Switching magnon chirality in artificial ferrimagnet

Chirality, an intrinsic degree of freedom, has been barely exploited as the information carriers in data transmission, processing, computing, etc. Recently the magnons in antiferromagnets were proposed to carry both right-handed and left-handed chiralities, shedding a light on chirality-based spintronics in which chirality-based computing architectures and chiral magnonic devices may become feasible. However, the practical platform for chirality-based spintronics remains absent yet. Here we report an artificial ferrimagnetic Py/Gd/Py/Gd/Py/Pt multilayer by which the switching, reading, and modulation of magnon chirality are demonstrated. In particular, the coexisting resonance modes of ferromagnetic and antiferromagnetic characteristics permit the high adjustability and easy control of magnon chirality. As a main result, we unambiguously demonstrated that Py precessions with opposite chiralities pump spin currents of opposite spin polarizations into the Pt layer. Our result manifests the chirality as an independent degree of freedom and illustrates a practical magnonic platform for exploiting chirality, paving the way for chirality-based spintronics.


Supplementary Note 2. The critical field (Htwist) at T > TM
Supp. The in-plane magnetization of Py(2.5 nm)/Gd(3 nm)/Py(2.5 nm)/Cu(6 nm) sample was studied at different temperatures. Supp. Fig. 2 (a) shows a typical hysteresis loop at T = 60 K. Twisted state is initialized at the critical field (Htwist). The temperature dependence of in-plane magnetization at H = 1000 Oe reveals the compensation temperature TM = 30 K of this sample (Supp. Fig. 2 (b)). According to the temperature evolution of Htwist shown in Supp. Fig. 2 (c), Gdaligned phase (region I) and twisted state (region II) as well as Py-aligned phase (region III) can be obtained by tuning the temperature and external field H. According to Fig. 2(c) and Supp. Fig. 2 (c), Py-aligned phase is always favorable for T ≫ TM unless applying an extremely large magnetic field. On the contrary, the temperature evolution of Htwist for T < TM is always sluggish with respect to that for T > TM. Such strong asymmetry in the temperature evolution of Htwist for T < TM and T > TM has been reported in Fe/Gd multilayer, which is due to the energy difference in the surface twisting and the bulk twisting of Fe (or Py) moments and Gd moments [3]. Htwist rises less abruptly in Py/Gd/Py sample than in Py/Gd/Py/Gd/Py sample, indicating a less rigid ferrimagnetic order in Py/Gd/Py trilayer. Thus we could produce an even more rigid ferrimagnetic order by increasing the repetition number of Py/Gd multilayer. It's worth noting that the monotonic decline of Htwist is synchronized with the reduction of the total magnetization when approaching TM, owing to the spinflop transition near TM 4 .
As shown in (b), the minimum number of stacks is Py/Gd/Py trilayer to achieve the Gd-aligned phase. The Py/Gd/Py/Gd/Py multilayer shows more well-defined compensation magnetization with respect to Py/Gd/Py trilayer. And Gd-aligned phase is not accessible in Py/Gd bilayer.  (6) sample (in nm) was measured at 1000 Oe in the temperature range between 20 and 150 K. The compensation temperature TM = 60 K was depicted in Supp. Fig. 3 (a). The Hall resistance of this sample was measured as a function of the out-of-plane (OOP) magnetic field. After the linear fitting of ordinary Hall effect (OHE) at high magnetic field (between 8 T and 9 T), we subtracted OHE from the signals and obtained the Hall resistance solely caused by anomalous Hall effect (AHE) RAHE. It has been widely accepted that AHE of rare-earth-transition-metal ferrimagnet is governed by the transition metal [5]. RAHE is proportional to the OOP component of the transition-metal magnetization. The 4f shell, which dominates the magnetic properties of rare-earth metal, is located far below the Fermi level [6].

Supplementary Note 3. The reversal polarity of anomalous Hall resistance at TM
As shown in Supp. Fig. 3 (b), the polarity of RAHE is reversed exactly at TM = 60 K, unambiguously confirming the reversal of Py magnetization with respect to the external magnetic field across TM. The compensation temperature TM concretely manifests the transition between Pyaligned phase and Gd-aligned phase. RAHE is not fully saturated in Supp. Fig. 3 (b) because the easy magnetization direction of this sample is in the sample plane. Py magnetic moment is oblique to the normal direction during the RAHE measurements.

Supplementary Note 4. Quantitative measurements of spin pumping
Supp. Fig. 4: Angular dependence of Vsym and Vasym (a) at T = 300 K and (b) at T = 10 K. The quantitative fittings were carried out by taking SRE into consideration. (c) Angular dependence of Hres at T = 300 K. The resonance field Hres is isotropic against θPy. The microwave frequency f is fixed at 13 GHz in these measurements.
The pure spin current across Py/Pt interface of the Py/Gd multilayer sample was generated and studied through spin pumping, recording the voltage signals V(H) by sweeping in-plane magnetic field (H). In order to distinguish the spin pumping voltage signals Vsp from Spin Rectification Effect (SRE), such as anisotropic magnetoresistance (AMR) and anomalous Hall effect (AHE), we carried out angular dependent measurements of V(H) signals following the conventional method in literatures [7,8].
V(H) signals are fitted by the combination of symmetric Lorentzian curve and antisymmetric Lorentzian curve.
Where Vsym and Vasym are the amplitude of symmetric curve and antisymmetric curve, respectively. Hres is the resonance field and ∆H is the linewidth corresponding to a half-width at half-maximum (HWHM). Figure 3(d) and (e) show the best fitting of V(H) signals at T = 300 K and T = 10 K, respectively. ∆H is ~ 150 Oe at 300 K and ~ 500 Oe at 10 K (f = 13 GHz), which is comparable with the literatures' results. A broader linewidth ∆H is observed at T = 10 K with respect to that at T = 300 K, due to the enhanced magnetic damping at low temperature. Such enhancement of magnetic damping originates from the significant magnetostriction of Gd film, while Gd has null magnetocrystalline anisotropy because of its null orbital moment [9,10]. We can also extract the Gilbert damping parameter which is 0.012 for Cu capping sample where spin pumping doesn't occur at Py/Cu interface. This value is in excellent agreement with the values reported in literatures. Angular dependences of Vsym and Vasym at T = 300 K and T = 10 K are plotted in Supp. Fig. 4(a) and (b). To extract the Vsp signals quantitatively, SRE induced by AMR and AHE are taken into account during the fitting.
Where Vsp is the spin pumping signals due to the pure spin current. and are the symmetric components induced by AHE and AMR, respectively. and are the antisymmetric components induced by AHE and AMR, respectively. θM is the azimuthal angle of magnetization. The Py/Gd multilayer is a polycrystalline film sample, magnetic anisotropy is expected to be absent in this system. This statement is supported by the isotropic angular dependence of Hres at T = 300 K (Supp. Fig. 4(c)). Thus θM is equivalent to the azimuthal angle of external field θH in our measurements. Specifically, θPy equals θH at T = 300 K and θH -180° at T = 10 K. For T = 300 K, the best fitting of Vsym yields Vsp = 282 nV, = -71 nV, = 31 nV, and = -85 nV, = 26 nV of Vasym fitting. The fitting results for T = 10 K are the following: Vsp = -371 nV, = -91 nV, = 23 nV, and = 85 nV, = -24 nV. It's worth mentioning that Vsp signal and SRE signal add up destructively at T = 300 K and constructively at T = 10 K, therefore Vsp is slightly higher than Vsym at T = 300 K and lower than Vsym at T = 10 K.
In light of Py-aligned phase at T = 300 K and Gd-aligned phase at T = 10 K, the Vsp signals against θPy have the opposite polarities in spite of the same MPy orientations. Thus we can conclude that the Vsp polarity of spin pumping is determined by the chirality of spin precession rather than the spin orientation. In addition, the microwave power Papp applied on the sample is Papp = 3.5 mW for T = 300 K and Papp = 4.5 mW for T = 10 K. Thus the spin pumping efficiency Vsp/Papp are comparable at these two temperatures. It's worth mentioning that the phases of SRE signals are opposite for T = 300 K and T = 10 K, as the result of the phase shifting between the precessional component of MPy and the induction current. To our surprise, the phase of induction microwave current can be modified by varying the temperature, which requires the further investigation in future.
Supp. Supplementary Figure 5(b) plots the Vsp signals against the microwave power Papp applied on the sample at T = 300 K. The linear dependence presented here rules out the possible nonlinear damping in our experiments [11]. This statement is further supported by Supp. Fig. 5(c) that the linewidth ∆H is barely changed versus Papp. The Vsp signals are generated as the result of the uniform MPy precession in the outermost Py layer.

Supplementary Note 5. Spin Rectification Effect and self-pumping in Py/Gd multilayer
Supp. Fig. 6: Spin pumping V(H) data of (a) Al2O3/Py/Gd/Cu, (b) Al2O3/Cu/Gd/Py/Cu and (c) Al2O3/Py/Gd/Py/Cu samples at 13 GHz. The line shape of V(H) data was fitted by symmetric Lorentzian curve for Al2O3/Py/Gd/Cu (green peak in (a)) and Al2O3/Cu/Gd/Py/Cu (cyan peak in (b)). The red fitting curve in (c) exhibits the superposition of two V(H) signals with opposite sign from Py/Gd and Gd/Py bilayers. The compensated self-pumping was observed in Al2O3/Py/Gd/Py/Cu. The voltage signals V(H) were mainly attributed to the spin pumping at Py/Pt interface and inverse spin Hall effect (ISHE) of Pt layer. However, it has been well studied that spin pumping signals can be contaminated by Spin Rectification Effect (SRE) [7], including anisotropic magnetoresistance (AMR) and anomalous Hall effect (AHE) [8,12 ]. In addition, ferromagnetic metal alone may produce a voltage signal via self-pumping [13 ]. To evaluate and exclude the possible contributions of SRE or self-pumping, we measured V(H) of several control samples without Pt electrode at room temperature. Supplementary Figure 6 (a) shows the voltage signal V(H) of Al2O3/Py/Gd/Cu sample. The negative V(H) was observed when sweeping in-plane magnetic field, which may result from SRE or self-pumping in Py/Gd bilayer sample. On the contrary, the positive V(H) of a smaller magnitude was observed in Al2O3/Cu/Gd/Py/Cu sample (Supp. Fig. 6 (b)). According to the opposite sign of V(H) shown in Supp. Fig. 6 (a)  To further demonstrate the compensated self-pumping of Py/Gd multilayer, we measured V(H) of several control samples at different microwave frequencies (11 GHz, 12 GHz, 13 GHz and 14 GHz). The opposite sign of V(H) in Py/Gd and Gd/Py bilayers was further confirmed, which was independent of the microwave frequencies. The tiny negative double-peak was observed in Al2O3/Py/Gd/Py/Cu sample, and such negative double-peak became further small and negligible in Al2O3/Py/Gd/Py/Gd/Py/Cu sample except for that at 14 GHz. The visible V(H) signal with the magnitude of 45 nV at 14 GHz established the upper limit of SRE voltage signal in this sample (Supp. Fig. 7 (d)). In consequence, the spin pumping voltage signals Vsp in Al2O3/Py/Gd/Py/Gd/Py/Pt sample were mainly attributed to the spin pumping at Py/Pt interface and inverse spin Hall effect (ISHE) of Pt layer. The compensated self-pumping was achieved in Py/Gd multilayers without Pt electrode.
Our Py/Gd multilayer samples were in Py-aligned phase at room temperature while MPy was much larger than MGd. Thus spin pumping from Py into Gd is expected to dominate self-pumping of Py/Gd multilayers. However, in light of the non-zero spin Hall angle of Py, the spin current backflow from Gd into Py should be taken into consideration as well [14]. The further investigation is required for the deep understanding of self-pumping in Py/Gd multilayers, which is beyond the scope of this work.
The visible V(H) signal is ~ 45 nV at 14 GHz for Al2O3/Py/Gd/Py/Gd/Py/Cu sample (Supp. Fig. 7 (d)). The angular dependence of this V(H) signal is presented in Supp. Fig. 8. The Vsym and Vasym signals have the same phase and similar amplitudes. The quantitative fitting yields the following results = -72 nV, = 27 nV and = -60 nV, = 18 nV, in accordance with the SRE signals obtained for Al2O3/Py/Gd/Py/Gd/Py/Pt sample (Supp. Fig. 4 (a)). According to these observations, the capping layer (Pt or Cu) has little impact on the SRE signals of Py/Gd multilayer, the SRE in this system is a bulk effect and dominated by the ferromagnetic multilayer. The SRE V(H) signal has the critical dependence on the microwave frequency (visible at 14 GHz and negligible at 13 GHz), which is an interesting topic and requires the further investigation in future.
To manifest SRE signals for the scenario where both FMR mode and exchange mode exist, we measured the V(H) signals of the Py/Gd multilayer (T = 20 K and f = 14 GHz) with Pt capping layer and Cu capping layer, respectively (Supp. Fig. 9 (a) and (b)). The Vsp signals govern the V(H) signals of the Pt capping sample, while the V(H) signals of the Cu capping sample are fully determined by SRE. The V(H) signals are normalized by the microwave power Papp applied on the samples. According to the quantitative fitting of V(H) signals at T = 10 K, the V(H) signals of FMR mode are mainly attributed to spin pumping signals Vsp, which is also true for other temperatures.
As shown in Supp. Fig. 9 (a) Fig. 9(c)). The SRE signals are dominated by Vasym component at 12 GHz and 14 GHz, and by Vsym component at 16 GHz. Meanwhile, the magnitudes of SRE signals are ~ 10 nV/mW at 12 GHz, ~ 25 nV/mW at 14 GHz and ~ 13 nV/mW at 16 GHz, all of which are one order of magnitude smaller than the V(H) signals of Pt sample ( Fig. 4(a)) and depend nonmonotonically on frequency. In analogy with the V(H) signals at T = 20 K, the SRE signals at T = 30 K cause a Vasym component of V(H) signals at 12 GHz and 14 GHz, and a minor V sym component at 16 GHz. Consequently, we can reach a qualitative conclusion that the V(H) signals of exchange mode in Pt capping sample are mainly attributed to the pure spin current due to spin pumping, SRE signals make the minor contributions to V(H) signals. It's worth mentioning that the quantitative evaluation of the Vsp signal of exchange mode is very challenging due to the coexistence of FMR mode and exchange mode. The superimposed V(H) lineshapes of FMR mode and exchange mode make the quantitative fitting impracticable. The magnetic system with the well separated FMR mode and exchange mode is desirable to reach such quantitative fitting.