Magnetoresistance effects · Magnetoresistance effects Anna S. Semisalova Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Germany Lomonosov

Dr. Anna Semisalova | Institute of Ion Beam Physics and Materials Research | www.hzdr.de

17-22 Sept. 2017, Bad Honnef, Germany

Magnetoresistance effects

Anna S. Semisalova

Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Germany

Lomonosov Moscow State University, Faculty of Physics, Russia

Bad Honnef Physics School on

Magnetism: From Fundamentals to Spin based Nanotechnology

Member of the Helmholtz AssociationPage 2

Dr. Anna Semisalova | HZDR | Institute of Ion Beam Physics and Materials Research | www.hzdr.de

Institute of Ion Beam Physics and Materials Research, HZDR



Spintronics

(also known as spin-electronics, magneto-electronics)

Electron = charge + spin

Idea: to use the spin in the

electronic devices

• Novel functionalities

• Higher speed

• Faster performance

• Lower power consumption

• …

Control,

Manipulation, and

Detection of spin state



Spintronics/nanomagnetism

Spintronicsapplications

Sensors

Magnetic recording

MRAM

Memristor applications

STT microwave devices

(oscillators)



What is Magnetoresistance?

Change of electrical resistivity of the material under the application of

magnetic field

∆𝑅

𝑅% =

𝑅 𝐻 − 𝑅(0)

𝑅(0)∙ 100

MR ratio:

Magneroresistance converts magnetic signal

into electrical signal

MR ratio at RT & at low H (~1 mT) is important for device applications

From: S. Yuasa, IEEE Distinguished Lecturer



Outline

0. Positive and negative magnetoresistance in metals

1. Anisotropic magnetoresistance – AMR

2. Giant magnetoresistance – GMR

Spin valve

GMR for hard disk drivers

3. Tunneling magnetoresistance - TMR

4. Magnetic Random Access Memory – MRAM

Amorphous vs. Epitaxial tunnel barrier

5. New twist - Magnetoresistance in antiferromagnets



Positive magnetoresistance effect – old good one

The force on an electron:

Ԧ𝐹 = 𝑚𝑑 Ԧ𝑣

𝑑𝑡= 𝑒𝐸 + 𝑒 Ԧ𝑣 × 𝐵

Kohler’s rule

∆𝜌

𝜌= 𝜔𝑐𝜏

2 =𝑒𝐵

𝑚𝜏

2

=𝑛𝑒2𝜏

𝑚

1

𝑛𝑒𝐵

2

∆𝝆

𝝆=

𝑹𝑯

𝝆

𝟐

𝑩𝟐 ∝𝑩

𝝆

𝟐

Change of carrier trajectory due to

Lorentz force

increase of carrier path (curling of

path)

increase of scattering events and

resistance



Negative magnetoresistance effect - introduction

Resistivity normalized to their values at TC of Ni, 631 K (from Gerritsen (1956))

Resistivity of ferromagnet:

𝜌𝑝𝑎𝑟𝑎 - const at T>TC

𝜌𝑓𝑒𝑟𝑟𝑜 ≈ 𝜌𝑝𝑎𝑟𝑎 1 −𝑀𝑠(𝑇)

𝑀𝑠(0)

2



Negative magnetoresistance effect - introduction

Resistivity of ferromagnet:

𝜌𝑝𝑎𝑟𝑎 - const at T>TC

𝜌𝑓𝑒𝑟𝑟𝑜 ≈ 𝜌𝑝𝑎𝑟𝑎 1 −𝑀𝑠(𝑇)

𝑀𝑠(0)

2

~1-m2(T)



Spin disorder resistivity

Resistance decreases, if magnetic field is applied,

due to splitting of d-band for majority - and minority

spin

Less scattering of s-electrons into d-band → higher

mobility

Above TC: Scattering ofboth spin orientations ofs-electrons into empty d-states possible

Below TC: No scatteringof s-electrons into emptyd-states for majority spins larger mean free path smaller resistance resistance increaseswhen approaching TC

(spin-disorder increases)



Negative magnetoresistance

External magnetic field suppresses spin-disorder and produces relative

shift of spin-subbands, similar to (but much weaker than) exchange field

negative contribution



Outline




Spin valve








Magnetoresistance for data storage technologies

Yuasa & Djayaprawira J. Phys. D: Appl. Phys (2007)

http://iopscience.iop.org/article/10.1088/0022-3727/40/21/R01/meta



Anisotropic Magnetoresistance (AMR)

180°0° angle θ 90°

θ

magnetic fieldcurrent

magnetic fieldcurrentcurrent

magnetic field

Pics from lectures of Prof. Dr. M. Farle

1857: W. Thomson (Lord Kelvin) –

demonstration of AMR in FM materials




Kohler’s rule for a ferromagnet:

∆𝜌

𝜌∝ 𝑎

𝐻

𝜌

2

+ 𝑏𝑀

𝜌

2

Ordinary magnetoresistance

Anomalous or anisotropicmagnetoresistance

Mc Guire, IEEE Trans.Magn. (1975)




▪ ∆𝜌/𝜌= 3 to 5% in bulk NiFe at room temperature▪ AMR decreases with the film thickness and pattern size due to

additional scattering (grain boundaries, interfaces)




Usual way of description:

𝜃 – angle between 𝑱 and 𝑴

𝜌 𝐻 =1

3𝜌∥ + 2𝜌⊥ + 𝜌∥ − 𝜌⊥ cos2 𝜃 −

1

3

𝜌av ∆𝜌

∆𝜌 𝐻 = 𝜌 𝐻 − 𝜌av

∆𝜌(𝐻)

𝜌av=∆𝜌

𝜌avcos2 𝜃 −

1

3

Resistivity in zero field for randomly demagnetized

sample




Usual way of description:

𝜃 – angle between 𝑱 and 𝑴

𝜌 𝐻 =1

3𝜌∥ + 2𝜌⊥ + 𝜌∥ − 𝜌⊥ cos2 𝜃 −

1

3

𝜌av ∆𝜌

∆𝜌 𝐻 = 𝜌 𝐻 − 𝜌av

Resistivity in zero field for randomly demagnetized

sample

𝝆 𝜽 = 𝝆⊥ + (𝝆∥ − 𝝆⊥)𝒄𝒐𝒔𝟐𝜽



Anisotropic Magnetoresistance (AMR) - schematic

resulting magnetic

moment

charge distribution due to

orbital motion of electrons

(no spherical symmetry for metals

with incompletely filled orbitals,

e.g. Fe (3d-metal))

rotation of magnetic moment

leads to rotation of charge distribution

(Spin-orbit coupling)

AMR is a consequence of an anisotropic mixing of spin‐up

and spin‐down conduction bands induced by the spin‐orbit

interaction

Lectures of Prof. Dr. M. Farle



Anisotropic Magnetoresistance (AMR) - schematic

resulting magnetic

moment

charge distribution due to

orbital motion of electrons

(no spherical symmetry for metals

with incompletely filled orbitals,

e.g. Fe (3d-metal))

I

cross section small

cross section large

rotation of magnetic moment

leads to rotation of charge distribution

(Spin-orbit coupling)

Lectures of Prof. Dr. M. Farle



AMR sensor application

Real-time monitoring of move direction,

under no-GPS coverage or rough/harsh

conditions

Lab4MEMS ©Analog Devices, Inc.

Pham et al., Sensors & Transduc. J. (2015)

Positioning

systems Mobile phones

Py AMR

- not good

Barber pole Py AMR

- good

MR heads (1992-1998)

http://www.sensorsportal.com/HTML/DIGEST/P_2769.htm



AMR sensor application

Real-time monitoring of move direction,

under no-GPS coverage or rough/harsh

conditions

Lab4MEMS ©Analog Devices, Inc.

MEMSIC, Inc.Pham et al., Sensors & Transduc. J. (2015)

3-axis AMR

magnetometer

Positioning

systems Mobile phones

Py AMR

- not good

Barber pole Py AMR

- good

MR heads (1992-1998)

http://www.sensorsportal.com/HTML/DIGEST/P_2769.htm



Outline




Spin valve








Giant Magnetoresistance

GMR

Nobel prize in physics (2007)

Baibich et al. PRL 61, 2472 (1988)Binasch et al. PRB 39, 4828 (1989)

Albert Fert

Université Paris-Sud,

Orsay, FrancePeter Grünberg

Institut für

Festkörperforschung,

Forschungszentrum

Jülich, Germany

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.61.2472

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.39.4828



Giant magnetoresistance – schematic description



Picture: Baibich et al. PRL 61, 2472 (1988) & Wikipedia

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.61.2472



GMR – non-magnetic layer thickness dependence

Fe/Cr system multilayer system

Parkin et al., PRL (1990)

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.64.2304



GMR basics

As long as spin-flip is negligible, charge current can be considered as

carried in parallel by two categories of electrons: spin up and spin

down (parallel and antiparallel to quantization axis)

Two current model (Mott 1930)

Scattering depends on the relative

orientations of the electron spins and

magnetic moments in sublattice: it is

weakest when they are parallel and

strongest when they are antiparallel



GMR – equivalent circuits for multilayer

𝑅𝐴𝑃 =𝑅↓↑+𝑅↑↑

2𝑅𝑃 =

2𝑅↓↑𝑅↑↑𝑅↓↑ + 𝑅↑↑

GMR=𝑅AP−𝑅P

𝑅P



“Spin-dependent scattering”

Paris, the Trendy-Shopping Street: Rue Vieille Du Temple

Pic - https://www.discoverwalks.com



“Spin-dependent scattering”

Paris, the Trendy-Shopping Street: Rue Vieille Du Temple

Pic - https://www.discoverwalks.com



GMR – measurements geometry

Spin up and spin down electrons are involved in conductivity

∆𝑅

𝑅𝐴𝑃=

𝛼 − 1

𝛼 + 1

2

Resistor model works if

CIP: mean-free paths of the electrons >>

thickness of the various layers

CPP: thickness << spin diffusion (flip)

length

𝛼 =𝑅↓↑

𝑅↑↑- spin scattering asymmetry



GMR in multilayers with two switching fields

Yamamoto et al. JMMM (1991)

Co(3nm)

Cu(5nm)

Py(3nm)

Cu(5nm)

×15

Magnetic Field (Oe)

Magnetic Field (Oe)

M/M

SM

R r

atio (

%)

80 K

RT

80 K

RT

MR r

atio (

%)

M

Magnetic Field (Oe)

CoPy

http://www.sciencedirect.com/science/article/pii/030488539190072I?via%3Dihub



GMR in multilayers with two switching fields

Yamamoto et al. JMMM (1991)

Co(3nm)

Cu(5nm)

Py(3nm)

Cu(5nm)

×15

Magnetic Field (Oe)

Magnetic Field (Oe)

M/M

SM

R r

atio (

%)

80 K

RT

80 K

RT

A significant step towards

applications of GMR in devices was

achieved by Parkin et al.:

GMR in sputtered multilayers

Parkin et al., PRL (1990)Magnetoelectronics, ed by M. Johnson, Elsevier (2004)

http://www.sciencedirect.com/science/article/pii/030488539190072I?via%3Dihub


https://www.elsevier.com/books/magnetoelectronics/johnson/978-0-12-088487-2



GMR - Spin Valve structure

Top type spin valve

Pics: Univ. of Leeds and here

http://www.stoner.leeds.ac.uk/Research/TutGMRSpin

https://www.intechopen.com/books/ferroelectric-materials-synthesis-and-characterization/biasing-effects-in-ferroic-materials




Top type spin valve

Pics: Univ. of Leeds and here

http://www.stoner.leeds.ac.uk/Research/TutGMRSpin

https://www.intechopen.com/books/ferroelectric-materials-synthesis-and-characterization/biasing-effects-in-ferroic-materials




First generation – top- or bottom-pinned spin valve

MR = 6 – 10%

AFM pinning layer

Pinned layer

Spacer

Free layer

Dieny et al. PRB (1991)Tsang et al. IEEE Trans. Magn. (1994)

Co, Co90Fe10,

Ni80Fe20/Co, Ni80Fe20/Co90Fe10

Co, Co90Fe10

Mn76Ir24, Mn50Pt50

Cu


http://ieeexplore.ieee.org/document/333909/



GMR - Spin Valve discovery

Dieny et al. PRB (1991)Dieny et al., JMMM (1991)Dieny et al., JAP (1991)

Py(15nm)

Cu(2.6nm)

Py(15nm)

FeMn(10nm)


http://www.sciencedirect.com/science/article/pii/030488539190311W?via%3Dihub

http://aip.scitation.org/doi/10.1063/1.348252



Effect of a thin layer inserted at the interfaces in spin valves

Parkin, PRL (1993)Sakakima et al., JMMM (2000)Veloso et al., APL (2000)

Non‐magnetic layers at interface and dead layers are source of strong

spin‐independent scattering and drastically reduces GMR

Additional thin FM layers (Co) at interface enhance GMR:

-> enhanced spin polarization

Specular spin valve with Nano Oxide Layers

MR = 15 – 20%


http://www.sciencedirect.com/science/article/pii/S0304885399007684#FIG3

http://aip.scitation.org/doi/abs/10.1063/1.1288672



Further improvement – synthetic layers

Synthetic antiferromagnet (SAF)Increase the exchange

field at the interface “pinned/exchange”

layers

Synthetic free layer (SF)Decrease the thickness

Guedes et al., JAP (2006)

http://aip.scitation.org/doi/full/10.1063/1.2162817



GMR for hard disk drives

First GMR read head – IBM, 1997

Picture: http://www.magnet.fsu.edu



HDD head evolution

Pic - pcguide.com, education.mrsec.wisc.edu



Outline




Spin valve








Tunneling Magnetoresistance (TMR)

Magnetic Tunnel Junctions (MTJ)



Julliere model of tunnel magnetoresistance (TMR)

Jullière, Phys. Lett. A (1975)Picture: http://moodera.mit.edu/Lecture of B. Dieny

TMR=𝑅AP−𝑅P

𝑅PP=

𝐷↑ 𝐸𝐹 −𝐷↓(𝐸𝐹)

𝐷↑ 𝐸𝐹 +𝐷↓(𝐸𝐹)

Spin polarization

Tunneling current in each spin channel

𝐽𝜎 ∝ 𝐷1𝜎 𝐸𝐹 × 𝐷2

𝜎 𝐸𝐹

Number of

candidates for

tunneling

Success rate

for candidate

Parallel configuration Antiparallel configuration

𝐽𝑃 ∝ 𝐷1↑𝐷2

↑ +𝐷1↓𝐷2

↓ 𝐽𝐴𝑃 ∝ 𝐷1↑𝐷2

↓ +𝐷1↓𝐷2

↑

TMR=2𝑃1𝑃2

1−𝑃1𝑃2P = 50% (Fe, Co):

TMR = 40-70%

http://www.sciencedirect.com/science/article/pii/0375960175901747?via%3Dihub

http://moodera.mit.edu/



Magnetic tunnel junctions

Chappert et al., Nat. Mater. (2007)Picture: http://moodera.mit.edu/

http://www.nature.com/nmat/journal/v6/n11/full/nmat2024.html#B31



MgO-based MTJ

Fully

epitaxial

Parkin et al., Nat. Mater. (2004)Yuasa et al., APL (2005)Yuasa et al., Nature Materials (2004)Yuasa et al., APL (2006)

Highly epitaxial MgO –

giant TMR was observed

https://www.nature.com/nmat/journal/v3/n12/full/nmat1256.html


http://www.nature.com/nmat/journal/v3/n12/full/nmat1257.html




MgO-based MTJ

Zhu & Park, Materials Today (2007)Ikeda et al., APL (2008)

Incoherent tunneling: Bloch

states are not conserved

Coherent tunneling:

Tunneling probability depends

on orbital symmetry

TMR 604% in Co20Fe60B20∕MgO∕Co20Fe60B20

Lectures of B. Dieny, S. Yuasa

http://www.sciencedirect.com/science/article/pii/S1369702106716935#fig1

http://aip.scitation.org/doi/abs/10.1063/1.2976435?journalCode=apl



Spin filtering

Picture: http://moodera.mit.edu/



MRAM

Photograph of the first MRAM product, a 4-Mbit

stand-alone memory (Freescale, 2006)

Magnetic

Random

Access

Memory

Chappert et al., Nat. Mater. (2007)

http://www.nature.com/nmat/journal/v6/n11/full/nmat2024.html#B31



MRAM - cell structure with perpendicular magnetic anisotropy

Magnetoresistive random access memory developed by Toshiba

Perpendicular Magnetic

Anisotropy:

Multilayers Co-Pt, Co-Pd, Co-Ni,

CoFe-Pt, CoFe-Pd, Co-Cr-Pt,

Alloys CoPt, FePt, CoCr, rare-

earth TM alloys

Picture - DOI: 10.5772/16539



Outline




Spin valve








Next generation – antiferromagnetic spintronics

Magneto-electronics, or spintronics, explores mainly ferromagnetic materials,

while AFM materials were given to secondary roles (exchange bias, etc.)

Advantages of AFM:

- Absence of stray fields

(minimized cross-talk

between AFM nanocrystals)

- Abundance

- Robustness General principle formulated by Louis Néel:

-> AMR! is a promising candidate to sense the magnetic state in AFM

“Effects in antiferromagnets depending on the square of the spontaneous magnetisation should show the same

variation as in ferromagnetic substances”

Critical milestone on the way of

implementation:

- no way to manipulate or even

probe the local AFM order

Neel’s Nobel Lecture

http://www.nobelprize.org/nobel_prizes/physics/laureates/1970/neel-lecture.pdf



AMR in antiferromagnetic semiconductor

TN = 240 K

Strontium iridate Sr2IrO4

AFM semiconductorPerovskiteSingle crystal, 500 µm thick

Point contact (PC) probe

PC resistance 𝑅 = 𝜌/2𝑎𝑎~45 nm ÷ 4.2 𝜇m

Wang et al., JAP (2015)Tsoi et al., PRL (1998)

http://dx.doi.org/10.1063/1.4913300

https://doi.org/10.1103/PhysRevLett.80.4281



AMR in antiferromagnetic semiconductor

TN = 240 K

Strontium iridate Sr2IrO4

AFM semiconductorPerovskiteSingle crystal, 500 µm thick

Wang et al., JAP (2015)Tsoi et al., PRL (1998)

Normalized AMR

1

0

𝑅 𝜃 − 𝑅𝑚𝑖𝑛

𝑅𝑚𝑎𝑥 − 𝑅𝑚𝑖𝑛

Max AMR: 14% at 77K

http://dx.doi.org/10.1063/1.4913300

https://doi.org/10.1103/PhysRevLett.80.4281



Perovskite named after…

Gustav Rose(1798 – 1873)

President of German Geological Society

Lev Perovsky(1792 – 1856)

Duke, mineralogist, Minister in Russia

Ural mountains

… Lev PerovskyMineral Calcium titanium oxide CaTiO3 found by Gustav Rose in Ural mountains in 1839

Pics: Wiki, here and here

https://chemicalstructure.net/portfolio/perovskite/

https://cosmolearning.org/images/russia-satellite-map-786/



Antiferromagnetic AMR in FeRh

Phase diagram of binary Fe-Rh compound

Pic - andrewsteele.co.ukHeidarian et al. PSSB (2017)

https://andrewsteele.co.uk/

http://onlinelibrary.wiley.com/doi/10.1002/pssb.201700145/full




Phase diagram of binary Fe-Rh compound

Heidarian et al. PSSB (2017)

http://onlinelibrary.wiley.com/doi/10.1002/pssb.201700145/full




Marti et al. Nature Materials (2014)





Marti et al. Nature Materials (2014)

Ordinary (Lorentz force ) MR




Summary

Spintronicsapplications

Sensors

Magnetic recording

MRAM

Memristor applications

STT microwave devices

(oscillators)






Documents

Magnetoresistance effects · Magnetoresistance effects Anna S. Semisalova Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Germany Lomonosov