MRAM

Simon Greaves1

1Research Institute of Electrical CommunicationTohoku University, Japan

4/2019

1 / 41

MRAM

Magnetic core memory

Field-written MRAM

STT MRAM

Other types of MRAM

2 / 41

Magnetic core memory

3 / 41

Magnetic core memory IA ferrite core memory with a

wire passing through the

centre.

An electric current passing

through the wire generates a

magnetic field.

If the magnetic field is large

enough the magnetisation of

the ferrite core can be

switched.

One of the earliest non-volatile memories was magnetic core

memory.

Information was stored based on the orientation (clockwise /

anticlockwise) of the magnetisation in a ferrite core.

4 / 41

Magnetic core memory II

Switching the magnetisation of a core

Cores are arranged in square

arrays. To change the

magnetisation of a core a current

pulse must be applied to two

orthogonal current lines.

The Oersted field from a single

current line is too small to switch

the core magnetisation.

At the intersection of two current

lines the Oersted field can switch

the core magnetisation.

5 / 41

Magnetic core memory III

Full wiring of a single core memory

To read data stored in a core a

current pulse is once again applied

to the X and Y drive lines.

If the core magnetisation switches a

current pulse is induced in the

sense line; readout is destructive.

Multiple 2D arrays of cores are

wired in parallel. The inhibit line is

used to prevent unwanted switching

in individual arrays.

6 / 41

Magnetic core memory IV

Section of core memory

Magnetic core memory dominated

computing between 1955 and 1975.

Densities reached around 40 bits

per cm2 and costs dropped to about

1 cent / 1 Yen per bit.

Core memory was eventually

replaced by DRAM technology.

7 / 41

Field-written MRAM

8 / 41

Hall cross device I

Hall cross with ferromagnetic layer on

top

The earliest magnetoresistive

device was based on a Hall cross.

A ferromagnetic layer on top of the

device produced a stray field that

varied depending on the

magnetisation.

The voltage measured across

S1 − S2 varied depending on the

direction of the stray field.

9 / 41

Hall cross device II

Resistance of MRAM device vs.

external applied field

The resistance of the device was

measured as a function of external

applied field.

The current was constant and the

Hall voltage was converted into a

resistance.

In zero field a difference in

resistance of about 2Ω was

measured.

∆RH/R0 ≈ 30, or a 3% change in

resistance.

10 / 41

Cross-tie memory

“0” and “1” states in a cross-tie memory

Two different states are

distinguished by the presence, or

absence, of a Bloch line and

associated cross-tie domain wall.

Writing is achieved by passing

currents through two orthogonal

wires simultaneously.

Problems include: low

magnetoresistance and high

probability of write error (≈ 1%).

11 / 41

AMR MRAM

Anisotropic magnetoresistance (AMR) is the change in resistance

as a function of magnetisation angle. Early devices used NiFe, with

an AMR of about 2%.

The stray field from the sense line distorted the NiFe

magnetisation, reducing the usable magnetoresistance to about

0.5% and the sense signal to 0.5 to 1 mV.

256K bit MRAM chips were manufactured. Read times were 250 ns

and write times 100 ns.12 / 41

Stoner-Wohlfarth MRAM I

An array of memory cells

located above the

intersections of two

orthogonal current lines.

Switching is via the Oersted

field.

Stoner-Wohlfarth MRAM stores information in magnetic tunnel

junctions (MTJ). Each cell has two magnetic layers: a pinned layer

and a storage layer. Here we discuss switching of the storage layer.

When currents Ix and Iy are applied the magnetisation of the cell at

the intersection of the two current lines should switch.

13 / 41

Stoner-Wohlfarth MRAM II

0 15 30 45 60 75 90Applied field angle, θ (°)

0.5

0.6

0.7

0.8

0.9

1

Sw

itch

ing

fie

ld,

Hc(θ

) /

Hk

y (easy axis)

H

x

θ

Hc (θ) / H

k

Switching field of a single domain

particle with uniaxial anisotropy.

θ = angle between applied field and

easy axis.

The discrete magnetic memory cells in MRAM should be single

domain with uniaxial anisotropy.

The switching field varies with applied field angle according to

Hc(θ)

Hk=(

cos2/3(θ) + sin2/3(θ))−3/2

14 / 41

Stoner-Wohlfarth MRAM III

-1 -0.5 0 0.5 1h

x

-1

-0.5

0

0.5

1

hy Stable

Unstable

Stoner-Wohlfarth astroid

If a cell is located above two

orthogonal current lines the field

from the lines is Hx = H sin θ and

Hy = H cos θ.

The switching threshold is

h2/3x + h

2/3y = 1, where hx = Hx/Hk

etc.

The Stoner-Wohlfarth astroid

shows the x and y fields needed to

switch the magnetisation of the

MRAM cell.

15 / 41

Stoner-Wohlfarth MRAM IV

In actual MRAM devices the cells have an elliptical shape in which

shape anisotropy helps to stabilise the magnetisation. In such

devices the Stoner-Wohlfarth asteroid is distorted.

The Stoner-Wohlfarth astroid is calculated at 0 K. At room

temperature the switching fields are reduced due to thermal

activation.

The cells in real devices have distributions of size, shape,

anisotropy etc. This makes it difficult to find a write condition that

will switch only the intended bit.

16 / 41

Toggle MRAM I

Structure of toggle MRAM cell Toggle MRAM cell and write lines

To overcome the problems of Stoner-Wohlfarth MRAM toggle

MRAM was developed.

The magnetic layers are synthetic antiferromagnets and the major

axis of the ellipse is at 45 to the write lines.

17 / 41

Toggle MRAM II

Writing operation

Current pulses are applied with a delay on one write line.

Each time the current pulses are applied the magnetisation

switches direction (toggles).

18 / 41

Toggle MRAM III

When a field is applied from one write line

the magnetisation of the two free layers

rotates as shown.

Suppose Hk = 0, the energy is given by

E(θ) = −Kex cos(2δ) − 2MsH sin(θ) sin(δ)

Minimising for δ we find

E(θ) = −

M2s H2

2Kexsin2(θ) + C

19 / 41

Toggle MRAM IV

Adding in Hk we get

E(θ) = MsHk

(

1 −

H2

HkHsat

)

sin2(θ)

where Hsat = 2Kex/Ms.

The toggle field is then given by

Hsw = (HkHsat)1/2

Toggle MRAM gives a much wider operating margin than

Stoner-Wohlfarth MRAM.

Toggle MRAM products were released into the market in 2006.

20 / 41

Toggle MRAM V

Data from Everspin Technologies

21 / 41

STT MRAM

22 / 41

Basic STT MRAM structure

Spin transfer torque (STT) MRAM devices contain a free layer (FL)

and a reference, or pinned, layer (RL).

The magnetisation of the free layer can be changed by passing a

sufficiently large current through the device.

The resistance of the device is different when the FL magnetisation

is parallel or anti-parallel with the RL magnetisation.

23 / 41

Magnetoresistance and spin polarisation

An electric current entering a ferromagnetic becomes spin

polarised, i.e. the majority of the electron spins align with the

magnetisation.

Spin polarisation P =J↑−J↓J↑+J↓

, where J↑/↓ is the current of electrons

with opposite spin.

The magnetoresistance of a F / NM / F structure can be written as

∆R/R = 2PP ′/(1 − PP ′), where P and P ′ are the spin

polarisations of the two F ferromagnets (NM = non magnet).

24 / 41

STT MRAM writing

Top: switching the free layer

from down to up.

Bottom: switching the free

layer from up to down.

Switching from anti-parallel to parallel: Electrons pass through the

pinned layer into the free layer.

Switching from parallel to anti-parallel: Electrons pass through the

free layer and are reflected from the pinned layer.

25 / 41

STT MRAM energy barrier I

Energy barrier to

switching, ∆ vs.

junction diameter in

perpendicular

magnetic tunnel

junction MRAM

devices

For high density storage the MRAM devices should be as small as

possible, but thermal stability must also be maintained.

For large devices the thermal stability factor ∆ saturates when

switching changes to a domain wall reversal process.

26 / 41

STT MRAM energy barrier II

Energy barriers for uniform

and domain wall reversal in

the free layer of a MRAM

device.

NEB = nudged elastic band.

Calculations of the energy barrier show that domain wall reversal is

energetically favourable once the MRAM device is sufficiently large.

In this example the energy barrier is approximately halved for

domain wall reversal.

27 / 41

Thermal stability I

MRAM devices are supposed to be non-volatile, but data retention

depends on the energy barrier.

The average time between thermally-induced reversals is given by

τ = τ0 exp

(

∆E

kbT

)

where τ0 is an attempt time (1/f0) of ≈ 1 ns.

For a given MRAM cell the probability of the cell not randomly

switching in time t is given by

Pn(t) = exp(−t/τ)

For N cells the probability of no cell switching becomes

PNn (t) = [Pn(t)]

N = exp(−Nt/τ)

28 / 41

Thermal stability II

The failure rate is given by

F (t) = 1 − exp(−Nt/τ) = 1 − exp

(

−

Nt

τ0exp

(

−

∆E

kbT

))

30 40 50 60 70 80 90 100Energy barrier, ∆E / k

bT

10-12

10-10

10-8

10-6

10-4

10-2

100

Fai

lure

rat

e, F

(t)

1 bit32 Mbit1 Gbit

49 67

73

Failure rate vs. energy barrier for t = 10 years

29 / 41

Thermal stability III

In order to read the state of a MRAM cell a read current must be

used. This current can disturb the cell magnetisation and increase

the probability of accidental switching.

If the critical current for switching is I0 and the read current is Iread ,

the energy barrier is reduced to

∆E = ∆E0

(

1 −

Iread

I0

)δ

where δ ≈ 2.

The failure rate expression thus becomes

F (t) = 1−exp(−Nt/τ) = 1−exp

(

−

Nt

τ0exp

(

−

∆E

kbT

(

1 −

Iread

I0

)δ))

30 / 41

Thermal stability IV

Although a constant read current would not be used, the effect on

the stability can be significant.

30 40 50 60 70 80 90 100Energy barrier, ∆E / k

bT

10-12

10-10

10-8

10-6

10-4

10-2

100

Fai

lure

rat

e, F

(t)

Iread

/ I0

00.10.2

Failure rate vs. energy barrier for t = 10 years when using a read

current. Assume δ = 2, N = 1, constant read current.

31 / 41

STT MRAM read and write currents

Ihigh and Ilow are the currents when the read voltage is applied.

IC0 is the minimum current to switch the device (t → ∞).

IWR is the current used to switch the device.

Distributions among devices set a minimum requirement on the

TMR needed to ensure reliable operation. Ilow − Ihigh > 20σI.

32 / 41

Other types of MRAM

33 / 41

Thermally assisted MRAM I

In thermally assisted MRAM (TA-MRAM) a current passes through

the device and heats one of the antiferromagnets above its

blocking temperature.

The device cools in the field from a second current line above the

device, setting the magnetisation direction of the storage layer.

34 / 41

Thermally assisted MRAM II

Two current lines are needed to switch the magnetisation of the

storage layer.

One current line is used to heat the device, the other to set the

magnetisation direction.

35 / 41

Thermally assisted MRAM III

The bias field from an antiferromagnet decreases with increasing

temperature, and reaches zero at the blocking temperature.

The direction of the bias field can be set by cooling the

antiferromagnet in a magnetic field.

36 / 41

Thermally assisted MRAM IV

One advantage of TA-MRAM is its resistance to external magnetic

fields.

The magnetisation of the storage layer can only be permanently

changed by heating the device.

37 / 41

Three terminal MRAM devices

There are two types of three terminal MRAM devices: domain wall

(DW) (left) and spin-orbit torque (SOT) (right).

The advantage of these devices is that the high write current does

not pass through the tunnel barrier, increasing the endurance of the

device.38 / 41

Conclusions

Although magnetoresistive memories have been around for a long

time it is only in recent years that they have become commercially

available.

Current products are based on STT-MRAM cells with perpendicular

magnetic anisotropy.

In the future devices using spin orbit torque are expected to be

introduced.

39 / 41

Sources

M. Julliere, Phys. Lett. 54A, p225, (1975), “Tunneling between

ferromagnetic films”.

M. Johnson, IEEE Trans. Magn. 34(4), p1054, (1998), “Hybrid

ferromagnet-semiconductor nonvolatile gate”.

L. J. Schwee, J. Appl. Phys. 53, p2762, (1982), “The concept and

initial studies of a crosstie random access memory”.

B. Dieny, “Introduction to magnetic random-access memory”, IEEE

Press.

B. N. Engel, IEEE Trans. Magn. 41, p132, (2005), “A 4-Mb toggle

MRAM based on a novel bit and switching method”.

A. V. Khvalkovskiy, J. Phys. D, Appl. Phys. 46, p074001, (2013),

“Basic principles of STT-MRAM cell operation in memory arrays”.

S. Bhatti, Materials Today 20, p530, (2017), “Spintronics based

random access memory: a review”.

40 / 41

Sources

H. Sato, Appl. Phys. Lett. 99, p042501, (2011), “Junction size

effect on switching current and thermal stability in CoFeB/MgO

perpendicular magnetic tunnel junctions”.

D. Apalkov, Proc. IEEE 104, p1796, (2016), “Magnetoresistive

random access memory”.

I. L. Prejbeanu, J. Phys. Cond. Matter. 19, p165218, (2007),

“Thermally assisted MRAM”.

S. W. Lee, Proc. IEEE 104, p1831, (2016), “Emerging

three-terminal magnetic memory devices”.

41 / 41