Mesoscopic Spintronics Taro WAKAMURA (Université Paris-Sud) Lecture 1
Today s Topics 1.1 History of Spintronics 1.2 Fudamentals in Spintronics Spin-dependent transport GMR and TMR effect Spin injection into diverse materials Spin current and spin relaxation Spin transfer torque
First of all... What is spintronics? Electronics and Spintronics Electron has: charge e Electronics Electron has: spin 1/2 Spintronics
Spintronics in our daily lives Magnetoresistive Random Access Memory (MRAM) Hard Disc Drive (HDD) How was spintronics born?
Spin-dependent transport Spin polarized current I : spin current I : spin current Pure spin current = = :Charge :Spin Flow of charge and spin I e ( = I + I ) 0 I S ( = I -I ) 0 Flow of spin only I S ( = I -I ) 0 Currents in ferromagnets?
Birth of Spintronics Giant Magneto-Resistance (GMR) effect Nobel Prize in Physics in 2007 Nonmagnetic metal Albert Fert Peter Grunberg
Birth of Spintronics Giant Magneto-Resistance (GMR) effect Fert s experiments Fe/Cr/Fe structure Antiferromagnetic coupling depending on the thickness of Cr Antiparallel Parallel Parallel Inplane magnetization curves Magnetoresistance (MR) ratio MR(%) = R AP R P R P x 100 ~ 50 % @ 4.2 K M.N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).
Birth of Spintronics Giant Magneto-Resistance (GMR) effect Grunberg s experiments Similar Fe/Cr/Fe structure, but measurements are at room temperature. Fe/Cr/Fe trilayer structure Small MR ratio: ~1.5 % G. Binasch et al., Phys. Rev. B 39, 4828 (R) (1989).
Birth of Spintronics Giant Magneto-Resistance (GMR) effect How can we explain the gigantic magnetoresistance effect? Electrical currents in ferromagnets are spin-polarized via s-d interaction Most of carries can pass through in the parallel alignment of the ferromagnets (= low R) Most of carries are scattered at the interface in the antiparallel alignment of the ferromagnets (= high R)
Birth of Spintronics Note: Exchange coupling between ferromagnetic layers Co/Ru/Co structure Fe/Cr/Fe structure Stuart Parkin (left) Coupling between ferromagnetic layers oscillates! S. S. P. Parikin et al., Phys. Rev. Lett. 64, 2304 (1990).
Birth of Spintronics Note: Exchange coupling between ferromagnetic layers Rudermann, Kittel, Kasuya, Yoshida (RKKY) interaction between magnetic moments via nonmagnetic layer can induce oscillating interaction. S 1 S 2 Conduction electron Spin density wave of Cr might play a role as well (Wang, Levy and Fry, PRL 1990).
Birth of Spintronics Tunneling Magneto-Resistance (TMR) effect Breakthrough by magnetic tunnel junction (MTJ) TMR in Fe/Al 2 O 3 /Fe multilayers MR ratio 18 % at room temperature T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 139, L231 (1995). Thanks to high-quality amorphous Al 2 O 3 tunnel barrier!
Birth of Spintronics Giant Magneto-Resistance (GMR) effect Julière s model
Birth of Spintronics Tunneling in a simple picture
Birth of Spintronics Tunneling in real materials Importance of symmetries of crystals
Birth of Spintronics Tunnel Magneto-Resistance (TMR) effect There are many Bloch states in Fe, and they have different spin polarization. e.g. D 1 state has high positive spin polarization, and D 2 state has negative spin polarization. Amorphous Al 2 O 3 mixes these states, thus decrease of net spin polarization. Decrease of MR ratio Incoherent tunneling
Birth of Spintronics Tunnel Magneto-Resistance (TMR) effect D 1 state with high spin polarization coherently couples D 1 evanescent wave in MgO tunnel barrier. High MR ratio is expected. Coherent tunneling
Birth of Spintronics Tunnel Magneto-Resistance (GMR) effect High tunneling probability of the D 1 state for parallel alignment High MR ratio
Birth of Spintronics Tunnel Magneto-Resistance (GMR) effect
Birth of Spintronics Tunnel Magneto-Resistance (GMR) effect Small lattice mismatch (3%) between Fe and MgO MgO with high crystallinity can be grown on Fe(001).
Birth of Spintronics Application of TMR to hard disk drives
Birth of Spintronics Application of TMR to hard disk drives
Brief Summary Spin-dependent transport is a key phenomenon for the birth of spintronics. One representative example is the giant magnetoresistance effect with metallic insertion layer between two ferromagnets. Giant magnetoresistance effect provoked intensive studies for systems with higher MR ratio, and replacing metallic layer with tunnel barrier (insulator) enables dramatically gigantic MR (TMR) Then, is it possible to transfer spin angular momentum without charge flow? If it is possible, Joule heating effects can be suppressed!
Pure spin currents Spin polarized current I : spin current I : spin current Pure spin current = = :Charge :Spin Flow of charge and spin I e ( = I + I ) 0 I S ( = I -I ) 0 Flow of spin only I S ( = I -I ) 0 Currents in ferromagnets?
Nonlocal spin injection and detection Easiest way: lateral spin valves Spin Polarized Current Pure Spin Current F side N side spin accumulation charge current + spin current spin current
Nonlocal spin injection and detection Lateral Spin Valve (LSV) structure V N F Spin Current V P DV V AP DV/I [m ] 0-1 DR -500 0 500 Magnetic field [Oe]
Nonlocal spin injection and detection Data evaluation Fitting equation where P I : spin polarization of tunneling junction l X : spin diffusion length of X DV/I [m ] 0 DR -1-500 0 500 Magnetic field [Oe] T. Wakamura et al., Appl. Phys. Exp. 4, 063002 (2011). 27
Hanle effect Another way to estimate t sf and D: the Hanle effect Larmor precession B L e B a 0 rotation NM S I B = 0 V b p/2 rotation NM B V/I 0 c p rotation NM 0 B B
Hanle effect Estimation of t p and D by the Hanle effect Time t N P (arb.) t=0 Pt () 44 46 48 Time (ps) B=0 D N = 500 cm 2 /s t = 40 ps V I 0 dt P( t)cos t 2 1 L t Pt ( ) exp exp p D 4D Nt Nt t 4 sf Diffusion Spin-flip V F. J. Jedema et al, Nature 416, 713 (2002).
Hanle effect First experimental report B (G) F. J. Jedema et al., Nature 416, 713 (2002). Information we can derive from the fitting of the Hanle curve: Diffusion coefficient (D), Spin polarization of Co (P), Spin diffusion length (l sf ) Many examples of the Hanle measurement for different materials: n-gaas (e.g. Lou et al., 2007), LaAlO 3 /SrTiO 3 2DEG (Reyren et al., 2013).
Key points of spin transport Spin can transfer information Spin transport in a long distance is preferable However Spins (to a certain quantized axis) are not conserved Charges are conserved on the contrary. Therefore, it is important to choose materials with long spin relaxation length or spin relaxation time. Then how does spin relaxation occur in materials?
Spin relaxation mechanism Spin relaxation mechanism A: Elliot-Yafet mechanism Periodic ion scattering containing phonon contribution e.g. Metals, Graphene B: D yakonov-perel mechanism Spin precesses along an effective magnetic field during momentum scattering. e.g. Semiconductors, Graphene J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999). Two mechanisms show different dependence of t s on t p. t s : spin relaxation time, t p : momentum relaxation time
Spin relaxation mechanism A: Elliot-Yafet mechanism Basic idea: impurity or phonon scattering + spin-orbit interaction Spin tilts a little every time the electron experiences momentum scattering. t t s p B: D yakonov-perel mechanism Basic idea: spin precession by random magnetic fields The system lack of inversion symmetry: E k E k Kramer s theorem: if Hamiltonian is time-reversal symmetric E k E k J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999). 33
Spin relaxation mechanism From two equations E k E k This can be regarded as a spin split caused by an effective k-dependent magnetic field (k): 1 Η ( k) Ω( k) 2 Electrons change their momentum after each momentum scattering process Random magnetic field between the scattering processes J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999). The smaller t p, the smaller the net magnetic field for spin becomes. (motional narrowing) Thus t s 1 t p 34
Spin relaxation from Hanle measurement Example: single-layer graphene case Single layer graphene t s D t p EY mechanism Bilayer graphene t s D -1 t p -1 DP mechanism H. Wei and R. K. Kawakami, Phys. Rev. Lett. 107, 047207 (2011). 35
Spin Transport in Materials Spin Transport in Various Materials Important issues in spintronics: efficient spin injection and detection (spin impedance mismatch problem) Search for materials with which long-range spin transport is possible Examples in metals: Ag, Al, Cu etc. (low spin-orbit materials) Y. Fukuma et al., Nat. Mater. 10, 527 (2011). 36
Spin Transport in Materials Spin Transport in Various Materials Spin currents can also be transferred through semiconductors (e.g. silicon, GaAs, LAO/STO) Gate control of spin transport is possible S. P. Dash et al., Nature. 462, 491 (2009). B (Oe) N. Reyren et al., Phys. Rev. Lett. 108, 186802 (2012).
Spin Transport in Materials Spin Transport in Various Materials New materials Carbon-based materials (graphene) Graphene Small spin-orbit interaction Good materials for transferring spin currents for a long distance (l sf ~ a few mm) N. Tombros et al., Nature 448, 571(2007).
Brief summary Spin angular momentum can be transferred with out any charge flow by means of spin currents. Spin currents can be easily generated by using ferromagnet-nonmagnet lateral spin-valve structures. The biggest difference between spin currents and charge currents is that spin currents are not conserved. Spin relaxation occurs by magnetic impurities or spin-orbit interaction. For the latter, the EY and DP mechanisms can be considered. Spin currents can be generated from ferromagnets. Then can spin currents affect magnetization of ferromagnets?
Spin transfer torque (STT) Spin(-polarized) currents flow of spin angular momentum Concept of STT When a current is passed through magnetic junction as shown in the right figure, spinpolarized current is injected into FM2 from FM1. If S 1 and S 2 is not parallel, a net torque is exerted on S 2 by injected spinpolarized current. Magnetization can be controlled by flowing a current.
Basics of spin dynamics Landau-Lifsitz Equation When a magnetic field is applied to a magnetic moment, the magnetic field exerts a magnetic torque 0 M x H eff 0 : gyromagnetic constant Magnetic moment continuously precesses around H In real systems, there is relaxation, thus phenomenological damping term
Basics of spin dynamics phenomenological damping term This equation implicitly assumes small damping (namely, the direction of M for the second term does not depend on t). Precisely speaking, damping is the force to prevent dm/dt. Gilbert proposes the following equation: These equations are equivalent by substituting Landau-Lifsitz-Gilbert (LLG) equation
Basics of spin dynamics For electrons from FM1 to FM2, three situations can be considered. (a) Reflection or spin scattering at the interface (b) Transmission (with presession) (c) Absorption of spin angular momentum by FM2
Basics of spin dynamics A spin points to (q,f) can be expressed as For example, in the case of (b), the phase shift for upspin and down spin electrons is and, respectively. Thus the spin function for the transmitted spin can be written as
Basics of spin dynamics If, the electron s spin completely flips. This angular momentum lost during the transmission transfers to FM2. In real materials, the phase shift should be random and averaged out for all electrons. Therefore the net angular momentum change becomes Spin-transfer-torque term proposed by Slonczewski John Slonczewski
Spin transfer torque (STT) Theory of STT Slonczewski s STT term
Spin transfer torque (STT) Magnetic domain wall motion driven by STT Spin transfer from electrons to magnetic moments move magnetic domail walls. Magnetic force microscope images A. Yamaguchi et al., Phys. Rev. Lett. 92, 077205 (2004).
Spin transfer torque (STT) A Magnetization switching by STT Electrons with minority spin carrier from nanomagnet scattered at the interface with Cu Exert torque on magnetization of nanomagnet AP AP A: Magnetic field driven magnetization switching P P B: STT driven magnetization switching Above the critical current, minor spin electrons reflected back from the thick Co layer transfer sufficient spin-angular momentum to the nanomagnet to force it into antiparallel alignment with the Co layer. B P AP F. J. Albert et al., Appl. Phys. Lett. 77, 3809 (2000).
Brief summary Spin(-polarized) currents are a flow of spin angular momentum, thus can exert a torque on magnetization (spin-transfer torque, STT). Magnetization dynamics can be described by Landau-Lifsitz-Gilbert (LLG) equation, and STT is expressed as a Sloczewski term. One can move magnetic domain walls by using STT with currents, and also switch magnetization with STT larger than Gilbert damping.