Spintronics and Magnetic Properties of Materials

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Spintronics and Magnetic Properties of Materials

• Natia L. Frank
• Department of Chemistry
• University of Washington
• Seattle, WA 98117

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The Earths Magnetic Field
Glatzmaier (Los Alamos)
Alerstam, Nature 2001
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Navigating the Earths 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 magnets 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
  Elizabeths 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.
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Quantum Mechanical Basis of Spin

• Rotation of the charge of an electron produces
  current loops with a magnetic moment directed
  along the rotation axisspin 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
• 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/cm3Gmol)
• 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 ? lt 0, 10-6 emu, ? independent
of H, origin field induced, paired electron
circulation. (b) Paramagnetism ? gt 0, 0 to10-4
emu, ? independent of H, origin angular momentum
of electron. No interactions between spins. (c)
Ferromagnetism ? gt 0, 10-4 to 10-2 emu, ?
dependent on H, spin alignment from dipole-dipole
interaction of moments or intramolecular exchange
coupling. high spin ground state. (d)
Antiferromagnetism ? gt 0, 0 to10-4 emu, ?
dependent on H, origin field induced, spin
pairing from dipole-dipole interaction or
intramolecular exchange coupling. low spin ground
state. (e) Ferrimagnetism ? gt 0, 10-4 to 10-2
emu, ? 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-
(b)
(c)
(d)
(e)
(a)
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Diamagnetism

• Theory of Diamagnetism Langevin (1905)
• Paired electrons produce a current loop that
  repels an external magnetic field.
• Diamagnetic susceptibilities are negative (c lt
  0), independent of field and temperature.
• Must be taken into account in the measurement of
  paramagnetic susceptibilities
• c ?p cdia
• Diamagnetic corrections can be calculated using
  Pascals constants and are always negative.

(Classical Langevin result)
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
Levitation at TltTc
YBa2Cu3O7 (YBCO)
YBa2Cu3O6
Images cortesy of ILL-France
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Paramagnetism

• Theory of Paramagnetism Curie (1907)
• Unpaired electrons produce an induced field that
  attracts an external magnetic field.
• Paramagnetic susceptibilities are positive (c gt
  0), dependent on field and temperature.

Random alignment of spins
Partial alignment of spins c increases
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Paramagnetism gbH vs. kT
Alignment of spins with field
Randomization of spins
m -gbS DE -2 gbSH 2 m?
???
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Fundamental Law in Magnetism Van Vleck
No angular momentum and no coupling between
ground and excited state magnetic moment -gbH
interacting with magnetic fieldHamiltonian
-gbH S operate Hamiltonian on spin wavefunction
two eigenvalues are obtained Ems gbH
(microscopic magnetization)
Macroscopic magnetization Application of
Boltzmann distribution Mf (NgbkT) For ms1/2
Valid for H / kTltlt1 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) After
  quantum mechanics (Van Vleck, 1931)
• c C/T, where C Curie Constant
  c Ng2b2 S(S1) / 3kT

Magnetic Moment
Susceptibility
Cu(H20)6(SO4)2 S 1/2
Ni(H20)6(SO4)2 S 1
Mn(H20)6(SO4)2 S 5/2
?? (emuK/cm3Gmol)
c (emu/cm3Gmol)
T(K)
T(K)
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Diamagnetism vs. Paramagnetism
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Paramagnetic Susceptibility of Conduction
Electrons
Pauli paramagnetism Only the fraction T/TF
contribute to the susceptibility.
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Field dependence of the Magnetization
Brillouin Function
M NgJmBBJ(x)
Assumptions made xltlt1 ( gJmBB ltlt kBT)
W. E. Henry
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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 behaviorThe 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
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).
Ferromagnetic exchange
Antiferromagnetic exchange
2J interaction between unpaired spins
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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.
Kinetic energy term (antiferromagnetic) and
potential energy term (ferromagnetic)
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Dimer Model for Magnetic Exchange
Hamiltonian
Summing over states isotropic Heisenberg
Hamiltonian
J E (S0) - E (S1) which is the isotropic
interaction parameter. In this case, J lt 0 is
antiferromagnetic coupling, while J gt 0 is
ferromagnetic coupling.
Bleaney Bowers (1952)
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Types of Magnetism
Diamagnetic
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Magnetic Ordering
T lt TcFerromagnet
T lt Tc Antiferromagnet
T gt Tc paramagnet
Fe (Tc 1043K) Ni (Tc 631K)
Cr (Tc 313K) Mn (Tc 95K)
NiO (Tc 523K) MnO (Tc 120K)
CrO2 (Tc 387K) CrBr3 (Tc 33K)
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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.
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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
Nature June 2000
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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.
0.090
0.200
(TheoryKondo)
(Experiment MacDonald)
Au(Fe)
0.08Fe
Resistance(?)
0.006Fe
minimum
0.074
0.184
T(K)
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Kondo effect in single-atom transistors
Park, Pasupathy Nature 2002