Voltage-Controlled Magnetic Anisotropy MRAM (VCMA-MRAM)

1. Theory

Definition: VCMA-MRAM is a magnetic tunnel junction memory in which an electric field across the MgO barrier changes the free layer’s perpendicular anisotropy, so the cell is written by a voltage rather than a current.
VCMA effect: The field changes the electron occupation of interface 3d orbitals, shifting interfacial anisotropy linearly: $K_{i} (E) = K_{i 0} - ξ E$ .
VCMA coefficient: Reported values for CoFeB/MgO are tens of fJ/(V m), while removing a $Δ \approx 70$ barrier at 1 V would need roughly 300 fJ/(V m).
Voltage-lowered barrier: The energy barrier falls linearly with voltage, reaching zero at a critical voltage $V_{c}$ .
Capacitive write: The write charges the junction capacitance, so energy is about $\frac{1}{2} C V^{2}$ , tens of attojoules for a 40 nm cell.

2. Working Principle

Precessional toggle write: A pulse drops the anisotropy near zero, the magnetization precesses around an in-plane field, and removing the pulse after half a period ( $t_{π} = π / γ H_{e x t}$ ) leaves it reversed.
Toggle behaviour: The final state depends on pulse length, not polarity, so the cell must be read before writing and pulse timing must be precise.
Damping limit: For long pulses the switching probability settles at 0.5, setting a narrow pulse-length window.
VCMA-assisted STT or SOT: A voltage lowers the barrier during a current write, reducing critical current as $I_{c 0} (1 - V / V_{c})$ while keeping retention and a deterministic bipolar write.
Read: TMR sensing at low bias, as in STT-MRAM.
Barrier stress: High fields across thin MgO raise breakdown concerns.

3. Applications

Current status: Research devices; not yet commercial.
Ultra-low-energy memory (target): Attojoule-class writes for energy-constrained caches and edge devices.
Write assist for STT and SOT (research): Voltage-lowered barriers to cut write current in other MRAM types.

Name	Formula	Related Formulae	Variables/Constants
Voltage-controlled anisotropy	$K_{i} (E) = K_{i 0} - ξ E$ $E = \frac{V}{t _{b}}$	$K_{e f f} (V) = K_{e f f} (0) - \frac{ξ V}{t _{b} t _{F}}$ $H_{k} (V) = H_{k} (0) - \frac{2 ξ V}{μ _{0} M _{s} t _{b} t _{F}}$	$K_{i} (E) : in t er f a c ia l ani so t r o p y e n er g y p er u ni t a r e a in an e l ec t r i c f i e l d E in t h e M g O ba r r i er$ $K_{i 0} : in t er f a c ia l ani so t r o p y a t z er o f i e l d$ $ξ : V C M A coe f f i c i e n t (c han g e o f t h e in t er f a c ia l ani so t r o p y p er u ni t f i e l d, in J / V m; t h e s i g n s h o w n i s f or t h e p o l a r i t y t ha t r e d u ces t h e p er p e n d i c u l a r ani so t r o p y)$ $E : e l ec t r i c f i e l d in t h e M g O ba r r i er$ $V, t_{b} : v o l t a g e a cr oss an d t hi c k n ess o f t h e M g O ba r r i er$ $K_{e f f} (V) : e f f ec t i v e p er p e n d i c u l a r ani so t r o p y e n er g y d e n s i t y o f t h e f r ee l a y er u n d er t h e v o l t a g e V (t h e o t h er t er m s o f K_{e f f} o n t h e S T T - M R A M p a g e a r e u n c han g e d)$ $t_{F} : t hi c k n ess o f t h e f r ee l a y er$ $H_{k} (V) : ani so t r o p y f i e l d u n d er t h e v o l t a g e V$ $μ_{0}, M_{s} : v a c uu m p er m e abi l i t y an d s a t u r a t i o n ma g n e t i z a t i o n$ $(l in e a r V C M A w i t h E = V / t_{b} : t h e scr ee nin g in t h e m e t a l an d an y q u a d r a t i c t er m see n in so m e s t a c k s a r e n e g l ec t e d, an d ξ i t se l f d e p e n d s o n t h e s t a c k)$
Energy barrier and critical voltage	$E_{b} (V) = E_{b 0} - \frac{ξ A}{t _{b}} V$	$V_{c} = \frac{E _{b 0} t _{b}}{ξ A} = \frac{K _{e f f} ( 0 ) t _{F} t _{b}}{ξ}$ $Δ (V) = \frac{E _{b} ( V )}{k _{B} T}$	$E_{b} (V) : e n er g y ba r r i er o f t h e f r ee l a y er u n d er t h e v o l t a g e V$ $E_{b 0} : e n er g y ba r r i er a t z er o v o l t a g e, e q u a l t o K_{e f f} (0) A t_{F}$ $ξ : V C M A coe f f i c i e n t$ $A : a r e a o f t h e j u n c t i o n$ $t_{b}, t_{F} : t hi c k n ess o f t h e M g O ba r r i er an d o f t h e f r ee l a y er$ $V_{c} : v o l t a g e a t w hi c h t h e p er p e n d i c u l a r ba r r i er v ani s h es (t h e ba r r i er i s t ak e n t o f a l l l in e a r l y an d t h e o t h er t er m s o f t h e ani so t r o p y t o s t a y co n s t an t)$ $K_{e f f} (0) : e f f ec t i v e ani so t r o p y e n er g y d e n s i t y a t z er o v o l t a g e$ $Δ (V) : t h er ma l s t abi l i t y f a c t or u n d er t h e v o l t a g e$ $k_{B}, T : B o l t z mann co n s t an t an d t e m p er a t u r e$
VCMA-assisted spin-transfer torque switching	$I_{c 0} (V) = \frac{4 e}{ℏ} \frac{α}{η} E_{b} (V) = I_{c 0} (0) (1 - \frac{V}{V _{c}})$	$E_{b} (V) = E_{b 0} (1 - \frac{V}{V _{c}})$	$I_{c 0} (V) : cr i t i c a l c u r r e n t f or s p in - t r an s f er s w i t c hin g w h e n a v o l t a g e V l o w er s t h e ba r r i er$ $I_{c 0} (0) : cr i t i c a l c u r r e n t a t z er o v o l t a g e (S T T - M R A M p a g e)$ $e, ℏ : e l e m e n t a r y c ha r g e an d r e d u ce d P l an c k co n s t an t$ $α, η : G i l b er t d am p in g co n s t an t an d s p in - t r an s f er e f f i c i e n cy$ $E_{b} (V), E_{b 0} : e n er g y ba r r i er w i t h an d w i t h o u t t h e v o l t a g e$ $V_{c} : v o l t a g e a t w hi c h t h e ba r r i er v ani s h es$ $(t h e v o l t a g e a cr oss t h e j u n c t i o n i s a l so t h e v o l t a g e t ha t d r i v es t h e s p in - t r an s f er c u r r e n t, so in a s in g l e - p u l se w r i t e V an d t h e c u r r e n t a r e l ink e d b y t h e j u n c t i o n r es i s t an ce)$
Precessional switching with a voltage pulse	$t_{π} = \frac{π}{ω} = \frac{π}{γ H _{e x t}}$	$ω = γ H_{e x t}$ $P_{s w} (t_{p}) = \frac{1}{2} [1 - exp (- \frac{t _{p}}{τ _{d}}) cos (ω t_{p})]$	$t_{π} : p u l se l e n g t h f or ha l f o f a p r ecess i o n p er i o d, a t w hi c h t h e ma g n e t i z a t i o n ha s r e a c h e d t h e o pp os i t e s i d e o f t h e p r ecess i o n co n e$ $ω : an g u l a r f r e q u e n cy o f t h e p r ecess i o n a r o u n d t h e in - pl an e f i e l d$ $γ : g y r o ma g n e t i c r a t i o (d e f in e d f or a f i e l d in A / m)$ $H_{e x t} : in - pl an e e x t er na l f i e l d ab o u t w hi c h t h e ma g n e t i z a t i o n p r ecesses w hi l e t h e p er p e n d i c u l a r ani so t r o p y i s c an ce l l e d b y t h e p u l se$ $P_{s w} (t_{p}) : p r o babi l i t y o f e n d in g in t h e o pp os i t e s t a t e a f t er a p u l se o f l e n g t h t_{p} (osc i l l a t es w i t h t h e p u l se l e n g t h, so i t i s a t o g g l e)$ $τ_{d} : d am p in g t im e o f t h e p r ecess i o n$ $t_{p} : p u l se l e n g t h$ $(t h e e x p r ess i o n f or P_{s w} i s t h e d am p e d cos in e o f t h e o u t - o f - pl an e co m p o n e n t, P_{s w} = (1 - m_{z}) /2 f or an ini t ia l m_{z} = + 1, an i l l u s t r a t i v e f or m)$ $(ω = γ H_{e x t} h o l d s o n l y i f t h e p u l se c an ce l s t h e p er p e n d i c u l a r ani so t r o p y co m pl e t e l y; a r es i d u a l ani so t r o p y c han g es t h e f r e q u e n cy . W i t h γ /2 π \approx 28 G H z / T, μ_{0} H_{e x t} o f t e n s o f m T g i v es t_{π} o f 0.1 t o 1 n s)$
Capacitive energy of a voltage write	$E_{w} = \frac{1}{2} C V^{2}$ $C = \frac{ε _{0} ε _{r} A}{t _{b}}$	$A = \frac{π d ^{2}}{4}$ $E_{w}^{'} = E_{w} + I V t_{p}$	$E_{w} : e n er g y s t or e d in t h e c a p a c i t an ce o f t h e j u n c t i o n d u r in g a v o l t a g e p u l se (t h e c a p a c i t i v e p a r t o f t h e w r i t e e n er g y)$ $C : c a p a c i t an ce o f t h e M g O ba r r i er$ $V : p u l se am pl i t u d e$ $ε_{0}, ε_{r} : v a c uu m p er mi tt i v i t y an d r e l a t i v e p er mi tt i v i t y o f M g O$ $A, d : a r e a an d d iam e t er o f t h e j u n c t i o n$ $t_{b} : t hi c k n ess o f t h e M g O ba r r i er$ $E_{w}^{'} : e n er g y in c l u d in g t h e J o u l e e n er g y o f t h e t u nn e l l in g c u r r e n t I d u r in g t h e p u l se o f l e n g t h t_{p}$ $(t h e c u r r e n t i s se t b y t h e r es i s t an ce o f t h e j u n c t i o n a t t h e p u l se v o l t a g e, so a hi g h r es i s t an ce - a r e a p r o d u c t l o w er s t h e seco n d t er m)$ $(c ha r g in g t h r o ug h a r es i s t an ce d r a w s C V^{2} f r o m t h e s u ppl y : C V^{2} /2 i s s t or e d an d t h e s am e am o u n t i s d i ss i p a t e d in t h e d r i v er; t h e s t or e d ha l f i s a l so l os t a t d i sc ha r g e u n l ess i t i s r eco v er e d)$

Important Questions

Ques: What is the VCMA effect, and what is its origin?

In a ferromagnet/MgO interface the perpendicular anisotropy is an interface effect that depends on the occupation of the 3d orbitals of the ferromagnet through the spin-orbit coupling. An electric field in the MgO changes the charge at the interface (by screening in the metal), changes the orbital occupation, and so changes the interfacial anisotropy linearly with the field, $K_{i} (E) = K_{i 0} - ξ E$ . The effect was predicted from first principles for Fe/MgO, seen in ultrathin Fe(Co) films in an electrolyte and then in solid-state Fe/MgO junctions, and later in CoFeB/MgO/CoFeB magnetic tunnel junctions. Because the effect is a field effect, the write is a voltage pulse, and not a current. Reference: C.-G. Duan et al., “Surface magnetoelectric effect in ferromagnetic metal films,” Phys. Rev. Lett. 101, 137201 (2008); M. Weisheit et al., “Electric field-induced modification of magnetism in thin-film ferromagnets,” Science 315, 349 (2007); T. Maruyama et al., “Large voltage-induced magnetic anisotropy change in a few atomic layers of iron,” Nat. Nanotechnol. 4, 158 (2009).

Ques: How does a VCMA cell write a bit, and why is it a toggle?

A voltage pulse across the MgO lowers the perpendicular anisotropy so that it is close to zero, and the magnetization precesses around the in-plane field $H_{e x t}$ . After half a precession period $t_{π} = π / γ H_{e x t}$ the pulse is removed and the anisotropy restores itself with the magnetization on the opposite side, so the state is reversed. Since the final state depends only on the pulse length and not on the polarity of the pulse, the same pulse takes up to down and down to up (a toggle, with an oscillating $P_{s w}$ ), so the cell must be read before it is written, and the pulse length must be controlled to a small fraction of the precession period. The damping makes $P_{s w}$ settle to 0.5 for long pulses, which sets a window for the pulse length. Reference: Y. Shiota et al., “Induction of coherent magnetization switching in a few atomic layers of FeCo using voltage pulses,” Nat. Mater. 11, 39 (2012); S. Kanai et al., “Electric field-induced magnetization reversal in a perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction,” Appl. Phys. Lett. 101, 122403 (2012).

Ques: How large does the VCMA coefficient need to be?

For the perpendicular barrier to vanish at a voltage $V_{c}$ the coefficient must be $ξ = K_{e f f} (0) t_{F} t_{b} / V_{c}$ . As an illustration, take $K_{e f f} (0) = 2 \times 1 0^{5}$ J/m $^{3}$ , $t_{F} = t_{b} = 1.2$ nm and $V_{c} = 1$ V: this gives $ξ \approx 2.9 \times 1 0^{- 13}$ J/(Vm), that is about 290 fJ/Vm (the same layer has $E_{b 0} \approx 3 \times 1 0^{- 19}$ J at a diameter of 40 nm, i.e. $Δ \approx 70$ at room temperature). The coefficients reported for CoFeB/MgO are typically about 30 to 100 fJ/Vm, with a few reports of a few hundred fJ/Vm in engineered stacks, so a cell with a thermal stability of this size cannot reach zero barrier at 1 V, and VCMA devices use a lower $Δ$ or a partial reduction of the barrier (the VCMA-assisted STT row), or a larger coefficient. Reference: P. Khalili Amiri and K.L. Wang, “Voltage-controlled magnetic anisotropy in spintronic devices,” SPIN 2, 1240002 (2012); F. Matsukura, Y. Tokura and H. Ohno, “Control of magnetism by electric fields,” Nat. Nanotechnol. 10, 209 (2015).

Ques: How much energy does a VCMA write need?

The write is a voltage pulse on a capacitor, so the energy is mostly $\frac{1}{2} C V^{2}$ stored in the junction, with an equal amount dissipated in the driver while charging (the supply delivers $C V^{2}$ ). For an MgO barrier of $t_{b} = 1.2$ nm and $ε_{r} = 9.8$ in a junction of 40 nm diameter, $C \approx 0.09$ fF, and at $V = 1$ V the energy is $E_{w} \approx 4.5 \times 1 0^{- 17}$ J, about 45 aJ stored, or about 90 aJ drawn from the supply. This is the capacitive part only: the tunnelling current during the pulse adds $I V t_{p}$ , which is small for a high resistance-area product barrier, and the circuit that drives the pulse, the line capacitance and the read-before-write are not included. The result is lower than the energy of a current write in the SOT example of the SOT-MRAM page (0.2 fJ) by a factor of about 2 to 4, with those omissions and with both examples using assumed parameters, so this is a comparison of two illustrations rather than of devices. Reference: P. Khalili Amiri et al., “Electric-field-controlled magnetoelectric RAM: progress, challenges, and scaling,” IEEE Trans. Magn. 51, 3401507 (2015); J. Grezes et al., “Ultra-low switching energy and scaling in electric-field-controlled nanoscale magnetic tunnel junctions with high resistance-area product,” Appl. Phys. Lett. 108, 012403 (2016).

Ques: How can VCMA be combined with STT or SOT?

A voltage across the MgO lowers the barrier, and the critical current of the STT switching is proportional to the barrier, so $I_{c 0} (V) = I_{c 0} (0) (1 - V / V_{c})$ in the assisted-switching row. The same junction therefore needs a lower current when the voltage is applied during the write, and the retention is not affected because the voltage is removed at the end of the write. The same applies to SOT, where the barrier enters the critical current density through the anisotropy field. The scheme gives a bipolar write with a reduced energy, without the toggle behaviour of the pure precessional write, but with the current-driven write path. Reference: W.-G. Wang, M. Li, S. Hageman and C.L. Chien, “Electric-field-assisted switching in magnetic tunnel junctions,” Nat. Mater. 11, 64 (2012); P. Khalili Amiri and K.L. Wang, SPIN 2, 1240002 (2012).

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