NYU NYU Spins Dynamics in Nanomagnets Outline

I. -Transport and Transfer Basics Andrew D. Kent –Giant (GMR) –Spin filtering and spin momentum transfer

II. Spin-Transfer Induced Dynamics Department of Physics, New York University –Landau-Lifshitz-Gilbert dynamics and spin-torque –Current threshold for excitations and stability diagrams

III. Experiments Lecture 1: Magnetic Interactions and Classical Magnetization –Point contacts, nanopillars Dynamics –dc transport, noise, high frequency characteristics Lecture 2: Spin Current Induced Magnetization Dynamics IV. Spin-Transfer MRAM Lecture 3: Quantum Spin Dynamics in Molecular Nanomagnets –Ultimate miniaturization of MRAM V. Summary

References

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*#9SE:# # Magnetoresistance (MR) !R/R The Two Channel Model of GMR Spin-dependent scattering of conduction electrons & change of scattering rate with an external field. Cu 0 [Ar].3d10.4s1 Cu [a.u.] Co DOS 0

[Ar].3d7.4s2

" e e" 0 E-EF

! ! Rspin-down = Rspin-up MR ! 0 Co

Resistance Rparallel << Ranti-parallel Rspin-down > Rspin-up MR ~ 1 % " R/R ~ 1-10 % " M e e"

! ! Key Idea!!! Spin Filtering by Ferromagnetic Layers If a magnetic layer acts as a spin-filter, then Parallel Antiparallel it must also experience a torque. low resistance state high resistance state Torque # % "

!

# $ I sin%

Ferromagnetic layers act spin polarizers and analyzers for an ! Slonczewski 1996 and Berger 1996 Seeds of the idea in Slonczewski, PRB 1989 Torques with Two Magnetic Layers

Reversing the direction of the current Electron flow (negative current) changes the sign of the torque fixed free Spin currents moving to the Torque # right exert a torque favoring parallel alignment % " (and a low resistance state) Electron flow (positive current) ! Spin currents moving to the left fixed free exert a torque favoring antiparallel alignment (and a high resistance state) # $ I sin% Spin-transfer is an interface effect: 2π Transverse spin coherence length: λc = kf↑ − kf↓ Stiles and Zangwill, PRB 2002

Spin Transfer – A new method to manipulate nanomagnets Dynamics: LLG+spin-torque (LLGS)

Spin current induced switching, Coherent dynamic precession. dmˆ dmˆ = −γmˆ × H" eff + αmˆ × + γaJ mˆ × (ˆm × mˆ P ) Charge current dt dt Spin current ! Heff damping [ˆm (ˆm mˆ )ˆm] − p − · p ¯hP J “fixed” ferromagnet aJ = mˆ 2eMst normal metal layer Spin-torque When the spin-torque exceeds “free” ferromagnet the damping, instabilities can precession occur! ! Also possible: bJ mˆ × mˆ P mˆ × Heff C. Oersted, 1819 J.C. Slonczewski, 1996 ‘Current-Induced Effective field’ γ/2π = 28 GHz/T z y New Physics: Thin film elements

! Insight into spin transport: injection, diffusion and coherence x

! Fundamentally new types of magnetic excitations ! Most of the theories are still untested H! = H! M (ˆm zˆ)ˆz + H (ˆm xˆ)ˆx eff − eff · K · Magnetic Excitations Stability Diagrams 2e α ! In-plane magnetization and field: J = M t(H + H +2πM ) c P s K eff mˆ ! H! H PS P

P/AP AP J 2e α ! Perpendicular magnetization and field: Jc = Mst(H 4πMeff ) ! P − 8 H>4πMeff H 4πM P/AP K ! eff ! 6 P Spin-current amplifies the motion for currents greater than a critical value: H 4 AP/PS AP 2e α mˆ Jc = Mst(H + HK +2πMeff) 2 PS ! P [T] Field Applied

0 0 0.05 0.1 J. Z. Sun, PRB 2000 J. Z. Sun, PRB 2000; Bertotti et al., PRL 2005, Chen et al PRB 2006 aJ [T]

Charge versus Spin Currents Experiments on Spin-Transfer In both cases there will be a current threshold at which the magnet will respond Geometries Charge current: magnet responds to the •Point contacts generated: Spin-Transfer Publications µoIc Nanopillars I Bc = Ic r • 2πr ∼ 120 •Nanowires Spin Current: there is a critical current density 100 •Nanorings Ic 2 Jc = Ic r Structures 2 80 Co πr ∼ •Spin-values 60 117 •Multilayers Cu 93 •Tunnel junctions 40 84 B •Single magnetic layers 56 Co 20 Materials 29 23 •Metallic ferromagnets 0 8 9 7 2 1 3 •Magnetic •Metallic antiferromagnets 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 In devices with radii less than Rmin: •Oxide ferromagnets The critical current due to the spin- Phenomena current will be less than that due to the •Current induced switching & precession charge current Rmin & 250 nm for Co •Current induced domain wall motion Experiments on Spin-Transfer

Point-contacts Pillars junctions

" Uniform precession of M " Hysteretic Switching of M H I H I M Co Cu M Co M P 8 7 6 5 I 3 M Co Cu Co

MP

Field applied perpendicular M. Tsoi et al. ; E.B.Myers et al.; Y. Ji et al., … J. A. Katine et al. ; J. Grollier et al.;… to the plane of the film 1998 2000

Microwave Oscillations of a Nanomagnet Driven Microwave Oscillations in Point Contact Geometries by a Spin-Polarized Current

Rippard et al. PRL 2004

Kiselev et al., Nature 2003 Theory on linewidth: Slavin 2007 week ending PPHHYYSSIICCA L R E V I E W L E T T E R S week ending PRLPRL 96,96, 227601227601Phase(2006)(2006) Locking of Two Spin-Torque Oscillators Spin-Transfer9 JUNE 2006 Induced Precession A nanomagnet oscillator P H Y S I C A L R E V I E W L E T T E R S week ending PRL 96, 227601 (2006) 9 JUNE 2006 Spin-TSpin-Transferransfer-Driven-Driven FFerromagneticerromagnetic Resonance of Individual Nanomagnets (a) 0 mA dc, 535 mT 0.52 mA dc vary strongly in peak shape and frequency as a function of 6 )

z 50 370 mT 30 mΩ J.J.C.C. SankeSankeyy,, PP..M.M. Braganca,Braganca, A.A.G.G.F.. Garcia, I. N. Krivorotov, R. A. Buhrman, and D. C. Ralph 990 µA rf H positive Idc, in a manner similar to A0, confirming that A1 ) 5 Ω Ω M Cornell University, Ithaca, New York 14853, USA Ω Ω 40 220 A rf Cornell University, Ithaca, New York 14853, USA and A2 (like A0) are associated with the PyCu layer. The / µ 4 2 (Received 4 February 2006; published 5 June 2006) m (Received 4 February 2006; published 5 June 2006) ( 50 Ω Ω FMR modes B0 and B1 that we identified with the Py layer Ω Ω 30 50 f 40 0mA dc 3 f r r ) I m I / 30 We demonstrate a technique that enables ferromagnetic resonance measurements of the normal modes ( -50 mΩ / do not shift significantly in f as a function of positive I . Ω We demonstrate a technique that enables ferromagnetic resonance measurements of the normal modes x dc 20

x r 20 i 2 mi m ( for magnetic excitations in individual nanoscale ferromagnets, smaller in volume by more than a factor of V 1 0 for magnetic excitations in individual nanoscale ferromagnets, smaller in volume by more than a factor of This is expected, because positive I is the wrong sign to e dc m 0 V w 0 5 6 7 8 5050comparedcomparedtotoindiindividualvidual ferromagneticferromagnetic samplessamples measured by other resonance techniques. Studies of the Ebels, et al., Nat. Mat (2007) 1 10 8 excite spin-transfer dynamics in the Py layer [7]. o 5 6 7 Freq. (GHz) resonance frequencies, amplitudes, linewidths, and line shapes as a function of microwave power, dc ADK, Nature Materials (2007) P week ending resonance frequencies, amplitudes, linewidths, and line shapes as a function of microwave power, dc There has been significant debate aboutP H Y whetherS I C A L theR E V I E W L0E T T E R8S0 µA rf 0 (b) current, and magnetic field provide detailed new information about the exchange, damping,Experiments:and spin- Kiselev et al., NaturePRL 96, (2003);227601 Krivorotov(2006) et al., Science 2005. 9 JUNE 2006 current, and magnetic field provide detailed new information about the exchange, damping, and spin- magnetic modes which contribute to the dc-spin-transfer- 10 11 12 7 8 9 transfer torques that govern the dynamics in magnetic nanostructures. (a) 0 mA dc, 535 mT 0.52 mA dc transfer torques that govern the dynamics in magnetic nanostructures. vary strongly in peak shape and frequency as a function of 6 Frequency (GHz) ) Frequency (GHz)

driven precessional signals correspond to approximately z 50 370 mT 30 mΩ 990 µA rf 60 H positive Idc, in a manner similar to A0, confirming that A1 ) 5 0.5 mA dc, 370 mT 60 (c) ) (d) uniform macrospin precession or to nonuniform spin-wave ) Idc =0 Ω Ω M Ω Ω 250 40 DOI: 10.1103/PhysRevLett.96.227601 PACS numbers: 76.50.+g, 72.25.Ba, 75.30.Ds, 75.75.+a z 220 A rf / 40 µ DOI: 10.1103/PhysRevLett.96.227601 PACS numbers: 76.50.+g, 72.25.Ba, 75.30.Ds, 75.75.+a and A2 (like A0) are associated with the PyCu layer. The 4Ω 0 4 2

m 370 A rf ) µ H m 43 m instabilities [17–20]. Our FMR measurements show di- ( 50 Ω ( Ω Ω FMR modes B0 and B1 that we identified with the Py layer Ω Ω 30 50 Ω Ω

Ω Ω 200 f 40f 0mA dc f 20

3 M r r r )

m I I I / / / 30

( -50 m / Ω rectly that,doatnotIshift, thesignificantlydc-driveninpeakf as afrequencyfunction ofispositiequalve Ito. 30 Ω 2 x

c dc m x 20i

x r 20 m i ( 2 mi 0 Ferromagnetic resonance (FMR) is the primary tech- separated by a 12 nm copper spacer (see details in [10]). 150 ( V m Ω Ω 1 0 Ω Ω Ferromagnetic resonance (FMR) is the primary tech- separated by a 12 nm copper spacer (see details in [10]).This is expected, because positive I is the wrong sign to e 08. 10. 12. dc m f V that of the lowest-frequency rf-driven mode, the one ex- 0 1 1.2 r 0.8 V w 0 I 5 6 7 8 Kaka et al., Nature 2005 and Mancoff et al. Nature 2005 1 10 m nique for learning about the forces that determine the We pattern the layers to have approximately elliptical cross / 8 excite spin-transfer dynamics in the Py layer [7]. o 6 7 nique for learning about the forces that determine the We pattern the layers to have approximately elliptical cross 100 ( 20 5Freq. (f/f0) pected to be most spatially uniform [13]. Higher values of x Freq. (GHz) P dynamical properties of magnetic materials. However, sections using ion milling. We focus here on one 30 There has been significant debate about whether the 0i 80 µA rf 0 (b) r I = I /3

e rf c dynamical properties of magnetic materials. However, sections using ion milling. We focus here on one 30 m Idc can also excite the spatially nonuniform mode A1 and 50 2 magnetic modes which contribute to the dc-spin-transfer- V 10 11 12 7 8 9 conconvventionalentional FMRFMR detectiondetection methodsmethods lacklack thethe sensitisensitivity 90 nm2 device, but we also obtained similar results in 40  w 10

Frequency (GHz) Freo quency (GHz) 2 2 even producedriven modeprecessionalhoppingsignalssocorrespondthat modeto approximatelyA1 can be 0 535 mT -24 mΩ

2 2  P to measure individual sub-100-nm-scale devices that are of 120 nm and 100 200 NYUnm samples. We use different 01.52 m µAA d crf, 370 mT 6060 I = 1.3I to measure individual sub-100-nm-scale devices that are of (c) ) dc c(d)

) I =0 excited whenuniformmodemacrospinA0 is precessionnot. or to nonuniform spin-wave 250 dc 0 z 40  Ω  370 A rf 40 ) µ H interest for fundamental physics studies and for a broad materials for the two magnetic layers so that bySpin-Transferapplyinginstabilitiesa Driven[17–20]. FMROur FMR measurements show di- m 43 mΩ interest for fundamental physics studies and for a broad In order to analyze the FMR peak shapes, we make the 7.0 7.5 8.0 ( 1.0 1.1 1.2 1.3 Ω Ω

Ω Ω 200 20f

M r I / rectly that, at I , the dc-driven peak frequency is equal to 30 /

2 Frequency (f/f ) range of memory and signal-processing applications. For perpendicular magnetic field H we can induce an offset c m Frequency (GHz) range of memory and signal-processing applications. For perpendicular magnetic field H we can induce an offset x 0 i simplifying assumption that the lowest-frequency modes ( 150 0 m Ω Ω Ω Ω 08. 10. 12. Measurement Principle that of the lowest-frequency rf-driven mode, the one ex- f V 1 1.2 this reason, many new techniques are being investigated angle between their equilibrium moment directions (both r 0.8 I this reason, many new techniques are being investigated angle between their equilibrium moment directions (both m A and B can be approximated by a macrospin model, / 0 0 100 ( 20 Freq. (f/f0) pected to be most spatially uniform [13]. Higher values of – Tulapurkar et al., Nature 2005 x for probing magnetic dynamics on small scales, including thethe spin-transfer torque and the small-angle resistance FIG.i 3 (color online). (a) r FMR I peak= I /3 shape for mode A0 at for probing magnetic dynamics on small scales, including e rf c – Sankey et al., PRL with2006 the SlonczeI can alsowskiexcformite theofspatiallythe spin-transfernonuniform modetorqueA [7].and m 50 dc 1 V Brillouin scattering [1] and FMR detected by Kerr micros- Idc 0 and different values ofw 10I rf: from bottom to top, traces 1–5 Brillouin scattering [1] and FMR detected by Kerr micros- even produce mode hopping so that mode A can be o (a) (b) Pulsed rThef in small-amplitude resonance is predicted [10] to1 have a ˆ0 535 mT -24 mΩ (a) P (b) span I 12 µA 80rf –340 A in equalI increments,= 1.3I and traces 5–10 copy [2], scanning probes [3,4], x rays [5], and electrical excited when mode A is not. rf 0 dc c copy [2], scanning probes [3,4], x rays [5], and electrical ) 0 ) simple Lorentzian line shape, ˆ S S span 3407–.0990 7.5A in8.0equal increments.1.0 1.1 (b)1.2 Bottom1.3 curve: spec-

Ω 32.9

Ω 32.9 In order to analyze the FMR peak shapes, we make the ( techniquestechniques[6].[6].HereHerewewedemonstratedemonstrate aa simplesimple nenew formform of (

Frequency (f/f ) simplifying assumption that2 the lowest-frequency modes tral densityFrequeofncdc-driy (GHvze) n resistance oscillations0 for mode A0, e e I = e FMRFMRthatthatusesusesinnovinnovatiativveemethodsmethods toto bothboth dridrivvee and detect e rf 0 c c c c A0 andVmixB0 fcan be approximated by a macrospin: model,(3) showing a peak with a half width at half maximum 13 MHz. n n n

n 2 I t I sin ωt FIG. 3 (color online). (a) FMR peak shape for mode A0 atˆ magnetic precession, thereby enabling FMR studies for the e a magnetic precession, thereby enabling FMR studies for the e † / 1 f f = a with the Sloncze( )=wski formo of( the0) spin-transfer0 torque [7]. r Top curve: FMR signal at the same bias conditions, showing the r t t 32.8 32.8 e I 0 and different values of I : from bottom to top, traces 1–5 e V ‡ ‰ ÿ † Š dc rf s f V s f miix The small-amplitude resonanceR is predicted [10] to have a first time on individual sub-100-nm devices and providing i first time on individual sub-100-nm devices and providing i ∆ o ˆ e phase-locking peak shape. Inset: Evolution of the FMR peak for e Idc H span I 80–340 A in equal increments, and traces 5–10 s R t − m t · m rf s R R Here f0 issimplethe unforcedLorentzian( )=precessionline shape,(1 frequencyˆ ( ) ˆ p.) The width ˆ e aadetaileddetailednenewwunderstandingunderstanding ofof theirtheir magneticmagneticIC modes.modes. We e 2 spanmode340A–9900 at370A in mTequal, Iincrements.dc 0, for(b)IrfBottomfromcurv30e:spec-A to 1160 A. R R Ref. Signal0 predicted for the PyCu layer in our experimental ge- ˆ exciteexciteprecessionprecessionnotnotbybyapplyingapplyingananacacmagneticmagnetic field as isis I2 = tral(c)densityEvolutionof dc-driof vtheen resistanceFMR signaloscillationsfor modefor modeA0 Ain0, the phase- Thermal fluctuations and ST: 32..7 Lock-in ometry is, to within 1%V errorf for  rfH >0 0:5 T: [10], (3) showing a peak with a half width at half maximum 13 MHz. done in other forms of FMR, but by using the spin-transfer Resonance: mix 0 2 locking regime at Idc 0:5 mA, 0H 370 mT, for (bottom to done in other forms of FMR, but by using the spin-transfer -2 -1 0 1 2 † / 1 f f0 =0 ˆ Sun, 2003 -2 -1 0 1 2 ‡ ‰ ÿ † Š Ttop)op curve:I fromFMR signal12 toat 370theˆ sameAbias, equallyconditions,ˆspacedshowingon thea logarithmic torquetorquefromfromaaLispin-polarizedspin-polarized and Zhang, 2004acaccurrentcurrent[7,8].[7,8].WWee detect thethe Magnetic Field (T)  f ; (4) phase-lockingrf peak shape. Inset: Evolution of the FMR peak for Here f0 is the unforced0 precession0 frequency. The width scale. (d) Results of macrospin simulations for the dc-driven ˆ mode A0 at 370 mT, Idc 0, for Irf from 30 A to 1160 A. resultingresulting magneticmagneticVisschermotionsmotions and Apalkovelectricallyelectrically 2005 .. WWee demonstratedemonstrate 16 A ) ) (c) (d) ˆ (c) ) (d) 2  predicted for the PyCu layer in our experimental ge- ) 2 C 0 (c)dynamicsEvolutionandof thetheFMRFMRsignalsignalfor[10].mode A0 in the phase- z 200 z A detailed studies of FMR in single nanomagnets as small as A 517 mT Determine14 anisotropieswhere and damping is the ofGilbert nanometerdamping scale magneticparameter elements. As predicted by detailed studies of FMR in single nanomagnets as small as ! 14 ometry is, to within 1% error for 0H > 0:5 T [10], locking regime at I 0:5 mA,  H 370 mT, for (bottom to H H dc 0 m 33 m ˆ ˆ / / ! Characterize the spin-transferEq. (3), interactionwe find that nearthe equilibriummeasured FMR peak for mode A G 12 3030 9090 55::55 nnmm ,, andand thethe methodmethod shouldshould bebe scalablescalable toto G 12 B1 0 top) Irf from 12 to 370 A, equally spaced on a logarithmic ( 150 ( Ω Ω

 f ; (4)   More recent experiments: Krivorotov et al., Science 2005469 mT ! Excite10 highly non-linear magnetization dynamics 0 0 scale.W(d)e notedResultsaboof macrospinve that thesimulationsFMR peakfor theshapedc-drichangesven from y 10 ininvvestigateestigatemuchmuchsmallersmallersamplessamplesasaswell.well. OurOur techniquetechnique isis y at Idc 0, for sufficiently smallˆvalues of Irf, is fit accu- m m A c 24 c 1 ( ( dynamics and the FMR signal [10]. 8 ˆ where is the Gilbert damping parameter. As predicted2 by a Lorentzian to a more complex shape for sufficiently large

n 8 100 n rately by a Lorentzian, the amplitude scales V I , and 2 similarsimilartotomethodsmethodsdedevelopedvelopedindependentlyindependently bybyTTulapurkar 2 mix rf e e B0 rf rf Eq. (3), we find that the measured FMR peak for/ mode A values of I . [See the detailed resonance shapes in I I 6 0 u u the width is independent of I , [Figs. 3(a) and 4(a)]. Our dc / etet al.al. [9][9] forfor radio-frequencradio-frequencyy detection,detection, butbut wewe will dem- / rf x x q 50 q We noted above that the FMR peak shape changes from

i 50 i 4 at Idc 0, for sufficiently small values of Irf, is fit accu- Figs. 3(b) and 3(c).] This shape change can be explained e (iii) e minimum measurable precession angle is 0:2 . For I > m onstrateonstrate thatthat thethe peakpeak shapesshapes measuredmeasured therethere werewere likelylikely m ˆ  2 rf r 420 mT r a Lorentzian to a more complex shape for sufficiently large (ii) A0 macrospiin rately by a Lorentzian, the amplitude scales Vmix Irf, and V

V  F 0 F 2 0:35 mA, the peak eventually shifts to higher frequency/ as a consequence of phase locking between Irf and the notnot simplesimple FMR.FMR. 0 (i) precessiion the width is independent of Irf, [Figs. 3(a) and 4(a)]. Our values of Idc. [See the detailed resonance shapes in 0 and the shape becomes asymmetric, familiar properties for Figs.large-amplitude3(b) and 3(c).] precessionThis shape changeexcitedcanbybeIexpdc [23lained–26]. When WWee havhavee achieachievveedd thethe follofollowingwing neneww results:results: (i)(i) We 2 4 6 8 10 12 14 16 0.0 0.2 0.4 0.6 minimum measurable precession angle is 0:2. For Irf >  asthea consequenceprecession frequencyof phase lockingincreasesbetweenwithI precessionand the ampli- measuremeasure magneticmagnetic normalnormal modesmodes ofof aa singlesingle nanomagnet,nanomagnet, Frequency (GHz) Magnetic Finonlineareld (T) 0:oscillators35 mA, the peak[21].eventuallyFrom theshiftsmagnitudeto higher frequencyof the rf frequencyandshiftthe shapein similarbecomessignalsasymmetric,[Fig.familiar3(b),propertiesinset], wefor large-amplitudetude, the rf currentprecessioncanexcforceited bytheIdc amplitude[23–26]. Whenon the low-f includingincluding bothboth thethe lolowest-frequencwest-frequencyy fundamentalfundamental mode the precession frequency increases with precession ampli- estimate thatnonlinearthe largestoscillatorsprecession[21]. Fromanglethewemagnitudehave achieof vedthe side of the resonance to be smaller than the equilibrium dc- andandhigherhigher-order-orderspatiallyspatiallynonuniformnonuniformmodes.modes. (ii)(ii) By com- FIG. 1 (color online). (a) Room-temperature magnetoresis-frequency shift in similar signals [Fig. 3(b), inset], we tude, the rf current can force the amplitude on the low-f paringparing thethe FMRFMR spectrumspectrum toto signalssignals excitedexcited byby a dc spin- tancetance as a function of field perpendicular to the sampleis approximatelyplane.estimate that40the. largest precession angle we have achieved sidedrivofenthetrajectoryresonance .toUnderbe smallerthesethanconditions,the equilibriumthedc-precession driphaseven trajectorylocks approximately. Under these conditions,out of phasethe precessionwith the applied rf polarizedpolarized current,current, wewe demonstratedemonstrate thatthat difdifferentferent dc biases Inset: Cross-sectional sample schematic, with arrows denotingThe peakisaapproximatelyshape for mode40. B0 is also to good accuracy typical equilibrium moment configuration in a perpendicularThe peak shape for mode B is also to good accuracy phasecurrentlocks(approximately 180 ),outgiofvingphasenegwithatitheveappliedvaluesrf of V . cancandridrivveedifdifferentferentnormalnormal modes.modes. (iii)(iii) FromFrom thethe resonanceresonance typical equilibrium moment configuration in a perpendicularLorentzian for small Idc, but with neg0 ative sign. This sign is f  mix Lorentzian for small I , but with negative sign. This sign is current (f 180 ), giving negative values of Vmix. lineline shapes,shapes, wewe distinguishdistinguish simplesimple FMRFMR fromfrom aa rregime of field. (b) Schematic of circuit used for FMR measurements.expected because when thedcPy moment precesses in reso- Frequencies on the high-f side of the resonance produce (c) FMR spectra measured at several values of magnetic field,expected because when the Py moment precesses in reso- Frequencies on the high-f side of the resonance produce phasephase locking.locking. (i(iv)v) FromFrom thethe resonanceresonance linelinewidths,widths, we nance, the positive current pushes the Py moment angle phasephaselockinglockingapproximatelyapproximatelyin phaseinwithphasethe withdrive andthe adrive and a at I values (i) 0, (ii) 150 A, and (iii) 300 A, offset verti-nance, the positive current pushes the Py moment angle dc closer to closerthe PyCuto themoment,PyCu moment,givinggivinga nega negatiativeveresistanceresistance positipositivevVe V.mixWe. Whaveehconfirmedave confirmedthis picturethisbypicturenumericalby numerical achieachieveve efficientefficient measurementsmeasurements ofof magneticmagnetic dampingdamping inin a cally.. Symbols identify the magnetic modes plotted in (d). Here mix singlesingle nanomagnet.nanomagnet. response.response.The FMRThe peakFMR peakshapesshapesfor forthethehigherhigher-order-order integrationintegrationof ofthe themacrospinmacrospinmodel model[Fig. 3(d)][Fig.[10].3(d)] [10]. Irf 300 A at 5 GHz and decreases by 50% as f increases rf modes A modes, A , andA1, AB2, andareBnot1 areasnotwellas wellfit fitbybyLorentzians.Lorentzians. RecentlyRecently, T,ulapurkarTulapurkaret al.et[9]al.measured[9] measuredsimilar peaksimilar peak OurOur samplessamples havhavee aa nanopillarnanopillar structurestructure [Fig.[Fig. 1(a), in-in- to 15ˆ GHz [10]. (d) Field dependence of the modes in the FMR1 2 1 to 15 GHz [10]. (d) Field dependence of the modes in the FMRWe plot the spectrum of dc-driven excitations for Idc shapes, and proposed that they were caused by simple set], consisting of two magnetic layers—20 nm of permal- We plot the spectrum of dc-driven excitations for Idc ˆ shapes, and proposed that they were caused by simple set], consisting of two magnetic layers—20 nm of permal- spectra. The solid line is a linear fit, and the dotted line would be0:52 mA, Irf 0 in Fig. 3(b). The width is much narrowerˆ FMR with a torque mechanism different from the 0:52 mA, Irf 0 in Fig.ˆ 3(b). The width is much narrower FMR with a torque mechanism different from the loyloy ((PyPy NiNi8181FeFe1919)) andand 55..55 nnmm ooff aa PyPy6565CuCu3535 alloy— thethe frequency of completely uniform precession. thanˆthe FMR spectrum for the same mode (inset), con- Slonczewski theory. We suggest instead that the peak ˆˆ than the FMRfirmingspectrumarguments thatfor thethelinesamewidthsmodein these(inset),two typescon-of shapesSlonczein wski[9] maytheorybe due. Weithere suggestto phaseinsteadlocking thatwith the peak firming armeasurementsguments thatarethedeterminedlinewidthsby difin ferentthesephysicstwo types[22].of thermallyshapes inexcited[9] precessionmay be dueat roomeithertemperatureto phase(ratherlocking with 0031-90070031-9007==0606==96(22)96(22)==227601(4)227601(4) 227601-1  2006 The American PhysicalmeasurementsSociety are determined by different physics [22].227601-3thermally excited precession at room temperature (rather 227601-3 NYU NYU Nanopillar Characteristics: DC Spin-Transfer Driven FMR

Perpendicular applied field Perpendicular Field, Idc =0, t=0.4 nm 2o [0.4 nm Co|0.8 nm Ni] x 3 50x150 nm2 junction I 3.6 nm Co/Ni • 20 nV/Hz1/2 H! 10 nm Cu noise level o 12 nm Co • ~2 precession • rf from 4 to 16 GHz with 2 GHz steps • Adjacent curves offset by 0.2 µV each In-plane applied! field

7 ( , • High field dV/dI shows current /4>? ' = induced excitations of free ,< 1

! layer at ~8 mA

:/; & .1 ,

- Mode that disperses to higher field with increasing frequency: %

829 ! Mirrors the FMR mode on a film of the same composition

!"# !"$ !# $ # "$ "# ! Enables determination of the easy-plane anisotropy and g-factor of an )*++,-./0123/4567 individual nanomagnet 25 2009Condensed Boulder Matter School, Physics Lecture Seminar, 2 Colorado State University, July 22, 2009 26 2009 Boulder School, Lecture 2

NYU NYU Mode Dispersion: Comparison of Films and Nanopillars Linewidth & Damping Normal modes 20 1 film

15 2 (GHz)

3 pillar 10 film 4 g =2.17 4πMeff =2.6 kOe 4 Frequency 3 pillar Dipole-exchange spin-wave modes 5 2 (Kalinilos and Slavin 1986) 1 + Dipole fields 0 0 2 4 6 8 10 Co thick layer ~500 Oe Magnetic Field (kOe) !Slope: ' = 0.036 ± 0.003 for the film; 0.033 ± 0.003 for the nanopillars ! The resonance frequency is consistent with excitation of the lowest lying mode of the !Intercept: "H0 = 284 ± 30 Oe for the film; 24 ± 15 Oe for the nanopillars element--shifted from the uniform FMR mode due to finite size effects and dipole fields from other magnetic layers W. Chen et al. Appl. Phys. Lett. 92, 012507 (2008) 27 2009 Boulder School, Lecture 2 W. Chen et al., J. Appl. Phys. 103, 07A502 (2008) 28 2009 Boulder School, Lecture 2 Spin Transfer MRAM Summary

• Spin-transfer interaction may enable the ultimate miniaturization of # Spin transfer is a new mechanism to manipulate nanoscale MRAM to limits set by thermal stability. magnets: • Why? Means of switching very high anisotropy nanomagnets ! Reversal ! Precession 1 ! Spin-waves +m -m U = HkMsV ≥ 40kBT 2 # Many basic and open questions about the interactions and magnetic excitations U 2e α 4e α Ic MsVHk = U ! Transport models ! ! P ! P ! Micromagnetics (beyond LLGS) Ic ∼ 50 µA ! Noise Potentially compatible CMOS # Great variety of phenomena, materials and structures technology! # New types of devices are possible that operate at the nanoscale and can be realized with present day technology

References • Review Articles: – Journal of Magnetism and Magnetic Materials 320 (2008): Jan. 2008 Current Perspectives – Handbook of Magnetism and Advanced Materials, Vol. 5, Spintronics and Magnetoelectronics, Edited by Parkin and Kronmüller 2007 – IBM J. Res. and Development 50(1) (2006)