Unconventional interlayer exchange coupling via chiral phonons in synthetic magnetic oxide heterostructures.

Chiral symmetry breaking of phonons plays an essential role in emergent quantum phenomena owing to its strong coupling to spin degree of freedom. However, direct experimental evidence of the chiral phonon-spin coupling is lacking. In this study, we report a chiral phonon-mediated interlayer exchange interaction in atomically controlled ferromagnetic metal (SrRuO3)-nonmagnetic insulator (SrTiO3) heterostructures. Owing to the unconventional interlayer exchange interaction, we have observed rotation of spins as a function of nonmagnetic insulating spacer thickness, resulting in a spin spiral state. The chiral phonon-spin coupling is further confirmed by phonon Zeeman effect. The existence of the chiral phonons and their interplay with spins along with our atomic-scale heterostructure approach unveil the crucial roles of chiral phonons in magnetic materials.

INTRODUCTION

Chiral phonon serves as a fundamental element in realizing nontrivial quantum mechanical phenomena. When chiral symmetry breaks in a crystal, chiral phonons emerge and can couple to spins leading to phenomena such as phonon Hall effect, optically driven effective magnetic field, AC Stark effect, topologically induced viscosity split, and pseudogap phase, as summarized in Table 1 (–). So far, thermal Hall and time-resolved spectroscopic measurements were used for identifying the dynamic signatures of chiral phonons (–). However, a static manifestation of chiral phonons determining a ground state with long-range spin ordering is lacking.

Table 1.

The chiral phonon–induced emergent spin states.

Phenomena	Systems	References
Phononic helicaledge state	Mechanical topologicalinsulator	(1)
AC Stark effect	CdTe quantum well	(2)
Phonon Hall effect	Honeycomb lattice,cuprates, paramagneticdielectrics	(10, 14, 16)
Optically driven effectivemagnetic field	ErFeO3 (perovskite)	(4)
Topologically inducedviscosity split	Weyl semimetals	(5)
Intervalley transfer ofphonon angularmomentum	WSe2 (honeycomblattice)	(6)
Topological magnon-phonon coupling	Honeycomb lattices	(7)
Pseudogap phase ofsuperconductor	Cuprates	(8)
Einstein–de Haas effect	Honeycomb, Kagome,triangle, and squarelattices	(3, 11, 12)
Dynamic multiferroicity	Perovskites
Resonant magnonexcitation	ErFeO3 (perovskite)	(13, 15)
Dzyaloshinskii-Moriya–type electromagnon	TbMnO3 (perovskite)
Inverse Faraday effect	DyFeO3 (perovskite)
Phonon Zeeman effect	Binary compounds, perovskites, andtransition metaldichalcogenides
Entanglement ofsingle-photon andphonon	WSe2 (honeycomblattice)	(9)
Static IEC	SrRuO3/SrTiO3superlattice	Current study

Synthetic magnetic heterostructures let us study an interlayer exchange coupling (IEC), which might originate from the chiral phonon–spin coupling, e.g., the spin polarization of hole carriers by elliptically polarized phonons (). In general, when two ferromagnetic (FM) layers are separated by a thin nonmagnetic-metallic (NM-M) spacer, the relative spin orientation of the FM layers is determined by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction via itinerant electrons (Fig. 1A). Here, the interlayer exchange constant (J) between the localized spins in the FM layers oscillates as a function of the spacer layer thickness (t) with the term cos(2kFt)/t, where kF and d are the Fermi wave vector of the itinerant electrons in the spacer and the dimensionality of the system, respectively (, ). Hence, both parallel and antiparallel spin ordering between the FM layers can be realized depending on t, where the antiparallel alignment is commonly referred to as synthetic anti-FM (sAFM) ordering. In contrast, for a nonmagnetic-insulating (NM-I) spacer without any itinerant carriers, J is known to decay monotonically and exponentially with t, above the quantum tunneling regime (, ). In the presence of chiral phonons, however, we propose that spins in the FM layers can indirectly interact with each other through an NM-I spacer via chiral phonon–spin coupling. Furthermore, depending on t, the interaction effectively changes the relative spin orientation (Fig. 1, B and C).

Fig. 1.

Chiral phonon–mediated IEC and resultant tSTO-dependent magnetic behavior of SRO/STO superlattices.

Schematic diagrams of IEC across (A) an NM-M spacer via free electron–mediated RKKY interaction and (B and C) NM-I spacers via chiral phonon–mediated interaction with different t. (D) In-plane M (T) curves of SRO/STO superlattices with systematically changing tSTO. (E) M (H) curves of the superlattices at 85, 50, and 5 K. The arrows indicate the directions of the H-field. (F) M (H) curves of the superlattices with different tSTO. The curves are measured at 5 K. (G) Oscillatory magnetic behavior of the M value as a function of tSTO. The values were obtained at 2 K with 0.01 T of in-plane H-field. The solid lines are a guide to the eye.

We used atomically designed SrRuO3/SrTiO3 (SRO/STO) superlattices to model the FM-M/NM-I/FM-M heterostructure. FM SRO (FM-M layer) is an excellent candidate for the realization of unconventional IEC, owing to its strong spin-phonon and spin-orbit coupling (–). A small Fermi energy mismatch between SRO and STO (NM-I layer) and their nonpolar nature highly suppresses the charge transfer across the interface (–). Furthermore, identical A-site ion (i.e., Sr) and similar in-plane lattice constants between SRO and STO provide coherent superlattice structures with fully strained states, i.e., without misfit dislocations, of which the configuration amplifies the experimental signal (, ). In particular, the FM molecular field of SRO layers breaks the degeneracy, enabling disparate population of the chiral phonons. The structural similarity of the perovskites and atomically sharp interfaces further facilitate the chiral phonon propagation, allowing chiral phonon spin interaction in the neighboring SRO layers.

We deliberately grew oxide superlattices with alternating α– and β–atomic unit cells (~0.4 nm) of SRO (tSRO) and STO (tSTO), respectively, repeated for γ times on STO (001) substrates, i.e., [α|β]γ, using pulsed laser epitaxy (see Materials and Methods and figs. S1 to S3) (, –). An intriguing oscillation in the in-plane magnetization is observed as a function of tSTO, indicating the presence of an unconventional IEC across the NM-I spacer. The noncollinear spiral spin state in the ground state responsible for the observed magnetic oscillation was visualized by polarized neutron reflectometry (PNR). We propose chiral phonon–spin coupling as a possible mechanism for the unconventional IEC across the NM-I spacer. In particular, we suggest that the angular momentum of the chiral phonons couple to the spins, leading to the spin spiral state in our superlattices. Strong spin-phonon coupling was indeed evidenced by confocal Raman spectroscopy. This previously unidentified type of long-range magnetic interaction yields an advanced understanding of the chiral phonons and accessible controllability of spiral spin states over them via atomic-scale heterostructuring. The spatial modulation of in-plane magnetization might further provide insight into the emergence of exotic spin orderings such as magnetic cone or fan (, ).

RESULTS

NM-I thickness–dependent oscillatory magnetization behavior

The SRO/STO superlattices exhibit an exotic in-plane magnetic behavior that has not been observed in single SRO films (Fig. 1, D to G, and fig. S4). Temperature (T)–dependent magnetization [M (T)] curves of the [6|β]10 superlattices along the in-plane direction commonly reveal a typical FM Tc = ~130 K, followed by an anomalous Néel-like downturn below ~80 K (Fig. 1D). Note that the out-of-plane M (T) shows the conventional FM behaviors of SRO with the same Tc and without any downturn, consistent with previous studies (fig. S5) (, –). Magnetic field (H)–dependent in-plane magnetization [M (H)] curves of the superlattices consistently support the AFM-like behavior, with a double hysteresis loop and a large coercive field of ~1.8 T appearing below ~80 K (Fig. 1, E and F, and fig. S6). Furthermore, H-dependent M (T) curves show a gradual disappearance of the downturn as H is increased, especially above the coercive field (fig. S6). Similar behavior was reported in low-dimensional materials and understood as the AFM-like IEC between the FM layers (, ).

A clear tSTO-dependent oscillation of in-plane magnetization was observed, demonstrating the presence of unconventional IEC. We extracted M (2 K, 0.01 T) values as a function of both tSRO and tSTO, which exhibit a distinct oscillation as a function of tSTO when tSRO ≥ 1.6 nm (Fig. 1G). Note that the oscillation of the net magnetization was directly picked up from the magnetization value. This underscores the intrinsic nature of the oscillation in our superlattices, distinguishing it from the oscillations observed in the exchange bias reported by other studies (–). For example, the SRO/NM-M/SRO heterostructure has shown exchange bias possibly originating from the RKKY interaction (), yet M (H) curves of the SRO/STO superlattices do not show any exchange bias. Superlattices with tSRO = 0.8 nm or less show negligible in-plane M (T) possibly owing to the reduced dimensionality (). However, M (2 K) of superlattices with fractional unit cells tSTO control also presents a portion of the magnetic oscillation (fig. S7). Figure 1F further shows that the M (H) curve for the superlattices with a thick STO layer (i.e., [6|18]10 superlattice, tSTO = ~7 nm) returns to the conventional single FM hysteresis loop with nearly the same saturation magnetization as the [6|6]10 superlattice. The downturn of M (T) with decreasing T also disappears for the [6|18]10 superlattice. These results indicate that an unconventional IEC plays a key role in the exotic AFM-like magnetic ground state of the superlattices with thin STO layers.

We fabricated more than 350 superlattices and measured the in-plane magnetization for more than 40 of those samples and achieved excellent reproducibility in both structural and magnetic properties (fig. S8). This confirms that the tSTO-dependent oscillation of the net magnetization in the superlattices is intrinsic and not originating from short-range ordering mechanisms such as spin-glass behavior. We note that the out-of-plane magnetization of the superlattices serves as the magnetic easy axis identical to the single SRO film (figs. S4 and S5) but does not exhibit the peculiar oscillatory behavior. The oscillation is observed only for the relatively small, in-plane magnetization, demonstrating a stronger susceptibility to the unconventional IEC. The small in-plane magnetization further complicates the application of conventional IEC analyses using the M (H) curves. Thus, to characterize the magnetic ground states of the superlattices, we focused on the in-plane magnetic behavior and spin structures at low-H fields below 80 K.

Synthetic spiral spin state

The depth profile of the spin vector orientation along the in-plane direction of each FM layer supports the IEC-induced spiral spin ordering (Fig. 2), and resultant STO-thickness–dependent oscillation of the net magnetization. Figure 2A shows the PNR spectra of the [6|4]10 superlattice measured at 5 K with 0.01 T in-plane H-field. R+ (R−) corresponds to the reflectivity measured with neutron spin parallel (antiparallel) to H. The superlattice peak at Q = ~1.6 nm−1 corresponds to the periodicity of the superlattice structures, consistent with the layer thicknesses obtained using x-ray reflectivity and scanning tunneling electron microscopy (STEM; figs. S2 and S3 and table S1). Spin asymmetry [S. A. = (R+ − R−)/(R+ + R−)] exhibits a distinct structure at Q = ~0.8 nm−1 (half of the superlattice peak Q value), indicating the existence of AFM-like ordering (Fig. 2B) (, , ). We focused on the result of [6|4]10 superlattice as the peak values at Q = ~0.8 and ~ 1.6 nm−1 provided the largest signal-to-noise ratio. We also did not carry out the spin-flip polarization because the PNR signals were estimated to be quite small (fig. S9) (). To characterize the synthetic spin structure of the superlattice, we assumed that each FM SRO layer has a single-spin orientation with an identical total magnetization, and the spin orientation of a neighboring layer has a relative angle difference of ϕ, depending on tSTO (text S1). The β- and γ-dependent M (2 K) were fit to result in ϕ = ~160° between the FM layers for tSTO = 1.6 nm, indicating a noncollinear spiral spin structure (fig. S10). Figure 2E visualizes the constructed spiral spin structure along the in-plane direction of the superlattice with nuclear (Fig. 2C) and magnetic (Fig. 2D) scattering length densities (SLDs). By examining numerous synthetic magnetic configurations, including the FM, sAFM, and spiral spin structures with varying ϕ, we confirmed that the structure shown in Fig. 2E indeed leads to a consistent in-plane simulation result of the experimental PNR spectra (figs. S12 to S15, table S2, and text S2). While the exact rotation of the spin directions from one SRO layer to the other can be a subject of debate based on our experimental and fitting errors, it is evident that collinear spin configurations including FM and sAFM cannot account for the observed experimental results.

Fig. 2.

Noncollinear spiral spin state of the SRO/STO superlattice.

(A) PNR spectra for the spin-up (R+) and spin-down (R−) polarized neutrons and (B) S. A. for [6|4] superlattice at 5 K. The measurement was performed with 0.01 T of in-plane H-field. The symbols and solid lines indicate experimental data and fit using the model in (C) to (E), respectively. The error bars represent 1 SD. (C) Nuclear SLD depth profile of the superlattice. (D) Magnetic SLD depth profile with x- and y-directional M values (M and M). Gray solid line is the absolute value of the total magnetic SLD for each SRO layer within the superlattice (~0.4 μB/Ru). The vertical dashed lines in (C) and (D) are guides to the eye. (E) Schematic diagram of the spin configuration in the SRO/STO superlattice. The top view displays the ϕ = 160° between the magnetization directions (S1 and S2) in the two neighboring SRO layers when tSTO = 1.6 nm. External H-field has been applied along the [010] direction (y).

Both the noncollinear spiral spin state and its tSTO-dependent behavior reflect the existence of a nonconventional IEC in the SRO/STO superlattice. Several mechanisms can be considered to understand the magnetic interaction, including the dipole-dipole interaction, magnetic anisotropy, RKKY, orange peel interaction, coupling to the defect states, interlayer Dzyaloshinskii-Moriya interaction, and chiral phonon–induced IEC (, , , –). First, the tSTO-dependent oscillatory behavior can rule out the dipole-dipole interaction and magnetic anisotropy, as they would only impose monotonic tSTO dependence (). Second, the RKKY cannot explain the interaction across the NM-I STO spacers (fig. S16 and text S3) (, ). Third, Néel suggested that a sizeable roughness at heterointerfaces can lead to an IEC across NM-I spacers (), yet our superlattices have a roughness in the order of an atomic unit cell (~0.4 nm; fig. S3). Fourth, recent studies proposed that Schottky defects or metallic in-gap states can result in an IEC (, ), which is absent in our SRO/STO superlattices with suppressed charge transfer (see text S4 for more details) (, ). Fifth, the interlayer Dzyaloshinskii-Moriya interaction can account for a noncollinear spiral spin state of synthetic magnetic layers. However, the Dzyaloshinskii-Moriya vector orientation should be defined along the in-plane direction of our experimental setup as was the case of other previously reported systems (, ), which is not consistent with the observed in-plane spiral spin structure.

Chiral phonon–mediated IEC

The last candidate, i.e., chiral phonon–spin coupling–induced IEC, is a plausible mechanism for elucidating the unconventional magnetic ground state, considering the facile formation and propagation of chiral phonons in the perovskite superlattices (, , , ). In particular, time-resolved optical spectroscopy has demonstrated that chiral phonons can dynamically mediate the long-range magnetic interaction across the NM-I spacer (). They proposed a chiral phonon–mediated long-range spin exchange Hamiltonian, which explicates with the angular momentum transfer mechanism via chiral phonons and spin-orbit interaction, through the insulating layers. As the chiral nature of the phonon breaks the mirror symmetry, one can anticipate the existence of an antisymmetric IEC.

For the SRO/STO superlattices, strong spin-phonon and spin-orbit coupling of SRO lead to the creation of the chiral phonons (–). In particular, the FM molecular field of SRO layers breaks the degeneracy, enabling disparate population of the chiral phonons. The structural similarity of the perovskites and atomically sharp interfaces further facilitate the chiral phonon propagation, allowing chiral phonon spin interaction in the neighboring SRO layers. Hence, we propose that spins in the FM layers can interact with each other through an NM-I spacer via chiral phonon–spin coupling, and the resultant unconventional magnetic ground state could be realized in the SRO/STO superlattices.

Chiral phonon–spin coupling evidenced by phonon Zeeman effect

The existence of chiral phonons and their coupling to spins in the SRO/STO superlattices was evidenced by T-dependent confocal Raman spectroscopy (see Materials and Methods). Figure 3 shows a distinct split of a phonon mode at ~367 cm−1 into two modes at ~358 (phonon A) and ~386 cm−1 (phonon B) below Tc, in addition to the conventional phonon anomaly at Tc originating from the strong phonon-spin coupling in SRO (, ). Lattice dynamical calculation indicated that the modes correspond to oxygen vibrations with orthogonal polarizations in the orthorhombic bulk SRO (). A superposition of the two orthogonal linear phonons with phase difference can create chiral phonons (insets of Fig. 3B) (), which are to be distinguished from the chiral phonons in hexagonal lattices (, ). The chiral phonon–spin coupling of SRO/STO superlattices was manifested by the phonon Zeeman splitting (), which appeared without an external H-field. This reveals that the FM molecular field in the SRO layer is strongly coupled to the chiral phonons (Fig. 3B). Whereas the two phonon modes are not degenerate in bulk SRO with orthorhombic structure, they should be degenerate in the thin film with a tetragonal structural symmetry, as shown for the high T results. From the T-dependent behavior, we believe that the degeneracy lifting below Tc is related to the opposite energy shift of the chiral phonons with opposite chirality under the FM molecular field. We also note that SRO has no structural phase transition below Tc (). The relative splitting of phonon frequency (∆ω/ω) of SRO/STO superlattice is ~0.076, similar to that of 4f rare-earth trihalides and Cd3As2 (, –). This indicates the strong effect of chiral phonon–spin coupling in SRO/STO superlattices. Although the population of phonon would decrease, the polarization of phonon can be enhanced with decreasing temperature, facilitating the magnetic interaction below Tc. In addition, the chiral phonon frequency (ω) is closely associated with the spatial spin rotation period (~3.6 nm) of the SRO/STO superlattices. Assuming the phonon velocity of SRO (vs) to be ~2 to 6 nm ps−1 (), the wavelength can be estimated as 2πvs/ω = ~1 to 3.6 nm for the chiral phonons showing the same order of magnitude to the periodicity of the synthetic magnetic oscillation. This correspondence suggests that chiral phonons created in the SRO layers can propagate across the NM-I STO spacers and induce IEC via chiral phonon–spin coupling.

Fig. 3.

Chiral symmetry breaking in SRO/STO superlattices.

(A) T-dependent confocal Raman spectra in z(xx) polarization of a [6|4] superlattice (the results of a [6|8] superlattices are in fig. S17). The symbols and solid lines represent experimental data and fit for the Raman spectra, respectively. Blue and red solid lines correspond to the A and B phonons, respectively, as described in the insets of (B). (B) T-dependent ω splitting below Tc. The insets schematically represent the expected chiral phonon modes of SRO. The dotted horizontal lines indicate (up) Tc of SRO and (down) the lowest T (10 K) of the measurement.

DISCUSSION

We have observed exotic spiral spin states with NM-I thickness–dependent oscillatory magnetic behavior, indicating the existence of IEC in atomically designed FM/NM-I heterostructures. The existence and the propagation of chiral phonons in the SRO/STO heterostructures would mediate the unconventional IEC via chiral phonon–spin coupling. We note that the microscopic mechanism of the unconventional IEC remains to be clarified and future theoretical studies are necessary. Nevertheless, the experimental observation itself provides a general intuition for understanding the emergent magnetic quantum phenomena, and the atomic-scale approach inspires the future combination of spintronics and phononics.

MATERIALS AND METHODS

Superlattice growth

We chose the SRO and STO heterostructures since this system highly suppresses the charge transfer between SRO/STO interfaces, demonstrating intrinsic low-dimensional SRO layers (, ). We deliberately synthesized the [α|β]γ superlattices, in which α–atomic unit cells layers of SRO and β–atomic unit cell layers of STO are systematically repeated for γ times along the growth direction, using pulsed laser epitaxy on (001) STO substrates. We controlled the number of atomic unit cells in the superlattices by using a customized automatic laser pulse control system programmed using LabVIEW. We ablated stoichiometric ceramic targets using a KrF laser (248 nm; IPEX868, Lightmachinery) with a repetition rate of 5 Hz and a laser fluence of 1.5 J cm−2. Both SRO and STO layers were deposited at 750°C and 100 mtorr of oxygen partial pressure for the stoichiometric condition of both materials. Note that atomically thin STO layers preserve their insulating behavior well (fig. S16).

Structural characterization

X-ray reflectivity and θ-2θ measurements were carried out by using high-resolution x-ray diffraction (HRXRD) of Rigaku Smartlab and PANalytical X’Pert XRD. We estimated the thickness of the superlattice period using Bragg’s law as where 𝛬, n, λ, and θ are the period thickness, superlattice peak order, x-ray wavelength, and nth-order superlattice peak position, respectively. We deduced the thickness of SRO and STO layer using x-ray reflectivity simulations, as shown in fig. S2. All the superlattices exhibit a small thickness deviation, below 1 atomic unit cell (~0.4 nm), corresponding to the atomic step size of the substrate. Atomic-scale imaging of the SRO/STO heterostructure was performed on a spherical aberration–corrected STEM (ARM200CF, JEOL) working at 200 kV with high-angle annular dark-field (HAADF) imaging mode. The incident electron probe angle was ~23 mrad, which translates to a probe size of ~0.78 Å. The angle range of the HAADF detector was 70 to 175 mrad. Cross-sectional thin samples for STEM observation were prepared by a dual-beam focused ion beam system (FIB; FEI Helios NanoLab 450) and the following low-energy Ar ion milling at 700 V (Fischione Model 1040, NanoMill) was conducted for 15 min to eliminate damaged surface layers from heavy Ga ion beam milling in the FIB system.

Magnetization measurements

T- and H-dependence of magnetization behavior were measured using a Magnetic Property Measurement System (MPMS; Quantum Design). Field-cooled M (T) curves were obtained from 300 to 2 K with 0.01 T of H-field. The M (H) curves were obtained at 5, 50, and 85 K.

Polarized neutron reflectivity

PNR experiments were performed on the Magnetism Reflectometer at the Spallation Neutron Source at Oak Ridge National Laboratory (SNS, ORNL). The measurements were performed in closed-cycle refrigerator systems with an external H-field by using a Bruker electromagnet. We used highly polarized neutrons (polarization efficiency of 99 to 98.5%) with wavelengths (λ) within a band of 2 to 8 Å. PNR spectra for two neutron polarizations (R+ and R−) were obtained by using time-of-flight method, where a collimated polychromatic neutron beam impinges a sample at a grazing incidence angle (δ). The reflectivity signal was recorded as a function of wave vector transfer, Q = 4πsin(δ)/λ (). Nuclear and spin structures of superlattices were simulated by using GenX (). To characterize the nuclear structure of the sample, we measured NR spectra at 300 K (fig. S12A). Saturation magnetization values were estimated to 0.4 μB/Ru using PNR spectra at 85 K with 1 T (> coercive field at 85 K) of in-plane H-field (fig. S12B), consistent with the result from MPMS. PNR is a depth-sensitive vector magnetometry method (). In saturation, the layer magnetizations are fully magnetized parallel to the external field. In this case, only non–spin-flip reflectivity curves, R++ and R−− exist, which correspond to two orientations of neutron polarization. The reflectivity curves have well-known characteristic features, like the oscillations determined by the total thickness and the Bragg peaks, corresponding to the periodicity of the superlattices. When the external magnetic field is released down to a small value of a guide field, the magnetizations in alternating SRO layers form a spiral structure, thus containing M and M components of magnetization. In this configuration, the reflected signal will contain both non–spin-flip (R++ and R−−, determined by the parallel component of the magnetization vector M) and spin-flip (R+– and R−+, determined by the perpendicular component of the magnetization vector M) neutrons so that the resulting reflectivity curves will correspond to R+ = R++ + R+– and R− = R−− + R−+. Our experiments were performed without spin-flip polarization analysis because the estimated experimental signal with spin-flip polarization is quite small (fig. S9). As it was demonstrated in (), without the full polarization analyses, the coupling angle between the magnetization vectors in the alternate magnetic layers can be effectively obtained through the data analyses by using the modulus of the magnetization vector obtained from the saturation and fitting only the alignment angles ϕ in the alternating SRO layers.

Confocal Raman spectroscopy

Raman spectra of SRO/STO superlattices were measured by using a confocal micro-Raman (Horiba LabRam HR800) spectrometer using a HeNe laser with a wavelength of 632.8 nm (1.96 eV). To enhance the Raman cross section of inelastic light scattering, we used the SRO/STO superlattice samples with 50 repetition numbers (). We used a grating with 1800 grooves per millimeter and a focused beam spot size of ~5 μm. The power was maintained below ~0.3 mW to suppress any heating effects. With the backscattering geometry, we used z(xx) configuration to detect the A and B phonon modes, which are expected to exhibit a strong spin-phonon coupling. We note that an anomaly of phonon B at Tc represents the strong spin-phonon coupling in SRO/STO superlattices, consistent with previous SRO heterostructures (, ). Lattice dynamical calculation suggested that the A and B phonon modes correspond to oxygen vibrations with orthogonal polarizations (Ag and B2g modes, respectively) in the orthorhombic bulk SRO (). To obtain high-quality Raman spectra, we precisely adjusted the z-directional beam position to achieve the optimal focus on the superlattice samples ().

Junction transport measurement

The junction transport measurement was performed on the superlattice with atomically thin STO layers. Tunneling transport geometry was used using Nb-doped (0.5 wt%) STO substrate as the bottom electrode and Au (~500 μm in diameter) as the top electrode. The top electrode was patterned on the surface of superlattices using RF sputtering with a shadow mask. T-dependent tunneling resistance of superlattices was recorded using a physical property measurement system (Quantum Design) with an excitation current of 0.3 μA.