Magnetoelectric phase transition driven by interfacial-engineered Dzyaloshinskii-Moriya interaction

Strongly correlated oxides with a broken symmetry could exhibit various phase transitions, such as superconductivity, magnetism and ferroelectricity. Construction of superlattices using these materials is effective to design crystal symmetries at atomic scale for emergent orderings and phases. Here, antiferromagnetic Ruddlesden-Popper Sr2IrO4 and perovskite paraelectric (ferroelectric) SrTiO3 (BaTiO3) are selected to epitaxially fabricate superlattices for symmetry engineering. An emergent magnetoelectric phase transition is achieved in Sr2IrO4/SrTiO3 superlattices with artificially designed ferroelectricity, where an observable interfacial Dzyaloshinskii-Moriya interaction driven by non-equivalent interface is considered as the microscopic origin. By further increasing the polarization namely interfacial Dzyaloshinskii-Moriya interaction via replacing SrTiO3 with BaTiO3, the transition temperature can be enhanced from 46 K to 203 K, accompanying a pronounced magnetoelectric coefficient of ~495 mV/cm·Oe. This interfacial engineering of Dzyaloshinskii-Moriya interaction provides a strategy to design quantum phases and orderings in correlated electron systems.

images indicate upward and downward ferroelectric domains. The ferroelectric switching disappears at 90 K. c, Temperature-dependent piezoresponse phase hysteresis of the I3/T6 superlattice. The coercive bias decreases when temperature increases from 3.7 K to 70 K and disappears at 90 K. Based on the above experiments and analysis, although there are Ti 4+ at one interface and mixed Ti 4+ /Ti 3+ at the other interface, we observe no distinguishable difference between the states of oxygen at the two interfaces. Therefore, most likely, the reason for the appearance of the Ti 3+ ion at the perovskite interface is not oxygen vacancies.
Then, in order to clarify the reason behind, we further investigated the oxidation state of Ir. Since the STEM-EELS is typically used to detect energy loss lower than 3 keV and not suitable for Ir-L edge, instead we carried out synchrotron X-ray absorption spectroscopy (XAS) at the BL39XU of Spring-8 Japan to collect the spectra near L3 edge of Ir in the (Sr2IrO4)3/(SrTiO3)6 superlattice and pure Sr2IrO4 thin film for comparison. The Ir L3 edge XAS spectra were collected by standard helicity reversal technique with a grazing incidence geometry (5.5° incidence angle). The partial fluorescence yield (PFY) mode was conducted, where the emissions were collected and energy-analyzed by a four-element silicon drift detector (Sirius 4, SGX Sensortech Inc.), respectively. As shown in Supplementary Fig. 8, the XAS peak position shifts to higher energy in the (Sr2IrO4)3/(SrTiO3)6 superlattice (inset Supplementary Fig. 8), compared to that in pure Sr2IrO4 thin film. This shift of XAS spectra implies that the valence of Ir increases in the superlattice compared to that in pure Sr2IrO4 thin film. Therefore, the appearance of the Ti 3+ near the interface is possibly due to the change of Ir oxidation state.  Temperature-dependent BLS were carried out on the I3/T6 superlattice, a signal near 74

Supplementary
GHz was observed, when increasing the temperature, this peak was dramatically suppressed as shown in Fig. 3c. The temperature-dependent intensity of the signal has a strong correlation with the result in Supplementary Fig. 2, indicating that the observed signal is from surface spin wave 4 .

Supplemental Note 3: Theoretical analysis for ME phase transition.
The effective spin Hamiltonian is expressed as 5 : Furthermore, the role of interfacial DMI on the temperature-dependent ME response is investigated based on symmetry analysis from Mermin-Wagner theorem 6 . SU (2) symmetry can be broken by the spin-orbit coupling, . For the case with = 0, the system becomes the isotropic Heisenberg model and the SU(2) symmetry persist the invariance, the critical temperature of order-disorder phase transition must be zero; for the case with ≠ 0, the SU(2) symmetry is broken slightly and the critical temperature of order-disorder phase transition becomes finite. Namely, considering the polarization or interfacial DMI in the superlattices, a finite temperature for the phase transition can be driven. For further studying the transition temperature, we may have the free energy in quasi-2D magnetic systems 7 : ∆F = 4π − B ln ( ) , where is a phenomenological parameter. The critical temperature ( ) can be estimated as 8 : B~( ln ( )) −1 . Therefore, the transition temperature increases with , namely, the transition temperature is proportional to the or polarization ( ∝ ∝ ). In order to clarify this relation between and , we estimate the interfacial DMI by conducting the BLS measurement. According to the equation 9 :

Supplementary
where is the strength of the interfacial DMI, is magnetic moment, is gyromagnetic ratio, is wave vector, and ∆ is the frequency shift between anti-Stokes and Stokes peaks in BLS spectra. With the same (~5 emu/cc), Firstly, in order to study the lattice distortion, we quantitively analyzed the octahedral rotations/distortions near the perovskite and Ruddlesden-Popper interfaces ( Supplementary Fig. 12). However, no distinguishable octahedral rotation exists at either interface. Therefore, we further calculated the layer-by-layer tetragonality (c/a ratio) based on HAADF images at room temperature, which provides higher signal-tonoise ratio and better contrast in the interface. As shown in Supplementary Fig. 13a  In addition, we also try to measure the off-center displacements of TiO columns with respect to the geometric mass center of the surrounding four Sr/Ba columns ( Supplementary Fig. 13f). The polarization of ultrathin BTO is much lower than the BTO bulk 11,12 . This will inevitably lead to a very small atomic displacement, which may be below the scanning noise and random specimen drift in acquiring STEM images (typically ~5 pm) 13 . Even so, we still observe a very little asymmetry of the off-center displacements in BTO/SIO superlattice as seen in Supplementary Fig. 13f, which is negligible in STO/SIO superlattice in Supplementary Fig. 13c.
The above structural analysis is summarized in Supplementary Fig. 14