Dr. Vadym Zayets

Abstract:

High- precision, high- reproducibility, high- repeatability measurement of magnetic and magneto- transport properties of ferromagnetic nanomagnets using the Hall effect

High-precision measurement of effect of spin-orbit torque (SOT effect): Dependence of magnetic and magneto- transport properties on electrical current

High-precision measurement of effect of voltage-controlled magnetic anisotropy (VCMA effect): Dependence of magnetic and magneto- transport properties on a gate voltage

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Measurements

(measurement 1) Measurement of Hall angle vs external perpendicular magnetic field

(1.1) Measurements of Hall angle, Anomalous Hall effect (AHE), Inverse Spin Hall effect (Sample dependence)

(1.2) Spin-orbit torque: Measurement of dependence of Hall angle, Anomalous Hall effect (AHE), Inverse Spin Hall effect on current magnitude and polarity.

(1.3) VCMA: Measurement of dependence of Hall angle, Anomalous Hall effect (AHE), Inverse Spin Hall effect on gate voltage

(measurement 2) Measurement of anisotropy field vs external perpendicular magnetic field

(2.1) Measurement of PMA & Anisotropy field

(2.2) Spin-orbit torque: ""Field- like torque" ""Damp- like torque". Measurement of dependence of PMA on the electrical current .

(2.3) VCMA: ""Field- like torque" ""Damp- like torque". Measurement of dependence of PMA on gate voltage.

(measurement 3) Measurement of magnetization switching under external perpendicular magnetic field

(3.1) Measurement of coercive field H_C, retention time, size of nucleation domain, parameter delta Δ

(3.2) Spin-orbit torque: Current dependence of magnetization switching parameters.

(3.3) VCMA: dependence of magnetization switching parameters on gate voltage.

(measurement 4) Measurement of magnetization switching under in-plane bias magnetic field

(4.1) Measurement of coercive field H_C, retention time, size of nucleation domain, parameter delta Δ

(4.2) Spin-orbit torque: Current dependence of magnetization switching parameters.

(4.3) VCMA: dependence of magnetization switching parameters on gate voltage.

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Details of Measurement Methods are here

 

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Volt 53B (Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm))

 

fabrication: EB only, 18/01/30 day3

MgO 220C/360C

Raw data Volt53.zip (.dat files and origin 9 files)

(7zip (free) download is here)

Conductivity: 0.04-0.06 S/m2

Anisotropy field H_anis =2.2 kGauss-6 kGauss

Coercive field = 200 Oe-330 Oe;

Hall angle measured=290- 750 mdeg

Intrinsic Hall angle of FeB= 1015 - 2625 mdeg;

Gap region etched: FeB is partially etched, stopped in middle of FeCoB

 

 

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magnetization- switching parameters:

retention time τ_ret

(gate): free18-> 10¹⁷ s; ud60-> 10²⁶ s; ud66-> 10¹⁰ s; ud67-> 10⁸ s;

(gap): ud60-> 10²⁶ s; ud66-> 10¹⁷ s;

size of nucleation domain:

(gate): free18-> 42 nm; ud60-> 69 nm; ud66-> 35 nm; ud67-> 33 nm;

(gap): ud60-> 64 nm; ud66-> 43 nm;

coercive field H_c:

(gate): free18-> 325 Oe; ud60-> 200 Oe; ud66-> 230 Oe; ud67-> 260 Oe;

(gap): ud60-> 230 Oe; ud66-> 330 Oe;

parameter Δ :

(gate): free18-> 130; ud60-> 270; ud66-> 100; ud67->60;

(gap): ud60-> 240; ud66-> 90;

 

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sizes of nanomagnets & conductivity σ

fabricated 18/01/30 day3

(ud 59): wire width: 400 nm; nanomagnet length: 10 μm; σ = 0.0446 S/m²

(ud 60): wire width: 1000 nm; nanomagnet length: 200 nm; σ = ? S/m²

(ud 66): wire width: 200 nm; nanomagnet length: 500 nm; σ = ? S/m²

(ud 67): wire width: 400 nm; nanomagnet length: 500 nm; σ = 0.0486 S/m²

(ud 68): wire width: 1000 nm; nanomagnet length: 500 nm; σ = 0.040 S/m²

(ud 73): wire width: 400 nm; nanomagnet length: 2000 nm; σ = 0.050 S/m²

(ud 39): wire width: 400 nm; nanomagnet length: 200 nm; σ = 0.0475 S/m²

(free 18): wire width: 1000 nm; nanomagnet length: 200 nm; σ = 0.04 S/m²

(free 68): wire width: 200 nm; lattice: stripe: 300 nm; gap 300 nm: ; σ = 0.064 S/m²

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Since the nanowire is double- layer, which consists of Ta and FeCoB layer, the Hall angle α_{Hall, FeB} in FeCoB can be calculated from measured Hall angle α_{Hall, measured} (See here) as

where

t_FeB, t_Ta, σ_FeB,σ_Ta are thicknesses and conductivities of FeCoB and Ta metals.

 

k_double=3.5

 

 

 

 

 

 

 

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(measurement 1) Measurement of Hall angle vs external perpendicular magnetic field Hz

 

 

 

Hall angle, Anomalous Hall effect (AHE), Inverse Spin Hall effect (Sample dependence)

Hall angle αHall 1st derivation ∂αHall/∂Hz 2nd derivation ∂2αHall/∂Hz2 αHall and therefore strength of AHE is substantially different for each nanomagnet ∂αHall/∂Hz is different for ~10 % for each sample with correspondent difference of ∂2αHall/∂Hz2, which means that the strength of ISHE is different for each nanomagnet

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

Fitting of Hall angle

The Hall angle α_Hall , its 1st derivation ∂α_Hall/∂H_z and its 2d derivation ∂²α_Hall/∂H_z² is simultaneously fitted by equation (See here)

where α_OHE is Hall angle of Ordinary Hall effect, α_AHE is Hall angle of Anomalous Hall effect and where α_ISHE is Hall angle of Inverse Spin Hall effect

There is an ambiguity for α_ISHE and α_AHE, which depends on unknown spin polarization sp

where sp is the spin polarization of conduction electrons, α_AHE,0.5 is α_AHE at sp=0.5, α_ISHE,0.5 is α_ISHE at sp=0.5

result of fitting:

sample:( free68 gate) α_ISHE,0.5= 410 mdeg; α_AHE,0.5=1401 mdeg; α_OHE=0.2 mdeg/kG; H_p=4.73 kG;

sample:( free18 gate) α_ISHE,0.5= 159 mdeg; α_AHE,0.5=816 mdeg; α_OHE=0.2 mdeg/kG; H_p=5.73 kG;

sample:( ud59) α_ISHE,0.5= 163 mdeg; α_AHE,0.5=2225 mdeg; α_OHE=0.2 mdeg/kG; H_p=5.84 kG;

sample:( ud60) α_ISHE,0.5= 165 mdeg; α_AHE,0.5=590 mdeg; α_OHE=0.2 mdeg/kG; H_p=5.06 kG;

sample:( ud66) α_ISHE,0.5= 274 mdeg; α_AHE,0.5=2324 mdeg; α_OHE=0.2 mdeg/kG; H_p=5.84 kG;

sample:( ud67) α_ISHE,0.5= 113 mdeg; α_AHE,0.5=1677 mdeg; α_OHE=0.2 mdeg/kG; H_p=6.01 kG;

sample:( ud68) α_ISHE,0.5=162 mdeg; α_AHE,0.5=767 mdeg; α_OHE=0.2 mdeg/kG; H_p=4.91 kG;

sample:( ud39) α_ISHE,0.5=392 mdeg; α_AHE,0.5=657 mdeg; α_OHE=0.2 mdeg/kG; H_p=6.18 kG;

 

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AHE & ISHE vs current & current polarity. SOT effect

Measurement 1. Dependence of Anomalous Hall effect (AHE) & Inverse Spin Hall effect (ISHE) on current and current polarity. Effect of Spin-Orbit Torque (SOT)

 

Spin-orbit torque. Hall angle, Anomalous Hall effect (AHE), Inverse Spin Hall effect vs current

fig.4a. Current- dependence of AHE (Hall angle αHall) fig.4b. Current- dependence of ISHE (∂αHall/∂Hz i)     fig.4c. Dependence of AHE on polarity of current j fig.4d. Dependence of ISHE on polarity of current j ΔAHE= (αHall(j)-αHall(-j))/2 ΔISHE= (ISHE(j)-ISHE(-j))/2 fig.4e. Hall angle αHall at different current j fig.4f.∂αHall/∂Hz at different different current j sample: ud59 gate. Dependence of AHE (αHall) is substantial and obvious sample ud59 gate. Dependence of ISHE is weak.

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

Features

(temperature)

dependence on current magnitude

(AHE vs I² ): strong 4-6 % decrease at current of 50 mA/ μm²; (fig.4a)

(ISHE vs I² ):weak 0.2 mdeg/kG decrease at 50 mA/ μm² (fig.4b)

(Spin- orbit torque)

dependence on current polarity

(AHE(I)-AHE(-I)): moderate ~0.6-0.8 % ; slope: both negative & positive; saturation: at 50 mA/ μm²; (fig.4c)

(ISHE(I)-ISHE(-I)): very small (~0.1 mdeg/kG) (fig.4d)

 

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AHE & ISHE vs gate voltage. VCMA effect

Measurement 1. Dependence of Anomalous Hall effect (AHE) & Inverse Spin Hall effect (ISHE) on gate voltage. Effect of Voltage-Controlled Magnetic Anisotropy (VCMA)

 

VCMA. Hall angle, Anomalous Hall effect (AHE), Inverse Spin Hall effect vs gate voltage

fig.5a. dependence of AHE (Hall angle αHall) on gate voltage fig.5b. dependence of ISHE (∂αHall/∂Hz) on gate voltage normalized change of AHE vs gate voltage. normalized AHE=(AHE(V)-AHE(V=1))/AHE(V).   fig.5c. Hall angle αHall at different different gate voltages fig.5d.∂αHall/∂Hz at different different gate voltages Sample ud66. Dependence on Vgate is clear Sample ud66. Data is noisy

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

Features

 

dependence on gate voltage

(AHE vs V_gate ): weak 0.4 % ; slope: unclear

(ISHE vs V_gate ): weak 0.2 mdeg/kG; slope: unclear

 

 

 

 

 

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(measurement 2) Measurement of anisotropy field vs external perpendicular magnetic field Hz

details about measurement method is here and here

Measurement of PMA. Anisotropy field

Anisotropy field Hanis Offset magnetic field Hoff . Scan is along wire. Offset magnetic field Hoff . Scan is perpendicularly to wire. Anisotropy field Hanis vs external perpendicular magnetic field Hz. Hanis is about 5 kG and variation from sample to sample is about 0.5 kG. Up to =2.5 kG, there is a peak and diversion from a strait line. There is a weak difference between positive and negative scans of Hz. Offset magnetic field Hoff measured when in-plane magnetic field is scanned along metallic wire. There is a substantial difference between samples and a substantial difference between positive and negative scans of Hz. At Hz =7 kG, Hoff = between 50-100 G for different samples. The dependence is linear with some periodical modulation. Offset magnetic field Hoff measured when in-plane magnetic field is scanned perpendicularly to metallic wire. There is a substantial difference between samples and a substantial difference between positive and negative scans of Hz. At Hz =7 kG, Hoff = between -10-40G for different samples. The dependence is slightly linear (nearly a constant) with a substantial periodical modulation.

details of this measurement method is here

Sample Volt53: Ta(3 nm)/ FeB(1.1 nm)/ MgO(7 nm)/ W(1 nm) /Ru(5 nm)

click on image to enlarge it

 

Spin-orbit torque vs PMA

Spin-orbit torque. Measurement of dependence of PMA on the electrical current j.

"Field- like torque". Current- dependence of offset field ∂Hoff/∂j. Scan is along wire. "Damp- like torque". Current- dependence of offset field ∂Hoff/∂j. Scan is perpendicularly to wire. ∂Hoff/∂j~ 0.1 Gauss/(mA/ μm2).E.g. at j=100 mA/ μm2, change of offset field ΔHoff=10 Gauss. There are clear oscillations. There is a substantial difference between positive and negative scans of Hz. ∂Hoff/∂j~ 0.18 Gauss/(mA/ μm2).E.g. at j=100 mA/ μm2, change of offset field ΔHoff=18 Gauss. There are clear oscillations. There is a substantial difference between positive and negative scans of Hz. Current- dependence of anisotropy field∂Hanis/∂j. Scan is along wire. Current- dependence of anisotropy field∂Hanis/∂j. Scan is perpendicularly to wire. ∂Hanis/∂j~ 0.8 Gauss/(mA/ μm2).E.g. at j=100 mA/ μm2, change of anisotropy field ΔHanis=80 Gauss. There are clear oscillations. Amplitude of oscillations increases at a larger Hz. There is a substantial difference between positive and negative scans of Hz. ∂Hanis/∂j~ 0.8 Gauss/(mA/ μm2).E.g. at j=100 mA/ μm2, change of anisotropy field ΔHanis=80 Gauss. There are clear oscillations. Amplitude of oscillations increases at a larger Hz. There is a substantial difference between positive and negative scans of Hz.

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

 

Spin-orbit torque. Measurement of dependence of anisotropy field Hanis and offset magnetic field Hoff on the electrical current j.

"Field- like torque". Dependence of offset magnetic field Hoff on current j. Scan is along wire. "Damp- like torque". Dependence of offset magnetic field Hoff on current j. Scan is perpendicularly to wire. Dependence of anisotropy field Hanis on current j. Dependence is linear. Slope is positive. Measurement is under perpendicular magnetic field H is + 0.8 kG. Dependence is linear. Slope is positive. Measurement is under perpendicular magnetic field H is + 0.8 kG. Hanis is proportional to j2 due to heating. Also, Hanis is proportional to polarity of current due to SOT effect (dependence is different for +j and -j current). Measurement is under perpendicular magnetic field H is + 0.8 kG. Dependence of offset magnetic field Hoff on perpendicularly applied magnetic field H. Scan is along wire. Dependence of offset magnetic field Hoff on perpendicularly applied magnetic field H. .Scan is perpendicularly to wire. Dependence of anisotropy field Hanis on perpendicularly applied magnetic field H . .

Data of Sample free18 gate

details of this measurement method is here

click on image to enlarge it

 

 

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VCMA vs PMA

 

VCMA. Measurement of dependence of PMA on gate voltage

dependence of anisotropy field on gate voltage ∂Hanis/∂V. Scan is along wire. dependence of anisotropy field on gate voltage ∂Hanis/∂V. Scan is perpendicularly to wire.     dependence of offset field on gate voltage ∂Hoff/∂V. Scan is along wire. dependence of offset field on gate voltage ∂Hoff/∂V. Scan is perpendicularly to wire.

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

 

 

 

Voltage-controlled magnetic anisotropy (VCMA). Measurement of dependence of anisotropy field Hanis and offset magnetic field Hoff on gate Voltage

Dependence of anisotropy field Hanis on gate voltage V "Field- like torque". Dependence of offset magnetic field Hoff on gate voltage V. Scan is along wire. "Damp- like torque". Dependence of offset magnetic field Hoff on gate voltage V. Scan is perpendicularly to wire. Hanis is linearly proportional to the gate voltage. Slope is negative. Measurement is under perpendicular magnetic field H is + 0.8 kG. Dependence is weak. Measurement is under perpendicular magnetic field H is + 0.8 kG. Dependence is weak.. Measurement is under perpendicular magnetic field H is + 0.8 kG. Dependence of anisotropy field Hanis on perpendicularly applied magnetic field H Dependence of offset magnetic field Hoff on perpendicularly applied magnetic field H. Scan is along wire. Dependence of offset magnetic field Hoff on perpendicularly applied magnetic field H. .Scan is perpendicularly to wire. . .

Data of Sample ud68

details of this measurement method is here

click on image to enlarge it

 

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(measurement 3) Measurement of magnetization switching under external perpendicular magnetic field Hz

SOT effect. Current dependence of magnetization switching parameters.

Coercive field HC Normalized change of coercive field HC vs current Dependence of HC on polarity of current j. SOT effect A substantial difference of HC from sample to sample (140-220 Oe). HC is reduced due to heating as HC~ j2. Additionally, coercive field linearly proportional to current HC~j due to SOT effect ΔHC= (HC(j)-HC(-j))/2. The change of HC with reverse of polarity of current. retention time Size of nucleation domain Delta Δ       Raw Data. Switching time vs applied magnetic field H and bias current. Raw Data. Switching time vs applied magnetic field H and bias current Dependence of HC on polarity of current j. SOT effect. Switching from spin-down to spin-up state. The left- side of hysteresis loop. Sample R71 gate Switching from spin-up to spin-down state. The right- side of hysteresis loop. Sample R71 gate ΔHC= (HC(j)-HC(-j))/2. The change of HC with reverse of polarity of current. Data of both gate and gap nanomagnet and from left and right- side switching of the hysteresis loop. Sample R71 gate

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

 

 

VCMA vs Coercive field

 

 

VCMA. Measurement of dependence of PMA on gate voltage.

dependence of normalized coercive field on gate voltage dependence of domain size on gate voltage

details of this measurement method is here

Sample Volt53: Ta(2.5 nm)/ FeBCo(x=0.3, 1 nm) MgO(5.1 nm)/ Ta(1nm)/ Ru(5 nm)

click on image to enlarge it

 

 

 

 

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(measurement 4) Measurement of magnetization switching under in-plane bias magnetic field

 

(fact 1) All parameters of thermo-activated switching (e.g. coercive field, retention time, parameter delta, size of nucleation domain) change substantially under external in-plane magnetic field H_x. There are several mechanisms for such change

(mechanism 1: major) The size H_x on nucleation domain changes under H_x.

Example: device ud66

(mechanism 2: minor) The PMA energy E_PMA on and therefore the energy barrier for the switching change under H_x.

Example: device ud67

(fact 2) The influence of in-plane magnetic field on switching parameters depends strongly on the number and distribution of fabricated defects and border irregularities in the nanomagnet. It makes the dependencies on H_x very different for nearly the same nanomagnets fabricated on same part of the same wafer.

 

Device ud66

(size): wire width: 200 nm; nanomagnet length: 500 nm;

 

 

magnetization switching parameters under in-plane bias magnetic field Hx

(up->down) corresponds to magnetization switching from up to down direction (left part of hysteresis loop); (down->up) corresponds to magnetization switching from down to up direction (right part of hysteresis loop);

Coercive field HC retention time Size of nucleation domain Substantial decrease of HC,up->down and substantial decrease under an increase of Hx (up->down switching): retention time is short and does not change at a negative Hx , but it sharply increases for a positive Hx. (down->up switching):The dependence is opposite. The retention time is short and does not change at a positive Hx , but it sharply increases for a negative Hx (up->down switching): size of a nucleation domain is small (~35 nm) and does not change at a negative Hx , but it sharply increases for a positive Hx. (down->up switching):The dependence is opposite. The retention time is short and does not change at a positive Hx , but it sharply increases for a negative Hx. (note) The dependence of the domain size on Hx is very similar to the dependence of retention time on Hx. Raw Data. Switching time vs applied magnetic field Difference of HC for up->down and down-> up magnetization switching Delta Δ Dependence of switching time on Hx is very substantial (black line) Difference of coercive field between magnetization switching from up to down direction (left part of hysteresis loop) and from down to up direction. It describes position of loop with respect to x- axis origin. The loop substantially (70 G) shifts to the left under negative Hx and to the right under positive Hx (red line) loop width. It is about 250 G and is is only slightly influenced by Hx The dependence of the delta on Hx is very similar to the dependencies of retention time and the domain size on Hx.

details of this measurement method is here

device ud66, in-plane magnetic filed Hx is applied along current (Hx || to current: 0 deg)

click on image to enlarge it

Coercive field

 

 

 

 

 

 

 

Device ud67

(size): wire width: 400 nm; nanomagnet length: 500 nm;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Device ud60

(size): wire width: 1000 nm; nanomagnet length: 200 nm;

magnetization switching parameters under in-plane bias magnetic field Hx

(up->down) corresponds to magnetization switching from up to down direction (left part of hysteresis loop); (down->up) corresponds to magnetization switching from down to up direction (right part of hysteresis loop);

Coercive field HC retention time Size of nucleation domain Slight decrease of HC under Hx   Size of nucleation domain is large (~65 nm) and it is only weakly influences by Hx Raw Data. Switching time vs applied magnetic field Difference of HC for up->down and down-> up magnetization switching Delta Δ Dependence of switching time on Hx is clear (black line) Difference of coercive field between magnetization switching from up to down direction (left part of hysteresis loop) and from down to up direction. It describes position of loop with respect to x- axis origin. The loop slightly shifts to the left under negative Hx and to the right under positive Hx (red line) loop width. It is about 210 G and is is only slightly influenced by Hx

details of this measurement method is here

Sample ud60, in-plane magnetic filed Hx is applied along current (Hx || to current: 0 deg)

click on image to enlarge it

 

 

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SOT effect + in plane bias field H_x

Device ud67

(size): wire width: 400 nm; nanomagnet length: 500 nm;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Device ud66

(size): wire width: 200 nm; nanomagnet length: 500 nm;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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VCMA effect + in-plane bias field H_x

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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I am strongly against a fake and "highlight" research