# Fileset
[BCR1441_SM.pdf](https://mdr.nims.go.jp/filesets/a9665da3-f864-48f2-9748-999961326759/download)
## Creator
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
## Rights
©2025 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)
## Other metadata
[Large magnetodielectric coupling in layered perovskite ](https://mdr.nims.go.jp/datasets/a7e3bbfd-4823-4e9f-ae9e-a68459ec7733)
## Fulltext
Supplementary Material for “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 E-mail: fujita.koji.5w@kyoto-u.ac.jp 1. Mössbauer spectroscopy To evaluate the valence state of europium ions and the local environment around Eu2+ ions, 151Eu Mössbauer effect measurements were performed at room temperature using a standard transmission geometry. A 151Sm2O3 source with 1.85 GBq activity provided the 21.5 keV γ-ray emission, and the velocity calibration was done with the magnetic hyperfine spectrum of α-Fe foil obtained using 57Co doped Rh as a 14.4 keV g-ray source. The Mössbauer spectrum of EuF3 was measured as a standard of Doppler velocity. Figure S1 shows the room-temperature 151Eu Mössbauer spectrum of n = 1 RP-type Eu2TiO4. Two absorption peaks are observed around 11.9(1) and 0.5(1) mm/s, assigned to Eu2+ and Eu3+, respectively. From the area ratio of the two absorption peaks, the fraction of Eu2+ relative to the total europium ions was estimated to be about 0.98(1). Since the effective Debye temperature of Eu2+ is usually lower than that of Eu3+ (e.g. 195 K for Eu2+ and 220 K for Eu3+ in EuPd3S4 [1]), it is expected that the real fraction of Eu2+ is higher than 98%. Note that the fraction of Eu2+ in the present sample is relatively larger than that in Eu2TiO4 as reported previously (~96%) [2]. The isomer shifts (δ = –11.9 mm/s) for Eu2TiO4 at room temperature is slightly larger than that of EuTiO3 (δ = –12.5 mm/s) [3], indicating a reduced coordination number for Eu2+ (CN = 9) than EuTiO3 (CN = 12). At 300 K, the Mössbauer spectrum can be interpreted in terms of pure quadrupole effects with quadrupole interactions eVzzQg = –6.1 mm/s. Since the Eu2+ site has fourfold symmetry, the asymmetry parameter η is regarded as zero. The fitting results for the Mössbauer data are summarized in Table S1. Fig. S1 Mössbauer spectrum of n = 1 RP-type Eu2TiO4 at room temperature. The black circles and red solid lines represent the experimental data and calculated curve, respectively. The green solid line shows the contribution from Eu3+ absorption. Table S1 The fitting parameters for Mössbauer spectrum of n = 1 RP-type Eu2TiO4 Table S2 Structural parameters of n = 1 RP-type Eu2TiO4 at 300 K obtained from refinement with an I4/mmm model against the SXRD data Site x y z Occ. U Eu1 4e 0 0 0.35414(2) 1 0.0050(5) Ti1 2a 0.5 0.5 0.5 1 0.004(21) O1 4c 0.5 0 0.5 1 0.008(10) O2 4e 0 0 0.15971(23) 1 0.0050(6) AEu2+ / AEu3+ δ (mm/s) eVzzQg (mm/s) Eu2TiO4 0.98 −11.9(1) –6.1(4) Eu2TiO4 [2] 0.96 −11.8 –6.6 EuTiO3 [3] 0.96 −12.5(1) 0 EuZrO3 [4] 0.94 −12.9(1) –10.20(37) 2. Molecular-field approximation In Eu2+-containing oxides with perovskite-type structure, the magnetic structure is predominantly determined by the nearest-neighbors (NN) and next-nearest-neighbor (NNN) exchange interactions between Eu2+ ions. In the case of cubic systems such as EuTiO3, these exchange interactions are characterized by the exchange constants J1 and J2, respectively. In the layered perovskite oxide, Eu2TiO4, however, there exist three types of NN of Eu2+ (J11, J12, J13) [see the inset of Fig. S2(a)] and two types of NNN Eu2+ (J21, J22) [see the inset of Fig. S2(b)]. We used the exchange interaction parameters obtained with the previous first-principles calculations [4]: 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. The calculation is done by the custom ruby code with internal molecular field components along the in-plane (x) and out-of-plane (z) directions: Hx = – (4J11 + 4J12 + J13 +4J21 + 4J22)×Sx Hz(z, h) = – (4J11 + 4J12 + J13 + 4J21 + 4J22) ×Sz – g·μB·h The total effective field is: |𝐻𝑒𝑓𝑓| = √𝐻𝑥2 + 𝐻𝑧2 , where x and z are the spin components, g is the Landé g-factor, μB is the Bohr magneton, and h is the external magnetic field. These equations were implemented using a self-consistent iterative approach to compute the average magnetization and the nearest-neighbor spin correlation as a function of temperature and magnetic field. In the molecular-field calculation, obtained as the products of on two sublattices in different magnetic fields are shown in Fig. S2(a). 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 The TC determined from the peak position of 𝛥〈𝑆𝑖 · 𝑆𝑗〉 is approximately 9.5 K [as shown in Fig. S2(b)], in good agreement with our experimental result. Table S3 Eu-Eu coordinates, distance, and direction in Eu2TiO4. Fig. S2 (a) Spin correlation function for Eu2TiO4 calculated using a molecular-field approximation at H = 0, 0.1, 0.5, 1, 3, and 5 T. (b) Temperature dependence of Δ obtained by subtracting data at H = 0.1, 0.5, 1, 3, and 5 T data from those at H = 0 T. The inserts show the NN interactions J1m (m = 1, 2, 3) and NNN interactions J2n (n = 1, 2) in Eu2TiO4 3. Phonon band structure and phonon model Based on the crystal symmetry, there are 18 types of optical phonon modes in I4/mmm Eu2TiO4. Among these, 7 infrared transverse optical (TO) modes mainly influence the dielectric properties. Our first-principles calculations reveal that the Eu (TO1) mode has the lowest frequency (see table S4), making it the dominant contributor to the dielectric properties. In this mode, Ti4+ and Eu2+ ions vibrate against the O2− octahedra within the a-b plane (see the inset of Fig. 2 in the main text), resembling the T1u mode in EuTiO3 [5]. NN NNN Coordinates Distance(Å) Direction J11 4 3.79123(1) <11√2> J12 4 3.88619(2) <100> J13 1 3.65819(5) <001> J21 4 5.49590(4) <110> J22 4 5.33711(4) <101> Fig. S3 (a) Phonon band structure of Eu2TiO4. The symmetry points are based on the √2 × √2 × 2 supercell. Table S4 Phonon frequencies (cm–1) and mode assignments at Γ point in Eu2TiO4 Irrep A2u(TO1) A2u(TO2) A2u(TO3) Eu(TO1) Eu(TO2) Eu(TO3) Eu(TO4) Freq (cm-1) 194 375 489 111 200 251 592 According to previous investigations of bulk EuTiO3 [5], a strong coupling between Eu spins and dielectric properties was realized through a modified T1u phonon mode. This was confirmed by an abrupt change in permittivity in different magnetic fields. In Eu2TiO4, this coupling is associated with the Eu(TO1) mode. The magnitude of the change in phonon frequency (ω0) with an applied magnetic field can be estimated from that of the permittivity. We speculate that the hybridization between Eu-4f/Ti-3d orbitals varies depending on the configuration of the Eu spins, which then modifies the Eu(TO1) mode frequency. As shown in Fig. 3(b) of the main text, the permittivity increases monotonically with the applied magnetic field and saturates at 3 T, reaching an increasement of approximately 22%. According to the Lyddane-Sachs-Teller (LST) relation, this increase in permittivity corresponds to a softening of the Eu(TO1) mode, with an estimated decrease in ω0 by 11%. The calculation follows the formula: 𝜀(𝜔) = 𝜀1(𝜔) − 𝑖𝜀2(𝜔) = 𝜀∞ + 4𝜋𝑁𝑒∗2/𝜇(𝜔02 − 𝜔2) + 𝑖𝛤𝜔 where N is the number of unit cells per volume, e* is the effective charge of ions, μ is the effective mass of ions, ω0 is the phonon frequency, and Γ is the scattering rate of the phonon. Fig. S4 Upper panel: Magnified view of the up-spin component of the PDOS in the energy region near the Eu 4f band of Eu2TiO4 at (a) ΔV = −7.3%, (b) 0%, and (c) +7.7%. Lower panel: Negative crystal orbital Hamilton populations (−COHP) for Eu-Ti interactions near the Fermi level at (d) ΔV = −7.3%, (e) 0%, and (f) +7.7%. The highest occupied state (Fermi level) is set to 0 eV. Fig. S5 (a), (b) Magnetic field dependence of (a) magnetization and (b) dielectric permittivity ratio [(ε(H)/ε(0T) at 1 MHz], for various temperatures (2, 3, 4, 5, 6, 7, 8, 9, and 10 K) in the range 0 T ≤ H ≤ 5 T. Reference: [1] M. Wakeshima et al., J. Solid State Chem. 157, 117 (2001). [2] Chia-Ling Chen and F. De S. Barros, Phys. Lett. A 38, 427 (1972). [3] C.-L. Chien, S. DeBenedetti, and F. D. S. Barros, Phys. Rev. B 10, 3913 (1974). [4] S. Li et al., J. Mater. Chem. C 11, 8383 (2023). [5] T. Katsufuji and H. Takagi, Phys. Rev. B 64, 054415 (2001).