Supplementary Material

Asymmetrical domain wall propagation due to the Dzyaloshinskii Moriya interaction in bifurcated PMA wire structure

J. Kwon et al.

1. Determination of the DW creation in the magnetic nanowire via current pulse injection into the

non-magnetic wire.

To confirm that the asymmetrical DW propagation can be replicated at reduced dimensions, nanowire

with width 500nm is patterned. A DW size in PMA has been proposed theoretically and experimentally in

less than few nanometer width. The narrow width wire in nano-scale can reduce the non-uniformity of

DW configuration and easily stabilized the magnetization in decreasing the magnetization volume from

2m to 500nm wide wire. Fig. S1(a) shows a SEM image and schematic illustration for DW creation by

current pulse injection along the injection line and the AHE measurement setup at the branches. The

AHE curves at the respective Hall bars, B1 and B2, for the Y-shaped structure with initial magnetization

along +Hz orientation is shown in Fig. S1(b) with and without created DW in the input wire. First, the

sample is magnetically saturated by applying a perpendicular field of +3 kOe along +Hz, up magnetized

state. The hysteretic reversal cycles in Rxy–Hz loops are observed at two Hall bars at the ends of U-shaped

branches having a constant dc current flow under applied perpendicular field, ±Hz. The observed Rxy

switching (Δ R ≈ ± 1.5 Ω) in the square hysteresis loops indicates a coercivity of ±1 kOe. The hysteretic

reversal cycles at each of Hall bars, B1 (square, blue) and B2 (circle, red) show that the Rxy values in the

magnetized state has a discrepancy, Δ R ≈ 0.25 Ω. The Rxy difference in between two Hall bars may be

due to non-uniform distribution of current in the U-shaped nano-structure as current is flowing from B2 to

B1. The other is distribution of local magnetization processes at each Hall bars due to structural defect at

the junction and curved shape of branches. We note that the hysteretic reversal obtained at each of the

branches concurrently, and the hysteresis loops at B1 and B2 have opposite Rxy change at the coercive

1

field. Rxy increases at B1 (square arrow) and decreases at B2 (circle arrow). The Rxy having opposite

polarity switching in the branches as the Hall voltage (V xy) are determined by the current direction in

electrical circuitry, as shown in Fig S1(a). The result indicates that the AHE at both branches comprising

of 500nm width wire shows same square hysteresis as comparing with 2m wide wire structure.

Fig S1: (a) Scanning electron microscopy (SEM) image of the fabricated 500nm wide wire device

comprising of DW input wire across a pulse injection line. The electrical setup for Hall measurement at

the Hall bars is schematically illustrated. (b) The measured AHE at each of branches with the

perpendicular field being swept. #1 and 2 denotes the reversal sequences in hysteresis at each of branches

2

with Δ R changes. Hpin is noted the pinning field of created DW. (c) DW creation probability by current

pulse passing through injection line. Determination of the DW creation as the function of pulse duration

time. (d) The shape of pulse signals with given duration times in constant voltage has been monitored by

the oscilloscope.

To investigate the DW creation in the nano-structure, a single current pulse injection via non-

magnetic injection line was used for creation and initializing the DW position near the injection line. The

magnetic field of +3 kOe was applied to prepare a single domain state along +Hz (up magnetized state) in

the magnetic wire. Afterwards, a single current pulse into the non-magnetic injection line has been

employed to create up-down DW by induced local Oersted field. Consequently, we examine the variation

of the Rxy–Hz loop as a single DW is created by current pulse injection. A successful DW creation has

been observed by detection of Rxy change at the pinning field, -87 Oe in the nanowire, as shown in Fig.

S1(b). Simultaneous Rxy change in each of branches has been observed the arrival of DWs at each of Hall

bars, which means that the two DWs present with a single DW creation in the structure. Prior to

investigation of two DWs in branches, deterministic creation of a single DW is investigated following the

pulse duration time increasing in Fig. S1(c). A created up-down DW is monitored by AHE measurement

as a created DW is pinned at the Hall bars. Deterministic a single DW creation is performed by pulse

injection repeating 20 times per each pulse duration time. The pinning field of the up-down DW

represents Rxy change at about –87 Oe as the field is increased towards –Hz (down magnetized). The failed

attempt with a short pulse duration time is not observed the Rxy change. The creation of DW is defined to

be successful when the Rxy change represented 100% at the pinning field, as seen in Fig. S1(c). A

successful DW creation requires appropriate current pulse injection parameters avoiding that a strong

pulse induces multiple DWs or damage in the nano-structure accompanying with Joule heating. Fig.

S1(c) shows that the DW creation with current density of pulse, J pulse ≈ 1.6 ×1011 A /m2 and lowest pulse

duration time 42ns has been observed the 100% DW creation in attempts. The lowest current pulse

parameter for 100% has been used to investigate a single DW motion in the input wire and the other DW

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creation at the junction due to the splitting in the 500nm wide nanowire system. On the other hand, the

higher current density of pulse, J pulse ≈ 3.6 ×1011 A /m2 has been observed 100% DW creation with pulse

duration time more than 17ns. Up-down and down-up chiral DW determined by a pulse with voltage

polarity and initial magnetized state. A nucleated single down-up DW in the wire is investigated, as the

initial magnetized state is up (+¿Mz) in the magnetic wire and current pulse, J pulse ≈ 1.6 ×1011 A /m2

injected via the injection line.

2. DWs pinning at the Hall bars in the nano-structure.

DW creation significantly relies on the duration time of the pulse as a critical current density

implicated. A creation of DW is observed as a current pulse with duration time above 40ns at the critical

intensity of pulse,V pulse=890 mV , which translate to current density, J pluse ≈ 1.6 ×1011 A /m2 via

injection line. A created DW relevant to a single pulse with various duration times is explored by AHE

measurement in Figs. S2(a) and (b). The dynamics of DW motion relies on the injected pulse parameter,

especially duration time, and the geometrical defects in the nano-structure. An up-down DW is able to

move along the DW input as the external field is increased towards –Hz. The created DW under control of

the duration times shows the various pinning behaviors at the Hall bars, which was not shown in 2m

wide wire device. At the pulse duration time below 47 ns, Rxy change in AHE observed a step at the

pinning field. The first step transition in Rxy change occurs at –100 Oe, indicates that the DW is depinned

from initial position and trapped at the Hall bar in B1, as shown in Fig. S2(a). For the B2, the first step

transition in Rxy change occurs at -50 Oe in Fig. S2(b). The result indicates that the DW in B2 is able to

reach earlier to the Hall bar than the DW in B1 as the field is increased towards –Hz. The second step

transition at approximately -120 ~ -150 Oe corresponds to the depinning of the DW through the center of

Hall bars at B1 and B2. For the comparison of Rxy step change in between B1 and B2, the step size is

quantitatively different. The first transition intensity in Rxy change shows a different between B1 and B2.

The Rxy change is Δ RB1≈ 0.25Ω at B1, and Δ RB2 ≈ 0.5 Ω at B2. However, the plateaus regions at B1

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and B2 are same as Δ H plateaus ≈ 50Oe. The step in Rxy change disappears and becomes a monotonic

switching as an increasing duration time more than 48 ns for the DW creation, as shown in both Figs.

S2(a) and (b). In case, the magnetization with DW motion relates to the down domain expanding. Note

that the step-like change in the Rxy implies the deformation of DW configuration so as to be passing the

Hall bar acting as an extrinsic barrier. The DW can be transformed to the DW equilibrium structure from

tilting Néel wall to non-linear DW face such as elongated DW at the Hall bars. 1,2 The geometrical defects

exist at the junction and Hall bars for the path of DW. The junction and Hall bars have a pinning potential

with geometrical defects such as the anti-notch and vertex, respectively.3,4 As well, the results indicate

that the pinning process at the Hall bars depends on the property of created DW such as Néel or Bloch

wall, and non-linear DW configuration in the input wire. The handedness dependence of field-driving

DW is also considerable to attribute the various DW depinning process at the Hall bars in B1 and B2.5,6

The Rxy change due to the DW is also investigated as the dc current varies in the AHE measurement in

Figs. S2(c) and (d). The DW at B1 shows a reliable Rxy value with switching at the pinning field as the

current increases in Fig. S2(c). However, DW in B2 has been observed the variation of the Rxy value. The

result shows that the base Rxy values of the up and down magnetized states of B1 in AHE has sustained a

constant, R xy ,down ≈ 1.7Ω, R xy ,up ≈ 2.5 Ω, as the current is increased in Fig. S2(c). On the contrary, the Rxy

value in magnetized states of B2 decreasesR xy ,up ≈ 2.7 Ω→ 2.2 Ω, R xy ,down ≈ 1.25 Ω→ 0.6 Ω as the

current is increased, as shown in Fig. S2(d). Decrement of Rxy in B2 implies that the magnetization states

at branch are also related to the DW motion corresponding to the current in the nano-structure. The

decrement of Rxy is able to include the measurement artifacts, that U-shape has locally non-steady

distribution of current density. A leakage current at the junction is also considerable as current flows

through U-shape structure. An injected single DW has been processed at the junction so as to produces

the other down-up DW by splitting. The DWs propagation directions due to the field are irrelevant to the

current flowing direction as the current flows through the branches. However, current may partially affect

to the magnetization process with DW motion in the nanowire with SOT effective field.

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Fig. S2. The AHE has been measured in order to monitor the varying of pinning fields in each of

branches after DW created in the nanowire by modulated current pulse parameters via injection line. The

DW pinning fields are monitored as function of various duration time in current pulse at (a) B1 and (b)

B2. The DW pinning fields are monitored as function of increasing current at (c) B1 and (d) B2.

3. Relationship between the magnetization and current-driven spin-orbit torque effect.

The spin transfer torque (STT) enables DW shift as polarized electrons from the charge currents

transfer their spin angular momentum to the local magnetic moment within the wire. The alternative

current driven mechanism is via the Spin-orbit torque (SOT). For the spin-orbit torque (SOT), two spin-

6

-250 -200 -150 -100 -50

1.0

1.5

2.0

2.5 70uA 80uA 90uA 100uA 110uA 120uA 130uA

Magnetic Field (Oe)

Rxy

()

-250 -200 -150 -100 -50

1.0

1.5

2.0

2.5

70uA 80uA 90uA 100uA 110uA 120uA 130uA

Rxy

()

Magnetic Field (Oe)

-300 -250 -200 -150 -100 -50 01.0

1.5

2.0

2.5

40ns 43ns 44ns 45ns 46ns 47ns 48ns

Magnetic Field (Oe)

Rxy

()

-300 -250 -200 -150 -100 -50 0

1.0

1.5

2.0

2.5 40ns 43ns 44ns 45ns 46ns 47ns 48ns

Rxy

()

Magnetic Field (Oe)

B1B2

(b)(a)

(d)(c)B2

B1

torque like terms are able to be expressed by the time evolution of the magnetization in the Landau-

Lifschitz-Gilbert (LLG) equation, 7 8

∂ M⃗∂ t

≈−γ M⃗ ×( ∂ E∂ M⃑

+aJ ( M⃗ × σ⃗ )+bJ σ⃗ )+α M⃗ × ∂ M⃗∂ t . (S1)

where M⃗ is the magnetization of ferromagnet, σ⃗ is the direction of accumulated spin polarized electrons at

the heavy-metal ferromagnet interface into the magnetic layer, which is determined by the direction of the

current, α is the Gillbert damping constant, γ is the gyromagnetic ratio. The current-induced effective

field comprises of ∆ H ≈ aJ M⃗ × ( M⃗ ×σ⃗ )+bJ M⃗ ×σ⃗ . For the case of spin-orbit torque, the coefficients of

the aJ and bJ are associated with the Slonczewski-like (SL) and Field-like (FL) term, respectively. The

SL torque effective fields have been studied for an embedded single magnetic layer asymmetrically

sandwiched between the heavy metals such as Pt, Ta, W. The effective fields from the torques have been

shown to enable high speed DW by current and voltage-induced effects. The effective fields

characterizing the SL and FL torque, are well known.9 10 The SHE arising in the heavy metal layer, gives

rise to spin polarized electron transverse to the flow of charge current, leading to a SL torque on the

ferromagnetic layer rather than a Field-like (FL) torque. For current flowing across a wire, σ⃗ acts in plane

transverse to the current flow. The rotation of magnetization in plane due to the current Je depends on the

given torques, T SL ≈ M⃗ ×(M⃗ × σ⃗ ) for a longitudinal one and T FL ≈ M⃗ × σ⃗ for a transverse one. For

example, the T FL can affect as an effective field, as σ⃗ and magnetization M⃗are orthogonal. For the

experiment, the effective fields are equivalent to the torques, T SL ≈ Δ HSL and T FL ≈ Δ H FL, relevant to the

direction along and transverse to current flow. The effective field is evaluated in phase with the AC

voltage excitation in the Hall voltage (V Hall) measurement. The magnetization oscillation in the wire can

be decomposed by harmonics measurement with an applied AC current with frequency f to modulate the

SOT amplitude. The oscillation contributes to the second harmonic in the Hall voltage (V Hall) which

provides a method to evaluate current-induced fields. The total V Hall can be described as

V Hall=V dc+V ω sin ωt+V 2 ωcos2 ωt+…. (S2)

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where V DC is independent on the AC excitation current in the total V Hall, V ω is first harmonic that relies

on the frequency of the AC excitation, and V 2ω is second harmonics which is the out-of-phase with

respect to the first harmonic. The V Hall follows the difference between the uniform up and down

magnetized states in PMA structure. We have evaluated the effective fields ( Δ HT , L) with respect to

current flow when the external in-plane field is swept along the x-axis (transverse field) and when it is

swept along the y-axis (longitudinal field). Here we assume that V ω andV 2 ω are proportional to the

amplitude of the AC excitation current. The V 2 ω is mostly sensitive to the effective field components

leading to the tilting of m̂ (deviation from uniform magnetization states). The effective fields from the

transverse and longitudinal V Hall measurement are obtained with the following equations.11 12

Δ HT ( L)=−2

∂V ω

∂ H ext ,T ( L )/∂2V 2 ω

∂ H ext ,T (L)2

. (S3)

where Δ HT ( L) is the transverse (longitudinal) effective field as variation of the AC V Hall measured with

in-plane field (H ext ,T ( L )) sweeping. The first (V ω) and second (V 2 ω) harmonics contributions for

quantitative effective field were measured in Pt/[Co/Ni]x4 film stack having perpendicular magnetic

anisotropy (PMA).

4. Measurement of V ω and V 2 ω components of the Hall voltage (V Hall).

The micro-wire has been prepared so as to enable high current density flow in the structure. Fig.

S3(a) illustrates the harmonics measurement setup to quantify the SL and FL torque by current-induced

effective field. The loop is reproduced with half amplitude of Hall resistance (Rxy) change in Fig. S3(b).

The constant sinusoidal AC current applied to the Hall cross geometry and measured the Hall voltage

using a lock-in amplifier. The in-plane field is also swept perpendicular and parallel to the current flow in

order to measure the transverse and the longitudinal components of the effective fields. The data of V ω is

fitted with a quadratic equation in external in-plane field up to ±600 Oe, as shown in Fig. S3(b). The

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second harmonic Hall voltage, V 2 ω has been obtained and exhibits a linear trend, as seen in Fig. S3(c),

and (d). The results of V 2 ω for the longitudinal measurement shows both positive and negative slope for

initial up and down magnetized state respectively, as seen in Fig. S3(c). For the transverse field sweep,

only a negative slope is observed, as seen in Fig. S3(d).

Fig. S3. (a) Illustration of electrical setup for a Hall bar device with Pt/[Co/Ni]x4. (b) The first harmonic

signal (V ω) shows quadratic dependence. (c, d) The second harmonic signal (V 2 ω) shows the linear

dependence as the in-plane field is applied to the transverse (H x) and the longitudinal (H y) respect to the

current direction with the initial magnetization state towards +z (solid circle) and –z (open circle).

5. Quantification of the current induced effective field, H L and HT .

9

+z+x+y

Vxy

Je

HT

HL

M

Ta

[Co/Ni]x4Pt

(b)(a)

(d)(c)

The SOT/current ratio in Pt/[Co/Ni]x4 is calculated to increase as the function of current density,

for both Δ HT and Δ H L about 5 Oe per 1010 A/m2, as shown in Fig. S4(a) and (b). The SOT/current ratio

indicates that the current-driven SOT can induce the magnetization due to the effective fields. As well,

the spin configurations within the DW can be changed by the strength of the effective field. Our work

suggests that the chiral DW in the Y-shaped structure has an efficient DW motion contributed by SL

torque with respect to the spin Hall effect (SHE). The Néel DW configuration would align with the wire

axis and the SL torque would drive its motion as the DW magnetization. The Néel DW motion in current

flowing branch with abrupt switching of Hall resistance may count on the SHE, which is relying on the

spin current from the bottom heavy-metal (Pt) layer. The different mechanism of FL torque is also

considered for DW configuration and motion at each of branches. Our result shows that the switching of

the Hall resistance at each branch occurs with the critical dc current density, Jdc current ≈ ± 6× 1010 A /m2.

The quantity of effective field in the critical current density of switching is estimated about 25 Oe. That

amount of effective field can induce a non-uniformity or transformation in DW configuration such as

tilting, which give more efficient motion of DW in the structure.

Fig. S4. (a, b) The transverse (Δ HT ) and longitudinal effective (Δ H L) field as function of the current

corresponds to the initial magnetization states pointing along +z (solid circle) and –z (open circle).

6. Micromagnetic simulation of an Up-Down Domain Wall with right hand tilt propagating in a T-shape structure.

10

1.5 2.0 2.5 3.0 3.5 4.0 4.5

-20

-10

0

10

20

HS

L (O

e)

J ( x1010 A/m2)

-Mz

+Mz

1.5 2.0 2.5 3.0 3.5 4.0 4.5

-20

-10

0

10

20

HFL

(Oe)

J ( x1010 A/m2)

-Mz

+Mz

(b)(a)

To gain an insight into the propagation of the DW at the bifurcation, micromagnetics simulations for

a T-shaped structure were carried out. Shown in Fig S5 are simulated spin configurations as DW

with a right-hand tilt propagates through a T-shaped structure.

Figure S5: Simulated spin configurations as a chiral Néel DW Up-Down, configuration with right hand tilt propagated through a T-shape junction. The DW expands asymmetrically at the bifurcation with a preferential propagation along the right hand side of the branch.

The structure is initially magnetized along the –z orientation and a DW with Up-Down configuration,

exhibiting a right-hand tilt, is injected into the system. As expected, the DW with right hand tilt

propagates asymmetrically along branch “B2” of the T-shaped junction. A clearer picture of the

propagation process is obtained in the T-shaped device. At the bifurcation, due to the initial right-

hand tilt of the DW, the expansion of the DW at the junction though having a crescent profile,

extends slightly towards branch “B” Fig S5-I. As the field is further increased, the domain expands

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within branch “B” due to the leading profile being on the right, Fig S5-II. Subsequently, as the

reversed domain expands within the junction, the DW within the branch “B” restores the right hand-

tilt and propagates through branch “B2”.

For branch “B1”, a slightly different process is observed. Following the depinning at the junction, the

DW within branch “B1” does not have the requisite right-hand tilt as imposed by the DMI. As such,

the DW undergoes a structural re-orientation of the spins within it to adopt the right-hand tilt. This

process undeniably slows down the DW propagation through branch “B1” while requiring additional

external energy for the DW stabilization.

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