Cavity mediated manipulation of distant spin currents using cavity-magnon-polariton
Lihui Bai, Michael Harder, Paul Hyde, Zhaohui Zhang, Can-Ming Hu, Y. P. Chen, John Q. Xiao
CCavity mediated manipulation of distant spin currents using cavity-magnon-polariton
Lihui Bai, ∗ Michael Harder, Paul Hyde, Zhaohui Zhang, and Can-Ming Hu
Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
Y. P. Chen and John Q. Xiao
Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA (Dated: June 2, 2017)Using electrical detection of a strongly coupled spin-photon system comprised of a microwavecavity mode and two magnetic samples, we demonstrate the long distance manipulation of spincurrents. This distant control is not limited by the spin diffusion length, instead depending on theinterplay between the local and global properties of the coupled system, enabling systematic spincurrent control over large distance scales (several centimeters in this work). This flexibility opensthe door to improved spin current generation and manipulation for cavity spintronic devices.
In spintronic devices information is carried by spin cur-rent, rather than charge current, and therefore informa-tion processing requires precise spin current manipula-tion. For this purpose Datta and Das [1] proposed thespin field-effect-transistor in which spin current is manip-ulated by a gate voltage via a local spin-orbit interactionin a semiconductor channel [2]. On the other hand the ex-change interaction is also commonly used to manipulatespin current. For example, the production of spin cur-rent can be realized via the spin-polarization of a chargecurrent in ferromagnetic materials and spin current canalso be absorbed by a local magnetization through spintransfer torque [3–6]. Devices exploiting either spin-orbitor exchange interactions for spin current control are typ-ically limited by the ∼ µ m spin diffusion length whichdepends on the spin-flip scattering time. Although thisis much larger than the ∼ nm range of the interactionsthemselves, a long distance ( (cid:29) µ m) spin manipulationwould be beneficial for spintronic applications. For exam-ple, the microwave power generated in spin valves due tospin transfer torque driven dynamics [7] could be greatlyenhanced using a long distance spin-interaction by en-abling phase-locking of several spin systems.In the field of cavity quantum electrodynamics thecorrelation of two distant ”atomic resonators” has al-ready been demonstrated using long range photon medi-ated interactions [8–11]. Such interactions are typicallyon the order of the photon wavelength and are there-fore much larger than those of either spin-orbit or ex-change interactions, approaching the limit of the spindiffusion length in optical systems with much larger cor-relations possible in microwave analogues. The recentobservation of strong magnon-photon coupling in ferro-magnetic/microwave cavity structures [12–16] opens thedoor to apply such photon mediated interactions in mag-netic systems to manipulate the magnetization and spincurrent [17–19].In this work, we experimentally studied the microwavemediated interaction between two magnetic systems,demonstrating spin current manipulation over a distanceof several cm. Using an electrical detection technique we are able to locally detect the spin currents in each mag-netic system via the spin pumping effect [16]. Althoughthe cooperativity of only one magnetic system was con-trolled, we find a simultaneous change in the spin currentof another magnetic system which is well separated andnot directly tuned. In this sense, we realized the manip-ulation of distant spin currents using the cavity-magnon-polariton. Control of the cooperativities is the key tosuch a cavity-mediated interaction and a coupling modelincluding both magnetic samples and a cavity mode isused to clearly highlight the effect of each photon-magnoncooperativity and to interpret the experimental observa-tions. This work offers a new way to coherently controlspin current and magnetization dynamics both directlyand over long distances, which we expect to play an im-portant role in the development of cavity spintronics.In our experiment we chose two pieces of yttrium irongarnet (YIG) on GGG substrates as the two magneticsystems due to their low Gilbert damping and low eddycurrent dissipation. The two nearly identical YIG sam-ples had dimensions of 10 mm × × µ m, asaturation magnetization of µ M s = 160 mT, a Gilbertdamping of α = 3 . × − and a Gyromagnetic ratioof γ = 27.6 × πµ GHz/T. An externally applied mag-netic field H determined the ferromagnetic resonance(FMR) frequency according to the Kittel equation ω r as ω r = ( ω + ω ω m ) / . Here, ω = γH and ω m = γM .The microwave magnetic field ( h ) driven magnetization( M ) precession, governed by the Landau-Lifshitz-Gilbert(LLG) equation, produced a non-equilibrium magneti-zation which generated a spin current through diffusion[20]. For the electrical detection of this spin current, plat-inum (Pt) strips were deposited on top of each piece ofYIG with a dimension of 10 mm × ×
10 nm. In thePt strips the spin currents were electrically detected byconversion into charge currents via the inverse spin Halleffect (ISHE). The spin current I s pumped by each sam-ple is linearly proportional to the voltage V SP detectedvia the ISHE, V SP ∝ I s ∝ Im ( m ∗ x m y ) [21] where m x and m y are the dynamical components of the magnetizationin each sample. a r X i v : . [ c ond - m a t . m t r l - s c i ] J un (a)−200 −100 0 100 200(b)−−V µ V θ = o θ = o θ = o θ = o θ = o V µ H (mT) −200 −100 0 100 200(c)−−V µ V θ = o θ = o θ = o θ = o θ = o µ H (mT) ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● . . . (d) M m h θ I s1 θ (degree) I s ( a . u . ) ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● . . . (e) θ (degree)I s2 FIG. 1. (Color online) Directly controlled spin current fromYIG1 and long distance manipulation of spin current fromYIG2. (a) Two YIGs coupled to a microwave cavity. Bytuning the YIG1 cooperativity, the YIG1 spin current wastuned. (b) The YIG1 voltage signal depends directly on theangle θ , which controls cooperativity of YIG1, while (c) thevoltage on YIG2 is also tuned by θ . The spin currents fromYIG1 and YIG2 as a function of angle θ are summarized in(d) and (e) respectively. To couple the magnetic samples, a cylindrical mi-crowave cavity made of oxygen-free copper was fabricatedwith a diameter of 36 mm and a height of 10 mm. Thecavity is designed to have a TM mode at ω c / π =6.34 GHz. The TM mode is chosen due to its wellsuited field profile with a microwave electric field alongthe cylindrical axis and a microwave magnetic field sur-rounding the electric field flux. This mode has an un-loaded damping of β = 0.0003 (Q = 1670). Denoting themicrowave magnetic field by h and the driving microwaveamplitude by h , the cavity mode frequency profile canbe written as h = ω h / ( ω − ω c + 2 iβω c ω ). Here, ω isthe microwave frequency.One of the YIG/Pt samples (labelled as YIG1) wasplaced on the lid of the cavity while another YIG/Pt sample (labelled as YIG2) was fixed on the bottom. Theexternal magnetic field H was applied in-plane for bothmagnetic samples and perpendicular to the Pt strip ofYIG2 in order to detect the maximum spin pumping sig-nal via the ISHE. The position of YIG1 with respect tothe microwave magnetic flux inside of the cavity was con-trolled by rotating the lid with the angle θ denoting theangle between the external magnetic field H and the localmicrowave magnetic field h at YIG1 as shown in Fig. 1(a). With only YIG1 loaded, the cavity mode frequencywas red shifted by 3% to 6.155 GHz while the dampingincreased to β = 0 . ω c = 5.960 GHzwith a damping of β = 0 . θ changed the cavity mode frequencyby less than 1% (much less than the shift due to loadingboth samples) and therefore this shift is not consideredin the detection and calculation of the spin currents. Thecoupling between the YIG samples and the cavity modewas characterized by measuring the microwave transmis-sion using a vector network analyzer (VNA) [12–16] whileelectrical detection was performed using a lock-in tech-nique with frequency modulation of 8.33 kHz [16] withspin pumping voltages on both YIG1 and YIG2 measuredsimultaneously.Spin currents were detected on both YIG1 and YIG2by sweeping the magnetic field H at a microwave fre-quency of 6 GHz, slightly detuned from the cavity modefrequency ω c . The microwave output power was 100 mW.As shown in Fig. 1 (b) and (c), the voltage signals haveLorentz line shapes and are anti-symmetric about themagnetic field H as expected for spin pumping voltages[22]. Rotating the angle θ from 0 ◦ to 90 ◦ by rotatingYIG1, the torque exerted on the magnetization of YIG1by the local microwave magnetic field was significantlyenhanced. Consequently, the amplitude of the spin cur-rent pumped by YIG1 is increased as shown in Fig. 1(b). Simultaneously the spin current pumped by YIG2was also detected as θ was tuned. Figure 1 (c) shows aclear systematic change of the spin current pumped byYIG2, even though YIG2 was spatially separated fromYIG1 and was not tuned directly. Contrary to the in-crease of spin current in YIG1, the amplitude of spincurrent from YIG2 decreases as θ is increased from 0 ◦ to90 ◦ .By adopting a Pt spin Hall angle of 0.0023 [22] to de-termine the ISHE coefficient, the detected voltages wereconverted to spin currents. The spin currents measuredfrom both magnetic samples are summarized in Fig. 1 (d)and (e) respectively. These panels systematically demon-strate the θ -dependence of the spin pumping voltages in-duced by the ISHE. Note that since the external mag-netic field H was not rotated during the measurement,the spin currents from both samples maintain the samesign. We found that YIG1 and YIG2 spin currents are µ H (mT)
145 155 165 175 ω π ( G H z ) . . . . θ = o YIG (b) |S | µ H (mT)
145 155 165 175 θ = o YIG (c) |S | µ H (mT)
140 150 160 170 ω π ( G H z ) . . . θ = o YIG + YIG (d) |S | µ H (mT)
140 150 160 170 θ = o YIG + YIG (e) |S | ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● θ (degree) C ( θ ) (a) FIG. 2. (Color online) (a) The cooperativity in a single YIGand cavity system is measured as a function of θ with a cal-culation according to Eq. (2). A microwave transmission S measurement of the ω − H dispersion is plotted for θ = 0 ◦ and 90 ◦ in (b) and (c) respectively. (d) and (e) display thetransmission for the cavity mode with both YIG1 and YIG2loaded at YIG1 angles of θ = 0 ◦ and 90 ◦ respectively. both strongly dependent on the angle θ with I s havinga | sin θ | dependence with the inverse behaviour shownby I s ; that is a maximum I s signal will correspond toa minimum I s signal and vice versa. Thus Fig. 1 il-lustrates the key experimental features demonstrating along distance manipulation of the spin current on YIG2by controlling the coupling between YIG1 and the cavitymode.The solid curves which are shown in Fig. 1 (d) and (e)have been calculated using a model of strongly coupledcavity-magnon-polaritons. To understand the manipu-lation of distant spin currents, we may start by under-standing the controllable coupling between one YIG anda cavity mode. In the linear coupling regime all mod-els of such strongly coupled systems reduce to that oftwo coupled oscillators, one representing the cavity modeand the other YIG FMR mode, with coupling strength κ [12–14, 16]. By defining the detuning parameters∆ c ≡ ( ω − ω c ) / (2 βω c ω ) and ∆ r ≡ ( ω − ω r ) / (2 αω r ω )and a cooperativity C ≡ κ ω m / (4 αβω c ), the normal mode dispersion and spin current are, respectively,∆ c ∆ r = 1 + C (1a) I s ∝ C (∆ c + ∆ r ) (1b)Strong coupling is defined as C > ω − H dis-persion and displays an anti-crossing when the coopera-tivity is nonzero, showing that the normal modes of theFMR/cavity system are only supported when both de-tunings, ∆ c and ∆ r , are inversely proportional. The keyto our technique for long distance control is that the dis-persion determined by Eq. (1a) is a global property ofthe coupled system (which can be measured through bothVNA and electrical techniques) while the spin current ofEq. (1b) depends both on the local properties throughthe cooperativity and the global properties through thedetunings ∆ c + ∆ r . Furthermore the spin current can be locally measured through electrical detection, enablingmultiple samples to be individually detected.The spin current can be directly controlled by tuningthe cooperativity and since the cooperativity depends onthe filling factor, this can be done by either changingthe number of spins in the magnetic material [12, 13] orchanging the local field distribution [14, 16]. By rotatingthe sample we can change the microwave magnetic fieldtorque on the magnetization and therefore C = C ( θ ) ∝ sin θ (2)Experimental results of the cooperativity as a functionof angle θ are summarized in Fig. 2 (a) (solid circles)and compared to the prediction of Eq. (2) (solid curve).Figures 2 (b) and (c) display the global ω -H dispersion ina microwave transmission spectrum S . When the coop-erativity C is close to 0, at θ = 0 ◦ , the maximum ampli-tude of | S | remains at the uncoupled cavity mode fre-quency ω c for all H , indicating the diminished coupling inthis configuration. However when the cooperativity is in-creased by setting θ = 90 ◦ , a clear anti-crossing feature isobserved near the crossing of the uncoupled cavity modeand the FMR dispersion, denoted by dashed lines respec-tively. This dispersion agrees well with the solid curveswhich are calculated based on Eq. (1a). With both mag-netic samples loaded, the microwave transmission S inFig. 2 (d) and (e) again shows that the dispersion canbe tuned by changing θ for YIG1. This illustrates howthe global properties of the coupled system will dependon the local tuning of one ferromagnetic sample. We em-phasize that the ω − H dispersion can be measured usingmicrowave transmission as shown here, or using electri-cal detection. However, the electrical detection methodalso allows us to locally detect the spin current of indi-vidual magnetic samples which is not possible throughmicrowave transmission.When two samples with a nearly identical resonanceresponse are placed inside the cavity, we can write thenormal mode dispersion and the spin current in YIG1and YIG2 as, respectively,∆ c ∆ r = 1 + C ( θ ) + C (3a) I s ∝ C ( θ )(∆ c + ∆ r ) (3b) I s ∝ C (∆ c + ∆ r ) (3c)Intuitively, as indicated by Eq. (3a), the dispersion oftwo magnetic samples (with the same FMR frequency)coupled to a cavity mode differs from Eq. (1a) only bythe sum of the cooperativities. This pattern holds forany number of magnetic samples. This feature explainsthe coupling strength enhancement between Fig. 2 (d)and (e) due to the increased number of spins. Further-more, the amplitude of the spin current produced in eachmagnetic sample, given by Eqs. (3b) and (3c) follows thesame structure as Eq. (1b). The only implicit differenceis that the detunings now satisfy a modified dispersiondepending on all cooperativities and therefore differ fromthe case of a single YIG sample.Figure 3 (a) and (b) shows the cavity-FMR detuning(∆ c − ∆ r ) dispersion following Eq. (3a) with the colorgradient indicating the spin current amplitudes for I s and I s respectively. The difference in color gradientbetween panels (a) and (b) highlights the difference be-tween the direct and long distance tuning respectively.Two normal modes are only excited when the detun-ings are either both positive or both negative. Basedon Fig. 3 (a) and (b) we can summarize the spin currentfeatures in such a coupled system as follows: (1) Thenormal modes of the coupled system rely on the sumof cooperativities of all magnetic samples with the cou-pling strength increasing when more magnetic samplesare added. (2) The spin current pumped by each mag-netic sample depends on both the global properties of thenormal mode detunings and the local cooperativity withthe cavity mode. (3) The amplitude of the spin currentfrom YIG1 (the directly tuned sample) is increased byincreasing C while the amplitude of spin current fromYIG2 (the distant sample) is decreased by increasing C .For comparison with the experimental observation wherewe measured the spin current by sweeping the magneticfield at a given microwave frequency (a fixed cavity modefrequency detuning of ∆ c = 7 . θ is increased from 0 ◦ to 90 ◦ . Along the arrow theamplitudes of both spin currents are plotted as a function ∆ c − − C ( θ ) increasing(a) |I s1 | (a.u.)0 0.24 ∆ c − − ∆ r−10 −5 0 5 10C ( θ ) increasing(b) |I s2 | (a.u.)0 0.24 C | I s | ( a . u . ) . . |I s1 |(c) C ( θ ) s2 | FIG. 3. (Color online) Following Eq. 3, the dispersion andamplitudes of both spin currents are plotted in (a) and (b) asa function of cooperativity C ( θ ). The color scales indicatethe amplitudes of both spin currents I s and I s while thegreen arrows indicate the change of C ( θ ) by tuning the angle θ . Along the arrows at a given cavity frequency detune ∆ c ,the amplitudes of both spin currents I s and I s are plottedas a function of the C in (c). of the C in (c). The solid curves in Fig.1 are I s | sin θ | and I s calculated from Eqs. (3b) and (3c), respectively.The factor of | sin θ | arising from the rotation of YIG1with respect to the magnetic field H due to the ISHEin the Pt layer. The agreement between experiment andmodel indicates that our long distance manipulation ofspin current in YIG2 is due to the cooperativity controlof YIG1. Therefore control of the cooperativities allowsus to control the dispersion of the strongly coupled sys-tem and thereby directly and remotely control the spincurrent amplitude in both samples simultaneously.In summary, we have electrically detected spin currentsfrom two YIG/Pt samples which both couple to a cav-ity mode. Via such a local detection technique we areable to distinguish the spin dynamics in each sample in-dividually and demonstrate the manipulation of distantspin currents, whereby controlling the cooperativity ofone magnetic sample will manipulate the spin currentin another sample well separated from the first. Sucha long distance manipulation originates in the local spincurrent dependence on the global coupling properties andthe ability to locally detect the spin system through elec-trical detection. 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