Spin orbit torque driven magnetic switching and memory. Debanjan Bhowmik

Transcription

1 Spin orbit torque driven magnetic switching and memory Debanjan Bhowmik

2 Spin Transfer Torque Fixed Layer Free Layer Fixed Layer Free Layer Current coming out of the fixed layer (F2) is spin polarized in direction of magnetizaton of M 2. This spin current acts on the magnetization of free layer F1 (M 1 ) and provides spin transfer Torque (Sonczweski torque) given by: η ( ) η : Srength of Slonczweski torque Spin transfer torque can be used for low power writing in magnetic memory (MRAM).

3 Alternative: Spin Orbit Torque Current flowing through ferromagnetic metal layer sees equivalent magnetic field, due to electric field at the interface. Current flowing through heavy metal layer Leads to accumulation of spin-polarized electrons at the interface. Two spin orbit torque terms: i. Field like torque: ii. Damping like torque:

4 Spin-Orbit Coupling Classical Electrodynamics, Jackson In laboratory frame of reference, say electric field is and magnetic field is 0. Anti-symmetric field strength tensor: A particle moves at velocity v in x-direction with respect to laboratory frame. Lorentzian transformation matrix: From reference frame of particle: g = 1 1- b 2 Electric field in laboratory frame of reference becomes magnetic field from particle frame of reference:

5 Spin-Orbit Coupling Electric field in laboratory frame of reference becomes magnetic field from particle frame of reference: If the particle is an electron, energy= : magnetic moment of electron : spin angular momentum of electron : Pauli spin matrix vector m: mass of electron Spin orbit coupling term in the Hamiltonian H SO = Is the spin orbit coupling coefficient.

6 Manchon, A. et al. Phys. Rev. B. 79, (2009). Rashba Effect j s Electric field is in Z direction due to Structral Inversion Asymmetry. : spin orbit coupling of conduction electrons in ferromagnetic metal : exchange coupling between conduction electrons and local moment of ferromagnet Since and This explains field like torque term:

7 Spin Hall Effect Similar in spirit to Rashba effect, but conduction electrons here are that of heavy metal And electric field can come from potential due to impurities (extrinsic spin Hall effect) or due to band structure of the metal (intrinsic spin Hall effect) A conduction electron in heavy metal experiences spin orbit coupling: An electron picks up an an anomalous velocity proportional to spin Hall angle:

8 Spin Hall Effect Electric field in x direction driving the electrons: z directed current due to electrons spin polarized in y direction: +y spin polarization ( ): -y spin polarization ( ): Net charge current = 0 Net spin current= Thus, spin Hall angle = Spin current/ Charge current

9 Spin Hall Effect in 5d transition metal (Ta) Spin Hall Angle (α SH ) Experimental Technique Non-local Spin Transport and Inverse SHE 0.15 Spin Torque FMR 0.12 Switching perpendicularly Magnetized CoFeB Reference M.Morota et al.,phys. Rev. B. 83, 2011 L.Liu et al., Science 336,2012 L.Liu et al., Science 336,2012 Possible Mechanisms: 1. Impurity scattering 2. Intrinsic Effects (first principle calculations predict opposite signs of Ta and Pt) T.Tanaka et al., Phys. Rev. B. 77,2008

10 Magnitude of spin current, from spin diffusion theory Electrons with spins in opposite direction lead to accumulation of spins across z direction, also leading to spin diffusion current. Spin dependent chemical potential: Spin current:

11 Magnitude of spin current, from spin diffusion theory Ferromagnetic metal on top Boundary conditions: Solution: spin current at z = W surface (interface with ferromagnet) Gets absorbed into the ferromagnet.

12 Magnitude of spin current, from spin diffusion theory W This spin current has spin polarization These spins get injected into the ferromagnetic metal layer. From spin transfer torque theory discussed before, ferromagnetic layer with magnetization M experiences : Damping like torque:

13 Spin orbit torque driven Magnetization dynamics: Equivalent spin transfer torque Easy axis Magnetic field: M 1 Anisotropy field Free layer Spin orbit torque: Tunnel barrier Electron Flow (J c ) M 2 Fixed layer t= thickness of ferromagnet, M s : saturation magnetization, θ= spin polarization

14 Need of an external magnetic field

15 Need of an external magnetic field

16 Trajectory for spin orbit torque switching Current density through Ta= 7.5 x 10 7 A/cm 2, spin Hall angle of Ta =0.12 Initial precession due to canceling of spin torque and damoing torque is absent here, leading to faster switching.

17 Trajectory for spin orbit torque switching Current density through Ta= 9 x 10 7 A/cm 2, spin Hall angle of Ta =0.12

18 Trajectory for spin orbit torque switching Current density through Ta= 1 x 10 8 A/cm 2, spin Hall angle of Ta =0.12

19 Switching time versus current density Advantage- Current density does not go up with decrease in switching time, unlike STT. Faster switching is possible. Disadvantage much higher value of current density needed.

20 Current density vs damping Advantage- Unike STT, switching current density is not directly proportional to damping factor, so more flexibility in terms of choosing materials.

21 External dc magnetic field needed to break the symmetry Landau Lifschitz Gilbert equation: M= magnetization, α= damping constant, γ= gyromagnetic ratio, σ= spin accumulation Not practical for a real SOTMRAM!! 21

22 Wedge shape of the magnet eliminates the need of an external magnetic field Fig I α < β Ta Direction of magnetization M driven by spin orbit torque Direction of final Magnetization M Fig II Ta +x +z -x -z α > β 22

23 Micromagnetic Simulation: Symmetry breaking due to wedge shape of the magnet y Spin Orbit Spin Torque orbit Off torque on M(magnetization): White arrow: In plane, Red: +z, Blue: -z; σ: spin accumulation Direction of M driven by σ +x -x Direction of final M +z -z

24 Micromagnetic Simulation: Symmetry breaking due to wedge shape of the magnet M(magnetization): White arrow: In plane, Red: +z, Blue: -z; Direction of M driven by σ Direction of final M +x +z -x -z Experimentally demonstrated the same phenomenon: L. You, O.J. Lee, D. Bhowmik et al. Proceedings of National Academy of Sciences 112(33) 2015 σ: spin accumulation 24

25 Device structure (STTMRAM and SOTMRAM) Advantages of SOTMRAM: i. Tunnel junction not damaged while writing. ii. Magnet is not switched while reading iii. Faster switching iv. More choice of materials Disadvantage of SOTMRAM: i. 2 transistors are needed per cell, hence more area occupied ii. Larger switching current density Kim et al. IEEE Transactions on Electron Devices 62, Lee et al. Proceedings of IEEE 104 (10), 2016