Current-induced domain wall motion in antiferromagnetically coupled structures: Fundamentals and applications

Yang, Enhancement of spin Hall effect induced torques for current-driven magnetic domain wall motion: inner interface effect, Phys.. Beach, Spin-orbit torques in Ta/ TbxCo100-x ferrimagn[r]

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aInstitute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam bToyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468- 511, Japan

a r t i c l e i n f o

Article history:

Received June 2018 Received in revised form September 2018 Accepted September 2018 Available online 17 September 2018

Keywords:

Antiferromagnet Ferrimagnet Spin-transfer torques Spineorbit torques Magnetization switching Domain wall motion

Perpendicular magnetic anisotropy

a b s t r a c t

The current-induced spin-torques provide an efﬁcient means of manipulating magnetization, intro-ducing the way for next generation spintronic devices During the past decades, studies have mainly focused on ferromagnetic materials In recent years, antiferromagnetically coupled structures have been found with more efﬁcient spin-toques and robust to magnetic noises This is because they have the strongly exchange-coupled magnetic sublattice structures, and the antiferromagnetic order parameter dynamics are different from those of the ferromagnetic ones As a result, the antiferromagnetically coupled structures offer a novel approach for reducing energy consumption as well as the immunity against external magnetic perturbation in spintronic devices In this review, we discuss current-induced domain wall motion under the action of different spin torques in a wide range of antiferromagnetically coupled materials New approaches and prospective applications of the antiferromagnetic structure-based devices are also discussed

©2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

1 Introduction

Magnetic materials are a central component in many

elec-tronic devices, such as data storage, sensors, motors etc After

the discovery of giant magneto-resistance (GMR) by Albert Fert

and Peter Grünberg in 1988

[1,2]

offered with the Nobel prize in

physics in 2007, the research on applications in spintronics has

speeded up quickly

[3

e

12] Then the spin-polarized current

excites the magnetization state and might eventually lead to the

magnetization reversal in multilayered structures of a

nonmag-netic (NM) layer sandwiched between two ferromagnonmag-netic (FM)

layers (Fig la)

[13

e

17]

and magnetic wires (Fig 1b)

[18]

There-fore, continuous efforts in the spintronics

ﬁ

eld, which use the

spins of conduction electrons to further reduce the size as well as

energy consumption of the magnetic devices, are important for

such applications.

As shown in

Fig 1a, a multilayered structure consists of FM1/

NM/FM2 where the in-plane FM1 is the pinned layer and supposed

to have much higher coercivity than that of the FM2 one The

electrons passing FM1 become spin-polarized along the direction of

FM1 magnetization The misalignment between the magnetization

directions of FM1 and FM2 will cause the conduction electrons to

lose the transverse component of their spin momentum This

mo-mentum is transferred to the local FM2 magnetization because of

total angular momentum conservation

[13,14] It means that the

magnetization of the FM2 can be excited or even reversed by the

injecting current without any applied external magnetic

ﬁ

elds.

Besides that, one of the most interesting consequences is the

pos-sibility of manipulating domain walls (DWs) position in nanowires

solely by an electric current: current-induced DW motion (CIDM)

effect (Fig 1b)

[19

e

24] This idea had been proposed for a long time

[25], but the nanotechnology had limited its approaches such as

micro-fabricating technique and effective methods for observing

magnetization The advantage of electric current with respect to

the effect of magnetic

ﬁ

eld is that it drives all domain walls in the

direction of electron

ﬂ

ow, whereas the magnetic

ﬁ

eld tends to

expand or shrink domains of opposite magnetizations

[25].

The majority of studies have been carried out for single NiFe

nanowires

exhibiting

in-plane

magnetic

anisotropy

(IMA)

[23,26

e

28] One of the highest DW velocities in NiFe exceeded

**Corresponding author Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

E-mail addresses:dobang.tti@gmail.com(D Bang),phamthach@toyota-ti.ac.jp

(P Van Thach)

Peer review under responsibility of Vietnam National University, Hanoi

https://doi.org/10.1016/j.jsamd.2018.09.003

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100 m/s in zero

ﬁ

eld

[29,30] This is convenient for designing

magnetic storage devices based on a shift register

[31,33] The DW

velocity can be enhanced with increasing temperature due to a

decrease of magnetization and pining strength

[33] On the other

hand, the DW velocity can be enhanced or suppressed depending

on the mutual magnitude and orientation of the

ﬁ

eld and current

[34,35] The velocity enhancement is also dependent on the

ﬁ

eld

range However, the current density required for inducing

magnetization switching and DW motion is of the order of 10

A/

m

, which justi

ﬁ

es the need for nanometer sizes with as small

cross-sections as possible, to minimize the injected current.

Growing interest has recently been devoted to the systems with

perpendicular magnetic anisotropy (PMA)

[36

e

44] The magnetic

wires contained very narrow Bloch walls, which contributed to

high spin transfer ef

ﬁ

ciency, as the DWs were displaced with a

current density of one order smaller than that of the in-plane

magnetic one Some systems with PMA, like Pt/Co/AlO

[36],

exhibited larger DW velocities compared to NiFe, up to 400 m/s

[37] Recently, a lot of papers have reported on current-induced DW

motion in PMA systems composed of different materials such as

FePt

[38], Co/Ni

[39

e

41], and Co/Pt

[42,44] However, the high

current density is still needed to drive DWs in the PMA wires, thus

limiting its practical applications Very low critical current densities

of the order of l0

A/m

have been reported for magnetic

semi-conductors, such as GaMnAs

[45,46] This is attributed to the low

spontaneous magnetization and high-carrier spin polarization of

this material

[47] But this approach is only achieved at low

tem-peratures due to the low Curie temperature of the semiconductor.

In the last seven years, an asymmetric (ASY) bilayer of a

perpendicular anisotropy FM and heavy metal (HM) with strong

spin

e

orbit coupling has attracted considerable interest for their

potential utility in spintronic elements In these systems,

current-induced spin

e

orbit torques (SOTs)

[48,49]

on the magnetization

can be induced by the Rashba effect at the interface (Fig 2a)

[37,50]

and by spin currents injected from the heavy metal due to the spin

Hall effect (SHE) (Fig 2b)

[49,51

e

56] SOTs have been identi

ﬁ

ed and

quanti

ﬁ

ed by a variety of techniques, including spin-torque

ferro-magnetic resonance

[53], quasistatic magnetization tilting probed

through harmonic voltage measurements

[54], and

current-induced hysteresis loop shift measurements

[57] In the bilayer

wires, DWs can be moved with high speed up to a few hundreds m/

s under current densities of the order of 10

A/m

in the opposite

direction to the direction of DWs motion in a single layer under the

effect of conventional spin-transfer torques (STTs) Unlike the FM

system, in antiferromagnetically (AF) coupled structures, their

angular momentum is not associated with the order parameter so

that spin dynamics in these structures is intrinsically much faster

than in FMs Up to now, a maximum DW velocity of up to 750 m/s

has been reported for Co/Ni/Co/Ru (t)/Co/Ni/Co wires with a

syn-thetic antiferromagnetic (SAF) structure Such a high DW velocity

can be achieved owing to the SAF structure that gives rise to a novel

torque associated with the antiferromagnetic exchange coupling

ﬁ

eld

[58] Current efforts are to optimize material structures for

realizing a high-speed and low-power magnetic memory based on

the CIDM Recently, current-driven relativistic N

eel order

ﬁ

eld as

well as DW motion in AFs where magnetic atoms have a local

environment with broken inversion symmetry have been predicted

theoretically and experimentally

[59

e

65] It has been

demon-strated that the antiferromagnetic DW can be moved in these AFs

with very high velocities which are orders of magnitude greater

than those in FMs due to the ef

ﬁ

ciency of the staggered spin

e

orbit

ﬁ

elds to couple to the order parameter and the exchange-enhanced

phenomena in AF texture dynamics Furthermore, the absence of a

Walker breakdown limit can keep the velocity of the

antiferro-magnetic DW up to values of few km/s

[61] Besides that, rare-earth

(RE) transition-metal (TM) alloys named ferrimagnetic alloys in

which the moments of RE sublattices are anti-ferromagnetically

coupled with those of TM sublattices are potential candidates for

realizing such high speed devices

[66

e

73] In ferrimagnetic alloys, a

negative exchange interaction between the RE and TM sublattices

can induce much faster DW motion at low current densities

[74]

and magnetic

ﬁ

elds

[75] Therefore, the AFs have led to the recent

development of spintronic-based devices with the ultimate speed

of magnetic dynamics

[59,76

e

79].

2 Current induced domain wall motion in wires based on

antiferromagnetically coupled structures

2.1 Synthetic antiferromagnetic bilayer wires

A synthetic antiferromagnetic structure composes of two

mag-netic sublayers of upper magmag-netic (UM) and lower magmag-netic (LM)

layers which are exchange-coupled via an ultrathin spacer layer

Fig 1.Schematic of an injecting current induces (a) in-plane magnetization exciting and magnetization switching in a multilayered structure of FM1/NM/FM2 and (b) domain wall (DW) motion in an in-plane magnetic wire

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DMI derived from the strong spin

e

orbit coupling and the

proximity-induced moment in Pt

[81

e

84] When

J

¼

0, the DW

with the magnetizations of

M

and

M

in the centre of the SAF

structure respectively, exhibits an anticlockwise N

eel structure.

When

J

s

0,

M

and

M

are rotated towards the spin accumulation

direction denoted by the magenta arrows (Fig 3b) and are

sub-jected to longitudinal

ﬁ

elds

H

and

H

, respectively, which are

composed of the corresponding DMI

ﬁ

elds and

H

, and

exchange-coupling

ﬁ

elds

H

and

H

, respectively (Fig 3c and d) Each of

magnetic coupling of bilayers also can be attributed to a change in

the DW velocity in a SAF wire by changing the thickness of the

spacer (Fig 5c) For the antiferromagnetically coupled wires with

Ru thicknesses of about and Å, the DW velocities are much

higher than those of the ferromagnetically coupled ones.

As mentioned above, theoretical estimations suggest the

possi-bility to substantially reduce the critical currents and tailor the

domain structure of antiferromagnetically -coupled wires at critical

currents above 10

A/m

, which are about one order of magnitude

below the highest value reported for the ferromagnetic structures.

However, most recent studies on the SAF wire have been focused on

only Co/Ni system

[85,86]

due to its strong coupling in the ultrathin

regime To optimize effectively the current-induced DW motion in

AFs, one must control the thickness and magnetization by changing

their compositions As such, antiferromagnetic compounds such as

Mn

Au and CuMnAs

[61]

and ferrimagnetic alloys such as the RE-TM

alloys offer additional advantages.

Fig 3.Schematic illustration of (a) DWs in a SAF wire and (b) Spin Hall current from an HM layer induced DWs motion in the SAF wire (c, d) Directions ofﬁelds and torques in the SAF bilayer, upper and lower panels correspond to the UF and LF, respectively Replotted from Ref 58 (Copyright 2015 Macmillan Publisher Limited)

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2.2 Current-induced DW motion in ferrimagnetic alloys

In the RE-TM alloys, where RE element (e.g., Tb, Gd, etc.) and TM

element (e.g., Co, Fe, etc.) sublattices are antiferromagnetically

coupled, the net magnetic moment can be tuned easily by varying

the RE-TM composition as shown in

Fig RE-TM alloy such as

Tb

e

Co

ﬁ

lms can be simply fabricated from a single target of TbCo

alloys or co-sputtering of two Co and Tb targets by using RF or DC

magnetron sputtering at room temperature without any

post-annealing processes At room temperature, pure Tb and Co are

paramagnetic and in-plane anisotropy ferromagnetic, respectively.

In form of an alloy or multilayers with alternating thin layers of Tb

and Co, however, the Tb and Co sublattices show a ferrimagnetic

order (Fig 6a)

[87,88] This ferrimagnetic order between the Tb and

Co sublattices may be con

ﬁ

rmed by observation of the

compensa-tion points (Fig 6b).

It has been reported that the critical current density to drive

domain wall motion strongly depends on the layered structure as

well as its composition

[68] The lowest critical current density of

about 1.5

10

A/m

and the highest slope of domain wall velocity

curve are obtained for the wire having thin Co sublayers and more

inner Tb/Co interfaces, while the largest critical current density of

2.6

10

A/m

is required to drive domain walls in the Tb

e

Co alloy

magnetic wire (Fig 7).

An enhancement of the antidamping torques by extrinsic spin

Hall effect due to Tb rare-earth impurity-induced skew scattering is

suggested to explain the high ef

ﬁ

ciency of current-induced domain

wall motion in the Co/Tb multilayer with more number of inner

interfaces (n) This study indicates an ef

ﬁ

cient way to reduce the

critical current density for DW motion through inner interface

engineering.

As discussed above, the effective SAF

ﬁ

lms are mostly limited in

ultrathin sublayers of a few Å and total

ﬁ

lm thickness of few

nanometers due to the dominance of interfacial effects Recently,

ultrafast

ﬁ

eld-induced DW motion has been observed in

GdFeCo-based ferrimagnets at the angular momentum compensation

temperature

[75,89,90] Because of different Land

e

g

-factors

be-tween the RE and TM elements, below the Curie temperature these

ferrimagnets have two special temperatures of the magnetization

compensation temperature (

T

), at which the two magnetic

mo-ments cancel each other, and the angular momentum

compensa-tion temperature (

T

), at which the net angular momentum

vanishes

[91,92] As a result, the nature of the dynamics of the

ferrimagnets changes from ferromagnetic to antiferromagnetic on

Fig 5.DW velocity as functions of (a) longitudinalﬁeld (Left and right panels: measured and calculated result), (b) current pulse densities for different thicknesses and (c) Ru spacer thickness (the orange and blue shaded regions correspond to ferromagnetic and antiferromagnetic couplings) Replotted from ref 56 (Copyright 2015 Macmillan Publisher Limited)

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approaching the

T

Furthermore, the net magnetic moment of

ferrimagnets is nonzero at

T

and can thus couple to an external

magnetic

ﬁ

eld as well as the ef

ﬁ

ciencies of

ﬁ

eld-induced DW

mo-tion As shown in

Fig 8, the DW velocity can reach up to over km/s

under around 100 mT

ﬁ

eld at temperature around

T

However, it

will be rapidly reduced when the temperature is far from the

T

.

In the following, a theory for the

ﬁ

eld-driven DW dynamics in

ferrimagnets is discussed brie

ﬂ

y The low-energy dynamics of a

DW in quasi-one-dimensional magnets is generally described by

Fig 7.(a) Schematic illustration of TbeCo basedﬁlms with different layered structures (b) Current density dependence of DW velocity for different magnetic wires (1.1-mm width) of A-, B-, and C-stack structures Replotted from Ref 68 (Copyright 2016 American Physical Society)

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two collective coordinates, its position (

X

) and angle (

4

), which

capture the translational and spin-rotational degrees of freedom

of the DW, respectively In ferromagnets, the force on

X

induces

the dynamics of

4

and vice versa Due to this coupling, the

mo-tion of a DW is limited by the Walker breakdown

[93] In

contrast, in antiferromagnets the dynamics of X and

4

are

in-dependent due to vanishing of the net spin density The DW

dynamics can be fast and be free from the Walker breakdown In

RE-TM alloys, the RE and TM moments can be easily controlled by

varying the composition or temperature, so that the

T

can be

designed for appropriate applications To date, the effect of

angular momentum compensation point on magnetization

dy-namics has attracted to studies of ferrimagnetic systems

[67,94,95] The lower threshold current density of one order of

magnitude, smaller power consumption, and higher speed than

those of FM systems would be a key to realizing spintronic

de-vices Finally, The improvement of DW velocity and reduction of

critical current density (

J

) by optimizing magnetic materials and

layered structures as functions of year are shown in

Fig It

clearly shows that the DW velocity is rapidly increased, while the

J

is reduced by a few orders of magnitude at room temperature

without applying any external

ﬁ

elds.

2.3 Prospective applications of the current-induced DW motion

based spintronic devices

Recently, magnetic nanostructures have been at the heart of a

multitude of devices ranging from applications of sensors to data

storage Probably the best known concept device is the racetrack

memory, which was proposed by IBM

[31,32,96]

based on the CIDM

effect As shown in

Fig 10, the racetrack memory can be designed

along lines in two and three dimensions or even in circular loops.

One of the key problems of the conventional hard drive is the

mechanical motion of the media, which can lead to failure in the

case of a mechanical shock In the case of the racetrack memory,

positions of domains as well as coded information can be moved

without using any mechanical motors On the other hand, the

racetrack only comprises one write or read element which can

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to the symmetry of the Y-shape, the two domains from inputs

arrive at the con

ﬂ

uence point at same time and then are combined

each other to continue moving to the output gate as a signal

“

l

”

for

the case of input (1, 1) For the case of input (1, 0) or (0, l), a single

domain will be trapped at the con

ﬂ

uence points due to the different

widths of the branches of inputs and output, so that the output

signal is

“

0

”

By using this concept device, memory and logic can be

netic process) and data processing (electronic transistors) It means

that these devices can potentially work faster with higher

energy-ef

ﬁ

ciency Additionally, other solutions such as magnetic

ﬁ

eld and

heat can be utilized to assist the CIDM for reducing the

J

Therefore,

it is believed that the new structures can be very promising to build

up future memory and logic devices performing ultra-high density

and speed.

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3 Conclusion

We have shown the key distinctions in current-induced

dynamics in ferromagnetic, antiferromagnetic and

ferrimag-netic structures As compared to the FM-ordered materials, the

AF-ordered ones have more ef

ﬁ

cient spin-toques, as well as

high DW motion speeds of up to few hundreds m/s and are

robust to magnetic noises This is because the AF materials

have a strongly exchange-coupled magnetic sublattice

struc-ture, and the antiferromagnetic order parameter dynamics are

different from those of the ferromagnetic ones However, these

effective SAF

ﬁ

lms are mostly limited to the ultrathin sublayers

of a few Å and the total

ﬁ

lm thickness of a few nanometers

due to the dominance of interfacial effects such as Rashba

ef-fect and DMI Alternatively, the RE-TM ferrimagnetic alloys are

not limited in these thin thickness regions The DW velocity

can reach over km/s under around 100 mT

ﬁ

eld at

temper-ature around the angular compensated tempertemper-ature The RE

and TM moments can be easily controlled by varying

compo-sition or temperature, so that the angular compensated

tem-perature can be designed for appropriate applications The

RE-TM ferrimagnetic alloys are therefore expected to provide a

new approach for reducing energy consumption as well as the

immunity against external magnetic perturbation in spintronic

devices, such as racetrack memories and spin logic gates.

Acknowledgments

This research was partially supported by the Ministry of

Edu-cation, Culture, Sport, Science and Technology, Japan - Supported

Program for Strategic Research Foundation at Private University

(2014

e

2020) and KAKENHI (Nos 17H03240 and 18K14128).

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