Layer thickness dependence of the Supplementary ... · Layer thickness dependence of the ....

Layer thickness dependence of the current-induced effective field vector in Ta | CoFeB | MgO

1

Supplementary information for

Layer thickness dependence of the current induced effective field vector in

Ta|CoFeB|MgO

Junyeon Kim1 Jaivardhan Sinha1 Masamitsu Hayashi1 Michihiko Yamanouchi23 Shunsuke

Fukami2 Tetsuhiro Suzuki4 Seiji Mitani1 and Hideo Ohno235

1National Institute for Materials Science Tsukuba 305-0047 Japan 2 Center for Spintronics Integrated Systems Tohoku University Sendai 980-8577 Japan 3Laboratory for Nanoelectronics and Spintronics Research Institute of Electrical Communica

tion Tohoku University Sendai 980-8577 Japan 4Renesas Electronics Corporation Sagamihara 252-5298 Japan 5WPI Advanced Institute for Materials Research Tohoku University Sendai 980-8577 Japan

S1 Sample preparation

Magnetron sputtering (DC and RF) is used to deposit the films on highly resistive silicon

wafers The wafer is covered with a 100 nm thick thermally oxidized (SiO2) layer The film

stacks used here is A (Ta wedge) Si-sub|dTa Ta|1 Co20Fe60B20|2 MgO|1 Ta B (CoFeB

wedge) Si-sub|1 Ta|tCoFeB Co20Fe60B20|2 MgO|1 Ta and C (reference) Si-sub|1 Ta|1

Co20Fe60B20|2 MgO|1 Ta (thickness units in nanometer) Note that the composition (in atomic

percent) of the CoFeB is different from our previous studies which were mostly Co40Fe40B201-

3 Using a linear shutter dTa and tCoFeB are varied from ~0 nm to ~ 2 nm on a single wafer

Since the substrate position can slightly vary with respect to the starting position of the linear

shutter the absolute value of the thickness may not agree with the designed thickness In

order to calibrate the thickness we use a film in which the thickness of each layer is well

defined (film C) and compare the transport properties (RXX RXY) with the wedge films

The thickness of the wedge films are calibrated so that RXX and RXY match with those of

film C

All films are annealed at 300 degC for one hour in vacuum after the film deposition Using

cross section transmission electron microscopy (TEM) we find that the Ta underlayer and the

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2

CoFeB layer are predominantly amorphous even after annealing at 300 oC (see Fig S1(c) for

an exemplary image) Due to the limit in the TEM resolution it is difficult to identify the Ta

underlayer thickness below which it does not form a continuous layer Photo-lithography and

Ar ion etching are used to pattern the Hall bar structure After the formation of the Hall bar a

conventional lift off process is used to form the contact electrodes made of 10 Ta|100 Au (see

Fig S1(a) for an exemplary optical microscopy image of the device) Prior to the deposition

of the contact electrodes we etch the region where the contacts are formed in order to avoid

large contact resistance due to the 2 nm thick MgO insulating layer Here the Ta capping

layer and nearly half of the MgO layer are etched As reported previously the etching of the

MgO layer results in reduction of the perpendicular magnetic anisotropy of the CoFeB layer3

The degree of reduction depends on how much the MgO layer is etched out etching half of

the MgO layer forces the magnetization easy axis of the CoFeB layer to point along the film

plane Schematic of the magnetization configuration of the device is shown in Fig S1(b)

Magnetization of the CoFeB layer is pointing out of plane where we evaluate the current

induced effective field ie at the Hall cross whereas it is directed along the film plane under

the contact electrodes (Ta|Au) Formation of such in-plane magnetized regions under the

contact electrodes can influence the magnetization switching we have shown that it can

reduce the out of plane coercive field However we consider that the in-plane magnetized

region has little effect on the evaluation of the current induced effective fields since it is far

away (~10 m) from the Hall cross and we limit the applied in-plane field smaller than the

magnetization switching field so that the magnetization of the Hall cross is mainly pointing

along the film normal

S2 Harmonic voltage measurements

The in-phase first harmonic Hall voltage signals measured simultaneously with the out of

phase second harmonic signals shown in Fig 2 are shown in Fig S2 The maximum

magnetization tilt angle estimated from the first harmonic Hall voltage signal is for example

~126 deg (~023 rad) for the data shown in Fig S2(a) It is not clear what causes the

small offset voltage in the second harmonic signals shown in Fig 2 The signal generator has

~0001 total harmonic distortion

S3 Resistance versus the wedge thickness

The thickness dependence of the measured wire resistance measured using the four point

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3

probe method is shown in Fig S3 for the Ta (S3(a)) and the CoFeB (S3(b)) wedge films

The wire resistance RXX is multiplied by the wire width (w 10 m) and divided by the length

between the two voltage probes (L 25 m) to obtain a normalized resistance RXX wL The

slope of 1(RXX wL) versus the wedge layer thickness gives the resistivity of the thickness

varying film We obtain ~191 middotcm for the Ta layer and ~111 middotcm for the CoFeB

layer

S4 Temperature dependence of the Hall resistance

In order to estimate the device temperature due to the Joule heating effect we show the

temperature dependence of normalized RXY in Fig S4(a) for dTa=03 09 and 13 nm 0XYR

corresponds to theRXY measured at room temperature (~295 K) using a small sense current

(IDC=10 uA for Fig S4(a) and VIN=05 V for Fig S4(b)) For dTa =13 nm (blue triangles) the

perpendicular magnetic anisotropy is not enough to hold the moments out of plane at ~400 K

and thus RXY is nearly zero at this temperature

The input voltage dependence of the normalizedRXY is shown in Fig S4(b) for the same

devices We observe a much smaller change in RXY 0XYR as VIN is varied compared to that

when the temperature is changed Using the results of Figs S4(a) and S4(b) we estimate the

device temperature as a function of the input voltage which is shown in Fig S4(c) For the

three devices measured we estimate the maximum device temperature to be within ~320 K

an increase of ~25 K from room temperature This value is reasonable since the maximum

current density passed along the Hall bar is only ~26x107 Acm2

S5 Derivation of Eq (1)

The magnetic energy of our system can be expressed as

2 22 cos cos sin sin sin cosu s s T L ZE K M M H H H (S51)

where Ku is the anisotropy constant (positive for out of plane easy axis) Ms is the saturation

magnetization and Hi=(TLZ) is the external field θ is the polar angle (with respect to the z

axis) and φ is the azimuthal angle (with respect to the x axis) of the magnetization We

define HT HL and Hz as the in-plane transverse field (directed along the x-axis in Fig 1(a)

ie transverse to the current flow) the in-plane longitudinal field (along the y-axis pointing

along the current flow) and the out of plane field respectively Assuming that the current




4

induced effective field and the external in-plane field are small enough so that the

magnetization tilt angle can be considered small ie θltlt1 the equilibrium tilt angle θ0 with

respect to the external field can be expressed as

0

cos sinT LH HD

(S52)

where 2 4u s s zD K M M H If the external field is directed along the film plane ie

Hz~0 which corresponds to our experimental condition D can be considered as a constant

(Note that if Joule heating takes place D varies with the current See section S6 for the

details)

The current applied to the wire can be expressed in terms of the wire resistance RXX and

the AC voltage with amplitude (VIN) and frequency

sin sinIN

XX

VI t I tR

(S53)

The resistance shows little dependence on the input voltage and thus can be assumed to be a

constant The current induced effective field Hmiddotsint can be decomposed into two

components the effective field directed transverse to TH and along LH the current

flow both lying within the film plane Here we assume that the effective field is in phase

with the AC voltage excitation Both components of the sinusoidal effective fields are added

to the external field in Eq (S52) to give the equilibrium magnetization tilt angle θ(VIN)

under the AC voltage application which reads

sin cos sin sin( ) T T L L

IN

H H t H H tV

D

(S54)

The EHE (Hall) resistance can be expressed using the magnetization tilt angle as

cos

2XY

XYRR

(S55)

where RXY corresponds to the difference in the EHE resistance between the two

magnetization states pointing along +z and ndashz Substituting Eq (S54) into (S55) and

assuming θ(VIN)ltlt1 gives

2 2

2 2 2 2

2 2

1 sin2 2 2

cos sin 2 cos sin

2 cos 2 sin 2( )cos sin

XYXY

T L T L

T T L L T L L T

R A BR tD D

A H H H HB H H H H H H H H

(S56)




5

Here the plusminus sign represents the state with magnetization direction pointing along +z

and ndashz respectively In obtaining Eq (S56) we neglect terms of O(HT(L)2) The Hall

voltage which is measured using the lock-in amplifier is VXY=RXYI Substituting Eqs

(S53) and (S56) into VXY and using the trigonometric identities we obtain the following

formula

2sin cos2XY DCV V V t V t (S57)

Here VDC represents terms that do not depend on The in-phase first harmonic V and the

out of phase second harmonic V2 voltages are expressed as

21

2 2XYR AV I

D

(S58a)

2 2

12 2 2

XYR BV ID

(S58b)

We substitute φ=0 when the external in-plane field is directed along the x axis (transverse

field) and φ=2 when it is pointing along the y axis (longitudinal field) To obtain Eq (1) in

the main text one needs to take the second derivative of Eq (S58a) and the first derivative

of Eq (S58b) with respect to the external field and take their ratio

S6 Effect of Joule heating on the current induced effective field

The magnitude of the current induced effective field may change due to changes in material

parameters caused by Joule heating There are three temperature dependent parameters that

can influence the effective field estimation the saturation magnetization (MS) the magnetic

anisotropy (Ku) and the extraordinary Hall effect resistance (RXY) Since the current passed

here is relatively low (maximum current density is ~26x107 Acm2 (VIN=30 V)) the

temperature rise is not significant (at most ~25 K above room temperature see Section S4)

We thus assume that most of the Joule heating related terms are small and consider terms that

are only linear with the temperature change See Ref 4 for the temperature dependence of

MS and Ku in a similar system the variation with temperature is more or less linear near room

temperature RXY also varies linearly with temperature within the temperature range of

interest as shown in Fig S4(a) Thus we assume the following form of MS Ku and RXY

( ) 1S SM T M T

(S61a)

( ) 1u uK T K T

(S61b)




6

( ) 1XY XYR T R T

(S61c)

Here and represent the change in MS Ku and RXY respectively when the temperature

changes by T For Joule heating the temperature rise is proportional to the square of

current and thus

2T I

(S62)

Here relates the change in the temperature with the amount of Joule heating (which is

proportional to the square of current) Substituting Eqs (S53) and (S62) into Eqs (S61a-

1c) give

2 2( ) 1 sinS SM T M I t

(S63a)

2 2( ) 1 sinu uK T K I t

(S63b)

2 2( ) 1 sinXY XYR T R I t

(S63c)

These equations explicitly show the time variation of each parameter due to the Joule heating

effect Substituting these parameters into Eqs (S52) and (S56) and retaining terms linear

with and result in the following form of the current induced effective field

2

( ) ( )2( ) ( )

2 12 14

MEAST L T L

T L T L

V DVH H TH H D

(S64)

where 2 4uS

S

KD MM

Note that ( )MEAST LH is the quantity we use to obtain the

current induced effective field from our measurements (see Eq (1) in the main text)

Equation (S64) shows that ( )MEAST LH varies as the Joule heating effect causes changes in RXY

MS and Ku To provide rough estimates of the effect of Joule heating we use ~83times10-4

~22times10-3 MS~794 emucm3 and Ku~44times106 ergcm3 from Yamanouchi et al4 ~22times10-3

and RXY~34 from Fig S4(a) (dTa~09nm) We find that ( )MEAST LH is larger than HT(L) by

less than 10 for a temperature increase of 25 K

S7 Effect of the Oersted field

The current flowing through the Ta layer can generate Oersted field which can act on the

CoFeB magnetization in sync with the transverse effective field The direction of the

Oersted field coincides with positive HTVIN here In order to estimate its effect we

calculate the Oersted field using the Biot-Savart law5 We assume the worst case where all




7

the current applied to the wire flows into the Ta layer (note that the resistivity of the Ta layer

is ~17 times larger than that of the CoFeB layer see S3) The Oersted field is calculated at a

position where the center of a 1 nm thick CoFeB layer is located (05 nm above the surface of

the Ta layer) For a fixed current density of 1x107 Acm2 the resulting Oersted field is ~06

Oe for a 1 nm thick Ta layer The Oersted field increases linearly with the Ta thickness

assuming a constant current density The results are plotted by the red solid line in Fig S5

together with the measured HTVIN (as shown in Fig 3(c)) We find that the effect of the

Oersted field is relatively small

References 1 S Fukami T Suzuki Y Nakatani N Ishiwata M Yamanouchi S Ikeda N Kasai and

H Ohno Appl Phys Lett 98 082504 (2011) 2 T Suzuki S Fukami N Ishiwata M Yamanouchi S Ikeda N Kasai and H Ohno

Appl Phys Lett 98 142505 (2011) 3 M Hayashi M Yamanouchi S Fukami J Sinha S Mitani and H Ohno Appl Phys

Lett 100 192411 (2012) 4 M Yamanouchi A Jander P Dhagat S Ikeda F Matsukura and H Ohno IEEE Magn

Lett 2 3000304 (2011) 5 T J Silva C S Lee T M Crawford and C T Rogers J Appl Phys 85 7849 (1999)




8

Figure captions

Fig S1 (a) Exemplary optical micrograph of the device The dark contrast region shows

the Hall bar formed from the film The width and length of the horizontal part of the Hall bar

is 10 m and 60 m respectively (b) Schematic image of the device corresponding to region

enclosed by the dotted line in (a) The magnetization direction of the CoFeB layer is

illustrated by the blue arrows The moments point along the film plane under the contact

electrodes (Ta|Au) whereas they are directed out of plane in other areas Note that the Ta

capping layer (on top of the MgO layer) is not shown in this image (c) Cross sectional

transmission electron microscopy image (courtesy M Kodzuka et al unpublished data) of a

typical film stack Sub|1 Ta|12 CoFeB|3 MgO|3 Ta (units in nanometer) The film is

annealed at 300 oC

Fig S2 In phase first harmonic signal Vas a function of in-plane field directed transverse

(a c) and parallel to (b d) to current flow for VIN=20 V Solid and open symbols represent

signals when the magnetization is pointing along +z and ndashz respectively The Ta wedge layer

thickness (dTa) is 01 nm for (a b) and 11 nm for (c d)

Fig S3 Inverse of the normalized resistance as a function of the wedge layer thickness The

resistance (RXX) measured using the four point probe method is multiplied by the wire width

(w) and divided by the distance between the two voltage probes (L) to obtain the normalized

resistance (a) Ta wedge film and (b) CoFeB wedge film The open symbols in (a) and (b)

are the inverse of the normalized resistance from the reference film (Si-sub|1 Ta|1 CoFeB|2

MgO|1 Ta)

Fig S4 (a) Environment temperature dependence of RXY normalized by its room

temperature value 0XYR (b) Normalized RXY as a function of the input voltage (VIN)

0XYR isRXY measured using the lowest VIN (typically 05 V) at room temperature (c)

Estimated device temperature plotted against VIN Symbols represent data from different Ta

thickness devices (Ta wedge film)

Fig S5 Calculated Oersted field divided by VIN (red solid line) plotted together with the

data from Fig 3(c) All current applied to the wire is set to flow within the Ta layer




Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2

Transverse LongitudinalTa 01 nm

Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)

CoFeB thickness (nm)

Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320

dTa (nm) 03 09 13Est

imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




2

CoFeB layer are predominantly amorphous even after annealing at 300 oC (see Fig S1(c) for

an exemplary image) Due to the limit in the TEM resolution it is difficult to identify the Ta

underlayer thickness below which it does not form a continuous layer Photo-lithography and

Ar ion etching are used to pattern the Hall bar structure After the formation of the Hall bar a

conventional lift off process is used to form the contact electrodes made of 10 Ta|100 Au (see

Fig S1(a) for an exemplary optical microscopy image of the device) Prior to the deposition

of the contact electrodes we etch the region where the contacts are formed in order to avoid

large contact resistance due to the 2 nm thick MgO insulating layer Here the Ta capping

layer and nearly half of the MgO layer are etched As reported previously the etching of the

MgO layer results in reduction of the perpendicular magnetic anisotropy of the CoFeB layer3

The degree of reduction depends on how much the MgO layer is etched out etching half of

the MgO layer forces the magnetization easy axis of the CoFeB layer to point along the film

plane Schematic of the magnetization configuration of the device is shown in Fig S1(b)

Magnetization of the CoFeB layer is pointing out of plane where we evaluate the current

induced effective field ie at the Hall cross whereas it is directed along the film plane under

the contact electrodes (Ta|Au) Formation of such in-plane magnetized regions under the

contact electrodes can influence the magnetization switching we have shown that it can

reduce the out of plane coercive field However we consider that the in-plane magnetized

region has little effect on the evaluation of the current induced effective fields since it is far

away (~10 m) from the Hall cross and we limit the applied in-plane field smaller than the

magnetization switching field so that the magnetization of the Hall cross is mainly pointing

along the film normal

S2 Harmonic voltage measurements

The in-phase first harmonic Hall voltage signals measured simultaneously with the out of

phase second harmonic signals shown in Fig 2 are shown in Fig S2 The maximum

magnetization tilt angle estimated from the first harmonic Hall voltage signal is for example

~126 deg (~023 rad) for the data shown in Fig S2(a) It is not clear what causes the

small offset voltage in the second harmonic signals shown in Fig 2 The signal generator has

~0001 total harmonic distortion

S3 Resistance versus the wedge thickness

The thickness dependence of the measured wire resistance measured using the four point




3






layer



























4




0

cos sinT LH HD

(S52)




details)



sin sinIN

XX

VI t I tR

(S53)









IN

H H t H H tV

D

(S54)


cos

2XY

XYRR

(S55)




2 2

2 2 2 2

2 2

1 sin2 2 2

cos sin 2 cos sin


XYXY

T L T L

T T L L T L L T

R A BR tD D


(S56)




5





formula




21

2 2XYR AV I

D

(S58a)

2 2

12 2 2

XYR BV ID

(S58b)

















( ) 1S SM T M T

(S61a)

( ) 1u uK T K T

(S61b)




6

( ) 1XY XYR T R T

(S61c)



current and thus

2T I

(S62)



1c) give


(S63a)


(S63b)


(S63c)




2

( ) ( )2( ) ( )

2 12 14

MEAST L T L

T L T L

V DVH H TH H D

(S64)

where 2 4uS

S

KD MM
















7

















8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




3






layer



























4




0

cos sinT LH HD

(S52)




details)



sin sinIN

XX

VI t I tR

(S53)









IN

H H t H H tV

D

(S54)


cos

2XY

XYRR

(S55)




2 2

2 2 2 2

2 2

1 sin2 2 2

cos sin 2 cos sin


XYXY

T L T L

T T L L T L L T

R A BR tD D


(S56)




5





formula




21

2 2XYR AV I

D

(S58a)

2 2

12 2 2

XYR BV ID

(S58b)

















( ) 1S SM T M T

(S61a)

( ) 1u uK T K T

(S61b)




6

( ) 1XY XYR T R T

(S61c)



current and thus

2T I

(S62)



1c) give


(S63a)


(S63b)


(S63c)




2

( ) ( )2( ) ( )

2 12 14

MEAST L T L

T L T L

V DVH H TH H D

(S64)

where 2 4uS

S

KD MM
















7

















8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




4




0

cos sinT LH HD

(S52)




details)



sin sinIN

XX

VI t I tR

(S53)









IN

H H t H H tV

D

(S54)


cos

2XY

XYRR

(S55)




2 2

2 2 2 2

2 2

1 sin2 2 2

cos sin 2 cos sin


XYXY

T L T L

T T L L T L L T

R A BR tD D


(S56)




5





formula




21

2 2XYR AV I

D

(S58a)

2 2

12 2 2

XYR BV ID

(S58b)

















( ) 1S SM T M T

(S61a)

( ) 1u uK T K T

(S61b)




6

( ) 1XY XYR T R T

(S61c)



current and thus

2T I

(S62)



1c) give


(S63a)


(S63b)


(S63c)




2

( ) ( )2( ) ( )

2 12 14

MEAST L T L

T L T L

V DVH H TH H D

(S64)

where 2 4uS

S

KD MM
















7

















8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




5





formula




21

2 2XYR AV I

D

(S58a)

2 2

12 2 2

XYR BV ID

(S58b)

















( ) 1S SM T M T

(S61a)

( ) 1u uK T K T

(S61b)




6

( ) 1XY XYR T R T

(S61c)



current and thus

2T I

(S62)



1c) give


(S63a)


(S63b)


(S63c)




2

( ) ( )2( ) ( )

2 12 14

MEAST L T L

T L T L

V DVH H TH H D

(S64)

where 2 4uS

S

KD MM
















7

















8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




6

( ) 1XY XYR T R T

(S61c)



current and thus

2T I

(S62)



1c) give


(S63a)


(S63b)


(S63c)




2

( ) ( )2( ) ( )

2 12 14

MEAST L T L

T L T L

V DVH H TH H D

(S64)

where 2 4uS

S

KD MM
















7

















8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




7

















8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




8

Figure captions










annealed at 300 oC










MgO|1 Ta)











Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




Ta|Au

Fig S1

CoFeB wire

60 m

Ta CoFeB MgO

Ta|Au

V

TaCoFeBMgO

Ta

5 nmSiO2




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




-1000 -500 0 500 1000-56

-49

77

84

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-56

-49

77

84

Mz

Mz

V (m

V)

HL (Oe)

-1000 -500 0 500 1000-77

-70

56

63

Mz

Mz

V (m

V)

HT (Oe)-1000 -500 0 500 1000

-77

-7056

63Mz

MzV (m

V)

HL (Oe)

Fig S2


Ta 10 nm Ta 10 nm

Ta 01 nm




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




0 1 20000

0001

0002

1(R

XX

wL

) (

-1)

Ta thickness (nm)

0 1 20000

0001

00021

(RX

Xw

L) (

-1)


Fig S3

(b)

(a)




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




280 320 360 40000

05

10

dTa (nm) 03 09 13

R

XY(T

)R

0 XY

Temperature (K)

0 10 20 30290

300

310

320


imat

ed T

emp

(K)

VIN (V)

0 10 20 300001

090

095

100

dTa (nm) 03 09 13

RX

Y(T

)R

0 XY

VIN (V)

Fig S4




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




00 05 10 15 200

1

2

3

4

02 04 06

00

03

Mz

Mz

HT V

IN (O

e V

)Ta thickness (nm)

HT V

IN (O

e V

)

Ta thickness (nm)

Fig S5




Layer thickness dependence of the Supplementary ... · Layer thickness dependence of the ....

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