Abstract
Harnessing the spin–momentum locking of topological surface states in conjunction with magnetic materials is the first step to realize novel topological insulatorbased devices. Here, we report strong interfacial coupling in Bi_{2}Se_{3}/yttrium iron garnet (YIG) bilayers manifested as large interfacial inplane magnetic anisotropy (IMA) and enhancement of damping probed by ferromagnetic resonance. The interfacial IMA and damping enhancement reaches a maximum when the Bi_{2}Se_{3} film approaches its twodimensional limit, indicating that topological surface states play an important role in the magnetization dynamics of YIG. Temperaturedependent ferromagnetic resonance of Bi_{2}Se_{3}/YIG reveals signatures of the magnetic proximity effect of T_{C} as high as 180 K, an emerging lowtemperature perpendicular magnetic anisotropy competing the hightemperature IMA, and an increasing exchange effective field of YIG steadily increasing toward low temperature. Our study sheds light on the effects of topological insulators on magnetization dynamics, essential for the development of topological insulatorbased spintronic devices.
Introduction
The development of spintronics relies crucially on control of spinpolarized currents, which carry spin angular momenta that can be utilized to manipulate magnetic moments through spintransfer processes. Spin currents can be generated by the spin Hall effect^{1} in a heavy metal, or by exploiting the spin structure of some twodimensional (2D) electron systems. A promising candidate of such a 2D system is the surface state of topological insulators (TIs). TIs are emergent quantum materials hosting topologically protected surface states, with dissipationless transport prohibiting backscattering^{2,3}. Strong spin–orbit coupling (SOC) along with time reversal symmetry (TRS) ensures that the electrons in the topological surface states (TSSs) have their direction of motion and spin locked to each other^{2,4,5}. The spin–momentum locking permits efficient interconversion between spin and charge currents. To date, several methods have been adopted to estimate the spincharge conversion efficiency of TIs, either by using microwaveexcited dynamical method^{6,7,8,9,10} (e.g., spin pumping and spin–torque ferromagnetic resonance (STFMR)) or thermally induced spin injection^{11}. Very large values of spincharge conversion ratio have been reported^{7,9,10}. Recently, TIs are shown to be excellent sources of spin–orbit torques (SOT) for efficient magnetization switching^{12}.
When a TI is interfaced with a magnetic layer, the interfacial exchange coupling can induce magnetic order in TIs by the magnetic proximity effect (MPE) and break the TRS^{13,14,15,16}. The resulting gap opening of the Dirac state is necessary to realize novel phenomena such as topological magnetoelectric effect^{17} and quantum anomalous Hall effect^{18,19}. Since the MPE and spintransfer process rely on interfacial exchange coupling of TI/ferromagnet, understanding the magnetism at the interface has attracted strong interests in recent years. Several techniques have been adopted to investigate the interfacial static magnetic properties, including spinpolarized neutron reflectivity^{15,20}, second harmonic generation^{21}, electrical transport^{14,22}, and magnetooptical Kerr effect^{14}. All these studies clearly indicate the existence of MPE resulting from exchange coupling and strong SOC in TIs. Specifically, a roomtemperature magnetic order induced by MPE in EuS/Bi_{2}Se_{3} has been reported recently^{15}. Through exchange coupling between the TSS and EuS layer, the induced magnetic moments exhibited perpendicular magnetic anisotropy (PMA) that can potentially open a gap of TSS. For TI/yttrium iron garnet (YIG) bilayer, however, the interfacial magnetic anisotropy and the resulting magnetization dynamics under the influence of TSS are still largely unknown. It is equally important to understand how the interfacial exchange coupling affects the magnetization dynamics of Bi_{2}Se_{3}/YIG because of the wide applications of YIG. For example, TIs can enhance the magnetic anisotropy, introduce additional magnetic damping, and greatly alter the dynamical properties of the ferromagnetic layer, as commonly observed in ferromagnet/heavy metals systems^{23,24,25}. The enhanced damping is visualized as larger linewidth of FMR spectra^{23,24,25}. Given the volatile surface band structure depending on the TI thickness^{26}, the adjacent materials^{27}, and the magnetism at the interfaces^{28}, experimental study on how the magnetization dynamically responds to the TSS is still lacking, which is a topic not only important for spintronics but also fundamental for physics.
In this work, we have investigated the magnetization dynamics via FMR in ferrimagnetic insulator YIG under the influence of the prototypical threedimensional (3D) TI Bi_{2}Se_{3}^{29}. We choose YIG as the ferromagnetic layer because of its technological importance, with high T_{C} ~550 K and extremely low damping coefficient α^{30}. When YIG is interfaced with TIs, its good thermal stability minimizes the interdiffusion of materials. Through the Bi_{2}Se_{3} thickness dependence study, we observed a strong modulation of FMR properties attributed to the TSS of Bi_{2}Se_{3}. The temperaturedependent study unraveled an effective field parallel to the magnetization direction existing in Bi_{2}Se_{3}/YIG. Such an effective field built up as the temperature decreased, which was utilized to demonstrate the zeroappliedfield FMR of YIG. Furthermore, we identified a possible signature of MPE of T_{C} as high as 180 K manifested as enhanced spin pumping in a fluctuating spin system, as well as a small emerging PMA at low temperature in competition with inplane magnetic anisotropy (IMA) extending to high temperature.
Results
Interfacial IMA in Bi_{2}Se_{3}/YIG
The roomtemperature FMR measurements were performed using a microwave cavity of frequency 9.76 GHz (Fig. 1a) and a broadband coplanar waveguide (Fig. 1b). The FMR spectra in Fig. 1c are compared for single layer YIG(12) and Bi_{2}Se_{3}(25)/YIG(12) bilayer (digits denote thickness in nanometer), showing a large shift of resonance field (H_{res}) ~317 Oe after the Bi_{2}Se_{3} growth plus a markedly broadened peaktopeak width ΔH for Bi_{2}Se_{3}/YIG. Figure 1d shows H_{res} vs. applied field angle with respect to the surface normal θ_{H} for YIG(12) and Bi_{2}Se_{3}(25)/YIG(12). Larger variation of H_{res} with θ_{H} in the bilayer sample was observed. When the applied field was directed in the film plane, clear negative H_{res} shifts induced by Bi_{2}Se_{3} were observed at all microwave frequencies f as shown in Fig. 1e. The data in Fig. 1d, e can be fitted in the scheme of magnetic thin films having uniaxial PMA, the strength of which is characterized by the effective demagnetization field 4πM_{eff} = 4πM_{s} − H_{an} − H_{int}, where 4πM_{s}, H_{an}, and H_{int} are the demagnetization field, the magnetocrystalline anisotropy field of YIG, and the interfacial anisotropy field induced by Bi_{2}Se_{3}, respectively. The fitting result shows an ~60% enhancement of 4πM_{eff} for the Bi_{2}Se_{3}(25)/YIG(12) bilayer sample. The large enhancement cannot be accounted for by an increase in the saturation magnetization M_{s}, which should amount to an additional magnetization of ~100 μ_{B}/nm^{2} for this sample. The MPE, even if it persists up to room temperature, is unlikely to induce the large amounts of magnetic moments. Furthermore, since the xray diffraction results in Supplementary Fig. 3(d) and (e) show that the YIG films did not gain additional strain after growing Bi_{2}Se_{3}, the enhanced anisotropy cannot result from the change of magnetocrystalline anisotropy. We thus attribute the change of anisotropy mostly to the H_{int}. Based on the above discussion, we obtain H_{int} = −926 and −1005 Oe from Fig. 1d, e, respectively (see Supplementary Note 2). The minus sign indicates the additional anisotropy points in the film plane.
The above observations suggested the presence of interfacial IMA in Bi_{2}Se_{3}/YIG. To verify this, we systematically varied the thickness of YIG, d_{YIG}, while fixing the thickness of Bi_{2}Se_{3}. Figure 2a presents the d_{YIG} dependence of 4πM_{eff} for single and bilayer samples. The 4πM_{eff} of single layer YIG was independent of d_{YIG} varying from 12 to 30 nm. In sharp contrast, 4πM_{eff} of Bi_{2}Se_{3}/YIG became significantly larger, especially at thinner YIG, which is a feature of an interfacial effect. The f and θ_{H}dependent FMR were performed independently to doubly confirm the trends. The interfacial IMA can be further characterized by defining the effective anisotropy constant K_{eff} = (1/2)4πM_{eff}M_{s} = (1/2)(4πM_{s} − H_{an})M_{s} − K_{i}/d_{YIG}, with the interfacial anisotropy constant K_{i} = M_{s}H_{int}d_{YIG}/2. The K_{eff}d_{YIG} vs. d_{YIG} data in Fig. 2b are well fitted by a linear function, indicating that the d_{YIG} dependence presented in Fig. 2a is suitably described by the current form of K_{eff}. The intercept obtained by extrapolating the linear function corresponds to K_{i} = −0.075 erg/cm^{2}.
TSSmodulated magnetization dynamics in Bi_{2}Se_{3}/YIG
To further investigate the physical origin of the IMA, we next varied the thickness of Bi_{2}Se_{3} (d_{BS}) to see how K_{i} evolved with d_{BS}. Figure 2c shows the d_{BS} dependence of K_{i}. Starting from the d_{BS} = 40 nm sample, the magnitude of K_{i} went up as d_{BS} decreased. An extremum of K_{i} −0.12 ± 0.02 erg/cm^{−}^{2} was reached at d_{BS} = 7 nm. An abrupt upturn of K_{i} occurred in the region 3 nm < d_{BS} < 7 nm. The K_{i} magnitude dropped drastically and exhibited a sign change in the interval. Furthermore, the K_{i} value of 0.014 erg/cm^{2} at d_{BS} = 3 nm corresponds to weak interfacial PMA.
The sizable interfacial IMA can be expected given the large SOC of Bi_{2}Se_{3}. One possible mechanism is that the electrons at the interface redistribute upon hybridization between the Fe dorbital of YIG and the Dirac surface state of Bi_{2}Se_{3}. Recent theoretical study on EuS/Bi_{2}Se_{3} bilayers indicates that in addition to the strong SOC, TSS play a crucial role in mediating the exchange coupling of the ions in the magnetic layer^{31}. The hybridization between TSS and the magnetic layer can overall enhance the magnetic anisotropy energy that is inherent at the interface^{31}. Although in general an interfacial magnetic anisotropy may not necessarily be related to the topological nature of materials, here we attribute the interfacial magnetic anisotropy of Bi_{2}Se_{3}/YIG to the TSS based on the unique d_{BS} dependence of K_{i}, that cannot be accounted for by the strain or chemical mixing effects. Note that possible interdiffusion of materials at the interface can also lead to an interfacial magnetic anisotropy. As shown in Supplementary Fig. 3(c), the transmission electron microscope (TEM) image reveals an ~1 nm interfacial layer. However, the interdiffusion is unlikely to play a dominant role in the interfacial magnetic anisotropy since K_{i} varied significantly with d_{BS} up to 40 nm, and cannot account for the modulated dependence of K_{i} with d_{BS}, especially under 20 nm. We now consider how the Bi_{2}Se_{3} band structure evolves with d_{BS}. Based on previous investigation on surface band structure of ultrathin Bi_{2}Se_{3}^{26}, d_{BS} = 6 nm was identified as the 2D quantum tunneling limit of Bi_{2}Se_{3}. When d_{BS} < 6 nm, the hybridization of top and bottom TSS developed a gap in the surface states. Spinresolved photoemission study later showed that the TSS in this 2D regime exhibited decreased inplane spin polarization^{32}. The modulated spin texture may lead to the weaker interfacial magnetic anisotropy than that in the 3D regime^{32,33}. We thus divide Fig. 2c into two regions and correlate the systematic magnetic properties with the surface state band structure. The sharp change of K_{i} around d_{BS} < 6 nm strongly suggests that the interfacial IMA in Bi_{2}Se_{3}/YIG is of topological origin.
The ΔH broadening in FMR spectra after growing Bi_{2}Se_{3} on YIG indicates that Bi_{2}Se_{3} introduced additional damping in YIG. Within the macrospin approximation, the damping enhancement can be normalized with respect to d_{YIG} by defining \(\Delta \tilde \alpha ={d_{{\mathrm Y} {\mathrm I} {\mathrm G}} \left( \alpha_{{\mathrm B} {\mathrm S}/ {\mathrm Y} {\mathrm I} {\mathrm G}}\alpha_{{\mathrm Y} {\mathrm I} {\mathrm G}} \right)}\), where α_{BS/YIG} and α_{YIG} are the damping coefficient of Bi_{2}Se_{3}/YIG and YIG, respectively. Figure 2d displays the d_{BS} dependence of \(\Delta \tilde \alpha\). Similar to K_{i} in Fig. 2c, \(\Delta \tilde \alpha\) increased as d_{BS} decreased, reached its maximum at d_{BS} = 7 nm with a very large value of ~0.27 nm, and then dropped abruptly in the interval of 3 nm < d_{BS} < 7 nm. For comparison, typical \(\Delta \tilde \alpha\) of Pt/YIG, in which efficient spin pumping giving rise to sizable \(\Delta \tilde \alpha\)^{24}, is indicated by the red dashed line. The inset shows ΔH vs. f data for Bi_{2}Se_{3} (7)/YIG(13) and YIG(13) fitted by linear functions. One can clearly see a significant change of slope, from which we determined α_{BS/YIG} − α_{YIG} to be 0.014. In general, the large damping enhancement can have multiple origins, including spinpumping effect, interlayer exchange coupling with other magnetic layers, and chemical reactions at the interface. However, the damping arising from the static exchange coupling from the MPE or any antiferromagnetic order at the interface is not expected at room temperature. Moreover, as previously mentioned, the slight interdiffusion at the interface is unlikely to be the major root cause of \(\Delta \tilde \alpha\) varying over the wide range of d_{BS}. Instead, considering the closed d_{BS} dependence of K_{i} and \(\Delta \tilde \alpha\), it can be seen that the trend of \(\Delta \tilde \alpha\) in Fig. 2d stemmed from the strong coupling between TSS of Bi_{2}Se_{3} and YIG—that is, the surface state band structure of Bi_{2}Se_{3} profoundly affected the damping of YIG^{6}. Through dynamical exchange, spin angular momenta were transferred from YIG to the TSS via the spinpumping effect. The spinpumping efficiency of an interface can be evaluated by the real part of spin mixing conductance g_{↑↓} using the following relation^{25}:
where g and μ_{B}, are the Landé g factor and Bohr magneton, respectively. The maximum g_{↑↓} value (d_{BS} = 7 nm) is calculated to be ~2.2 × 10^{15} cm^{−2}, about three times larger than that of a typical Pt/YIG sample. The large g_{↑↓} of Bi_{2}Se_{3}/YIG implies an efficient spin pumping to an excellent spin sink of Bi_{2}Se_{3}. Note that the trend in Fig. 2d is distinct from that of the normal metal (NM)/ferromagnetic metal (FM) structures. In NM/FM, the g_{↑↓} increases with increasing NM thickness as a result of vanishing spin backflow in thicker NM^{34}. It is worth noting that the conducting bulk of Bi_{2}Se_{3} can dissipate the spinpumpinginduced spin accumulation at the interface^{6,35}. In this regard, the d_{BS} = 7 nm sample has the largest weight of surface state contribution to g_{↑↓}. Such unconventional d_{BS} dependence of g_{↑↓} implies that TSS plays a dominant role in the damping enhancement.
Spinpumping signature of MPE and observation of the exchange effective field
Since the effects of TSS are expected to enhance at low temperature, we next performed temperaturedependent FMR on Bi_{2}Se_{3}/YIG. Two bilayer samples Bi_{2}Se_{3}(25)/YIG(15) and Bi_{2}Se_{3}(16)/YIG(17), and a single layer YIG(23) were measured for comparison. Figure 3a, b shows the H_{res} vs. f data at various temperatures T for YIG(23) and Bi_{2}Se_{3}(25)/YIG(15). The H_{res} of both samples shows negative shifts at all f with decreasing T. The data of YIG(23) can be reproduced by the Kittel equation with increasing M_{s} of YIG at low T. In sharp contrast, Bi_{2}Se_{3}(25)/YIG(15) exhibited negative intercepts at H_{res}, and the intercepts gained their magnitude when the sample was cooled down. This behavior of nonzero intercept is common for all of our Bi_{2}Se_{3}/YIG samples. Note that the Kittel equation in its original form cannot produce an intercept. To account for the behavior, a phenomenological effective field H_{eff} is added to the Kittel equation, i.e.,
The solid lines in Fig. 3b generated by the modified Kittel equation fitted the experimental data very well.
Figure 3c, d presents the T dependence of H_{res} and ΔH for the YIG(23) and two Bi_{2}Se_{3}/YIG samples. As we lowered T, all of the samples had decreasing H_{res}, which was viewed as the effect of the concurrently increasing M_{eff} and H_{eff} as seen in Fig. 3a, b. On the other hand, ΔH built up with decreasing T. We first examined ΔH of the YIG(23) single layer. The ΔH remained relatively unchanged with T decreasing from room temperature, and dramatically increased below 100 K. The pronounced T dependence of ΔH or α has been explored in various rareearth iron garnet and was explained by the slowrelaxation process via rareearth elements or Fe^{2+} impurities triggered at low T^{36}. For sputtered YIG films, specifically, the increase in ΔH was less prominent in thicker YIG, indicating that the dominant impurities were located near the YIG surface^{37}. Distinct from that of YIG(23), the ΔH progressively increased for the bilayer samples. We were not able to detect FMR signals with ΔH beyond 100 Oe due to the limited sensitivity of our coplanar waveguide. However, one can clearly see that, for Bi_{2}Se_{3}(25)/YIG(15) and Bi_{2}Se_{3}(16)/YIG(17), ΔH broadened owing to increased spin pumping at first. For Bi_{2}Se_{3}(25)/YIG(15), the ΔH curve gradually leveled off, and intersected with that of YIG(23) at T ~40 K. The seemingly antidamping by Bi_{2}Se_{3} at low T may be related to the modification of the YIG surface chemistry during the Bi_{2}Se_{3} deposition. Additional analyses are needed to verify the scenario, which is, however, beyond the scope of this work. For the Bi_{2}Se_{3}(10)/YIG and Bi_{2}Se_{3}(7)/YIG samples, the damping had increased to such large magnitude below 150 K, and FMR could not be easily detected.
In both H_{res} and ΔH curves, humplike features located at T = 140 and 180 K (indicated by the arrows) were revealed for Bi_{2}Se_{3}(25)/YIG(15) and Bi_{2}Se_{3}(16)/YIG(17), respectively. We note that the humps are reminiscent of spin pumping into a fluctuating magnet close to its magnetic ordering temperature. As pointed out by Ohnuma et al.^{38}, the spinpumping efficiency is governed by the momentum sum of imaginary part of dynamical transverse spin susceptibility \(\chi _k^R\) of the spin sink:
where k is the wave vector and ω_{rf} is the microwave angular frequency. For a ferromagnet, the \(\chi _k^R\) is known to be divergent near its T_{C}^{39}. Therefore, an enhancement of spin pumping is expected as the spin sink is close to its magnetic phase transition point^{38,40,41}. In our system, a possibly newly formed magnetic phase would be the interfacial magnetization driven by the proximity effect, namely, T_{C} = 140 and 180 K for our Bi_{2}Se_{3}(25)/YIG(15) and Bi_{2}Se_{3}(16)/YIG(17), respectively. In fact, the T_{C} values of our samples are in good agreement with the reported T_{C} of 130 and 150 K in TI/YIG systems^{14,22}.
Using Eq. (2), we further determine the T dependence of 4πM_{eff} and H_{eff} of YIG(23) and the two bilayers samples, as shown in Fig. 3e, f. The 4πM_{eff} of YIG(23) became larger monotonically as previously discussed, while the 4πM_{eff} of the bilayer samples increased before reaching a maximum when T was around 150 K, and then decreased slightly at low T. We further calculate the interfacial anisotropy field H_{int} using \(4\pi M_{{\mathrm{eff}}}^{{\mathrm{BS}}/{\mathrm{YIG}}}  4\pi M_{{\mathrm{eff}}}^{{\mathrm{YIG}}} \approx  H_{{\mathrm{int}}}\). The inset of Fig. 3e shows the T dependence of H_{int}. The magnitude of H_{int} increased as the samples cooled down from room temperature at first. Upon crossing the temperature regions where the humplike features are located, H_{int} magnitude started to decrease with further decreasing T. Although the samples exhibit interfacial IMA (H_{int} < 0) within the temperature range of our measurement, further extending the trend of Bi_{2}Se_{3}(16)/YIG(17), specifically, leads to interfacial PMA (H_{int} >0) below 40 K. The turning of H_{int} curves around 150 K implied that a competing magnetic anisotropy was emerging, which favored perpendicular direction and effectively diminished the IMA that persisted up to room temperature. Observing that the turning of H_{int} curves were in the vicinity of the individual hump temperature, we thus attribute the interfacial PMA to MPE in Bi_{2}Se_{3}/YIG. Our scenario is further supported by a theoretical model that considers the direct exchange coupling of TSS and an adjacent magnetic layer^{31,42}. In this model, the calculated total electronic energy in the system with MPE indicates that PMA is in favor.
To independently show the effect of strong interfacial exchange coupling in Bi_{2}Se_{3}/YIG, we have performed electrical transport measurements at low T. As shown in Supplementary Fig. 7, we observed a clear negative magnetoresistance (MR) of Bi_{2}Se_{3}/YIG, which is distinct from weak antilocalization (WAL) effect typical of Bi_{2}Se_{3} films without magnetic perturbation. Detailed analyses show that the MR data can be well reproduced if we assume that the TRS is broken and electrons are magnetically scattered at the bottom surface of Bi_{2}Se_{3} (see Supplementary Note 4), which may be an indication of the presence of MPE in our Bi_{2}Se_{3}/YIG sample. However, we did not detect anomalous Hall effect in our samples, which might be obscured by the bulk conduction of Bi_{2}Se_{3} in the transport measurements.
The H_{eff} of the bilayer samples, again, shows different T evolution than that of the bare YIG in Fig. 3f. H_{eff} built up with decreasing T in bilayers while the H_{eff} of the YIG single layer was T independent and close to zero. Phenomenologically, the H_{eff} resembles the exchange bias field of interlayer exchange coupling in an antiferromagnet/ferromagnet interface. However, we would like to exclude the possibility of exchange bias for the following two reasons. First, as shown in Supplementary Fig. 6, we did not observe shifts of magnetization hysteresis loop which is characteristic of an exchange bias effect^{43}. Secondly, extending the field sweep to reversed applied field, we found that the FMR spectrum was symmetric with respect to the zero applied field, indicating that the direction of H_{eff} followed that of M. The observation is distinct from the magnetization pinning of exchange bias, in which the H_{eff} direction is fixed depending on the interfacial magnetic structure. The fact that H_{eff} existed only in FMR measurement suggests that it comes from spinpumpinginduced spin imbalance at the interface as previously reported^{44}. Through exchange coupling to the magnetic layer, the nonequilibrium spin density 〈S〉_{neq} of the TSS gives rise to fieldlike torque:
where Δ_{ex} is the exchange coupling constant^{45}. STFMR experiments on NiFe/Bi_{2}Se_{3}^{9} and CoFeB/Bi_{2}Se_{3}^{46} showed large T_{FL} comparable to the damplike torque owing to spin–momentum locking of TSS. Since spin pumping is the reciprocal process of STFMR, one can expect that the T_{FL} appears as an exchange effective field in spin pumping. Moreover, we noticed that the T dependence of H_{eff} in Fig. 3f resembles that of T_{FL} in CoFeB/Bi_{2}Se_{3}^{46}, which implies that H_{eff} and T_{FL} share the same origin. Although a large T_{FL} can originate from other systems with strong SOC such as Rashbasplit quantum well state^{45}, which is likely to coexist with the TSS in Bi_{2}Se_{3}/YIG^{47}, the T_{FL} from Rashba state is expected to decrease with decreasing Rashba coefficient at low T^{48}. Here, we highlight that H_{eff} monotonically increased at low T. The unique T dependence of H_{eff} suggests that it is likely to originate from TSS.
Zerofield FMR of Bi_{2}Se_{3}/YIG
Finally, we demonstrated that the TSSmodulated magnetic anisotropy and H_{eff} in Bi_{2}Se_{3}/YIG are strong enough to induce FMR without an applied field H_{ext}, which we term zerofield FMR. Figure 4a displays T evolution of FMR first derivative spectra of Bi_{2}Se_{3}(25)/YIG(15) at f = 3.5 GHz. The spectral shape started to deform when the H_{res}was approaching zero. The sudden twists at H_{ext} ~ + 30 (−30) for positive (negative) field sweep arose from magnetization switching of YIG, and therefore led to hysteric spectra. The two spectra merged at 25 K and then separated again when T was further decreased. Figure 4b shows the microwave absorption intensity I spectra with positive field sweeps. We traced the peak position of I spectrum H_{peak} using the red dashed line, and found it coincided with zero H_{ext} at the zerofield FMR temperature T_{0} ~25 K. Below 25 K, H_{peak} moved across the origin and one needed to reverse H_{ext} to counter the internal effective field comprised of the demagnetization field 4πM_{s}, H_{int}, and H_{eff} (Fig. 4e). It should be pointed out that the presence of H_{int} alone would be inadequate to realize zerofield FMR. Only when H_{eff} is finite would the system exhibit intercepts as we have seen in Fig. 3b. We further calculate T_{0} as a function of microwave excitation frequency f (Fig. 4f) using Eq. (2) and the extracted H_{eff} of Fig. 3f. We obtain that, with finite H_{eff} persisting up to room temperature, zerofield FMR can be realized at high T provided f is sufficiently low. However, we emphasize that it is advantageous for YIG to be microwaveexcited above 3 GHz. When f < 3 GHz, parasitic effects such as threemagnon splitting^{49,50} take place and significantly decrease the microwave absorption in YIG. Here, we demonstrate that the strong exchange coupling between Bi_{2}Se_{3} and YIG gave rise to zerofield FMR in the feasible high frequency operation regime of YIG. Further improvement of interface quality of Bi_{2}Se_{3}/YIG is expected to raise H_{eff} and T_{0} for roomtemperature, field free spintronic application.
Discussion
Most experiments probing the spin transfer or spin–charge interconversion at TSS used FMs as the spin source/detector. The pitfall of FMs is that the constituent transition metals are chemically reactive with chalcogenides. Severe reactions can occur when an FM is deposited on a TI, forming new species that complicated the system under study. Even if an ideal TI/FM interface is achieved, theoretical study suggests that the electron doping from the FM can significantly shift the Fermi level of TIs and destroy the spin texture^{27}. Besides, for SOT generation, currentshunting by FM reduces the current flowing in the TI and diminishes the SOT strength. Therefore, ferromagnetic insulators such as YIG is a far better platform to study the coupling mechanism between TSS and magnetic layers.
We attribute the hightemperature interfacial IMA to the enhanced exchange coupling of Fe^{3+} ions in YIG mediated by TSS based on the d_{BS} dependence of K_{i} in Fig. 2c. We emphasize that, although the model in ref. ^{42} predicts a PMA originated from direct exchange coupling between TSS and a magnetic layer, in reality, other contributions of magnetic anisotropy dependent on the detailed interfacial atomic structure can arise. As illustrated in ref. ^{31}, in addition to the PMA from MPE, the stress anisotropy energy of EuS can also be magnified by the strong SOC of Bi_{2}Se_{3}, which would not necessarily be PMA for a material system other than EuS/Bi_{2}Se_{3}. Other factors such as the Fermi energy of Bi_{2}Se_{3} can have pronounced effects on the exchange coupling constant and total anisotropy energy^{31}. Given the multiple sources of magnetic anisotropy that are possibly influenced by TSS, an indepth theoretical study will be needed to precisely describe the hightemperature interfacial IMA and the emerging lowtemperature PMA of Bi_{2}Se_{3}/YIG.
The TSSmodulated magnetization dynamics presented in this work have important implications. Firstly, the electronic structure of TI/ferromagnetic insulator interface has a pronounced influence on the magnetization dynamics. It should be noted that the strong coupling between the TSS and YIG can potentially modify the TSS of pure Bi_{2}Se_{3}. Since the spin texture of TSS is critical for spin transport, an insertion layer may be needed to decouple YIG and Bi_{2}Se_{3} for spintronics devices. The interface structure, in turn, depends strongly on the sample fabrication process. For example, Wang et al.^{8} reported a markedly different d_{BS} dependence of g_{↑↓} from the one shown in Fig. 2d. Specifically, our samples show larger \(\Delta \tilde \alpha\) when d_{BS} was approaching the 2D limit. Note that the linewidth broadening observed in this work is overall larger than that reported in ref. ^{8} mainly because we have chosen thinner YIG films. The discrepancy in the d_{BS} dependence of g_{↑↓} may be reconciled by the different sample characteristics by comparing the TEM images and the surface morphology of Bi_{2}Se_{3}, etc.
Secondly, although the interface spin structure is of great interest to investigate, it has been difficult to measure with spinpolarized photoemission techniques because of the limited probing depth. Spin pumping provides another route to resolve the problem, since it has proven to be a powerful tool to probe magnetic phase transition of ultrathin films^{40,41}. Here, we extended the concept and used spin pumping to study the MPE in Bi_{2}Se_{3}/YIG. The indicators of MPE are shown in Fig. 3c, d. Further testing of the validity of this method will depend on the improvements in the sample quality, such as a sharper interface and lowering the carrier density of Bi_{2}Se_{3}.
Lastly, the observations of large K_{i}, \(\Delta \tilde \alpha\) at room temperature, and H_{eff} at low temperature in Bi_{2}Se_{3}/YIG echo the theoretical predictions of the magnetization dynamics of a perpendicularly magnetized layer interacting with TSS^{51,52,53}. According to these models, the gap opening of TSS due to broken TRS leads to topological (inverse) spin galvanic effect^{51,52}, anisotropic shifts of FMR frequency^{52}, and anisotropic damping^{53}. Despite the fact that an interfacial PMA showed up at low temperature in Bi_{2}Se_{3}/YIG, the bilayer sample still exhibited a gross inplane anisotropy due to the shape anisotropy of YIG. However, the notable modulation of the YIG properties presented in this work is a promising start to examine these models. We expect ferromagnetic insulators with PMA, such as strained TmIG^{54}, will offer new opportunities to realize the phenomena.
In summary, we have investigated the magnetization dynamics of YIG in the presence of interfacial exchange coupling and TSS of Bi_{2}Se_{3.} The significantly modulated magnetization dynamics at room temperature are shown to be TSSoriginated through the Bi_{2}Se_{3} thickness dependence study. The temperaturedependent study reveals a possible signature of MPE and an emerging PMA that compensates the hightemperature IMA, with a spinpumpinginduced effective field increasing toward low temperature. The underlying mechanism of these phenomena calls for further theoretical modeling and understanding. To our knowledge, this is the first work that links the magnetization dynamics of the magnetic layer to TSS, showing that FMR and spin pumping can be effective techniques to probe the interface magnetic properties. Moreover, the TSSmodulated dynamics are a cornerstone for future investigation on novel physics such as topological inverse spin galvanic effect, and further raise several interesting topics. For example, how the H_{eff}, a quantity that comes from the nonequilibrium process of spin pumping, depends on the spin texture of TSS and the interfacial magnetic anisotropy will be an important question to answer. Temperaturedependent FMR with outofplane setup should provide us with valuable information. Therefore, understanding the interplay between these phenomena and further manipulating them will be a step forward toward developing TIbased spintronics.
Methods
Sample preparation and structural properties
The YIG thin films were deposited on (111)oriented gadolinium gallium garnet (GGG) substrates by offaxis sputtering at room temperature. The GGG(111) substrates were first ultrasonically cleaned in order of acetone, ethanol, and DIwater before being mounted in a sputtering chamber with the base pressure of 2 × 10^{−7} Torr. For YIG deposition, a 2inch YIG target was sputtered with the following conditions: an applied rf power of 75 W, an Ar pressure of 50 mtorr, and a growth rate of 0.6 nm/min. The samples were then annealed at 800 °C with an O_{2} pressure of 11.5 mtorr for 3 h. Supplementary Fig. 1(a) displays the atomic force microscopy (AFM) image of the YIG surface, showing a flat surface with a roughness of 0.19 nm. Supplementary Fig. 1(b) shows the highangle annular darkfield (HAADF) image of YIG/GGG. The YIG thin film was epitaxially grown on the GGG substrate with excellent crystallinity. No crystal defects were observed at the YIG bulk and YIG/GGG interface.
The YIG/GGG samples were annealed at 450 °C in the MBE growth chamber for 30 min prior to Bi_{2}Se_{3} growth at 280 °C. The base pressure of the system was kept about 2 × 10^{−10} Torr. Elemental Bi (7N) and Se (7N) were evaporated from regular effusion cells^{55}. As shown in Supplementary Fig. 3(a), streaky reflection highenergy electron diffraction (RHEED) patterns of Bi_{2}Se_{3} were observed. Supplementary Fig. 3(b) displays the surface morphology of 7 quintuple layer (QL) Bi_{2}Se_{3} taken by AFM. The image shows layerbylayer growth of Bi_{2}Se_{3} with the step heights ~1 nm, which corresponds to the thickness of 1 QL. The surface roughness of our 7 QL Bi_{2}Se_{3} is ~0.28 nm within a layer. The layer structure of Bi_{2}Se_{3} was also revealed by the HAADF image shown in Supplementary Fig. 3(c). Despite the highquality growth of Bi_{2}Se_{3}, an amorphous interfacial layer of ~1 nm formed. The excellent crystallinity of our samples was verified by clear Pendellösung fringes of the synchrotron radiation xray diffraction (SRXRD) data shown in Supplementary Fig. 3(d). The fringes of YIG(444) peak do not show clear changes before and after the growth of Bi_{2}Se_{3}, indicating that the lattice parameter in the normal direction of YIG remains unchanged. To check the lattice parameter of inplane direction, we also performed inplane radial scans of YIG/GGG(22–4) peaks. Supplementary Fig. 3(e) shows that the peaks position measured before and after growing Bi_{2}Se_{3} is perfectly matched, indicating the absence of Bi_{2}Se_{3}induced strains in YIG that might contribute additional magnetic anisotropy^{56}. Supplementary Fig. 3(f) displays the xray reflectivity (XRR) data of our Bi_{2}Se_{3}(6)/YIG(50) sample. From the fit to the data, we extract the Bi_{2}Se_{3} surface roughness and Bi_{2}Se_{3}/YIG interface roughness to be 0.16 nm and 0.22 nm, respectively. Note that the interface roughness of Bi_{2}Se_{3}/YIG is close to that of YIG surface (0.19 nm), which means the interdiffusion at the interface is at minimal, if any.
FMR measurement setup
To investigate the magnetic properties of Bi_{2}Se_{3}/YIG, roomtemperature angle and frequencydependent FMR measurements were performed independently using a cavity and coplanar waveguide, respectively (Fig. 1a, b). For the temperaturedependent FMR, the coplanar waveguide was mounted in a cryogenic probe station (Lake Shore, CPXHF), which enables samples to be cooled as low as 5 K. The external field is modulated for lockin detection in all of the measurements. The modulation amplitude was kept below 1/4 of the FMR linewidth to avoid serious spectral distortions. The microwave source power was no larger than 5 dBm.
Data availability
The experimental data of this work are available from the corresponding authors upon reasonable request.
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Acknowledgements
We would like to thank Prof. Mingzhong Wu, Dr. Hsin Lin, and Dr. Tao Liu for their helpful discussion. We would also like to thank Dr. Jauyn Grace Lin for her technical support and Dr. ChienTing Wu for the TEM analyses. The work is supported by MoST 1052112M007014MY3, 1062112M002010, 10626228002001, and 1052112M001031MY3 of the Ministry of Science and Technology in Taiwan.
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Y.T.F. designed the experiment, collected the FMR data, and analyzed the data. K.H.M.C., C.C.T., C.C.C., and C.N.W. fabricated the samples. C.K.C. performed the XRD measurements and S.R.Y. performed the transport measurements. S.F.L. provided scientific supports. J.K. and M.H. supervised the project. Y.T.F. and J.K. wrote the manuscript with the comments of all the authors.
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