Control of the Bose-Einstein Condensation of Magnons by the Spin-Hall Effect
Michael Schneider, David Breitbach, Rostyslav Serha, Qi Wang, Alexander A. Serga, Andrei N. Slavin, Vasyl S. Tiberkevich, Björn Heinz, Bert Lägel, Thomas Brächer, Carsten Dubs, Sebastian Knauer, Oleksandr V. Dobrovolskiy, Philipp Pirro, Burkard Hillebrands, Andrii V. Chumak
aa r X i v : . [ phy s i c s . a pp - ph ] F e b Control of the Bose-Einstein Condensation of Magnons by the Spin-Hall Effect
Michael Schneider, ∗ David Breitbach, Rostyslav Serha, Qi Wang, Alexander A. Serga, AndreiN. Slavin, Vasyl S. Tiberkevich, Bj¨orn Heinz, Bert L¨agel, Thomas Br¨acher, Carsten Dubs, SebastianKnauer, Oleksandr V. Dobrovolskiy, Philipp Pirro, Burkard Hillebrands, and Andrii V. Chumak Fachbereich Physik and Landesforschungszentrum OPTIMAS,Technische Universit¨at Kaiserslautern, D-67663 Kaiserslautern, Germany Faculty of Physics, University of Vienna, A-1090 Vienna, Austria Department of Physics, Oakland University, Rochester, MI, USA INNOVENT e.V. Technologieentwicklung, Jena, Germany (Dated: February 2021)Previously, it has been shown that rapid cooling of yttrium-iron-garnet/platinum (Pt) nano struc-tures, preheated by an electric current sent through the Pt layer leads to overpopulation of a magnongas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Halleffect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnonsdepending on the electric current and applied field orientations. Here we demonstrate that the in-jection or annihilation of magnons via the SHE can prevent or promote the formation of a rapidcooling induced magnon BEC. Depending on the current polarity, a change in the BEC thresholdof -8% and +6% was detected. These findings demonstrate a new method to control macroscopicquantum states, paving the way for their application in spintronic devices.
The formation of a Bose-Einstein condensate (BEC)can be achieved by a decrease in the temperature forreal-particle systems [1], or in a quasi-particle system bythe injection of bosons resulting in an increase in thechemical potential. The latter has been demonstratedexperimentally for exciton-polaritons [2, 3], photons [4, 5]or magnons [6–12]. In the case of magnonic systems theinjection was realised by the parametric pumping mecha-nism [9–11, 13], allowing for the injection of a large num-ber of magnons at a given frequency, via the spin-Seebeckeffect [14] or by the mechanism of rapid cooling, as it wasshown recently [15]. The method of rapid cooling makesuse of the application of a DC heating pulse and the sub-sequent rapid cooling of yttrium iron garnet (YIG)/Ptnano structures. The heating generates a high popula-tion of magnons being in thermal equilibrium with thephononic system. A rapid decrease in the phononic tem-perature results in the break of the equilibrium. Sincethe lifetime of magnons is larger than the phonon cool-ing rate in the experiment an overpopulation of magnonsover the whole magnon spectrum is generated. This over-population results in a redistribution of magnons fromhigher to lower energies. In this way, if the temperatureof the heated YIG film is high enough and the coolingprocess is fast enough, the magnon chemical potential isincreased to the minimal energy of the magnon systemand the BEC formation process is triggered.In the previous experiments, a Pt or Al layer was usedto heat the YIG nano structure [15]. For a Pt heater anadditional generation of a spin-polarized current trans-verse to the YIG/Pt interface due to the spin Hall effect(SHE) is expected [16–19]. The resulting spin currentis known to act on the magnetization dynamics in theYIG via the spin transfer torque (STT) [20–25]. TheSHE-STT contribution, which can be easily checked bythe variation of the current polarity with respect to the magnetization orientation in the YIG film [22], was notobserved in the original experiments [15]. The reason wasthe large YIG film thickness of 70 nm (STT is an inter-face effect) and the high quality of the Pt layer grown bymolecular beam epitaxy that results in a small spin Hallangle [26].Here, we investigate a similar structure but with asmaller YIG film thickness of 34 nm [27] and with thePt layer deposited by a sputtering technique to achievea pronounced SHE-STT effect. Using such YIG nanostructures, we are now able to investigate the influenceof the SHE-STT effect on the formation of the magnonBEC by rapid cooling. We show that the magnons an-nihilated or injected by the STT effect while the currentpulse is applied, strongly influence the threshold of theBEC formation.Figure 1 shows the structure under investigation and asketch of the experimental setup. The structure consistsof a 2- µ m-wide YIG/Pt stripe (34 nm/7 nm) on a (111)gadolinium gallium garnet (GGG) substrate. The YIGstructure was fabricated using electron-beam lithographywith subsequent argon-ion milling [28]. Afterwards a 3- µ m-long Pt layer was deposited on the waveguide using aRF-sputtering technique. To establish electrical contactsto the platinum pads, Ti/Au-leads (10 nm/150 nm) witha distance of 2 µ m between the inner edges were fabri-cated by electron beam evaporation. In the presentedexperiments DC pulses of a duration of τ P = 100 nsare applied to the Pt pad. Standard ferromagnetic res-onance (FMR) measurements were performed on tworeference pads on the same sample, one bare and onecovered with platinum. These yielded Gilbert-damping-constants of α YIG = 1 . × − for the bare YIG pad and α YIG | Pt = 1 . × − for the YIG/Pt pad, correspondingto a spin mixing conductance of g ↑↓ = 5 . × m − [29]. The magnetization dynamics is measured by means T i / A u c on t ac t p a d YIG PtGGG substrate DC pulse2 µm
Pulseeneratorg
LaserBLS-Fabr -P roty énterferometeri Photo etectorn-d T r i gge r i ng BLS time-traces x y
Focalspotscan-line T i / A u c on t ac t p a d FIG. 1. Colored scanning-electron microscopy-image of thestructure under investigation and sketch of the experimentalsetup. The structure consists of a 2- µ m-wide and 34-nm-thickYIG stripe. A 3- µ m-long and 7-nm-thick platinum-heater isplaced on top and contacted by Ti/Au-leads separated by adistance of 2 µ m. of Brillouin light scattering spectroscopy (BLS). A laserbeam with 457 nm wavelength and 5 . ± . | U | = 1 . | j C | = 1 . × A m − .Figure 2(a) shows the reference experiment with anexternal field µ H aligned parallel to the long axis ofthe waveguide, parallel to the direction of the current j C ( µ H ext k j C ). In this geometry, no contribution of theSHE-STT effect is expected and the application of the current pulse only results in a Joule heating-induced in-crease of the YIG/Pt temperature. While the DC pulseis applied (black box in the figure), the BLS intensitydecreases, as originally investigated in Ref. [31]. Fur-ther, the spectrum of thermal magnons shifts to lowerfrequencies due to the decrease in the saturation mag-netization [15, 32]. After the DC pulse is switched offat t = 100 ns, the heat-dissipation-induced rapid coolingtriggers the formation of the BEC at the bottom of thespectrum [15]. The BEC manifests itself as a pronouncedpeak in the magnon intensity. The accompanying fre-quency increase is due to the cooling.The contribution of the SHE can be switched on byrotating the magnetic field by 90 ◦ , hence pointing alongthe short axis of the stripe [see insets in Figs. 2(b,c)], i.e.perpendicular to the direction of the DC current [22].In this geometry the SHE-STT contribution can bedamping- or anti-damping like [16, 33]. The change inthe effective damping can also be described by the an-nihilation or injection of magnons [22], or by the changein the magnon chemical potential µ [17, 21]. In the casewithout a STT-contribution [Fig. 2(a), pulse duration of τ P = 100 ns and a voltage of U = 1 . µ , thus suppressing BEC formation.In the case of the SHE-STT-induced magnon injectionprocess [Fig. 2(c), j C ,x < , µ H ext ⊥ j C ] the SHE-STTeffect enhances the magnon redistribution, which is man-ifested by the even higher BLS intensity measured afterthe DC pulse, compared to Fig. 2(a).For a better comparison of the three cases describedabove, Figs. 2(d,e) depict the extracted BLS spectra atthe time frames marked in Figs. 2(a-c). The BLS in-tensity during the pulse duration for the STT injectingmagnons [dashed red line in Fig. 2(d)] is more than onemagnitude larger compared to the case without a SHE-STT contribution [black curve in Fig. 2(d)]. The increasein intensity is observed although the BLS sensitivity issignificantly decreased at higher temperatures [31]. Inaddition, in the case of a SHE-STT induced magnon an- (1) (2) (3) (1) (2) (3) (1) (2) (3) B L S f r equen cy ( G H z ) Time (ns) Time (ns) Time (ns) j c µ x t H j c µ x t H j c µ x t H B L S i n t en s i t y ( a r b . un i t s ) . . . (a) (b) (c) x y x y x y j c || µ H j c ⊥ µ H (d) (e) BLS spectra application during DC-pulse (1)
Heated,STT injection Thermal (×7) (3)
Heatedwithout STT (×7)HeatedSTT-annihilation(×7)00.51.01.52.02.53.0 B L S i n t en s i t y ( a r b . un i t s ) B L S i n t en s i t y ( a r b . un i t s ) Thermal (×7) (3)
Rapid cooling,STT-annihilation(×7)Rapid cooling,without STTRapid cooling,STT-injection
BLS spectra after DC-pulse application (2) j c || µ H j c 0 ext ⊥ µ H FIG. 2. BLS intensity color-coded (log-scale) as a function of the BLS frequency and time. The duration of the 100-ns longheating DC pulse with an amplitude of | U | = 1 . (1) , as shown in (a-c). For comparison, thermal spectra extracted in time frame (3) forthe field pointing along the short (filled grey curve) and long axis (filled yellow curve) of the waveguide. (e) BLS spectra afterthe DC pulse extracted in time frame (2) , as shown in (a-c), thermal spectra as in (d). nihilation [solid red line in Fig. 2(d)], the BLS intensityseems to be decreased compared to the case without SHE-STT contribution [black line in Fig. 2(d)]. In addition,a large shift of the magnon frequency is observed for anSHE-STT-injection with respect to the non-heated, ther-mal spectra [filled curves in Fig. 2(d), for two different di-rections of µ H ext ], which is in the range of ∆ f = 1 GHz.The shift is caused by the decrease in saturation magne-tization due to the large number of magnons injected viathe SHE-STT mechanism.Note that a purely thermal excitation of magnons takesplace over the whole spectral range [Fig. 2(a), black solidline in Fig. 2(d)]. The subsequent decrease of the satu-ration magnetization leads to a decrease in the BLS in-tensity [31]. In contrast, for a STT-injection of magnonsthe BLS intensity increases [Fig. 2(c), red dashed line inFig. 2(d)], in spite of the heating-induced decrease of theBLS sensitivity (which does not depend on the field ori-entation). The reduction of the BLS sensitivity is givenby the decrease in the saturation magnetization that canbe treated as a thermally-induced increase of the num-ber of magnons over the whole magnon spectrum [34]. Thus, the fact that the BLS intensity in Fig. 2(c) in-creases rather than decreases during the heating processsuggests that the SHE-STT mechanism injects magnonsprimarily into the low energy part of the spectrum acces-sible with micro focused BLS.Figure 2(e) depicts the spectra after pulse termina-tion during the rapid cooling process. It can be seen,that the STT-annihilation of magnons suppresses theBEC formation, the rapid cooling process causes onlya minor increase of the BLS intensity (compare the solidred line with the thermal spectrum for the same geome-try, grey filled curve). The SHE-STT driven injection ofmagnons (red dashed line) causes a larger BLS intensitycompared to the case without a SHE-STT contribution(black dashed line).The presented results in Fig. 2 show that the SHE-STT effect can control the BEC formation process via theinjection or annihilation of magnons. To investigate thethreshold of the BEC formation process in the presenceof the SHE-STT effect, we first characterize the state ofthe magnon system right before the cooling takes place.Figure 3(a) shows the inverse BLS intensity as a func- Fit /I n t. B L S i n t en i s t y ( a r b . un i t s ) I I n t U U th = - 0.95 V (b)(a) End of pulse1.0 1.4 1.8 2.2×3 ⊥ µ j c 0 ext H ⊥ µ j c 0 ext H j c 0 ext ⊥ µ H c 0 ext j ⊥ µ H (c) j H c 0 ext ||µ j c, x > 0 j c, x < 0 After pulse j c 0 ext ⊥ µ H After pulse
STT-injectedsubtracted I n t. B L S i n t en i s t y ( a r b . un i t s ) I I n t
80 ThresholdwithoutSTTThresholdSTT-injection ThresholdSTT-annihilation ( )d
Absolute voltage | (V) |U Absolute voltage | (V) |U Absolute voltage | (V) |U Threshold ofSTT-induceddampingcompensation
FIG. 3. (a) Inverse BLS intensity as a function of the voltage for the application of a continuous DC current. The linear fit yieldsa threshold for the damping compensation of U th = − .
95 V. (b) Integrated BLS intensity at the end of the applied DC pulse(integration interval τ P − < t < τ P ) as a function of the absolute value of the voltage. The external field of µ H ext = 110 mTis aligned perpendicular to the direction of the current. The SHE-STT effect either injects (“+”-sign data points) or annihilates(“ − ”-sign data points) magnons. (c) Integrated BLS intensity after the pulse is switched off ( τ P < t < τ P + 95 ns) as a functionof the absolute value of the voltage. The blue curves correspond to the situation in (b), the black curves show the referencecurve for µ H ext k j C , without a SHE-STT contribution. (d) Integrated intensity as in (c), the residual signal caused by thedecaying STT-injected magnons is subtracted. Due to the injection or annihilation of magnons via the STT the thresholds areshifted with respect to the case without a SHE-STT contribution (pink line). tion of the applied voltage, now for an applied continu-ous DC voltage instead of a DC pulse. The linear fit ofthe inverse BLS intensity yields the threshold voltage forthe STT-induced damping compensation [20], which isfound to be U = − .
95 V. Thus, for the voltages appliedin the pulsed experiments, the SHE-STT effect compen-sates the damping and should lead to the formation ofauto-oscillations after a sufficiently long time [33].Figure 3(b) shows the BLS intensity integrated overthe whole frequency range shown in Fig. 2 and integratedover the last 8 ns of the applied DC pulse as a function ofthe voltage. This BLS intensity at the end of the pulseis corresponding to the final magnon intensity in the fre-quency range accessible with BLS, which is the low fre-quency region of the spectrum. The “+”-sign data pointscorrespond to the direction in which the STT effect in-jects magnons, the “ − ”-sign data points correspond tothe case when the STT effect annihilates magnons (anegative voltage corresponds to a positive current den-sity in x -direction and results in an injection of magnonsas indicated by ”+”-sign data points). We observe anincreasing BLS intensity at the end of the pulse withhigher voltages, indicating an increasing STT-injection.After reaching its maximum at a voltage of U = 1 .
45 Vthe BLS intensity decreases again, which is attributed toa decreased spin mixing conductance due to the heating[35], and a decreased BLS sensitivity at higher temper-atures [31]. The decreasing BLS intensity for oppositecurrent polarity is a superposition of the annihilation ofmagnons due to the SHE-STT effect and the decreasingBLS sensitivity.In the following, the effect of the changed magnon pop-ulation at the end of the pulse on the threshold voltage of the BEC formation is investigated. The applied DC pulsevoltage defines the temperature increase achieved by theJoule heating, and, therefore, it defines the number of ex-cess magnons redistributed in the process of rapid cool-ing. Thus, the investigation of the BLS intensity as afunction of the applied voltage yields threshold informa-tion.Figure 3(c) shows the BLS intensity after thepulse is switched off, integrated in the time interval τ P < t < τ P + 95 ns. As a reference, the black curvesshow the integrated BLS intensities without a SHE-STTcontribution ( µ H ext k j C ). These two curves (positiveand negative current polarity) show a sudden increase ata voltage of U = 1 .
42 V, which is the threshold of theBEC formation without a SHE-STT contribution. Forthe case of a STT-annihilation (bright blue graph) a pro-nounced threshold at a higher voltage of U = 1 .
51 V isobserved.In the case of STT-injection, the BLS intensity aftertermination of the pulse (dark blue curve) is the interplayof the rapid cooling induced magnon redistribution andthe (decaying) STT-injected magnons during the pulse.To investigate if these two contributions are a linear su-perposition or if the SHE-STT effect driven injection in-fluences the redistribution process, we need to subtractthe intensity originating from an exponential decay ofthe STT-injected magnons. This intensity can be de-rived as I STT ( t ) = I STT t = τ P exp[ − t − τ p ) /τ m ], where I STT t = τ P is the intensity at the end of the pulse [integrated valueshown in Fig. 3(b)], and τ m the magnon lifetime. Fittingthe time evolution of the BLS intensity for the lowestvoltages applied (for STT-injection, without a contribu-tion of the rapid cooling mechanism) reveals τ m = 34 ns.Thus, by using the starting intensity of the SHE-STTeffect injected magnons we can calculate the expectedmagnon intensity after the pulse if no rapid cooling pro-cess would take place. The experimental BLS intensityafter the pulse with the calculated STT-contribution sub-tracted is shown in Fig. 3(d). For U > .
30 V we find thatthe intensity after the end of the pulse is larger than theintensity given by the finite lifetime of the STT-injectedmagnons. This lowest voltage that leads to an increaseof the number of magnons above the STT-injected levelis identified as the threshold of the BEC formation. Insummary, the shift of the BEC formation threshold isfrom U = 1 .
42 V down to 1 .
30 V or up to U = 1 .
51 V,corresponding to a relative change of -8% or +6% respec-tively.The decreasing intensity at higher voltages [
U > .
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