NYU NYU Spins Dynamics in Nanomagnets Outline I. Spin-Transport and Transfer Basics Andrew D. Kent –Giant magnetoresistance (GMR) –Spin filtering and spin momentum transfer II. Spin-Transfer Induced Magnetization 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 !"#$%&'()#*#+,)#-)./'()-)"+/#0$#1(2"3)(&4/#&(0'5#.()#6%/57.8)6#97)$+:#+0&)+,)(#;%+,#+,0/)#0$#<)(+4/# &(0'5#9(%&,+:=#>,)#8?.@%/#."6#@?.@%/#()5()/)"+#+,)#()/%/+."A)#A,."&)#."6#)@+)(".7#-.&")+%A#$%)76B#()/5)A? 1 2009 Boulder+%C)78=# School,>,)# Lecture)@5)(%- 2 )"+/#/,0;#.#-0/+#/%&"%$%A."+#")&.+%C)#-.&")+0()/%/+."A)#$0(#+,)#+(%7.8)(#./#;)77#./# 2 2009 Boulder School, Lecture 2 Physics 2007+,)#-'7+%7.8)(/=#>,)#/8/+)-/#+0#+,)#(%&,+B#%"C07C%"&#7.(&)#/+.AD/#0$#7.8)(/B#/,0;#.#6)A()./10/15/2007)#0$#()/% 08:19/+." 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A.+%0"/#."6#5.+)"+)6#+,)#6%/A0C)(8=#<(0-#+,%/#C)(*8#9#-SE0:-# )"+#+,)#.().#0$#+,%"#$%7-#-.&")+%/-#()/).(A,# # A0-57)+)78#A,."&)6#6%()A+%0"#%"+0#-.&")+0)7)A+(0"%A/=## http://nobelprize.org/nobel_prizes/physics/laureates/2007/ # Page 1 of 1 >,)#6%/A0C)(8#0$#&%."+#-.&")+0()/%/+."A)#%--)6%.+)78#05)")6#+,)#600(#+0#.#;).7+,#0$#");#/A%)"+%$%A#."6# +)A,"070&%A.7#50//%3%7%+%)/B#%"A7'6%"&#.#+()-)"60'/#%"$7')"A)#0"#+,)#+)A,"%^')#0$#6.+.#/+0(.&)#."6#-.&")+%A# /)"/0(/=#>,0'/."6/#0$#/A%)"+%/+/#.77#.(0'"6#+,)#;0(76#.()#+06.8#;0(D%"&#0"#-.&")+0)7)A+(0"%A#5,)"0-)".# ."6#+,)%(#)@570(.+%0"=#>,)#/+0(8#0$#+,)#1OT#)$$)A+#%/#.#C)(8#&006#6)-0"/+(.+%0"#0$#,0;#.#+0+.778#'")@? 5)A+)6#/A%)"+%$%A#6%/A0C)(8#A."#&%C)#(%/)#+0#A0-57)+)78#");#+)A,"070&%)/#."6#A0--)(A%.7#5(06'A+/=# *#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 electric current! 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 Applied Field [T] 0 0 0.05 0.1 J.