Theory of Spin Diode Effect

Piotr Ogrodnik

Warsaw University of Technology and Institute of Molecular Physics Polish Academy of Sciences

NANOSPIN Summarizing Meeting, Kraków, 11-12th July 2 016

Outline:

o What is the spin diode effect ?

o Analytical model

o Applications: TMR/GMR/AMR structures

o Extensions of the model – GMR nanowire

o Summary

What is the spin diode effect ?The idea is very simple (A. Tulapurkar et al., Nature 438, 330-342 (2005) )

• magnetoresistive element: AMR, GMR, TMR

Then we pass the a.c. current through this elementIf the current is the source of driving force for magnetization dynamics then we can measure Vdc (spin diode voltage) that results from the mixingof a.c. current and oscillating resistance of the element.

��

0

10

5

10-1

0

1

Vdc

Time

RF current: ��.�.

Oscillating resistance: R(t)

Spin diode DC voltage:�� � ��.�. ⋅ ��

�����

Model (1)What is measured ? Output voltage:

a.c. current oscillating resistance

��The amplitude of resistance changes:

� � � �� � �∥ � �� cos� �

TMR, GMR structures:�– the angle between two magnetic moments

AMR structures:�– the angle between magnetic momentand current density vector �ΔR ≡ �∥ � ��; �� � � )

Model (2)

AMR: �� � �2�sin��cos����

�� �1

2�sin����

%&' � �(%Δ�

� ��sin��cos��)*��+

%&' � �(%Δ�

4� ��sin��)*��+

TMR/GMR:

The goal is to calculate -. for specific system

-. may be derived from LLG/LLGS equation

I

Model (3) Calculations ��:

STT term in standard form for multilayer systems i.e. 0∥ 123 12 31� � 0��12 31��

or for non-uniform magnetization distribution:

(magnetization distribution within the sample has to be assumed), Such a torque effectively acts on averaged magnetic moment of thesample 1 (macrospin with nonhomogenities..)

�45 67 3 8 9 ⋅ : 5 67 ;

<=>> � �?@

A �AB

�AC�AD�A'EFG�AHC�AIJ

magneto--crystalline

anisotropy

shape anisotropy

Magnetic energy:

Zeeman-like Interactions

Interlayer coupling

Interaction with

Oersted field (in the case: ? 3 <�= � K)

Magnetoelastic energy

Model (4)LLG equation in spherical coordinates with STT Slonczewski-like and field-like terms:

We assume that magnetic moment oscillates harmonically around stationary point, sothe solutions for two angles describing 1 are in the form:

Model (5)Linearization of RHS

Ψ - phase shift between 1 and driving-force (a.c. current)

if dynamics is driven by Oersted field, we use derivatives with respect to MEJ (instead of % )

- symmetric contribution to the Vdc lineshape

- antisymmetric contribution to the Vdc lineshape

Applications(1):TMR nanopillar with perpendicular anisotropy – first comparison with the experiment.

A = N�2 cos�� � sin�sinO �1C MJPQ ∙ SU �UV

�WXSUYZ[SU

N�2-isV biasvoltage dependent

Energy with perpendicular anisotropy:

Application (2) – GMR structure in CIP configurationZiętek et al., Phys. Rev. B 91, 014430 (2015)

107 108 109 1010

-10

-5

0

5

107 108 109 1010

-10

-5

0

5

107 108 109 1010

-10

-5

0

5

196 Oe 61 Oe 32 Oe

Vdc (m

V)

Frequency (Hz)

1.8 2.0 2.2 2.4 2.6-50

0

50

Hco

up (

Oe)

Cu layer thickness (nm)

Application (3) – GMR sample in CIP configuration (the influence of IEC on the out-of-resonance Vdc signal driven by Oersted field)Ziętek et al., APL 107, 122410 (2015)

Additional energy term (IEC): A'EFG � �1 ⋅ M'EFG RKKY interaction

Extension of the spin diode model - GMR nanowires. Motivation :

Thick(25nm) magnetic (Co) layer

Thin (5nm) magnetic (Co) layer

Cu (7 nm) spacer

Results – relations of dispersion

The best fits:

2000 1500 1000 500 00

5

10

15

Magnetic Field Oe

Freq

uenc

yG

Hz

thick layer: d = 10 nm, K = 20 kJ/m3 , Ms= 1.4 Tthin layer: d = 5 nm, K = 35kJ/m3, Ms = 1.3 TSpacer thickness: 30 nm (corresponding to dipolar coupling fields: 60 Oe (in thick layer) and 113 Oe (in thin layer)

2000 1500 1000 500 00

5

10

15

Magnetic Field Oe

Freq

uenc

yG

Hz

thick layer: d = 10 nm, K = 35 kJ/m3 , Ms= 1.4 Tthin layer: d = 5 nm, K = 20kJ/m3, Ms = 1.3 TSpacer thickness: 30 nm (corresponding to dipolar coupling fields: 60 Oe (in thick layer) and 113 Oe (in thinlayer)

Thin layer (fixed 5 nm)

2000 1500 1000 500 00

5

10

15

Magnetic Field Oe

Freq

uenc

yG

Hz

More realistic Cu thickness = 7 nmdipolar fields are large...

2000 1500 1000 500 00

5

10

15

Magnetic Field Oe

Freq

uenc

yG

Hz

and with reduced magnetocrystalline anisotropy (in both layers ~0.1 kJ/m3)

Thick layer = 10 nm

More realistic: thick layer = 20 nm

2000 1500 1000 500 00

5

10

15

Magnetic Field Oe

Freq

uenc

yG

Hz

Thick layer, and thin layer: K = 100 J/m3 Ms= 0.9 T

Best fit for:

Spacer thickness: 17.5 nm (corresponding to dipolar coupling fields: 67 Oe (in thick layer) and 306 Oe (in thin layer)

The conclusion from f(H) within macrospin model:The best fit is for thick layer (~10nm) and very thick Cu spacer (30 nm) with very high magnetocrystalline anisotropy (20-40kJ/m3) and high saturation magnetization (1.3 -1.4 T).

Vdc lineshapes (for the best f(H) fit):

Dynamics driven only by STT:

4 6 8 10 12

20

10

0

10

20

Frequency GHz

Spi

ndi

ode

volta

geV

dca.

u.

H 200 Oe

4 6 8 10 12

2. 10 13

1. 10 13

0

1. 10 13

Frequency GHz

Spi

ndi

ode

volta

geVd

ca.

u.

H 1500 Oe

4 6 8 10 120.00001

0

0.00001

0.00002

0.00003

0.00004

0.00005

Frequency GHz

Spi

ndi

ode

volta

geV

dca.

u.

H 1500 Oe

without coupling -> peaks still symmetric

Vdc lineshapes (for the best f(H) fit):

Dynamics driven only by Oersted field:

4 6 8 10 12600

400

200

0

200

400

Frequency GHz

Spi

ndi

ode

volta

geV

dca.

u.

H 200 Oe

4 6 8 10 12

0.00006

0.00004

0.00002

0

0.00002

0.00004

0.00006

Frequency GHz

Spi

ndi

ode

volta

geV

dca.

u.

H 1500 Oe

Playing with the parameters (phase shift, amplitudes of STT and Oersted field) makes possible to get lineshapes similar to experimental ones.

2 4 6 8 10 12

15

10

5

0

5

10

Frequency GHz

Spin

diod

evo

ltage

Vdc

a.u.

H 120 Oe

4 6 8 10 120.0001

0.00005

0.0000

0.00005

Frequency GHz

Spi

ndi

ode

volta

geV

dca.

u.

H 1500 Oe

Summary (short):

• In some cases the model (macrospin) agrees well with theexperimental results

• However, in the case of strongly coupled layers the theoretical analysis becomes very difficult because of number of free parameters