Transcript Tutorial_Frank_Magnetism

Spintronics and Magnetic Properties of Materials
Natia L. Frank
Department of Chemistry
University of Washington
Seattle, WA 98117
UW Bio-Molecular Magnetism Group
The Earth’s Magnetic Field
Glatzmaier (Los Alamos)
UW Bio-Molecular Magnetism Group
Alerstam, Nature 2001
Navigating the Earth’s Magnetic Field
Magnetoreception:
How organisms use magnetic information to control and direct their behavior
•Magnetotaxis: movement along field lines: alignment
•Menotaxis (Kuhn) compass orientation with respect to external field
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Early Magnetism
Origin of the name “magnetism”: Magnesia (Thessaly, Greece)
Greeks: Lodestone FeO-Fe2O3 “leading stone or compass”
“The magnet’s name the observing Grecians drew From the
magnetick region where it grew”- Lucretius Carus 100B.C.
“The nails of whose shoes and the tip of whose staff stuck fast in a
magnetick field while he pastured his flocks”-Pliny the Elder(Magnus)
Greek Writings: Lodestone appeared as early as 800 B.C.
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Gilbert: The Father of Magnetism
1600. William Gilbert: “ Father of
Magnetism “ b. 1544. London
physician, physics by hobby. Queen
Elizabeth’s personal physician. d.
1603 plague. “ it is easy for men of
acute intellect to slip and err”.
Treatise “ On the Magnet: Magnetic
Bodies Also, and On the Great
Magnet the Earth; a New
Physiology, Demonstrated by Many
Arguments and Experiments”
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Magnetic Field Vector H
The density of lines is proportional to the magnitude
of the magnetic field vector.
Fk
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m1 m 2
r0
2
r
H
m
2 r0
r
Quantum Mechanical Basis of Spin
Rotation of the charge of an electron produces current loops with a magnetic
moment directed along the rotation axis:spin angular momentum.
Origin of magnetic moment: orbital angular momentum(a) and spin angular
momentum(b).
Bohr Magneton (mB or b ) = eh/4pmc = 9.27 x 10-21 erg/Oe
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Magnetization (M) and Induction(B)Vectors
Magnetic dipole moment: m :
m = 1 when a force of 1 dyne is experienced in a field of 1 oersted.
Magnetic Induction, B = H + DH measured in gauss (G) and H in oersted (Oe)
Intensity of magnetization (magnetic dipole moment / unit volume) = M (emu/cm3)
In cgs units, DH = 4pM, therefore, B = H + 4pM.
The magnetic induction is equal to the external field corrected for the magnetization
of the substance.
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Magnetic Susceptibility and Permeability
When the vectors B, H and M are parallel, it is useful to define the magnetic
permeability(m) and magnetic susceptibility(c) of a substance:
B  mH
M c/H
Define M/H = cV where cV is the volume magnetic susceptibility and is
dimensionless.
Gram Susceptibility, cg = cV / r (cm3 g-1) where r is the density
Molar Susceptibility, cM = cg *molecular weight and is in units of
(emu/cm3•G•mol)
The magnetic susceptibility and permeability characterize the type of
magnetism observed:
diamagnetism, paramagnetism, ferromagnetism, or antiferromagnetism
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Types of Magnetism
(a) Diamagnetism: c < 0, 10-6 emu, c independent of H, origin field induced, paired electron
circulation.
(b) Paramagnetism c > 0, 0 to10-4 emu, c independent of H, origin angular momentum of
electron. No interactions between spins.
(c) Ferromagnetism c > 0, 10-4 to 10-2 emu, c dependent on H, spin alignment from dipole-dipole
interaction of moments or intramolecular exchange coupling. high spin ground state.
(d) Antiferromagnetism c > 0, 0 to10-4 emu, c dependent on H, origin field induced, spin pairing
from dipole-dipole interaction or intramolecular exchange coupling. low spin ground state.
(e) Ferrimagnetism c > 0, 10-4 to 10-2 emu, c dependent on H, origin field induced, spin pairing
(antiferromagnetic coupling) of two species with different magnetic moments from dipole-dipole
interaction or intramolecular exchange coupling. leads to net magnetization
Unpaired e-
Paired e-
(a)
(b)
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(c)
(d)
(e)
Diamagnetism
Theory of Diamagnetism: Langevin (1905)
• Paired electrons produce a current loop that repels an external magnetic field.
c
•
•
•
m0 Nm
B

m0 NZe2
6m
r2
(Classical Langevin result)
Diamagnetic susceptibilities are negative (c < 0), independent of field and
temperature.
Must be taken into account in the measurement of paramagnetic susceptibilities:
c= cp + cdia
Diamagnetic corrections can be calculated using Pascal’s constants and are
always negative.
Nijmegen High Field Magnet Laboratory, Netherlands
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Superconductors: The Perfect Diamagnet
Superconductivity:
1911: Heike K. Onnes noted that the resistance of a frozen mercury rod suddenly
dropped to zero when cooled to the boiling point of helium (4.2 Kelvin).
The conductivity occurs with zero resistance, and probably involves the formation of
“Cooper pairs”. The mechanism of cooper pair formation is still under investigation.
Meissner effect: Magnetic fields are excluded from superconductors below their Tc
YBa2Cu3O7 (YBCO)
Images cortesy of ILL-France
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YBa2Cu3O6
Levitation at T<Tc
Paramagnetism
Theory of Paramagnetism: Curie (1907)
•
•
Unpaired electrons produce an induced field that attracts an external magnetic
field.
Paramagnetic susceptibilities are positive (c > 0), dependent on field and
temperature.
apply Field (H)
B
Random alignment of
spins
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Partial alignment of
spins: c increases
Paramagnetism: gbH vs. kT
Alignment of spins with field
m = -gbS
DE = -2 gbSH = 2 m
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Randomization of spins
Fundamental Law in Magnetism: Van Vleck
No angular momentum and no coupling between ground and excited state:
magnetic moment= -gbH
interacting with magnetic field:Hamiltonian: = -gbH S
operate Hamiltonian on spin wavefunction: two eigenvalues are obtained: E=ms gbH
mm  E / H
(microscopic magnetization)
Macroscopic magnetization: Application of Boltzmann distribution M=f (NgbkT)
For ms=1/2:

gbH 
gb H  
 exp 
  exp
 
Ngb 
2kT 
2kT  
M
gb H 
gbH 
2 
exp
 exp 


 2kT 
 2kT 

Valid for H / kT<<1
H large, T low: Msat = N gb S
H moderate, T moderate: Curie Law
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Paramagnetism: Curie Law
The dependence of the magnetic susceptibility with temperature for spin only systems is
governed by the Curie Law.
Before quantum mechanics:(Curie, 1900)
c = C/T, where C = Curie Constant
After quantum mechanics: (Van Vleck, 1931)
c = Ng2b2 S(S+1) / 3kT
Magnetic Moment
Susceptibility
5
c (emu•K/cm3•G•mol)
c (emu/cm3•G•mol)
2
[Cu(H20)6](SO4)2 S = 1/2
1.5
[Ni(H20)6](SO4)2 S = 1
[Mn(H20)6](SO4)2 S = 5/2
1
0.5
0
0
20
40
60
80
T(K)
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100
120
4
m(BM )  2.828 cT
3
2
1
0
0
50
100
150
T(K)
200
250
300
Diamagnetism vs. Paramagnetism
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Paramagnetic Susceptibility of
Conduction Electrons
Pauli paramagnetism: Only the fraction T/TF contribute to the susceptibility.
3Nm 2
M
H
2kB TF
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Field dependence of the Magnetization
Brillouin Function
M = NgJmBBJ(x)
2S  1  1
 x 
2S  1
BJ (x) 
coth
x 
coth 
 2S  2S
2S 
2S
x  gJmB B /k B T
Assumptions made:
x<<1 ( gJmBB << kBT)
W. E. Henry
UW Bio-Molecular Magnetism Group
“Spin-only” Magnetism
Spin only magnetism refers to systems in which there is no orbital angular
momentum, and no exchange interactions (No spin orbit coupling, g-anisotropy,
zero field splittings, exchange interactions)
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Deviations from “Ideal behavior”:
The Curie-Weiss Law
Deviations from Curie Law behavior may be due to
internal electronic structure ( g-anisotropy, ZFS,
spin-orbit coupling) or magnetic exchange
interactions which lead to an additional mean field,
causing a different distribution of spin states. If the
mean field is small relative to the splitting of original
states, the magnetic susceptibility follows the Curie
Weiss Law:
c
C
T 
where  is essentially a mean field parameter.
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Magnetic Exchange Interactions
Magnetic exchange interactions between two spin containing units depends to a first
approximation on the orbital overlap either directly through space (direct exchange) or
through bond (spin delocalization, spin polarization or superexchange).
S=1
S=0
2J
2J
S=1
Ferromagnetic
Antiferromagnetic
exchange
exchange
2J = interaction between unpaired spins
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S=0
What is Exchange???
Exchange interaction: spin dependent coulomb energy
Exchange energy ( Exchange Field): If two atoms i and j have spin angular momentum
Sih/2p and Sjh/2p, respectively, then the exchange energy between them can be
described in terms of the exchange integral Jex.
E ex  2J ex Si  S j
(e1  e 2 ) 2
J ex  2k 
U
Kinetic energy term (antiferromagnetic) and potential energy term (ferromagnetic):
(e1  e2 ) 2
4(b  l)2
J AF  

U
U
UW Bio-Molecular Magnetism Group
JF  2k
Dimer Model for Magnetic Exchange
Hamiltonian:
H  2  Jij Si S j
Summing over states: isotropic Heisenberg Hamiltonian
H  2JS1  S2
J = E (S=0) - E (S=1) which is the isotropic interaction parameter. In this case, J < 0 is
antiferromagnetic coupling, while J > 0 is ferromagnetic coupling.
c
2Ng2 b 2 / kT
Bleaney Bowers (1952)
3  exp(2J / kT)
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Types of Magnetism
Diamagnetic
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Magnetic Ordering
T > Tc: paramagnet
T < Tc:Ferromagnet
Fe (Tc = 1043K)
Ni (Tc = 631K)
CrO2 (Tc = 387K)
CrBr3 (Tc = 33K)
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T < Tc: Antiferromagnet
Cr (Tc = 313K)
Mn (Tc = 95K)
NiO (Tc = 523K)
MnO (Tc = 120K)
Long Range Order: Antiferromagnetism
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Long Range Order: Ferromagnetism
Large magnetization energies
associated with ferromagnetism give
rise to formation of domain walls.
Driving force?
Magnetostatic energy.
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Hysteresis: Hard and Soft Magnets
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Single Domain Particles
First postulated in 1930 by Frenkel and Dorfman
Single domain particles cannot be demagnetized (no domain walls), their
magnetization can only be reversed by rotation.
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Magnetic Nanoparticles
Behavior of nanoparticles is a function of structure, size, and interactions in the
material.
single domain
Hc
multidomain
Superparamagnetic
D
Dc
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Spintronics
Spintronics: Spin-polarized charge transport
Spin orientation of conduction electrons has is a slow process (ns), compared
to the rate of electron momentum decay (fs).
Applications:
quantum computing, (each spin corresponds to a bit “qubit”)
magnetic information storage(GMR)
magnetic hard drives
M-RAM (GMR-RAM)
nonvolatile programmable logic(AND, OR, NAND and NOR gates)
NY Times, (IBM) 2001
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Nature June 2000
Magnetoresistance
Prinz(1998)
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Spin Valves
A general magnetic field sensor made of GMR multilayers (iron-nickel with silver)
(Institute of Physics)
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Dilute Magnetic Semiconductors (DMS)
Can spin polarized transport be realized in semiconductor structures?
semiconductor quantum dots, atoms, or molecules quantum bits (qubits) for
quantum computing and quantum communication.
ferromagnetic semiconductors = charge transport and magnetic storage.
Challenges: ferromagnetic material ( with high Tc)
effective spin-injection (100% ideally)
resistivity comparable to that of a semiconductor for effective band matching.
Mn-based zinc-blende III-V and II-VI magnetic semiconductors:
hole-mediated exchange based on the Zener model (double exchange) correctly
predicts the magnetic exchange in these systems.
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RKKY Theory
The phenomenon of magnetic exchange in electron-delocalized solid state materials
was described for magnetically dilute semiconductors by Kondo, Heeger and Ruderman and
Kittel, Kasuya, and Yosida.
Indirect exchange interaction between the two magnetic ions that occurs through electron
scattering and hyperfine interactions between the scattered electron and magnetic nucleus.
The conduction gas is magnetized in the vicinity of the magnetic ion; the second ion
perceives the magnetization of the first, leading to an interaction between them, known as
the Friedel or RKKY interaction.
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Kondo Effect
The Kondo Effect is a minimum in the electrical resistivity-temperature curve of dilute
magnetic alloys at low temperatures.
Anomalously high scattering probability: dynamic nature of the scattering of the
exchange coupling, and of the sharpness of the Fermi surface at low temperatures.
The spin dependent contribution to the resistivity is dependent on the exchange
energy, nearest neighbors, and strength of exchange scattering.
(Experiment: MacDonald)
0.090
0.200
(Theory:Kondo)
Resistance()
Au(Fe)
0.08%Fe
0.006%Fe
minimum
0.074
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0.184
T(K)
Kondo effect in single-atom transistors
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Park, Pasupathy Nature 2002