Toggle Magnetic Random Access Memory (Toggle MRAM)

1. Theory

• Definition: Toggle MRAM is a field-written magnetic RAM whose free layer is a synthetic antiferromagnet (SAF), switched by two overlapping current pulses on a word line and a bit line, and read through the tunnel magnetoresistance of the junction.
• Read element: A magnetic tunnel junction whose resistance is low for parallel and high for antiparallel magnetizations (details on the STT-MRAM page).
• Stoner-Wohlfarth astroid: Describes the field combinations that switch a single-domain magnet; conventional field MRAM wrote cells at the edge of this astroid.
• Half-select problem: In conventional field MRAM, cells on only one active line see fields near the astroid, so cell variation causes write failures or disturbs.
• Synthetic antiferromagnet: Two ferromagnetic layers coupled antiparallel through a Ru spacer, with the easy axis at $45^{\circ }$ to the write lines.
• Spin-flop: In a field the SAF moments scissor to lie nearly perpendicular to the field, which is the basis of toggle switching.
• Shape anisotropy: The elongated cell’s demagnetizing factors set the anisotropy field $H_k=(N_w-N_L)M_s$.

2. Working Principle

• Write sequence: Word line on, bit line on, word line off, bit line off, so the field rotates by $90^{\circ }$ and carries the flopped moment pair around.
• Toggle action: When the field is removed, the two layer moments have swapped, so every write reverses the bit regardless of field direction.
• Read-before-write: The cell is read first and toggled only if the stored value differs from the new data.
• Large write margin: Only the fully selected cell sees enough rotating field to flop, so half-selected cells are not disturbed.
• Field from current: Each line field is about $I/2\pi d$, needing milliampere currents and tens of picojoules per write.
• Scaling limit: Smaller cells need higher switching fields while line cross-sections shrink, so electromigration and crosstalk prevent scaling.

3. Applications

• Industrial and automotive non-volatile memory: Fast, unlimited-endurance storage for controllers, data logging and black-box recorders.
• Aerospace and defence: Radiation-tolerant memory for satellites and avionics, where magnetic storage is immune to charge upsets.
• RAID and storage controllers: Non-volatile write caches that survive power loss without batteries.

Name	Formula	Related Formulae	Variables/Constants
Stoner-Wohlfarth energy and astroid	$\frac{E}{V}=K_u{\sin }^2\varphi -{\mu }_0{M}_{s}H\cos \left(\varphi -\psi \right)$	${\left(\frac{H_x}{H_k}\right)}^{2/3}+{\left(\frac{H_y}{H_k}\right)}^{2/3}=1$ $H_{sw}\left(\psi \right)=\frac{H_k}{{\left({\cos }^{2/3}\psi +{\sin }^{2/3}\psi \right)}^{3/2}}$ $H_k=\frac{2K_u}{{\mu }_0{M}_s}$	$\begin{array}{r}E/V:magneticenergydensityofa\\ single-domainferromagneticlayer(the\\ Stoner-Wohlfarthmodel)\end{array}$ $\begin{array}{r}{K}_u:uniaxialanisotropyenergydensity\\ (theshapeanisotropyinapatternedcell)\end{array}$ $\varphi :angleofthemagnetizationfromtheeasyaxis$ $\begin{array}{r}{\mu }_0,M_s:vacuumpermeabilityandsaturation\\ magnetization\end{array}$ $\begin{array}{r}H,\psi :magnitudeoftheappliedfieldand\\ itsanglefromtheeasyaxis\end{array}$ $\begin{array}{r}{H}_x,H_y:componentsofthefieldalongthe\\ easyaxisandthehardaxis(theastroid\\ istheboundaryofthefieldsthatswitch\\ thelayer)\end{array}$ $\begin{array}{r}{H}_k:anisotropyfield,whichisthe\\ switchingfieldalongtheeasyaxisand\\ alsothefieldneededalongthehardaxis\end{array}$ $\begin{array}{r}{H}_{sw}\left(\psi \right):switchingfieldattheangle\psi (it\\ is{H}_k/2at45degrees)\end{array}$
Shape anisotropy and switching field	$H_k=\left(N_w-N_L\right)M_s$	$\Delta =\frac{{\mu }_0{M}_s{H}_{k}V}{2k_{B}T}$ $H_k\propto \frac{\Delta k_{B}T}{M_{s}V}$	$\begin{array}{r}{H}_k:anisotropyfieldfromtheshapeofan\\ elongatedcell\end{array}$ $\begin{array}{r}{N}_w,N_L:demagnetizingfactorsalongthe\\ widthandalongthelengthofthecell(N_w\\ islargerthan{N}_L)\end{array}$ $M_s:saturationmagnetization$ $\Delta :thermalstabilityfactor$ $\begin{array}{r}{\mu }_0,k_B,T:vacuumpermeability,Boltzmann\\ constantandtemperature\end{array}$ $V:volumeofthefreelayer$ $\begin{array}{r}(forafixed\Delta theswitchingfieldrises\\ asthevolumefalls,soasmallercell\\ needsalargerwritefield)\end{array}$
Field of a write line	$H=\frac{I}{2\pi d}$	$H={\eta }_f\frac{I}{2\pi d}$ $I\approx \frac{2\pi dH}{{\eta }_f}$	$\begin{array}{r}H:magneticfieldatthefreelayerfrom\\ thecurrentinawriteline,takenasa\\ longthinwire\end{array}$ $I:currentinthewriteline$ $\begin{array}{r}d:distancefromthecentreofthelineto\\ thefreelayer\end{array}$ $\begin{array}{r}{\eta }_f:fieldenhancementfactorofa\\ flux-concentratingcladdingaroundthe\\ line(equaltoonewithoutit)\end{array}$ $\begin{array}{r}(thefieldofareallineoffinitewidth\\ islowerthanthatofathinwire)\end{array}$
Synthetic antiferromagnet free layer	$\frac{E}{A}=-J_{ex}\cos \left({\varphi }_1-{\varphi }_2\right)+{\sum }_{i=1,2}\left[K_u{t}_i{\sin }^2{\varphi }_i-{\mu }_0{M}_s{t}_{i}H\cos \left({\varphi }_i-\psi \right)\right]$	$H_{ex}=\frac{-J_{ex}}{{\mu }_0{M}_s{t}_F}$ $H_{sf}=\sqrt{H_k\left(2H_{ex}-H_k\right)}\approx \sqrt{2H_{ex}{H}_k}$ $H_{sat}=2H_{ex}-H_k\approx 2H_{ex}$	$\begin{array}{r}E/A:magneticenergyperunitareaoftwo\\ identicalferromagneticlayerscoupled\\ throughathinnon-magneticspacer(the\\ Stoner-Wohlfarthmodelforeachlayer)\end{array}$ $\begin{array}{r}{J}_{ex}:interlayerexchangecouplingenergy\\ perunitarea,negativeforthe\\ antiferromagneticcoupling(Ruspacer)\end{array}$ $\begin{array}{r}{\varphi }_1,{\varphi }_2:anglesofthemagnetizationsof\\ thetwolayersfromtheeasyaxis\end{array}$ $\begin{array}{r}{t}_i:thicknessoflayeri(equalto{t}_{F}for\\ abalancedpair)\end{array}$ $\begin{array}{r}{K}_u,M_s,H,\psi :anisotropyenergydensity,\\ saturationmagnetization,appliedfield\\ anditsangle\end{array}$ $H_{ex}:exchangefieldofthecoupling$ $H_k:anisotropyfieldofonelayer$ $\begin{array}{r}{H}_{sf}:spin-flopfieldatwhichthetwo\\ momentsturnperpendiculartothefield\\ andbecomenearlyparalleltoeachother\\ (forthefieldalongtheeasyaxis)\end{array}$ $\begin{array}{r}{H}_{sat}:saturationfieldatwhichthetwo\\ momentsarealignedwiththefield\end{array}$ $\begin{array}{r}(bothderivedforabalancedpairwiththe\\ fieldalongtheeasyaxis:intheflopstate\\ \cos \theta =H/(2H_{ex}-H_k),and{H}_{sf}iswhereits\\ energyequalsthatoftheantiparallelstate;\\ theantiparallelstatestaysmetastableup\\ to\sqrt{H_k\left(2H_{ex}+H_k\right)},andtheapproximations\\ holdfor{H}_{ex}\gg H_k)\end{array}$
Toggle write window	$H_{eff}=\sqrt{H_x^2+H_y^2}$	$H_{sf}<H_{eff}<H_{sat}$ $\psi =\arctan \frac{H_y}{H_x}=45^{\circ }$	$\begin{array}{r}{H}_{eff}:magnitudeofthefieldwhentheword\\ lineandthebitlinearebothon(the\\ fieldsofthetwolinesareperpendicular\\ toeachother)\end{array}$ $H_x,H_y:fieldsofthetwolinesatthecell$ $\begin{array}{r}{H}_{sf},H_{sat}:spin-flopandsaturationfields\\ ofthesyntheticantiferromagnetforthe\\ fielddirection\psi (at\psi =45^{\circ }theydifferfromthe\\ easy-axisvaluesofthepreviousrow;\\ seeD.C.Worledge,Appl.Phys.Lett.84,\\ 4559(2004))\end{array}$ $\begin{array}{r}\psi :angleofthefieldfromtheeasyaxis\\ ofthecell,whichis45degreesfromboth\\ lines(hencethecellisrotatedby45\\ degreestothelines)\end{array}$ $\begin{array}{r}(thepulsesequenceturnsononeline,\\ thentheother,thenturnsoffthefirst\\ andthenthesecond,sothefield\\ directionrotatesby90degrees;acell\\ withonlyonelineonseesafieldbelow\\ thespin-flopfieldanddoesnottoggle)\end{array}$
Write energy of the two lines	$E_w={\sum }_{k=x,y}{I}_k^2{R}_k{t}_k$	$I_k=\frac{2\pi d{H}_{line}}{{\eta }_f}$	$\begin{array}{r}{E}_w:Jouleenergyinthetwowritelines\\ foronewriteoperation\end{array}$ $\begin{array}{r}{I}_k:currentinlinek(thewordlineor\\ thebitline)\end{array}$ $\begin{array}{r}{R}_k:resistanceoflinekoverthelength\\ thatcarriesthecurrent\end{array}$ $\begin{array}{r}{t}_k:timeforwhichthecurrentflowsin\\ linek(thesequenceofthepulses\\ overlaps)\end{array}$ $\begin{array}{r}d,{\eta }_f:distancetothefreelayerand\\ claddingenhancementfactor(previous\\ rows;dismeasuredfromthecentreof\\ theline)\end{array}$ $\begin{array}{r}{H}_{line}:fieldthatthelinemustprovideat\\ thecell(afractionofthewindowfield\\ H_{eff})\end{array}$

Important Questions

Ques: Why was toggle MRAM developed, and what does the synthetic antiferromagnet do?

In a conventional field-written MRAM the free layer is switched by the sum of the fields of a word line and a bit line, according to the Stoner-Wohlfarth astroid. A cell on only one of the two lines (half-selected) sees a field that is also close to the astroid, so cell-to-cell variation of the switching field gives either an unwritten selected cell or a disturbed half-selected one, and the margin is small. Toggle MRAM replaces the single free layer with a synthetic antiferromagnet (two ferromagnetic layers coupled by a Ru spacer) with the easy axis at 45 degrees to the lines, and writes with a sequence of pulses. The spin-flop transition gives a field window in which only the selected cell flops and the half-selected cells do not, and the margin is much larger. Reference: L. Savtchenko, B.N. Engel, N.D. Rizzo, M.F. Deherrera and J.A. Janesky, Method of writing to scalable magnetoresistance random access memory element, U.S. Patent 6,545,906 (2003); B.N. Engel et al., “A 4-Mb toggle MRAM based on a novel bit and switching method,” IEEE Trans. Magn. 41, 132 (2005).

Ques: How does the write sequence reverse the cell, and why is it a toggle?

With the easy axis at 45 degrees, a field along one line turns the two antiparallel moments of the synthetic antiferromagnet into the spin-flop state, in which they are almost perpendicular to the field and the net moment follows the field. The pulse sequence turns on the word line, then the bit line (both on), then turns off the word line, then the bit line, so that the field direction rotates by 90 degrees. The pair of moments is carried round by the rotating field, and when the field is removed it relaxes into the easy axis with the two moments exchanged, so the layer that was up becomes down and the other way. The final state does not depend on the direction of the fields, only on the sequence, so every write reverses the cell (a toggle), and the stored state has to be read first and the cell written only if it differs from the data. This is a cost of the method that STT and SOT writes with a direction of current do not have. Reference: D.C. Worledge, “Spin flop switching for magnetic random access memory,” Appl. Phys. Lett. 84, 4559 (2004); B.N. Engel et al., IEEE Trans. Magn. 41, 132 (2005).

Ques: What current and energy does a field write need?

With the line-current row, a required field at the cell of 50 Oe (about 4000 A/m) and a distance of 200 nm from the line to the free layer give $I\approx 2\pi dH/{\eta }_f\approx 5$ mA with no cladding. With a line resistance of 100 $\Omega$, a pulse of 10 ns and two lines, the Joule energy is $E_w\approx 2\times (5\mathrm{mA}{)}^2\times 100\Omega \times 10\mathrm{ns}\approx 50$ pJ. The numbers are illustrative; a cladding lowers the current, and the real lines have a width, a thickness and a resistance that depend on the design. The energy is larger by orders of magnitude than that of a spin-torque write, which is one reason for the move to STT. Reference: B.N. Engel et al., IEEE Trans. Magn. 41, 132 (2005); M. Durlam et al., “A 1-Mbit MRAM based on 1T1MTJ bit cell integrated with copper interconnects,” IEEE J. Solid-State Circuits 38, 769 (2003).

Ques: Why does field writing not scale to smaller cells?

For a given thermal stability factor $\Delta ={\mu }_0{M}_s{H}_{k}V/2k_{B}T$ the anisotropy field rises as the volume falls, so the switching field goes up as the cell shrinks. The field of a line at a given distance falls with the line current and the distance, so the current has to rise, while the cross-section of the line falls. The current density in the lines is then limited by electromigration (a reliability topic), and the field also reaches neighbouring cells (crosstalk) with a distance that becomes comparable to the cell pitch. These limits are not present in a spin-torque write, where the current goes through the cell and scales with its area. Reference: A.V. Khvalkovskiy et al., “Basic principles of STT-MRAM cell operation in memory arrays,” J. Phys. D 46, 074001 (2013); B.N. Engel et al., IEEE Trans. Magn. 41, 132 (2005).

Ques: How is the shape anisotropy of the cell estimated?

For a single-domain cell of elongated shape the anisotropy field is the difference between the demagnetizing factors across and along the long axis, $H_k=(N_w-N_L)M_s$, which can be calculated for a rectangular prism or approximated by an ellipsoid. The factors depend on the aspect ratio and on the thickness, so the switching field is set by the geometry and the thickness of the layer as well as by the material. Real cells have edge roughness and edge domains, and the switching field of an individual cell deviates from the macrospin value, which is the source of the cell-to-cell variation that limited conventional MRAM (a general observation; the Aharoni paper below gives the demagnetizing factors, and the Stoner-Wohlfarth paper the single-domain model). Reference: A. Aharoni, “Demagnetizing factors for rectangular ferromagnetic prisms,” J. Appl. Phys. 83, 3432 (1998); E.C. Stoner and E.P. Wohlfarth, “A mechanism of magnetic hysteresis in heterogeneous alloys,” Phil. Trans. R. Soc. A 240, 599 (1948).

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