ELECTRONIC PUMPING OF QUASIEQUILIBRIUM BEC MAGNONS

Transcription

1 ELECTRONIC PUMPING OF QUASIEQUILIBRIUM BEC MAGNONS Scott A. Bender Rembert A. Duine (Utrecht) Yaroslav Tserovnya arxiv:.38

2 OUTLINE BEC realizations pumped collective excitations in CM BEC exciton polaritons and photons in microcavities BEC parametrically pumped magnons Spin pumping by magnons Spin-torque induced magnon BEC vs classical instabilities Dynamic phase diagram/experimental proposal/feasibility (YIG)

3 BEC IN SOLID STATE Exciton polaritons in semiconductor microcavities: Deng et al., Science (00); Kasprza et al., Nature (006); Balili et al., Science (007) Photons in an optical microcavity: Klaers et al., Nature (00)

4 BEC OF MAGNONS Parametric microwave pumping magnons in YIG: Demoritov et al., Nature (006) Demidov et al., PRL (008) YIG is material choice due to its low Gilbert damping

5 SPIN PUMPING BY MAGNONS Parametrically pumped magnons induce ISHE voltage torque pumping Bauer and YT, Physics (0) Sandweg, Serga, Saitoh, Hillebrands et al., PRL (0) cf. Berger, PRB (996)

6 SPIN TORQUE VS SPIN PUMPING The traditional picture torque Slonczewsi, JMMM (996) is accompanied with rmodynamic reciprocal called pumping: YT, Brataas, and Bauer, PRL (00)

7 SPIN-TRANSFER RECIPROCITY Interaction magnetic textures and electric (charge// heat) currents: τ torque f pumping m(r,t) jc(r,t), jq(r,t) t m αm t m = γm H eff + τ ˆL t j +ˆρj = E + f YT and Meclenburg (008) YT and Wong (009)

8 SPIN-MAGNON EXCHANGE Kajiwara, Saitoh et al., Nature (00)

9 OUR GOAL We want to develop a viable dc-transport route to inducing BEC magnons in magnetic thin-film heterostructures 7&8"("* :*!"#$%&'()*+,-* q &44%53/*63%/*.("/$0'()*+-* 39* 39* 39* #45"*0$))3"'* 0("/$0("*3%30')("#* 7&8"("* q 39* #45"*0$))3"'* Microwave agitation ferromagnet is replaced by electronic pumping Bender, Duine, and YT, arxiv (0)

10 FI/NM INTERFACIAL EXCHANGE ˆV int = q V q ĉ q â â +H.c.!""#$%&'(!)*%+,'-%#&' 0 0,*&3,4.'%#%,4.*5' F %*%.)/' 67!3#$'8#,9!&%&:' S tot = S R = T R ( µ) N R

11 ground-state magnon energy; magnons begr is Fermi-level Bose-EinsteinHere, condensed when µl =.density states conduction electrons and current (per is straightforward to calculate from3 3 acial area A) j flowing into insulator VL V R d d V V uctorthe in terms temperatures and chemical poten0 total (z axis) current 3 3 A gr (π)!"#$%&'()*+,-* (π).("/$0'()*+-* to lowest order in V int using Fermi s golden rule: 39* δ ( F ) δ ( F ), (5) z d SL 39* :* j= = j + jex, (3) A dt F is Fermi energy (assumed to be39* much larger where than temperature) VR volume 39* conduce ground-state, jand, and excited, jexand, magnon tor. Notethat current density ibutions are functions magnon chemical po-j is only present in N (µ, Taccumulation rmodynamic limit phase, µl contribution =. On ground-state (condensed) magnon L L )/VL : al µlconsists, electron µ =inµbec, µ or hand, density jex (carrying ir temperatures TL and TR. In -current rmody jdensity = π ( µ ) g (4)in transfer excited magnon states) via c limit, -current j V, describing R n. is present both normal and BEC phases after some manipula flow ground-state magnons into and and, out is density states conduction can be written as contribution nsulator, is Here, proportional to Fermi-level number groundas well astions, grrmal magnon electrons and magnons N per insulator volume VL, n = Vex ( ) ( µ jex =π V d 3 )3gR gl ( ) V d d L R V V A g [nb (βl ( R µl ))(π) nb (π) (βr ( µ))], (6) δ ( F ) δ ( F ), (5) terms if T energy-dependent density magnon which is in enhanced L <T R SPIN TRANSPORT EQUATIONS 7&8"("* 7&8"("* &44%53/*63%/* #45"*0$))3"'* q 0("/$0("*3%30')("#* #45"*0$))3"'* q FIG. n = to th fall in forma We ature that or lo

12 sum condensate tot L ccur-l c αdl αdl esent in to that shown in figure, crossing point j /αd would c L s determined by accumulaanipulafall in magnon normal phase = 0), thus precluding a BEC nd ground-state en- (nwhere excited magnon flux jc = jex (µ formation. FIG.. Behavior nand predicted by rate equation, applied magnetic field), independent, as long as µl is anchored b as = jtotdepends / dl = on jc / d αn /.atif j πsign jexn,which both temα = Vopposite ( µ) gr /dl, L c,had tobiases. that shown inhenceforth sufficiently figure, on crossing point jc /αd tial Note is regime magnetic layer thicness. The L would Wethat focus where temperin atures normal phase (nleft 0), thussubsystems precluding a BEC = n fall conductor could, inn princibose-einstein condensed system both and right are fixed so thus fall, (6) to formation. insulator required as depicted Fig.. In fir thatuntil any energy gain or regimes, loss, independent in gain )and nby "-*%') tained and system undergoes that α < 0) > jc /αdl, n or loss, is completely absorbed or resupplied rmal 0 (0) magnon./0) <saturating 3%#() reservoirs. At fixed T density excited magnons ion. In a recent experiment by tially until at a value Ms c L j pendent ( j jac monotonic We henceforth focus on cregime where 0magnetization nex becomes function µl temperalone. is Let ferromagne n pumping into a metal by mag< dl and αd LBohr α magneton). us both suppose left right subsystems are fixed furr that accumulation µin inthis so right byatures presence parametrically case, magnonis independent become diffusion insuthata any energy between gain or loss, independent from gain ition, reservoir current tions important ultimately and n exceeds Vsq α 4) lator and fixed. If total density magnons from a rmal gradient as disbe treated more carefully or loss, is completely absorbed or resupplied by rmalhere. This is > 0 ( critical BEC density n (corresponding toa µ ors Ref. [0] made use swaser (i.e.,magnons -wave c L = ), analog jcexcited reservoirs. At fixed T density L (7) nex diffusion reaches and remains pinned at> this value, nc, andin cont wherein along a ward in Ref. and observed nex becomes a monotonic function µl 0) [8] alone. Let only nreciprocally, is free to vary. to In ours BEC(in phase, n, time YIG) in a magnetic insulator ectable Hall signal. ates inus furr suppose that accumulation µ in right dependence n is given by d be used to generate accusecond regime, µ > but n (0) < jc reservoir is independent diffusion from insu a metal via Hall effect; j < 0), n decreases towards zero, and c ace are jc density magnons jc lator and fixed. If total exceeds αt/ ulation may n drive magnons ters normal phase. The two regime + n (0) e, last(8) n (t) = ate curαd critical BEC densityαd ncl (corresponding = which L toj µ< L 0), ), to j > 0 and are mor c c cumula!"#$%&'()*(+,-") BEC RATE EQUATION

13 DYNAMIC PHASE DIAGRAM "# n tot (t) /n tot (0) "# n tot (t) /n tot (0)!"#$%&$'&()*+$ n (t) /n tot (0) n ex (t) /n tot ( ) n tot (t) /n tot ( ) $%&'()#*%#+,-# n (t) /n tot ( ) n ex (t) /n tot ( ) 3 4 5!$#!"# αt αt &-./)+# 0)',# j c < 0 34# j c > 0 T L /T R "# 0 %&'()*+,#-.#&-./)+# β R ( µ )

14 EXPERIMENTAL PROPOSAL Starting with classical -torque instability in YIG/PT bilayer Kajiwara, Saitoh et al., Nature (00) reduce Pt SHE current slightly below its critical value rmally anchor YIG layer relative to Pt by a cool substrate The larger YIG/PT temperature difference, wider subcritical current window for BEC phase

15 DETECTION AND OUTLOOK The pro--principle for transport-induced BEC magnons can be confirmed by Brillouin light scattering or detection coherent microwave emission (with BEC coherence reflected in characteristic scaling signal with lateral size YIG/Pt bilayer) The dc steady-state realization BEC would open new avenues for realization superfluidity, macroscopic coherent phenomena, and nonlocal transport scenarios that are not feasible in a traditional microwave-pumped realization magnon condensates First condensed-matter realization BEC bosonic excitations in an electrically-driven system?

16 SUMMARY The quantized form -transfer torque and pumping captures both classical Gilbert damping and torque-driven instabilities This description also provides a natural language for discussing dilute electronically-pumped magnon gases, which can condense in a steady-state dc transport regime, requiring (SHE) current-induced classical instability in a magnetic insulator film with low intrinsic Gilbert damping (compared to pumping): d µm cooling magnetic layer relative to normal-metal layer (Seebec) optical/microwave/nonlocal transport probes to confirm coherence condensate