chapter 4: spin dependent transport (lecture #5)...module: magnetism on the nanoscale, ws 2020/2021...
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module: magnetism on the nanoscale, WS 2020/2021
chapter 4: spin dependent transport (lecture #5)
Dr. Sabine Wurmehl; [email protected]
Dresden, November, 23rd, 2020
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reminder: free electron model & ….Formation of metallic Na
according to band theory
Fermi surface (model) density of states (DOS)
Fermi distribution or DOS „in reality“
DOS k2 E1/2
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Landau diamagnetism
reminder: magnetic properties in metals- spin contribution
Zeemann splitting
for a metal in magnetic field • only electrons at Fermi energy contribute
• localized system: all unpaired electrons contribute
• in metals, spin of electrons leads to Pauli susceptibility cP
• cP is temperature independent
𝐻 = ½ 𝑚 (𝐩+𝑒𝐀)2 ± 𝜇𝐵𝐁
Pauli paramagnetism
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with magnetic field:
k-vectors condense on tubes paralell to field
reminder: magnetic properties in metals- orbital contribution
harmonic oscillator plane wave
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reminder: structure modifications and electronic correlations in the series BaT2As2 (T = Cr, Mn, Fe, Co, Ni, Cu)
S. Selter, F. Scaravaggi et al. Inorg. Chem. (2020)
Question:
What are potential reasons to not get g from all
members of the series???
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from discussion (simplified):
no full information about DOS from gamma if:
• semiconducting or insulating ground state (here: BaMn2As2)
• spin density wave gap is present (afm) (here: BaFe2As2)
• superconductivity present (sc gap)
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reminder: RKKY interaction
Ruderman–Kittel–Kasuya–Yosida.
https://www.researchgate.net/profile/Puspamitra_Panigrahi/publication/252771578/figure/download/fig1/AS:669380048351236@1536604048549/RKKY-interaction-the-interaction-of-magnetic-spins-mediated-by-conduction-electrons.ppm
local magnetic polarizes conduction electrons which in turn couples to another local moment at distance r
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RKKY interaction in metals
local magnetic polarizes conduction electrons which in turn couples to another local moment at distance r
indirect, itinerant exchange interaction between magnetic moments mediated by conduction electrons
• long ranged
• oscillating dependance of JRKKY on r fm or afm
• description by second-order perturbation theory
𝐽𝑅𝐾𝐾𝑌 ∝ cos(2𝑘𝐹𝑟)𝑟3
https://www.researchgate.net/profile/Heinz_Horner/publication/1940273/figure/fig1/AS:497194916474880@1495551913737/RKKY-interaction.png
https://www.researchgate.net/profile/Puspamitra_Panigrahi/publication/252771578/figure/download/fig1/AS:669380048351236@1536604048549/RKKY-interaction-the-interaction-of-magnetic-spins-mediated-by-conduction-electrons.ppm
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module: magnetism on the nanoscale, WS 2020/2021
chapter 4: spin dependent transport (lecture #5)
Dr. Sabine Wurmehl; [email protected]
Dresden, November, 23rd, 2020
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4.0 intro „spindependent transport“
• study of spin dependent transport was fostered in ~1980s
• interesting from a fundamental point of view
• highly attractive: application in spintronics
charge + spin of electron for data processing, storage & read-out
magnetic „bit“
spintronics
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spindependent transport
Is there an elegant way to monitor spin state by „easy“ way of measurement?
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magnetoresistance
is there an elegant way to monitor spin state by „easy“ way of measurement?
measurement of resistance in response to magnetic field!
magnetoresistance
𝜎 = 𝑒2N(𝐸𝐹)𝑣𝐹2 𝜏/3
scales with
• DOS N(EF)
• Fermi velocity v
• scattering time t mean free path l1
𝜎= 𝜚
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magnetoresistance- definition
𝑀𝑅≔Δ𝑅
𝑅= 𝑅 𝐻 −𝑅(0)
𝑅(𝐻)
known since long time: MR in metals is ~ few % (1857)
new discoveries in late 80s dramatic increase of MR ratio!
GMR ~ 50%
TMR ~1000%
CMR even larger
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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positive MR in non-magnetic metals
(also called normal MR)
in any metal conduction electrons are scattered at impurities, phonons, defects, grain boundaries, ….
conductivity depends on „scattering events“
parametrized by mean free path l
l is the distance that an electrons travels between two scattering events
𝑙 ∝ 𝜎 𝑙 = 𝜈𝐹𝜏
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mean free path
𝑙 ∝ 𝜎 𝑙 = 𝜈𝐹𝜏
mean free path is small compared to Fermi wave length
:= conductivity
l := mean free path
t:= mean time between scattering events
𝜆𝐹:= Fermi wave length
kF:= Fermi wave vector
mean free path large compared to Fermi wave length
𝑘𝐹𝑙 ≫ 1
𝑘𝐹𝑙~1
distance l is large enough
electron wave at 2nd scatterer is plane wave again
distance l is small
superposition of incoming and backscattered wave
𝜆𝐹 = 2𝜋/𝑘𝐹
https://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel2.pdf
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mean free path with or without magnetic field
(a) without field (b) with field
scattering process is different with or without applied magnetic field
(c) mean free path in field
https://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel2.pdf
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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negative magnetoresistance in ferromagnets
http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel2.pdf
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resistance in ferromagnetsabove and below fm order
T. SHINJO
Spin Dependent Transport in Magnetic Nanostructures.
In: Experiments of Giant Magnetoresistance, pages 1–46.
Taylor & Francis MG Books Ltd, Bodmin (2002)
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electronic transport in 3d metals
• 3d metals have both s and d electrons at Fermi level
• s electrons have much smaller effective mass broader bands
• s electrons are relevant charge carrier in 3d metals
• N.F. Mott: resistance is determined by scattering of s electrons in free d states
E
s
d
EF
σ = nse2τs
ms∗ +
nde2τd
md∗
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scattering of s in d states above and below TC
https://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel2.pdf
high scattering rate of s electrons in d states
high resistance
• d states split, majority bands are now below EF
• no scattering of majority s electrons in majority d bands
lower resistance
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negative magnetoresistance in ferromagnets
application of magnetic field increases ordering of spins viz. spin polarization
enhances effect of lower resistance in ferromagnet below TC
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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anisotropic magnetoresistance
MR depends on orientation between field and current
origin: spin orbit coupling affects s-d scattering differently, depending on direction of field
SOC lowers symmetry of wave functions by mixing of states
anisotropic scattering
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asymmetric charge distribution due to SOC
http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel3.pdf
energy of (a) and (b) is not the same
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anisotropic magnetoresistance
http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel3.pdf
J H
longitudinal MR
J H
transversal MR
1857 Thomson
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two current model
http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel3.pdf
spin flips are possible!
higher resistance!
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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colossal magnetoresistance (CMR)
• negative MR related to spin disorder
• observed in mixed valent manganites (Jonker and Santen 1950s)
…courtesy Laura Corredor Bohorquez…..
𝐶𝑀𝑅 ≔ −𝑅 𝐻 −𝑅(0)
𝑅(𝐻)= - Δ𝑅
𝑅
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et al.
La3+substituted by Sr2+
mixed valency of Mn3+/4+
compositional range that
shows transition from
paramagnetic-semiconducing
to ferromagnetic-metallic
state
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magnetic field changes spin order
spin-order and resistivity strongly linked in manganites
application of magnetic field shifts insulator-metal transition
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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giant magnetoresistance
• spindependent transport in multilayers
• 2 magnetic layers seperated by thin layer of non-magnetic metal
• started research hype in field of spintronics
Grünberg und Fert 1986
Nobelprice in 2007
P. Grünberg und A. Fert
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S. S. P. Parkin 2002
giant magnetoresistance
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M. Baibich, A. Fert et al. Phys. Rev. Letters 61, 2472 (1988)
G. Binasch, P. Grünberg et al. Phys. Rev. B 39, 4829 (1988)
Giant Magneto-ResistanceGMR:= DR/R=
𝑅𝑝−𝑅𝑎
𝑝
𝑅𝑝
„1“
„0“
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http://www.spintec.fr/IMG/pdf/spin-valves.pdf
two geometries
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http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel5.pdf
resistor network
GMR:= DR/R=𝑅𝑝−𝑅𝑎
𝑝
𝑅𝑝
scattering rates for ,
parallel alignment
low resisitance r+
antiparallel alignment
high resistance r-
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http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel5.pdf
resistor network
GMR:= DR/R=𝑅𝑝−𝑅𝑎
𝑝
𝑅𝑝
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http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel5.pdf
scattering of s electrons
in d states
strong scattering,
high resistance
low scattering,
low resistance
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http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel5.pdf
GMR
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RKKY in multilayersMR as fct of spacer thickness
Parkin et al. Phys. Rev. Lett. 64, 2304 (1990)
Wang et al. EPL 87 47001 (2009)
Parkin et al. Phys. Rev. B 44, 7131(R) (1991)
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origin of MR dependence of spacer thickness
Parkin et al. Phys. Rev. Lett. 64, 2304 (1990)
accepted model: quantum interference
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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J. S. Moodera et al. Phys. Rev. Lett. 80, 2941 (1998)
Tunneling Magneto-Resistance (TMR)
early days:
• thin insulating tunnel barrier Al2O3
• two ferromagnetic layers: Simple ferromagnets as Co, Ni-Fe
Ni-Fe (permalloy)
Co
nm thin layer of Al2O3
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TMR in Co-Al2O3-Permalloy
J. S. Moodera et al. Phys. Rev. Lett. 80, 2941 (1998)
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Data: J. S. Moodera et al. Phys. Rev. Lett. 80, 2941 (1998)
Scheme adapted from: T. Graf et al. Prog. Sol. State. Chem. 39, 1 (2011)
Ni-Fe (permalloy)
Co
nm thin layer of Al2O3
Model: M. Julliere, Phys. Lett. A 54, 225 (1975)
tunneling Magneto-Resistance (TMR)
20% TMR ratio
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Model: M. Julliere, Phys. Lett. A 54, 225 (1975)
Julliere model
∆𝑅
𝑅𝑇𝑀𝑅=𝑅𝐴−𝑅𝑃
𝑅𝐴=
2𝑃1𝑃2
1+𝑃1𝑃2with P=
𝑁↑−𝑁↓
𝑁↑+𝑁↓
tunneling depends on the density of states!
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eV
barrier thickness
t
EF
barrier height f
metal 1metal 2
I12 (E) N1 (E-eV) N2 (E) T2 x f(E-eV) [1-f(E)] , T2 exp (-ctf)
I21 (E) N1 (E-eV) N2 (E) T2 x [1- f(E-eV)] f (E)
Integration and small voltages only yield:
I DOS1 DOS2 (E) x ∫ [f(E-eV)- f (E)]dE, for low T ∫ =eV
I/V DOS1 (EF) DOS2 (EF)
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add-on: majority and minority states
https://www.researchgate.net/publication/293815864_Current_Driven_Magnetization_Dynamics_in_Ferromagnets_and_Antiferromagnets/figures?lo=1
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TMR
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Inomata et al. Appl. Phys. Lett. 86, 232503 (2005) http://www.pha.jhu.edu/~wgwang/pics/DMTJ%20TEM.jpg
deterioration by temperature dependence and interface
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http://www.jst.go.jp/sicp/ws2009_sp1st/presentation/15.pdf
impact of barrier on TMR
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Courtesy S. Yuasa (AIST)
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Coherent tunneling – band filtering
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Concept: R. de Groot et al. Phys. Rev. Lett. 50, 2024 (1983)
J. Kübler et al. Phys. Rev. B 28, 1745 (1983)
goal: material with 100% spin polarization at Fermi energy
Scheme: T. Graf et al. Prog. Sol. State. Chem. 39, 1 (2011)
optimized materials for TMR
∆𝑅
𝑅𝑇𝑀𝑅=
2𝑃1𝑃21+𝑃1𝑃2
with P=𝑁↑−𝑁↓
𝑁↑+𝑁↓Julliere model:
Good: Better:
P:= spin polarization
N:= DOS
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ideal materials for spin dependent transport
Felser et al. Angew. Chem. Int. Ed. 2007, 46, 668 – 699
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improvement of TMR stacks
TMR overview: T. Graf et al. Prog. Sol. State. Chem. 39, 1 (2011)
2012
Liu et al. Appl. Phys. Lett. 101, 132418 (2012)
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Liu et al. Appl. Phys. Lett. 101, 132418 (2012)
TMR in Co2MnaSig Heusler films
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zoo of magnetoresistance effects
• positive magnetoresistance in non-magnetic metals
• negative magnetoresistance in ferromagnetic metals
• anisotropic magnetoresistance (AMR); MR: 3-4%
• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T
• giant magnetoresistance (GMR); MR up to 100% at RT
• tunnelling magnetoresistance (TMR); MR up to 1000%
• powder magnetoresistance (PMR)
intrinisc MR effects
extrinisc MR effects
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