Introduction

Heterostructures of transition metal perovskites (ABO3) provide a fertile ground to study emergent phenomena of correlated electrons and a promising route to new functional devices using quantum effects. Since the collective behavior of electrons at an oxide interface can differ strongly from that in the component materials, superlattices show a plethora of properties such as metal-to-insulator transition1, high Néel temperature2,3, formation of a two-dimensional electron gas4, superconductivity5, orientation-dependent magnetism6,7, and charge-ordered ferroelectricity8. The presence of layers of A-site cations with different valence can induce charge and/or orbital ordering at the B-sites, which can lead to a ground state differing fundamentally from those of the component materials8. In addition, layer-by-layer deposition9,10 offers the possibility to induce ferroelectric polarization in heterostructures of inversion-symmetric compounds11.

SrCrO3 is a metallic d2 perovskite with the nonpolar tetragonal space group P4/mmm and C-type antiferromagnetic (C-AFM) ordering below the Néel temperature of 100 K12. It undergoes a metal-to-insulator transition under high pressure due to bond instability13 and exhibits \({d}_{xy}^{1}{d}_{xz}^{0.5}{d}_{yz}^{0.5}\) orbital ordering14,15. In a superlattice with SrTiO3, it undergoes a metal-to-insulator transition under tensile strain due to a nonpolar-to-polar structural transition, inducing a ferroelectric polarization of 41 μC/cm2 at +3% strain, for example, while adopting G-AFM ordering (zero magnetization)12. YCrO3 is a semiconducting d3 perovskite with the nonpolar orthorhombic space group Pbnm, G-AFM ordering below the Néel temperature of 141.5 K16, and ferroelectric polarization of 2 μC/cm2 due to off-centering of the Cr cations below 473 K17. While these results are based on polycrystalline samples, recently, high-quality single crystals have been synthesized at high temperatures, and crystal structure and magnetization measurements have been performed18,19. Single crystalline YCrO3 shows a Néel temperature of 140 K and weak ferromagnetism at higher temperatures due to spin canting, combined with in-plane antiphase tilting and out-of-plane in-phase tilting of the O octahedra (a−a−c+ tilting pattern in Glazer’s notation)18. It is particularly interesting to explore the electronic and magnetic properties of the SrCrO3/YCrO3 superlattice, as both component materials lack magnetization and ferroelectric polarization while their electronic and magnetic properties can be controlled by strain engineering20,21,22,23. The average nominal valence of Cr is 3.5+ due to the Sr2+ and Y3+ states of the A-site cations. However, because of the strong Coulomb interaction, one may speculate that half of the Cr cations will realize a nominal valence of 3+ and the other half a nominal valence of 4+. As a result, a Mott-insulating state with charge, orbital, and/or magnetic ordering may be achieved.

Motivated by the new functionalities offered by superlattices and straintronics, we study the dependence of the multiferroic properties of the SrCrO3/YCrO3 superlattice under epitaxial strain. The superlattice turns out to be semiconducting despite the metallic nature of SrCrO3. We show that magnetic states can be realized with large ferroelectric polarization despite the fact that the individual compounds show no ferroelectricity. The combination of large magnetization with large ferroelectric polarization gives rise to robust multiferroism, enabling multistate memory applications. Monte Carlo simulations are used to predict the critical temperatures of the magnetic phases.

Results

First-principles calculations

We find that the SrCrO3/YCrO3 superlattice (Fig. 1a) adopts the monoclinic space group P21 due to a combination of the layered A-site cation ordering with an a−a−c+ tilting pattern (like YCrO3). The P21 symmetry is also obtained when we start the structure optimization from other possible GdCrO3-type symmetries (space groups Pna21 and Pca21). We obtain A-AFM ordering without strain and a transition to FM ordering at +1% strain (Fig. 1b) with a large magnetization of 5 μB per formula unit. The occupation matrix and projected densities of states show that the superlattice adopts a checkerboard charge ordering with Cr3+ (d3) and Cr4+ (d2) states (Fig. 1c) throughout the considered range of strain. In other words, the nearest B-site neighbors of the Cr3+ ions are Cr4+ ions, and vice versa. This d3-d2 charge ordering creates a breathing distortion of the O octahedra with expansion around the Cr3+ ions and contraction around the Cr4+ ions, which is confirmed by the appearance of long and short bonds, respectively.

Fig. 1: Magnetic ordering.
figure 1

a Structure and exchange paths connecting the Cr3+ and Cr4+ ions, b strain dependence of the total energy, and c considered magnetic orderings.

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To understand the orbital occupations in detail, we investigate the projected densities of states, finding that in the spin-majority channel, the valence/conduction band edge is predominantly due to hybridized Cr3+/Cr4+ 3d and O 2p orbitals (Fig. 2a), representing covalent Cr-O bonds. The presence of Y3+ ions distorts the O octahedra around the Cr4+ ions as compared to SrCrO3, with four Cr-O bonds becoming shorter (1.89, 1.92, 1.96, and 1.98 Å instead of 2.05 Å). The bond lengths of the neighboring Cr3+ ions change slightly to accommodate these distortions but stay similar to those of YCrO3. As a result of the modified bonding environment of the Cr4+ ions, the degenerate dxz and dyz states of SrCrO3 (occupied by one electron) split such that the dxz orbital carries one electron and the dyz orbital remains empty, opening a small bandgap in the spin-majority channel (Fig. 2b). The electronic band structure indicates that the FM phase is an indirect narrow bandgap semiconductor (Fig. 2c).

Fig. 2: FM phase.
figure 2

a, b Projected densities of states and c electronic band structure (black/red lines represent the spin-majority/spin-minority channel) of the FM phase at +5% strain. d Electronic band structure when the spin-orbit coupling is taken into account. Analogous results at +1% strain are shown in Supplementary Fig. 1.

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While the superlattice realizes A-AFM ordering without strain and under compression, it realizes FM ordering under tension. To understand this observation, we measure the octahedral Cr3+-O-Cr4+ angles (Fig. 3a). The in-plane angles of 146° to 153° result in FM in-plane exchange (Cr3+-Cr4+; Goodenough-Kanamori rules24,25). Under tension, the out-of-plane angles do not exceed the in-plane angles, and FM ordering is favored. Under compression, however, the out-of-plane angles exceed the in-plane angles, and the out-of-plane exchange becomes AFM, resulting in A-AFM ordering. We notice that the magnetocrystalline anisotropy switches from in-plane to out-of-plane between +1% and +2% strain (Fig. 3b).

Fig. 3: Strain effects.
figure 3

Strain dependence of the a in-plane and out-of-plane Cr3+-O-Cr4+ angles, b magnetocrystalline anisotropy energy, and c magnetic coupling constants.

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Next, we extract the magnetic coupling constants using a Heisenberg spin Hamiltonian. We consider the in-plane nearest-neighbor coupling J1, out-of-plane nearest-neighbor coupling J2, and next-nearest-neighbor couplings J3 and J4 (Fig. 1a), assuming that the spin vectors are collinear with length one, as their magnitude later will be taken into account in the Monte Carlo simulations. The magnetic coupling constants are obtained by solving the coupled equations E1 = E0 + 8J1 − 4J2 − 8J3 − 8J4 (A-AFM), E2 = E0 − 8J1 + 4J2 − 8J3 − 8J4 (C-AFM), E3 = E0 − 8J1 − 4J2 + 8J3 + 8J4 (G-FiM), E4 = E0 + 8J1 + 4J2 + 8J3 + 8J4 (FM), E5 = E0 + 8J3 − 8J4 (G-FiM with one Cr3+ spin flipped), and E6 = E0 − 8J3 + 8J4 (G-FiM with one Cr4+ spin flipped), where E0 is the lattice energy and E1 to E6 are the total energies of the magnetic orderings obtained from density functional theory. We find that J1 is always positive (FM) while J2 is negative (AFM) without strain and under compression but positive under tension. J3 (Cr3+ to Cr3+) is always slightly negative. J4 (Cr4+ to Cr4+) is slightly positive under compression, indicating a weak spin frustration, and slowly increases under tension to overtake J1 between +3% and +4% strain (Fig. 3c), which is attributed to the decreasing out-of-plane Cr3+-O-Cr4+ angles (Fig. 3a). The simultaneous increase of J2 and J4 is the prime reason for the A-AFM to FM transition. To compute the critical temperatures of the magnetic phases, we execute Monte Carlo simulations with Gaussian moves26 for our Heisenberg model in a 12 × 12 × 12 supercell, using 100,000 sweeps for thermalization and 80,000 additional sweeps for data collection. The Néel temperature of the A-AFM phase is found to be 90 K without strain and 50 K at −5% strain, for example, and the Curie temperature of the FM phase is found to be 115 K at +5% strain (Fig. 4).

Fig. 4: Temperature effects.
figure 4

Temperature dependence of the a magnetic susceptibility at −5% (A-AFM phase), 0% (A-AFM phase), and +5% (FM phase) strain, with the peak marking the critical temperature, b magnetization at +5% strain when both the nearest-neighbor and next-nearest-neighbor couplings are considered, and c specific heat at −5%, 0%, and +5% strain.

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We next turn to the projected densities of states and electronic band structure of the A-AFM phase at −5% strain (Fig. 5). In agreement with the zero magnetization, the densities of states of the two spin channels are identical. The orbital hybridizations at the valence and conduction band edges are the same as in the case of the FM phase, and we obtain an indirect narrow bandgap semiconductor again. While spin-orbit coupling was not included in previous studies of SrCrO3 and YCrO3 due to a minor impact on the electronic and magnetic properties12,27, we find that in the case of the SrCrO3/YCrO3 superlattice, the bandgap increases significantly from 0.2 to 0.7 eV in the FM phase at +5% strain (Fig. 2d) and from 0.3 to 0.6 eV in the A-AFM phase at −5% strain (Fig. 5c), for example.

Fig. 5: A-AFM phase.
figure 5

a Projected densities of states and b electronic band structure of the A-AFM phase at −5% strain (spin channels degenerate). c Electronic band structure when the spin-orbit coupling is taken into account.

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Since both the FM and A-AFM phases are semiconductors, we next calculate the ferroelectric polarization. Finite in-plane ferroelectric polarization results from unequal in-plane antipolar displacements of the Sr2+ and Y3+ cations due to their different ionic radii and oxidation states (Fig. 6a). We find differences of 0.032b, 0.028b, and 0.026b (0.16, 0.15, and 0.15 Å) at −5%, 0%, and +5% strain, respectively, which are much larger than those of the FM superlattices reported in ref. 11 due to the larger distortions of the O octahedra of the SrCrO3/YCrO3 superlattice. The obtained ferroelectric polarizations of 13.5, 12.1, and 11.0 μC/cm2 along the b-axis (in-plane) at −5%, 0%, and +5% strain, respectively, correspondingly are much larger than those reported in ref. 11. The antipolar displacements of the nearest-neighbor Sr2+ ions and of the nearest-neighbor Y3+ ions are equal along the a-axis, i.e., they do not result in ferroelectric polarization. The energy barrier to switch the ferroelectric polarization is found to be 0.27 eV at 0% strain (Fig. 6b).

Fig. 6: Ferroelectric polarization.
figure 6

a In-plane antipolar displacements and b energy barrier to switch the ferroelectric polarization at 0% strain.

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Discussion

In summary, we predict by first-principles calculations large hybrid-improper ferroelectric polarization for the superlattice composed of the perovskites SrCrO3 and YCrO3. A Cr3+-Cr4+ checkerboard charge ordering is found without strain as well as under strain. We demonstrate that the formation of a superlattice is able to induce multiferroism even in perovskite oxides lacking both magnetism and ferroelectricity individually. The SrCrO3/YCrO3 superlattice adopts an A-AFM ordering without strain and under compression, while it becomes FM with a magnetization of 5 μB per formula unit at +1% strain. We find that the checkerboard charge ordering results in a band insulator with a narrow indirect bandgap. While FM metals are common, the combination of FM ordering with p-type semiconductivity is a rare phenomenon and interesting for spintronics applications. Monte Carlo simulations demonstrate magnetic critical temperatures of 50 K for the A-AFM phase at −5% strain and 115 K for the FM phase at +5% strain, for example. The hybrid-improper ferroelectric polarization is due to a large difference between the antipolar displacements of the Sr2+ and Y3+ cations (which can be controlled by strain) and its magnitude approaches that of conventional ferroelectric oxides such as BaTiO3. Similar multiferroic phases can be expected to occur in superlattices with other transition metal ions that support multiple valence states.

Methods

We perform first-principles calculations within the framework of density functional theory using the Quantum-ESPRESSO code28. The projector-augmented wave method and ultrasoft pseudopotentials are adopted. We employ the generalized gradient approximation of Perdew-Burke-Ernzerhof for the exchange-correlation functional and account for electronic correlations in the transition metal 3d orbitals by considering an onsite Coulomb interaction29 of the established literature value of 4 eV, which reproduces the experimental lattice constants of SrCrO3 (experiment: 3.87 Å; theory: 3.81 Å)14 and YCrO3 (experiment: 3.84 Å; theory: 3.79 Å)18,30. We have checked that the magnetic ground state of the superlattice does not change for onsite Coulomb interactions of 2, 3, and 5 eV. A cutoff of 90 Ry is used for the plane waves and a cutoff of 640 Ry for the augmentation charge. The Brillouin zone is sampled on an 8 × 8 × 6 Monkhorst-Pack k-mesh in the structure optimization, which is found to provide convergence of the total energy, and on a 14 × 14 × 12 Monkhorst-Pack k-mesh in the calculation of the electronic band structure and density of states. The total energy convergence criterion is set to 10−8 Ry. All structures are optimized until the Hellmann-Feynman forces stay below 10−5 Ry/Bohr. The ferroelectric polarization is calculated by the Berry phase approach31 on a 10 × 50 × 10 Monkhorst-Pack k-mesh to achieve convergence.

We set the in-plane lattice constants of SrCrO3 and YCrO3 equal (a = b = 3.80 Å) to mimic (001) epitaxial growth. The length and angle of the out-of-plane lattice vector are optimized for each strain value simultaneously with the atomic positions. This procedure is executed for different magnetic orderings to capture the strain effect on the relative energies of these orderings. Since SrCrO3 and YCrO3 have a lattice mismatch of only 0.5% (lattice constants of 3.81 and 3.79 Å, respectively), realization of a 1:1 superlattice is experimentally feasible thanks to recent developments in layer-by-layer deposition techniques10.