fig. 4(c)], the PDOS for Ti in Eu2TiO4 is significantly larger, indicating a stronger hybridization between Eu 4f and Ti 3d orbitals.  To further illustrate the covalent bonding interactions between Eu 4f and Ti 3d orbitals, we employed the COHP method [32]. In COHP analysis, the negative value represents bonding interactions, while the positive value corresponds to antibonding interactions. A comparison of the −COHP in the energy range −1 eV to 1 eV near the Fermi level between Eu2TiO4 and EuTiO3 is displayed in Fig. 4(d). Integrating the –COHP curves up to the Fermi level provides the integral –COHP (−ICOHP) value, which qualitatively correlate with the strength of corresponding bonds. The larger positive value of −ICOHP in Eu2TiO4 (0.2 band-1) than in EuTiO3 (0.17 band-1) indicates the stronger bonding between Eu and Ti atoms in Eu2TiO4, implying the enhanced AFM interaction within the Pv layers. We expect that this stronger bonding interaction can contribute to the large MD coupling observed in Eu2TiO4. Moreover, Figure 4(e) plots the variation in −ICOHP against the isotropic lattice volume change (ΔV). For both Eu2TiO4 and EuTiO3, the −ICOHP increases with lattice volume decreasing. Interestingly, the variation in −ICOHP with ΔV is pronounced in Eu2TiO4 compared to EuTiO3, which indicates that the layered structure of Eu2TiO4 offers a more volume-sensitive mechanism for tuning the bonding interaction between Eu 4f and Ti 3d orbitals. Namely, the pseudo-uniaxial strain resulting from the intrinsic physical nature of the layered perovskite structure provides a versatile platform to study the complex interplay between static electrical and magnetic properties. It is interesting to explore the possibility of inducing ferroelectricity in Eu2TiO4 by epitaxial strain or chemical substitution, though care must be taken to mitigate potential conductivity issues.  FIG. 4. (a) Site-projected PDOS of Eu2TiO4. The zero of energy is placed at the highest occupied state. (b) and (c) Magnified view of the up-spin component of the PDOS in the energy region near the Eu 4f band in (b) Eu2TiO4 and (c) EuTiO3. (d) Comparison of −COHP between Eu2TiO4 and EuTiO3 without volume change (ΔV = 0%) and (e) variations of integral −COHP (−ICOHP) between Eu2TiO4 and EuTiO3 with isotropic volume change (ΔV = −14.3%, −7.3%, 0%, 7  +7.7% and +15.8%). V. CONCLUSIONS In conclusion, an FM layered perovskite oxide, n = 1 RP-type Eu2TiO4, exhibits a large MD coupling around TC. The magnitude of the MD coupling (approximately 22% at 3T) is three times larger than that of bulk EuTiO3. A combined study of structure analysis and first-principles calculations suggests that the enhanced MD coupling in Eu2TiO4 arises from the interplay of RS and Pv layers in the quasi-2D structures. The AFM superexchange interactions via the B-site Ti 3d state, which compete with indirect FM interactions via the Eu 5d state, are crucial to the mechanism responsible for the enhanced MD coupling. Our study highlights that this layered structure provides a distinctive approach to regulating MD coupling, opening interesting possibilities for innovative MD material design. ACKNOWLEDGMENTS The authors would like to thank Prof. K. Tanaka and Mr. T. Wakamatsu for supporting the electron-beam evaporation. The computation was carried out using the computer resources offered under the category of General Projects by the Research Institute for Information Technology, Kyushu University. This work was supported by the Grant-in-Aid for the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant No. JP22K04686, JP21H04619, JP23K23043, JP25K08265 JP24K21688, and JP25K01500). K.F. acknowledges grants from the Okura Kazuchika Memorial Foundation, Izumi Science and Technology Foundation, Sumitomo Electric Industries, JFE 21 Century Foundation, and Iwatani Naoji Foundation. SXRD experiments were performed on BL02B2 at SPring-8 with the approval of Japan Synchrotron Radiation Research Institute (JASRI) (Proposal Nos. 2023A1498, 2023B1654, 2024A1510).[1] H. Schmid, Multi-ferroic magnetoelectrics, Ferroelectrics 162, 317 (1994). [2] S. W. Cheong and M. Mostovoy, Multiferroics: a magnetic twist for ferroelectricity, Nat. Mater. 6, 1 (2007). [3] K. Dunnett, J.-X. Zhu, N. A. Spaldin, V. 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