Spin-Orbit Torque Magnetic Random Access Memory (SOT-MRAM)

1. Theory

• Definition: SOT-MRAM is a three-terminal magnetic memory in which a magnetic tunnel junction sits on a heavy-metal (or topological) channel; an in-plane write current in the channel switches the free layer by spin-orbit torque, and a separate read current flows through the junction.
• Spin Hall effect: Strong spin-orbit coupling deflects opposite spins sideways, turning a charge current into a transverse spin current that enters the free layer.
• Channel materials: Pt (${\theta }_{SH}\approx 0.1$), $\beta$-Ta and $\beta$-W (a few tenths), and topological insulators; the useful figure of merit is ${\theta }_{SH}^2/{\rho }_N$, not ${\theta }_{SH}$ alone.
• Interface losses: Spin memory loss, backflow and finite channel thickness reduce the effective spin Hall efficiency ${\theta }_{eff}$.
• Separate read and write paths: The write current never crosses the MgO barrier, removing STT’s read-write conflict and barrier stress.
• Damping-like and field-like torques: The damping-like torque drives switching; the field-like torque acts like an effective field.

2. Working Principle

• Write: Current through the channel injects spin current into the free layer; the torque is maximal from the start, so there is no incubation delay and sub-nanosecond switching is possible.
• Perpendicular layers need symmetry breaking: Without an in-plane field the damping-like torque leaves up and down equally likely; exchange bias, in-plane layers, tilted anisotropy, structural asymmetry or an added STT give field-free switching.
• Critical current density: Depends on $M_s{t}_F$, the anisotropy field and the in-plane field, divided by ${\theta }_{eff}$.
• Current shunting: Part of the write current flows through the conductive free layer and is wasted.
• Read: TMR sensing through the junction, as in STT-MRAM.
• Write energy: $E_w=I_N^2{R}_{ch}{t}_p$, of order sub-femtojoule for illustrative values, but with an extra transistor per cell.

3. Applications

• Current status: In development, with 300 mm process integration demonstrated; not yet in volume products.
• High-speed non-volatile caches (target): Replacement for SRAM in L1/L2 and last-level caches, combining fast, high-endurance writes with zero standby power.

Name	Formula	Related Formulae	Variables/Constants
Spin Hall charge-to-spin conversion	${\mathbf{J}}_s={\theta }_{SH}\frac{\hslash }{2e}\hat{\sigma }\times {\mathbf{J}}_c$	${\theta }_{SH}=\frac{2e}{\hslash }\frac{J_s}{J_c}$ ${\theta }_{SH}=\frac{{\sigma }_{SH}}{{\sigma }_N}$	$\begin{array}{r}{\mathbf{J}}_s:spincurrentdensity(flowofangular\\ momentumperunitarea)producedbythe\\ spinHalleffectinthechanneland\\ flowingtowardtheinterfacewiththe\\ ferromagnet\end{array}$ $\begin{array}{r}{J}_s,J_c:magnitudesofthespincurrent\\ densityandofthechargecurrentdensity\end{array}$ $\begin{array}{r}{\theta }_{SH}:spinHallangle,theratioofthespin\\ current(inunitsof\hslash /2e)tothecharge\\ current\end{array}$ $\begin{array}{r}\hslash ,e:reducedPlanckconstantand\\ elementarycharge\end{array}$ $\begin{array}{r}\hat{\sigma }:unitvectoralongthespin\\ polarization,whichliesintheplaneof\\ thefilmandisperpendiculartothe\\ chargecurrent\end{array}$ ${\mathbf{J}}_c:chargecurrentdensityinthechannel$ $\begin{array}{r}{\sigma }_{SH}:spinHallconductivityofthechannel\\ material,expressedinunitsof(\hslash /2e)so\\ thatithastheunitsof{\sigma }_N\end{array}$ $\begin{array}{r}{\sigma }_N:electricalconductivityofthechannel\\ material\end{array}$ $\begin{array}{r}(thesignandthedirectionof\hat{\sigma }depend\\ ontheconventionandonthesignof{\theta }_{SH})\end{array}$
Effective spin Hall efficiency of a thin channel	${\theta }_{eff}={\theta }_{SH}{T}_{int}\left[1-\mathrm{sech}\left(\frac{t_N}{{\lambda }_{sf}}\right)\right]$	${\theta }_{eff}\to {\theta }_{SH}{T}_{int}\left(t_N\gg {\lambda }_{sf}\right)$	$\begin{array}{r}{\theta }_{eff}:effectiveefficiencywithwhichthe\\ chargecurrentinthechannelproducesa\\ torqueontheferromagnet\end{array}$ ${\theta }_{SH}:spinHallangleofthechannelmaterial$ $\begin{array}{r}{T}_{int}:spintransmissionofthe\\ channel/ferromagnetinterface(between\\ zeroandone)\end{array}$ $t_N:thicknessofthechannel$ ${\lambda }_{sf}:spindiffusionlengthinthechannel$ $\begin{array}{r}(achannelmuchthinnerthanthespin\\ diffusionlengthconvertslittlecurrent,\\ sotheefficiencysaturatesfora\\ thicknessofafew{\lambda }_{sf})\end{array}$ $\begin{array}{r}(drift-diffusionresultusedinthe\\ spin-torqueFMRanalysisofL.Liuetal.,\\ Phys.Rev.Lett.106,036601(2011);T_{int}is\\ aphenomenologicalfactorhere)\end{array}$
Figure of merit of the channel material	$FoM=\frac{{\theta }_{SH}^2}{{\rho }_N}$	$P_{ch}\propto J_c^2{\rho }_N\propto \frac{{\rho }_N}{{\theta }_{eff}^2}$	$\begin{array}{r}FoM:figureofmeritofachannelmaterial\\ (largervaluesgivealowerwritepower)\end{array}$ ${\theta }_{SH}:spinHallangle$ ${\rho }_N:resistivityofthechannelmaterial$ $\begin{array}{r}{P}_{ch}:powerdissipatedperunitvolumeof\\ thechannelduringawrite\end{array}$ $\begin{array}{r}{J}_c:chargecurrentdensityneededfor\\ switching,whichfallsas1/{\theta }_{eff}\end{array}$ $\begin{array}{r}{\theta }_{eff}:effectivespinHallefficiency\\ (previousrow)\end{array}$ $\begin{array}{r}(scalingestimateatafixedgeometry:it\\ ignoresshunting,contactresistanceand\\ thethicknessdependenceof{\rho }_N;some\\ paperscompare{\theta }_{SH}/{\rho }_{N}or{\sigma }_{SH}instead)\end{array}$
Current shunting through the ferromagnet	$J_N=\frac{I_w{\sigma }_N}{w\left({\sigma }_N{t}_N+{\sigma }_F{t}_F\right)}$	$\frac{I_N}{I_w}=\frac{{\sigma }_N{t}_N}{{\sigma }_N{t}_N+{\sigma }_F{t}_F}$	$\begin{array}{r}{J}_N:currentdensityinthechannelwhen\\ thefreelayerisconductiveandshunts\\ partofthecurrent\end{array}$ $\begin{array}{r}{I}_w:totalwritecurrentthroughthe\\ channelandthelayersaboveit\end{array}$ $w:widthofthechannel$ $\begin{array}{r}{\sigma }_N,t_N:conductivityandthicknessofthe\\ channel\end{array}$ $\begin{array}{r}{\sigma }_F,t_F:conductivityandthicknessofthe\\ ferromagneticlayer\end{array}$ $\begin{array}{r}{I}_N:partofthecurrentthatflowsinthe\\ channel(parallelconductionmodel)\end{array}$ $\begin{array}{r}(thin-filmconductivitiesdependon\\ thickness,andinterfaceresistanceis\\ neglected)\end{array}$
Torque on the free layer: damping-like and field-like	$\frac{d\mathbf{m}}{dt}=-\gamma \mathbf{m}\times {\mathbf{H}}_{eff}+\alpha \mathbf{m}\times \frac{d\mathbf{m}}{dt}-\gamma H_{DL}\mathbf{m}\times \left(\mathbf{m}\times \hat{\sigma }\right)-\gamma H_{FL}\mathbf{m}\times \hat{\sigma }$	$H_{DL}=\frac{\hslash {\theta }_{eff}{J}_N}{2e{\mu }_0{M}_s{t}_F}$	$\begin{array}{r}\mathbf{m}:unitvectoralongthemagnetizationof\\ thefreelayer\end{array}$ $\begin{array}{r}\gamma :gyromagneticratio(definedforafield\\ inA/m)\end{array}$ $\begin{array}{r}{\mathbf{H}}_{eff}:effectivefield(anisotropy,\\ demagnetizingandappliedfields)\end{array}$ $\alpha :Gilbertdampingconstant$ $\begin{array}{r}\hat{\sigma }:spinpolarizationdirectionofthe\\ spincurrent(intheplane,perpendicular\\ tothechargecurrent)\end{array}$ $\begin{array}{r}{H}_{DL},H_{FL}:equivalentfieldsofthe\\ damping-likeandthefield-liketorque(in\\ A/m)\end{array}$ ${\theta }_{eff}:effectivespinHallefficiency$ $J_N:chargecurrentdensityinthechannel$ $\begin{array}{r}e,\hslash ,{\mu }_0:elementarycharge,reduced\\ Planckconstantandvacuumpermeability\end{array}$ $\begin{array}{r}{M}_s,t_F:saturationmagnetizationand\\ thicknessofthefreelayer\end{array}$ $\begin{array}{r}(thedamping-liketermhastheformofthe\\ spin-transfertorqueoftheSTT-MRAMpage,\\ with\hat{\sigma }intheplaceofthereference\\ direction\mathbf{p})\end{array}$
Critical current density with an in-plane field	$J_{c0}=\frac{2e}{\hslash }\frac{{\mu }_0{M}_s{t}_F}{{\theta }_{eff}}\left(\frac{H_k}{2}-\frac{H_x}{\sqrt{2}}\right)$	$\frac{H_k}{2}>\frac{H_x}{\sqrt{2}}$	$\begin{array}{r}{J}_{c0}:criticalchargecurrentdensityinthe\\ channelfortheswitchingofa\\ perpendicularfreelayer(zero\\ temperature,macrospin)\end{array}$ $\begin{array}{r}e,\hslash ,{\mu }_0:elementarycharge,reduced\\ Planckconstantandvacuumpermeability\end{array}$ $\begin{array}{r}{M}_s,t_F:saturationmagnetizationand\\ thicknessofthefreelayer\end{array}$ ${\theta }_{eff}:effectivespinHallefficiency$ $H_k:anisotropyfieldofthefreelayer$ $\begin{array}{r}{H}_x:in-planemagneticfieldappliedalong\\ thecurrentdirection,whichbreaksthe\\ symmetryanddefinesthefinalstate(the\\ relatedconditionkeeps{J}_{c0}positive)\end{array}$ $\begin{array}{r}(K.-S.Leeetal.,Appl.Phys.Lett.102,\\ 112410(2013),writteninSI;macrospin,\\ zerotemperature,H_{x}wellbelow{H}_k,\\ field-liketorqueneglected)\end{array}$
Write current, channel resistance and write energy	$I_N=J_{N}w{t}_N$	$R_{ch}=\frac{{\rho }_N{L}_{ch}}{w{t}_N}$ $E_w=I_N^2{R}_{ch}{t}_p$	$\begin{array}{r}{I}_N:writecurrentinthechannel(flows\\ betweentwoterminalsandnotthroughthe\\ tunneljunction)\end{array}$ $J_N:currentdensityinthechannel$ $\begin{array}{r}w,t_N,L_{ch}:width,thicknessandlengthof\\ thechannelunderthejunction\end{array}$ $R_{ch}:resistanceofthechannel$ ${\rho }_N:resistivityofthechannelmaterial$ $E_w:Jouleenergyofawritepulseoflength{t}_p$ $t_p:writepulseduration$

Important Questions

Ques: How does an SOT-MRAM cell differ from an STT-MRAM cell?

An SOT-MRAM cell has three terminals. The magnetic tunnel junction sits on top of a heavy-metal (or topological) channel, and the write current flows in the plane of the channel between two terminals, while the read current flows through the junction between the third terminal and one of the channel terminals. The in-plane current produces a spin current by the spin Hall effect, and the spin current exerts a torque on the free layer. The writing therefore does not stress the tunnel barrier with a high current, and the read and write paths are separate, which removes the conflict between the read and write of an STT cell. The cost is an extra transistor and terminal per cell, and in a perpendicular cell a symmetry-breaking field. Reference: A. Manchon et al., “Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems,” Rev. Mod. Phys. 91, 035004 (2019); G. Prenat et al., “Ultra-fast and high-reliability SOT-MRAM: from cache replacement to normally-off computing,” IEEE Trans. Multi-Scale Comput. Syst. 2, 49 (2016).

Ques: What is the origin of the spin Hall effect, and which materials are used?

A charge current in a material with strong spin-orbit coupling deflects the spin-up and spin-down electrons in opposite directions, so a transverse spin current appears. The origin is intrinsic (the Berry curvature of the band structure, which gives a ${\sigma }_{SH}$ independent of the scattering) or extrinsic (skew scattering and side jump from impurities). The first demonstrations of switching used Pt, then $\beta$-Ta and $\beta$-W, with reported spin Hall angles of about 0.05 to 0.1 for Pt, about $-0.12$ to $-0.15$ for $\beta$-Ta (Liu 2012) and about $-0.3$ for $\beta$-W (Pai 2012), the negative sign meaning the opposite spin direction to Pt, and topological insulators and alloys were reported later with larger values. A high ${\theta }_{SH}$ in a high-resistivity material does not give a low write power, which is the point of the figure of merit ${\theta }_{SH}^2/{\rho }_N$. Reference: J.E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett. 83, 1834 (1999); J. Sinova, S.O. Valenzuela, J. Wunderlich, C.H. Back and T. Jungwirth, “Spin Hall effects,” Rev. Mod. Phys. 87, 1213 (2015); L. Liu et al., “Spin-torque switching with the giant spin Hall effect of tantalum,” Science 336, 555 (2012); C.-F. Pai et al., “Spin transfer torque devices utilizing the giant spin Hall effect of tungsten,” Appl. Phys. Lett. 101, 122404 (2012).

Ques: Why does a perpendicular free layer need an in-plane field, and how can this be avoided?

The damping-like torque tilts the magnetization toward the in-plane spin direction $\hat{\sigma }$, which is perpendicular to the easy axis. The torque is the same for the two final states, so without a symmetry-breaking element the magnetization relaxes to up or down with equal probability. An in-plane field along the current (the $H_x$ term in the critical-current row) makes the switching deterministic, and its direction sets the final state. A field is not practical in a chip, so field-free options are used: an exchange bias or an in-plane magnetized layer that gives an effective $H_x$, a tilted anisotropy, a lateral structural asymmetry of the channel, and an additional spin-transfer torque from the junction. Each adds a layer or a process step. Reference: I.M. Miron et al., “Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection,” Nature 476, 189 (2011); K.-S. Lee, S.-W. Lee, B.-C. Min and K.-J. Lee, “Threshold current for switching of a perpendicular magnetic layer induced by spin Hall effect,” Appl. Phys. Lett. 102, 112410 (2013).

Ques: Why is SOT switching fast?

In an STT cell the spin polarization is collinear with the magnetization in the initial state, so the torque is zero at $\theta =0$ and the reversal starts only after an incubation time set by the thermal initial angle ${\theta }_0$ (the $\ln (\pi /2{\theta }_0)$ term of the precessional switching time on the STT-MRAM page). In an SOT cell the spin polarization $\hat{\sigma }$ is perpendicular to the magnetization from the start, so the torque is at its maximum immediately and there is no incubation delay. Sub-nanosecond switching has been reported, and the switching time falls with the overdrive current. No switching-time expression is given on this page, because the published macrospin results depend on the field and the field-like torque. Reference: K. Garello et al., “Ultrafast magnetization switching by spin-orbit torques,” Appl. Phys. Lett. 105, 212402 (2014); K. Garello et al., “SOT-MRAM 300mm integration for low power and ultrafast embedded memories,” IEEE Symp. VLSI Circuits (2018).

Ques: How much energy does an SOT write need?

With the write-energy row, an example: a channel of width $w=100$ nm, thickness $t_N=5$ nm and length $L_{ch}=200$ nm, resistivity ${\rho }_N=20\mu \Omega$cm, a critical current density of $10^7$ A/cm${}^2$ and a pulse length of 1 ns. The current in the channel is $I_N=J_{N}w{t}_N=50\mu$A, the channel resistance is $R_{ch}=80\Omega$, and the energy is $E_w=I_N^2{R}_{ch}{t}_p\approx 0.2$ fJ. This uses assumed numbers for the geometry and the current density, and ignores the shunting of the current through the free layer, the overdrive that a fast pulse needs and the in-plane field. The current also flows in the channel, not in the junction, which is what allows a higher current without stressing the barrier. Reference: A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019); K. Garello et al., IEEE Symp. VLSI Circuits (2018).

Ques: What does the interface do to the efficiency?

The spin current produced in the channel has to cross the interface to reach the free layer. Spin memory loss and spin backflow at the interface reduce the spin current that is absorbed, which is described by the transmission $T_{int}$, and the finite thickness of the channel reduces the spin accumulation (the $1-\mathrm{sech}(t_N/{\lambda }_{sf})$ factor). Measured values of the spin Hall angle depend on the method (spin-torque ferromagnetic resonance, harmonic Hall, spin pumping), and the apparent value in a given stack is the effective one, so the values quoted for a material should be compared at the same thickness and interface. Reference: L. Liu et al., “Spin-torque ferromagnetic resonance induced by the spin Hall effect,” Phys. Rev. Lett. 106, 036601 (2011); J.-C. Rojas-Sanchez et al., “Spin pumping and inverse spin Hall effect in platinum: the essential role of spin-memory loss at metallic interfaces,” Phys. Rev. Lett. 112, 106602 (2014).

Related pages in this vault: Spin-Transfer Torque Magnetic Random Access Memory (STT-MRAM), Voltage-Controlled Magnetic Anisotropy MRAM (VCMA-MRAM), Toggle Magnetic Random Access Memory (Toggle MRAM), Magnetoresistive Random Access Memory (Toggle and STT-MRAM), Hall Effect System, Magnetic Materials and Magnetic Circuits, Magnetic Force Microscope (MFM).