Crystal structure and magnetic properties of EuZrO₃ solid solutions

Abstract

It is theoretically proposed that perovskite-type EuZrO₃ becomes a ferromagnet when the lattice volume is increased or the structure is changed from orthorhombic to cubic in contrast to the fact that the stable phase of EuZrO₃, the structure of which is orthorhombic, is antiferromagnetic. To investigate the change in crystal structure and magnetic properties of EuZrO₃ with the variation of lattice volume, we have synthesized polycrystals of solid solutions A_xEu_1−xZrO₃ (A = Ba, Ca, Sr); Eu²⁺ is substituted by group 2 elements with different ionic radius to realize the change in lattice volume and crystal structure of EuZrO₃. The stable magnetic structure of EuZrO₃ solid solutions is tuned with the change of lattice volume. In particular, the ferromagnetic state is stabilized by the increase in lattice volume, which experimentally verifies the prediction by the first-principles calculations. Furthermore, this phenomenon is explainable in terms of the competition between ferromagnetic and antiferromagnetic interactions that is highly related to the volume variation and the rotation of ZrO₆ octahedron. The present results indicate that the magnetic structure can be systematically tuned by controlling the chemical pressure in solid solutions.

---

1. Introduction

Multiferroics display two or more primary ferroic orderings, such as ferroelectricity (FE), ferro-, antiferro-, or ferri-magnetism, ferrotoroidicity, and ferroelasticity in a single-phase, and the coupling between these multiple order parameters leads to novel effects, specifically, the magnetoelectric (ME) effect.^1–3 Much attention has been paid to the multiferroic properties of perovskite-type oxides the composition of which is denoted by ABO₃, especially since the discovery of enhancement of polarization in constrained thin films of ferroelectromagnet BiFeO₃ and manipulation of the electric polarity of TbMnO₃ with a magnetic field.^4,5 Currently, studies of ABO₃ perovskite oxides with ME effect have focused on several compounds including divalent europium-based perovskite oxides with a general formula of EuMO₃ (M: group 4 elements).⁶ For the multiferroic EuMO₃, the correlation between magnetic and dielectric properties through the spin-lattice coupling was experimentally demonstrated for EuTiO₃ (paraelectric and G-type antiferromagnetic).^7–9 Specifically, the dielectric constant manifests a drastic drop at the antiferromagnetic phase transition temperature, i.e., the Néel temperature (T_N), due to the hardening of soft phonon modes and subsequent saturation disruption of the dielectric constant at low temperature. The decrease of dielectric constant can be suppressed by applying a magnetic field below T_N and the dielectric constant is altered by 7% at 1.5 T, corresponding to a large ME effect.⁹ Moreover, ferromagnetism of EuTiO₃ (ETO) induced by an external electric field exhibits another aspect of ME effect.¹⁰ Such an ME effect was observed for EuZrO₃ as well.¹¹ For magnetic properties closely related to the ME effect of EuMO₃, the critical balance was proposed between the antiferromagnetic (AFM) superexchange interaction via the nd orbitals of M elements and ferromagnetic (FM) indirect exchange interaction via the Eu 5d states based on the hybrid Hartree–Fock density functional calculations.¹²

Due to the strong correlation between the degrees of freedom in crystal structure and order parameters related to the dielectric and magnetic properties, ME effects can be modified via various engineering techniques.^13–22 Density functional theory (DFT) calculations and subsequent experiments have proposed that through the strain engineering, ETO thin film deposited on a substrate can be converted from a paraelectric (PE)-AFM phase to a FE-FM phase.^23,24 A change in the magnetic interactions of FM ordering induced by engineering techniques in EuMO₃ is anticipated to modify the ME effects. The influence of engineering techniques including strain and stress as well as lattice volume change on the magnetic structure and properties of ETO has been studied theoretically and experimentally. DFT calculations revealed that when a biaxial compressive strain is induced in the surface, both FM and FE states become stable in ETO thin films.²³ This was supported by the appearance of nanometer-sized FM clusters in ETO films when an electric field is applied under a moderate compressive strain.¹⁰ The observation of FM properties has been also reported for ETO thin films with a in-plane biaxial tensile strain and a vertical strain.^25–27 Furthermore, it was suggested by the hybrid Hartree–Fock density functional calculations that the lattice volume-expanded EuMO₃ prefers the FM interaction through the Eu 5d states to the AFM one via the M nd states, as a consequence of the reduced hybridization of the Eu 4f and M nd orbitals.²⁸ The volume expansions induced by the lattice mismatch between ETO thin films and different substrates can change the magnetic ground state of ETO from AFM to FM, experimentally supporting the theoretical calculations.²⁹ Based on the critical balance between AFM superexchange interaction via the M nd orbitals and FM indirect exchange interaction via Eu 5d states, the FM state resulting from the modification of crystal structure of EuMO₃ by engineering techniques was confirmed by the works mentioned above. However, those works were conducted on biaxially strained EuMO₃ thin films, and the strain engineering was restricted by the substrate and could not realize three-dimensionally isotropic volume change. On the other hand, a uniform three-dimensional strain-induced negative pressure was realized by Zhao et al.³⁰ in a composite thin film of EuTiO₃ in which MgO phases of cylindrical shape were embedded. They observed the FM state in the ETO nanocomposite film and explained the magnetic state in terms of a different critical balance between the out-of-plane AFM nearest exchange interaction and the in-plane FM exchange interaction. Thus, the mechanism of the magnetic interaction in EuMO₃ under three-dimensional strain or stress remains controversial.

EuZrO₃, another kind of EuMO₃, shows an orthorhombic crystal structure (Pbnm) and exhibits structural distortions associated with octahedral rotations, thereby having a lower symmetry than the ETO which adopts the ideal cubic (Pm3̄m) perovskite structure.^31–34 As for the magnetism, Eu²⁺ ions in EuZrO₃ favor the G-type AFM structure, which has been verified by the analysis of the sign and magnitude of the magnetic exchange constants based on the Heisenberg spin Hamiltonian.^6,35 This theoretical analysis along with experimental observations of the AFM transition at 4.1 K indicates that EuZrO₃ is magnetically similar to ETO.^11,34 Moreover, the calculations by Akamatsu et al. propose that the exchange coupling constant also can be varied by the lattice volume, showing its potential for modulating the magnetic order.²⁸ This prediction provided an insight that not only the volume expansion of lattice but the decrease of octahedral rotation involved in the structural change from orthorhombic Pbnm to cubic Pm3̄m structures leads to the weakening of the AFM interaction via Zr 4d orbitals and even triggering the occurrence of FM order in EuZrO₃. Furthermore, the calculations extended an understanding of the competition between AFM superexchange interaction via the M nd orbitals and FM indirect exchange interaction via Eu 5d states in EuMO₃.

A chemical pressure, often observed in solid solutions, can induce the three-dimensional strain or stress, which is important to clarify the mechanism of magnetic interaction in EuMO₃ as mentioned above, and can change the lattice volume as well as crystal structure that has influence on the magnetic interactions and structures.^29,36,37 The formation of solid solutions through the A-site cation substitution has been reported to modulate the lattice volume and the accompanying structural evolution of ABO₃ perovskite oxides.^38–43 The alkaline earth metal zirconates AZrO₃ (A = Ba, Ca and Sr) have different crystal structures and crystal lattice volumes at room temperature; the structure is cubic Pm3̄m for A = Ba and orthorhombic Pbnm for A = Ca and Sr.^44–48 Thus, the substitution of the A-site (Eu²⁺) by group 2 elements has the potential to induce variations in lattice volume and crystal structure and to fine-tune the magnetic properties of EuZrO₃. In this study, we aimed to qualitatively verify the theoretical prediction deduced by Akamatsu et al. and reveal the underlying intrinsic mechanism of tuning the relative strengths of the competing magnetic interactions by changing the lattice volume for EuZrO₃.²⁸ The change of magnetic ordering state of EuZrO₃ with a systematic variation in the lattice volume was experimentally elucidated by an A-site substitution. Through a conventional solid-state reaction method, the A-site (Eu²⁺) substitution was realized by group 2 elements (Ba, Ca, and Sr) with different ionic radii. The lattice volume, crystal structure, local environment, chemical state of europium ions, and magnetic properties of solid solutions A_xEu_1−xZrO₃ (A = Ba, Ca, and Sr) were investigated using powder X-ray diffraction (XRD), high-resolution X-ray fluorescence spectrometry (HRXRF), and superconducting quantum interference device (SQUID) magnetometer. We found that the solid solutions based on EuZrO₃ are AFM even when Sr²⁺ or Ca²⁺ is incorporated and an enhanced AFM behavior is observed in Ca_0.3Eu_0.7ZrO₃ while the ferromagnetic ordering occurs in Ba_0.3Eu_0.7ZrO₃. Overall, this study demonstrates the correlation between magnetic structure at low temperatures and the lattice volume of the EuZrO₃ solid solutions. It is an important point that under the scenarios of three-dimensional chemical pressure, the present study provides direct evidence to control the competition between AFM and FM interactions among Eu²⁺ ions by changing the ZrO₆ octahedral rotation.

2. Results and discussion

2.1. Structural characterization

The structural characterization was performed at room temperature in the present study. It is known that EuZrO₃ takes the orthorhombic Pbnm structure with the lattice parameters at room temperature (a = 5.8192 Å, b = 8.1958 Å, and c = 5.7958 Å) and 1.4 K (a = 5.8163 Å, b = 8.1854 Å, and c = 5.7816 Å).⁴⁹ For BaZrO₃ with space group Pm3̄m and SrZrO₃ with space group Pbnm, the normalized molar volume approximately changes from 1.000 to 1.003 and 1.000 to 1.004, respectively, when the temperature is varied from 4.2 to 300 K.⁵⁰ In addition, CaZrO₃ with Pbnm structure has an average volume thermal expansion coefficient of 8.5192 × 10⁻⁶ K⁻¹ at temperatures from approximately 0 to 350 K. Thus, the crystal structures of the A_xEu_1−xZrO₃ series remains stable even if the temperature is varied from room temperature (300 K) to very low temperature.⁵¹

The powder X-ray diffraction (XRD) patterns of the A_xEu_1−xZrO₃ series recorded at ∼300 K are shown in Fig. 1. Each of the samples is almost entirely composed of a single phase with perovskite structure, although a trace amount of ZrO₂ is detectable as an impurity phase in most of the A_xEu_1−xZrO₃ series (Fig. S1, ESI†). Compared to pure EuZrO₃, the diffraction peaks systematically shift to lower angles upon the incorporation of the larger Ba²⁺. This result confirms an increase in the unit lattice volume of Ba_xEu_1−xZrO₃ solid solutions, as the ionic radius of Ba²⁺ in coordination number (CN) 8 (1.61 Å) is larger than that of Eu²⁺ (1.43 Å) in CN 8.⁴⁸ In contrast, oposite diffraction peak shifts are observed when the Eu²⁺ is substituted by Ca²⁺ in CN 8 (1.37 Å), indicating a smooth lattice contraction for all synthesized members of Ca_xEu_1−xZrO₃. Additionally, since the ionic radius of Sr²⁺ in CN 8 (1.44 Å) is almost the same as Eu²⁺, no apparent peak shift is observed for Sr_xEu_1−xZrO₃ as shown in Fig. 1.⁴⁸ All trends in XRD patterns indicate that the replacement of Eu²⁺ with group 2 elements is indeed an effective strategy for compositional tuning of lattice volume by utilizing the chemical pressure.

Fig. 1 The powder X-ray diffraction (XRD) patterns of A_xEu_1−xZrO₃ (0 ≤ x ≤ 1), where A is Ca, Sr, or Ba. The right panel shows enlarged patterns of the most intense peak for samples.

Part of the result of Rietveld analysis is illustrated in Fig. 2. All the patterns were well described by assuming that the sample was composed of a single-phase. Based on the refinement results, all the solid solutions are assigned to most probable space group. Fig. 2a confirms that EuZrO₃ is identified as an orthorhombic unit cell with space group Pbnm and the lattice constants, which are in good agreement with the values reported previously.^33,34 Moreover, the XRD patterns of Ca_xEu_1−xZrO₃ and Sr_xEu_1−xZrO₃ solid solutions are assigned to orthorhombic Pbnm structure, coincident with the fact that EuZrO₃, CaZrO₃ and SrZrO₃ have the same structure.^44–46 For Ba_xEu_1−xZrO₃ solid solutions, because BaZrO₃ takes a cubic structure with Pm3̄m space group at room temperature, the phase is changed from orthorhombic Pbnm to cubic Pm3̄m with an increase in Ba concentration.^44,47,52 The Pbnm and Pm3̄m structure are represented by a⁻a⁻c⁺ and a⁰a⁰a⁰ of Glazer notation, respectively.³² The sequence of phases in the Ba_xEu_1−xZrO₃ series at room temperature and the accompanying crystal symmetry can be deduced as follows (Table 1): 0 ≤ x ≤ 0.3, orthorhombic Pbnm (a⁻a⁻c⁺); 0.4 ≤ x ≤ 0.6, orthorhombic Ibmm (a⁻a⁻c⁰); x = 0.7, tetragonal I4/mcm (a⁰a⁰c⁻); and 0.80 ≤ x ≤ 1, cubic Pm3̄m (a⁰a⁰a⁰).²⁸ These deductions agree with the results given by Howard and Stokes for structural transition of ABO₃ perovskites. All of the fitted patterns are given in Fig. S1 (ESI†).^38,53

Fig. 2 X-ray diffraction profiles measured at room temperature (red crosses) and calculated profiles obtained by Rietveld analysis (black solid curves) for (a) EuZrO₃, and (b) Ba_0.3Eu_0.7ZrO₃. The vertical ticks (green) indicate the positions of the Bragg reflections, and the bottom solid lines (blue) correspond to the difference between the observed and the calculated intensity.

Table 1 Refined Structural Parameters for A_xEu_1−xZrO₃ with A = Ba, Ca, and Sr (0 ≤ x ≤ 0.9)

BaxEu1−xZrO3	a (Å)	b (Å)	c (Å)	V (Å^3)	Space group	R wp (%)	R B (%)	S
x = 0	5.79674(4)	5.81988(4)	8.19624(5)	276.511(3)	Pbnm	2.316	4.799	1.746
x = 0.1	5.82575(8)	5.81277(7)	8.20967(9)	278.010(5)	Pbnm	10.29	6.814	2.208
x = 0.2	5.83588(8)	5.84784(8)	8.23440(11)	281.017(6)	Pbnm	10.12	7.702	2.200
x = 0.3	5.84151(11)	5.87189(11)	8.24788(16)	282.908(9)	Pbnm	10.77	8.171	2.370
x = 0.4	5.86280(13)	5.85745(12)	8.27547(19)	284.188(10)	Ibmm	5.573	3.922	3.719
x = 0.5	5.88447(10)	5.87592(9)	8.28320(14)	286.405(8)	Ibmm	3.681	4.087	2.466
x = 0.6	5.90892(12)	5.89129(12)	8.31516(18)	289.460(10)	Ibmm	5.315	4.192	3.608
x = 0.7	5.90694(10)	5.90694(10)	8.32721(14)	290.552(8)	I4/mcm	7.046	5.115	4.647
x = 0.8	4.18186(3)			73.1322(9)	Pm3̄m	6.544	4.316	3.956
x = 0.9	4.18862(2)			73.4873(7)	Pm3̄m	6.110	5.148	3.695

---

CaxEu1−xZrO3	a (Å)	b (Å)	c (Å)	V (Å^3)	Space group	R wp (%)	R B (%)	S
x = 0.1	5.77804(6)	5.81272(6)	8.17967(9)	274.723(5)	Pbnm	2.529	4.348	2.154
x = 0.2	5.75758(6)	5.80380(6)	8.16325(9)	272.781(5)	Pbnm	2.437	8.470	2.927
x = 0.3	5.75090(5)	5.79130(5)	8.16550(8)	271.953(4)	Pbnm	2.452	4.521	2.505
x = 0.4	5.72996(14)	5.80064(15)	8.15116(20)	270.923(11)	Pbnm	3.554	7.375	2.638
x = 0.5	5.71224(20)	5.79369(20)	8.13813(28)	269.331(16)	Pbnm	11.84	8.138	2.638
x = 0.6	5.69244(15)	5.78965(16)	8.11824(21)	267.554(12)	Pbnm	4.261	6.172	4.664
x = 0.7	5.65930(7)	5.77553(7)	8.07929(10)	264.075(6)	Pbnm	3.626	3.741	3.414
x = 0.8	5.64155(6)	5.77700(7)	8.07081(9)	263.037(5)	Pbnm	3.580	3.658	3.982
x = 0.9	5.61377(9)	5.75465(10)	8.03228(13)	259.485(7)	Pbnm	5.085	2.238	4.467

---

SrxEu1−xZrO3	a (Å)	b (Å)	c (Å)	V (Å^3)	Space group	R wp (%)	R B (%)	S
x = 0.1	5.79485(2)	5.81957(2)	8.19647(3)	276.413(2)	Pbnm	2.817	5.870	0.246
x = 0.2	5.79604(2)	5.81993(2)	8.20028(4)	276.616(2)	Pbnm	2.748	3.294	0.216
x = 0.3	5.79672(19)	5.82203(20)	8.19981(28)	276.732(17)	Pbnm	8.621	7.278	2.205
x = 0.4	5.79668(2)	5.82164(2)	8.20036(4)	276.730(2)	Pbnm	2.131	3.408	2.252
x = 0.5	5.79763(4)	5.82151(4)	8.20247(6)	276.841(4)	Pbnm	10.32	6.961	2.278

---

Gradual changes in the lattice constants and volume induced by A-site isovalent substitution are found from the results of refinement (Table 1), and the correlation between the composition x and the lattice volume for the A_xEu_1−xZrO₃ series is clearly seen in Fig. 3. All the compositional dependences of lattice volume follow the Vegard's law.^54,55 The lattice volume linearly increases, linearly decreases, and remains constant with Ba, Ca, and Sr concentrations, respectively, confirming the formation of all-proportional solid solutions.

Fig. 3 Compositional dependence of the lattice volume of unit cell (V) at room temperature for the solid solutions A_xEu_1−xZrO₃. The difference in shape and color of the symbols correspond to the difference in the space groups and the alkaline earth metal elements, respectively. The background color represents the structure of the solid solutions; yellow for orthorhombic, pale green for tetragonal, and pale blue for cubic.

2.2 Magnetic properties

The temperature dependence of magnetic susceptibility χ (T) was obtained via field-cooling (FC) process under an applied magnetic field of 100 Oe for A_xEu_1−xZrO₃. The results are illustrated in Fig. 4. The χ(T) curve for the zero-field-cooling (ZFC) process coincides with that for the FC process within experimental errors. The magnetic phase transition temperatures (Néel temperature, T_N and Curie temperature, T_C) were acquired by taking the 1st derivation of χ(T) curves. The results are summarized in Table 2. Since the presence of a trace trivalent europium (6%) is confirmed by ¹⁵¹Eu Mössbauer spectroscopy and high-resolution X-ray fluorescence spectrometry (Fig. S2 and S3, ESI†), both Curie paramagnetism of Eu²⁺ and Van Vleck paramagnetism of Eu³⁺ are taken into consideration for analyzing the magnetic susceptibility of A_xEu_1−xZrO₃ solid solutions in the high-temperature region. In the present case, the following equations were used:

χ = nχ_Eu²⁺ + (1 − n)χ_Eu³⁺ + χ₀ (1)

Fig. 4 Temperature dependence of magnetic susceptibility χ (T) for (a) Ba_xEu_1−xZrO₃, (b) Ca_xEu_1−xZrO₃, and (c) Sr_xEu_1−xZrO₃ solid solutions.

Table 2 Néel Temperature (T_N), Curie temperature, (T_C), Weiss Temperature (θ_W), and saturation magnetization (M_S) of A_xEu_1−xZrO₃

BaxEu1−xZrO3	Transition temperature (K)	θ W (K)	M S (μB)
x = 0.0	T N = 4.1	−0.19(2)	7.80(1)
x = 0.1	T N = 3.5	0.11(1)	7.28(5)
x = 0.2		0.12 (1)	7.45(1)
x = 0.3	T C = 3.1	0.67(1)	7.19(3)
x = 0.4		0.16(1)	7.33(3)
x = 0.5		0.15(2)	7.39(1)

---

CaxEu1−xZrO3	Transition temperature (K)	θ W (K)	M S (μB)
x = 0.0	T N = 4.1	−0.19(2)	7.80(1)
x = 0.1	T N = 4.0	−0.22(1)	7.13(2)
x = 0.2	T N = 3.1	−0.45(2)	7.07(2)
x = 0.3	T N = 3.0	−0.86(1)	7.18(6)
x = 0.4	T N = 2.9	−0.27(1)	7.31(4)
x = 0.5		−0.09(1)	7.58(2)

---

SrxEu1−xZrO3	Transition temperature (K)	θ W (K)	M S (μB)
x = 0.0	T N = 4.1	−0.19(2)	7.80(1)
x = 0.1	T N = 3.8	−0.12(1)	7.31(10)
x = 0.2	T N = 3.3	−0.07(1)	6.90(4)
x = 0.3	T N = 2.8	−0.14(3)	6.98(1)
x = 0.4	T N = 2.2	−0.09(1)	7.81(2)
x = 0.5		−0.075(7)	7.61(2)

---

In eqn (1), n is the molar ratio of Eu²⁺ to the total europium ions the value of which is 0.94 (Fig. S2 and S3, ESI†), χ₀ is the temperature-independent term. χ_Eu²⁺ is the magnetic susceptibility of Eu²⁺ according to the Curie–Weiss law [eqn (2)], where N is the number of magnetic moment, k_B is the Boltzmann constant, μ_B is the Bohr magneton, and M_B is the effective number of Bohr magnetons with the theoretical value of 7.94. χ_Eu³⁺ is the magnetic susceptibility of trivalent Eu ions based on the Van Vleck paramagnetism [eqn (3)], where a (a = λ/k_BT) is the ratio of the multiplet width with the value of 370 cm⁻¹ for the spin–orbit coupling constant λ.^56,57 The experimental data are fitted well with the theoretical curves (Fig. S4, ESI†). The Weiss temperature (θ_W) obtained by the fitting was also listed in Table 2.

The present EuZrO₃ sample manifests a clear AFM transition (T_N = 4.1 K) in line with the previous study.^11,34 The A_xEu_1−xZrO₃ (A = Ca, Sr) solid solutions also exhibit AFM behavior for x = 0.1–0.4 while PM behavior is observed for x = 0.5 due to the dilution of magnetic moment assigned to Eu²⁺ ion. Besides, Ba_xEu_1−xZrO₃ solid solutions with x = 0.1 and 0.2 show AFM-like behavior. When x reaches 0.3, the compound exhibits FM behavior; the magnetization drastically increases below T_C with a decrease of temperature.⁵⁸ For x = 0.4 and 0.5, since significant magnetic dilution reduces the spin–spin interactions, magnetic ordering is not observed and the compounds show PM behavior.

The Weiss temperature, θ_W, reflects the magnitude and the sign of the magnetic interaction among Eu²⁺ ions. For Ba_xEu_1−xZrO₃, as the fraction of Ba is increased, θ_W initially increases from −0.19 (x = 0) to 0.67 (x = 0.3), and subsequently decreases to 0.15 (x = 0.5). The change of sign of θ_W from negative to positive when x increases from 0 to 0.3 suggests that the dominant interaction is switched from AFM to FM when the fraction of Ba is increased up to x = 0.3. The switch of magnetic interaction reflects the fact that the AFM and FM interactions compete with each other in EuZrO₃. The value of θ_W is decreased dramatically above x = 0.4 and the compounds are PM even at low temperatures as indicated by Fig. 4(a). For Sr_xEu_1−xZrO₃, due to the weakening of AFM interaction caused by the magnetic dilution with an increase in the fraction of Sr, θ_W is gradually increased to approach 0 from a negative value with the increase of x. For Ca_xEu_1−xZrO₃, θ_W is negative independent of the composition, suggesting that the AFM interaction is dominant in all the solid solutions of this system. There seems a tendency that θ_W deceases, takes a minimum at x = 0.3, and then increases as the fraction of Ca is increased. Overall, the lattice expansion induced by the substitution of Ba²⁺ for Eu²⁺ inhibits the AFM interaction, leading to a situation that FM state is dominant. In contrast, enhancement of AFM interaction is realized through the lattice compression in Ca_xEu_1−xZrO₃. For Sr_xEu_1−xZrO₃, the value of θ_W is negative and increases to approach zero with an increase in the fraction of Sr. This phenomenon simply indicates that the magnetic structure is changed from AFM to PM by the dilution of magnetic moments belonging to Eu²⁺ because the lattic volume is almost independent of the composition of Sr_xEu_1−xZrO₃ due to the fact that the ionic radius of Sr²⁺ and Eu²⁺ is almost the same as each other.

The magnetic field (μ₀H) dependence of magnetization (M) at 2 K for A_xEu_1−xZrO₃ is illustrated in Fig. 5. The data at low μ₀H are magnified in the insets. For Sr_xEu_1−xZrO₃ at low μ₀H, the continuous increase of slope of the M–H curves indicates the gradual weakening of AFM interaction due to the dilution of Eu²⁺ ions. On the other hand, a decrease in the slope at low μ₀H indicates an enhanced AFM interaction for Ca_0.3Eu_0.7ZrO₃. For Ba_0.3Eu_0.7ZrO₃, an abrupt increase in the slope at around 1000 Oe is found and the hysteresis loop is observed unlike A_0.3Eu_0.7ZrO₃ (A = Sr and Ca) in Fig. S5 (ESI†), corresponding to the FM states of Ba_0.3Eu_0.7ZrO₃ for Eu²⁺ spins. This FM state can also be confirmed by the steep increase of magnetic susceptibility with decreasing temperature below T_C when a magnetic field of 100 Oe is applied. Furthermore, Fig. 5 demonstrates that the saturation magnetization (M_S) for the A_xEu_1−xZrO₃ series ranges from 7.19 μ_B to 7.80 μ_B (also summarized in Table 2). These values are almost identical to the theoretical magnetic moment of Eu²⁺ (7 μ_B), suggesting that almost all the europium ions are present as a divalent state in the A_xEu_1−xZrO₃ solid solutions. This fact indicates that the reduction process of Eu³⁺ into Eu²⁺ by using ZrN is effective.

Fig. 5 Dependence of magnetization on magnetic field at 2 K for (a) Ba_xEu_1−xZrO₃, (b) Ca_xEu_1−xZrO₃, and (c) Sr_xEu_1−xZrO₃.

Since the linear relationship between the lattice volume and composition x is found, the compositional change can directly reflect the variation of lattice volume and accompanying crystal structural change of EuZrO₃. Therefore, the compositional dependence of magnetic properties and crystal structure can lead to the relationship between the lattice volume and magnetic order. Here it should be noted that we can reasonably discuss magnetic properties at very low temperatures in terms of the crystal structure at room temperature because the crystal structure remains stable for EuZrO₃, BaZrO₃, SrZrO₃, and CaZrO₃ even when the temperature is varied from room temperature to very low temperature as described in section 2.1. According to the simple mean field theory, the Weiss temperature depends on the number of magnetic moment as well as the magnitude of magnetic interaction. Thus, it is thought that the parameter, θ_W/(1−x), reflects the magnitude of magnetic interaction between Eu²⁺ ions in the first approximation. In Fig. 6, we present the lattice volume dependence of θ_W/(1−x). It is found that θ_W/(1−x) is apt to increase with an increase in the lattice volume. It is worth noting that the tuning of magnetic interaction and the resultant magnetic transition are considered to be induced by the lattice expansion and shrinkage rather than the changes in crystal symmetry since the crystal structure retains orthorhombic Pbnm in the range of lattice volume shown in Fig. 6. The results elucidate the relationship between the lattic volume and magnetic order which has been predicted by the theoretical calculations for EuZrO₃.²⁸

Fig. 6 The value of θ_W/(1−x), in which θ_W is Weiss temperature and x is the concentration ratio of alkaline earth metal elements, is plotted against the lattice volume. The dashed line represents the fitted linear regression line.

2.3 Microscopic origin of magnetic behavior

To get a better understanding of the effect of the variation of lattice volume on the magnetic behavior, the origin and magnitude of the effect are discussed from a microscopic point of view. The cooperative rotation of ZrO₆ octahedra needs to be taken into account since it has been microscopically verified on the basis of first principles calculations that the octahedral rotation, related to the change of lattice volume of the orthorhombic structure, facilitates the AFM superexchange interactions between Eu²⁺ ions via vacant 4d state of Zr⁴⁺ in the orthorhombic EuZrO₃.²⁸ For the series of Ba-substituted solid solutions, an increase in the lattice volume is accompanied by the continuous conversion of the crystal structure from Pbnm (a⁻a⁻c⁺) to Ibmm (a⁻a⁻c⁰), I4/mcm (a⁰a⁰c⁻), and then Pm3̄m (a⁰a⁰a⁰) at room temperature. For the series of Ca- and Sr-substituted solid solutions, the crystal structure retain Pbnm (a⁻a⁻c⁺) even when the fraction of Ca and Sr is altered. Fig. 7 illustrates the octahedral rotations with two types of angles θ^a− and θ^c+ and the relationship between these rotation angles and the lattice volume. Here the lattice volume and the corresponding θ^a− and θ^c+ were extracted from the data for EuZrO₃, Ba_xEu_1−xZrO₃ and Ca_xEu_1−xZrO₃ solid solutions with the structure of Pbnm (a⁻a⁻c⁺). It is found that both θ^a− and θ^c+ are increased with the decrease of lattce volume. As the relationship between the magnetism and the lattice volume is verified in Fig. 6, the result shown in Fig. 7 indicates that the AFM interaction is weakened by descending the octahedral rotations, leading to the situation that the FM interaction is more dominant. Consequently, the present experimental result supports the theoretical suggestions that the octahedral rotation has great influence on the overlap between the Eu²⁺ 4f orbital and the Zr⁴⁺ 4d orbital and hence, changes the magnitude of AFM interaction between Eu²⁺ ions via 4d state of Zr⁴⁺ in EuZrO₃.

Fig. 7 Schematics of ZrO₆ octahedral rotations (tilt angles) along the (a) a-axis and (b) c-axis in an orthorhombic Pbnm structure (a⁻a⁻c⁺). The europium atoms are shown as green spheres, the zirconium atoms as purple spheres and the oxygen atoms as red spheres. The rotation angles θ^a− and θ^c+ are defined in (a) and (b), respectively. (c) The relation between the lattice volume and the octahedral rotation angles θ^a− and θ^c+ for orthorhombic Ca_xEu_1−xZrO₃ (0 ≦ x ≦ 0.3), EuZrO₃, Ba_xEu_1−xZrO₃ (0 ≦ x ≦ 0.3), respectively.

3. Conclusions

We experimentally provide an insight into the relative strengths of the competing magnetic interactions between Eu²⁺ ions in EuZrO₃, which is dependent on the lattice volume and crystal structure, as suggested by the first principles calculations. The variation of lattice volume was realized by synthesizing EuZrO₃-based solid solutions; Eu²⁺ was replaced by alkaline-earth metal ions with different radii, that is Ba, Sr, and Ca. The experimental results indicate that the magnetic ground state of EuZrO₃ can be switched from AFM to FM by increasing the lattice volume. This is consistent with the first-principles calculations reported previously. Furthermore, the results also demonstrate that there is a strong coupling between the magnetic structure and the rotation of ZrO₆ octahedra. Specifically, the AFM superexchange interaction between Eu²⁺ ions via Zr 4d state is enhanced by the rotations of the ZrO₆ octahedra. The expansion of lattice volume and concomitant reduction of ZrO₆ octahedral rotation lead to the situation that the FM indirect exchange interaction via Eu²⁺ 5d state overcomes the AFM interaction via Zr⁴⁺ 4d state.

4. Experimental details

4.1. Sample preparation

Polycrystalline A_xEu_1−xZrO₃ (A = Ba, Ca; x ≤ 0.9 and Sr; x ≤ 0.5) were synthesized by the conventional solid-state reaction method. The stoichiometric mixture of reagent-grade Eu₂O₃, ZrO₂, ACO₃, and ZrN (both 99.9% pure, sourced from Kanto Chemicals, Japan) with the molar ratio of 2–2x, 3 + x, 4x and 1−x was pressed into a pellet. The ZrN was added as a reducing agent to convert Eu³⁺ into Eu²⁺. The pellet was sintered in a carbon crucible at 1300 °C for 10 h under a reducing atmosphere of Ar (97 vol%)/H₂ (3 vol%). The resultant EuZrO₃ pellet was greenish-yellow, while the solid solutions of Ba_xEu_1−xZrO₃, Ca_xEu_1−xZrO₃, and Sr_xEu_1−xZrO₃ were light greenish, light yellow, and light greenish-yellow, respectively.

4.2. Measurements of structural and magnetic properties

The crystal structure and purity of the sintered materials were characterized by XRD at room temperature using Cu Kα radiation (RINT2500, Rigaku). Structural parameters were determined by Rietveld refinement of the X-ray diffraction data using RIETAN-FP.^59–61 In order to estimate the structural distortions related to the ZrO₆ octahedral rotations, the two rotation angles θ^a− and θ^c+ shown in Fig. 7 were determined by performing VESTA based on the Rietveld refinement results.^27,62 The chemical valence states of europium ions in A_xEu_1−xZrO₃ were examined using HRXRF spectroscopy, Eu₂O₃ was used as a reference for trivalent Eu ions. Peak position corrections were performed using Mn Kα₁₂ standard spectra for each sample measurement. A Savitzky-Golay smoothing method was used (smoothing points = 7) to pretreat data before analysis.⁶³ The valence state of europium ions of EuZrO₃ was evaluated using the ¹⁵¹Eu Mössbauer spectrum in a standard transmission geometry at room temperature, which employed γ-ray source of ¹⁵¹Sm₂O₃. The velocity calibration was done with the magnetic hyperfine spectrum of α-Fe foil using ⁵⁷Co γ-ray source. In addition, the Mössbauer spectrum of EuF₃ was utilized as a Doppler velocity standard.⁶⁴ To understand the influence of structural change on the magnetic properties of solid-state solutions A_xEu_1−xZrO₃, temperature and magnetic field dependence of magnetization was measured using the superconducting quantum interference device magnetometer (MPMS, Quantum Design). The temperature dependence of magnetic susceptibilities was measured in a range of 2–300 K under both ZFC and FC processes at an external magnetic field of 100 Oe. The field dependence of magnetization was recorded at 2 K under magnetic fields up to 5 T.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by JSPS KAKENHI, Grant-in-Aid for Challenging Research (Exploratory), Grant Number 21K19025. The authors are grateful to Michiru Yamashita and Hirokazu Izumi at Hyogo Prefectural Institute of Technology for their help with HRXRF measurement.

Notes and references

1. H. Schmid, Ferroelectrics, 1994, 162, 317–338.
2. R. Ramesh and N. A. Spaldin, Nat. Mater., 2007, 6, 21–29.
3. N. A. Spaldin and R. Ramesh, Nat. Mater., 2019, 18, 203–212.
4. J. Wang, J. Neaton, H. Zheng, V. Nagarajan, S. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. Schlom and U. Waghmare, Science, 2003, 299, 1719–1722.
5. T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T.-H. Arima and Y. Tokura, Nature, 2003, 426, 55–58.
6. H. Akamatsu, K. Fujita, H. Hayashi, T. Kawamoto, Y. Kumagai, Y. Zong, K. Iwata, F. Oba, I. Tanaka and K. Tanaka, Inorg. Chem., 2012, 51, 4560–4567.
7. T. Katsufuji and H. Takagi, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 64, 054415.
8. A. Bussmann-Holder, E. Liarokapis and K. Roleder, Sci. Rep., 2021, 11, 1–8.
9. H. Wu and W. Shen, Solid State Commun., 2005, 133, 487–491.
10. P. Ryan, J. Kim, T. Birol, P. Thompson, J. Lee, X. Ke, P. Normile, E. Karapetrova, P. Schiffer and S. Brown, Nat. Commun., 2013, 4, 1–8.
11. T. Kolodiazhnyi, K. Fujita, L. Wang, Y. Zong, K. Tanaka, Y. Sakka and E. Takayama-Muromachi, Appl. Phys. Lett., 2010, 96, 252901.
12. H. Akamatsu, Y. Kumagai, F. Oba, K. Fujita, H. Murakami, K. Tanaka and I. Tanaka, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 214421.
13. M. Itoh, T. Shimura, J.-D. Yu, T. Hayashi and Y. Inaguma, Phys. Rev. B: Condens. Matter Mater. Phys., 1995, 52, 12522.
14. T. Ishihara, H. Matsuda and Y. Takita, J. Am. Chem. Soc., 1994, 116, 3801–3803.
15. P. Radaelli, G. Iannone, M. Marezio, H. Hwang, S. Cheong, J. Jorgensen and D. Argyriou, Phys. Rev. B: Condens. Matter Mater. Phys., 1997, 56, 8265.
16. M. Uehara, S. Mori, C. Chen and S.-W. Cheong, Nature, 1999, 399, 560–563.
17. J. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. Li, S. Choudhury, W. Tian, M. Hawley and B. Craigo, Nature, 2004, 430, 758–761.
18. K. J. Choi, M. Biegalski, Y. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche, Y. Chen, X. Pan and V. Gopalan, Science, 2004, 306, 1005–1009.
19. M.-W. Chu, I. Szafraniak, R. Scholz, C. Harnagea, D. Hesse, M. Alexe and U. Gösele, Nat. Mater., 2004, 3, 87–90.
20. D. G. Schlom, L.-Q. Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer and J.-M. Triscone, Annu. Rev. Mater. Res., 2007, 37, 589–626.
21. D. G. Schlom, L.-Q. Chen, C. J. Fennie, V. Gopalan, D. A. Muller, X. Pan, R. Ramesh and R. Uecker, MRS Bull., 2014, 39, 118–130.
22. Y. Yokoyama, Y. Yamasaki, M. Taguchi, Y. Hirata, K. Takubo, J. Miyawaki, Y. Harada, D. Asakura, J. Fujioka and M. Nakamura, Phys. Rev. Lett., 2018, 120, 206402.
23. C. J. Fennie and K. M. Rabe, Phys. Rev. Lett., 2006, 97, 267602.
24. J. H. Lee, L. Fang, E. Vlahos, X. Ke, Y. W. Jung, L. F. Kourkoutis, J.-W. Kim, P. J. Ryan, T. Heeg and M. Roeckerath, Nature, 2010, 466, 954–958.
25. K. Kugimiya, K. Fujita, K. Tanaka and K. Hirao, J. Magn. Magn. Mater., 2007, 310, 2268–2270.
26. K. Fujita, N. Wakasugi, S. Murai, Y. Zong and K. Tanaka, Appl. Phys. Lett., 2009, 94, 062512.
27. Y. Lin, E.-M. Choi, P. Lu, X. Sun, R. Wu, C. Yun, B. Zhu, H. Wang, W. Li and T. Maity, ACS Appl. Mater. Interfaces, 2020, 12, 8513–8521.
28. H. Akamatsu, Y. Kumagai, F. Oba, K. Fujita, K. Tanaka and I. Tanaka, Adv. Funct. Mater., 2013, 23, 1864–1872.
29. K. Tanaka, K. Fujita, Y. Maruyama, Y. Kususe, H. Murakami, H. Akamatsu, Y. Zong and S. Murai, J. Mater. Res., 2013, 28, 1031–1041.
30. R. Zhao, C. Yang, H. Wang, K. Jiang, H. Wu, S. Shen, L. Wang, Y. Sun, K. Jin and J. Gao, Nat. Commun., 2022, 13, 2364.
31. M. Shafer, J. Appl. Phys., 1965, 36, 1145–1152.
32. A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem., 1972, 28, 3384–3392.
33. V. Viallet, J.-F. Marucco, J. Saint, M. Herbst-Ghysel and N. Dragoe, J. Alloys Compd., 2008, 461, 346–350.
34. Y. Zong, K. Fujita, H. Akamatsu, S. Murai and K. Tanaka, J. Solid State Chem., 2010, 183, 168–172.
35. B. Alho, E. Nóbrega, V. de Sousa, A. M. G. Carvalho, N. De Oliveira and P. Von Ranke, J. Appl. Phys., 2011, 109, 083942.
36. J. Coey, M. Viret and S. Von Molnar, Adv. Phys., 1999, 48, 167–293.
37. G. Cuono, F. Forte, A. Romano, X. Ming, J. Luo, C. Autieri and C. Noce, Phys. Rev. Mater., 2021, 5, 064402.
38. B. Kennedy, C. Howard, G. Thorogood and J. Hester, J. Solid State Chem., 2001, 161, 106–112.
39. L. Li, B. J. Kennedy, Y. Kubota, K. Kato and R. F. Garrett, J. Mater. Chem., 2004, 14, 263–273.
40. C. J. Howard, G. R. Lumpkin, R. I. Smith and Z. Zhang, J. Solid State Chem., 2004, 177, 2726–2732.
41. N. L. Henderson, X. Ke, P. Schiffer and R. E. Schaak, J. Solid State Chem., 2010, 183, 631–635.
42. Y. Ren, R. Küngas, R. J. Gorte and C. Deng, Solid State Ion., 2012, 212, 47–54.
43. M. Y. Liu, T. L. Sun, X. L. Zhu, X. Q. Liu, H. Tian and X. M. Chen, J. Am. Ceram. Soc., 2021, 104, 6393–6403.
44. H. D. Megaw, Proc. Phys. Soc., 1946, 58, 133.
45. H. Koopmans, G. Van De Velde and P. Gellings, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1983, 39, 1323–1325.
46. B. J. Kennedy, C. J. Howard and B. C. Chakoumakos, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 4023.
47. A.-M. Azad, S. Subramaniam and T. W. Dung, J. Alloys Compd., 2002, 334, 118–130.
48. R. D. Shannon, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 1976, 32, 751–767.
49. M. Avdeev, B. J. Kennedy and T. Kolodiazhnyi, J. Condens. Matter Phys., 2014, 26, 095401.
50. K. Knight, J. Mater. Sci., 2020, 55, 6417–6428.
51. A. Shukla, V. Parey and N. Gaur, AIP Conf. Proc., 2016, 020011.
52. E. Slonimskaya and A. Belyakov, Glass Ceram., 2001, 58, 54–56.
53. C. J. Howard and H. T. Stokes, Acta Crystallogr., Sect. B: Struct. Sci., 1998, 54, 782–789.
54. L. Vegard, Z. Phys., 1921, 5, 17–26.
55. A. R. Denton and N. W. Ashcroft, Phys. Rev. A: At., Mol., Opt. Phys., 1991, 43, 3161.
56. J. Van Vleck, The Theory of Electric and Magnetic Susceptibilities, Clarendon, Oxford, 1932.
57. L. Holmes, R. Sherwood, L. Van Uitert and S. Hüfner, Phys. Rev., 1969, 178, 576.
58. Y. Zong, K. Fujita, H. Akamatsu, S. Murai and K. Tanaka, Phys. Status Solidi C, 2011, 8, 3051–3054.
59. H. Rietveld, Acta Crystallogr., 1967, 22, 151–152.
60. D. L. Bish and S. Howard, J. Appl. Crystallogr., 1988, 21, 86–91.
61. F. Izumi and K. Momma, Solid State Phenom., 2007, 15–20.
62. K. Momma and F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276.
63. T. Konishi, J. Kawai, M. Fujiwara, T. Kurisaki, H. Wakita and Y. Gohshi, X-Ray Spectrom., 1999, 28, 470–477.
64. G. Shenoy and B. Dunlap, Nucl. Instrum. Methods, 1969, 71, 285–291.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3tc00888f

---