CMR_Formal_Presentation2

Colossal Magnetoresistance

Dr. Cammerata

Colossal Magnetoresistance

Definition

Why the interest?

Brief History

Materials

Causal Forces

Implications for Industry

Colossal MagnetoresistanceDefinition

Colossal magnetoresistance (CMR)

It is the property of some materials in which the electrical resistance changes by orders of magnitude when an external magnetic field is applied to them.

)0(

)0()(

)0( R

RHR

R

R

Technological Interest

• The global market for nanomagnetic materials and devices will rise at an AAGR (average annual growth rate) of 22.6% from $4.3 billion in 2004 to reach nearly $12.0 billion in 2009.

• Information storage applications account for the vast majority – over 90% – of today’s market and will continue to dominate in 2009.

Source: Mindy Rittner, Ph.D.GB-293 Nanomagnetics: Materials, Devices and MarketsPublished December 2004 BCC, Inc., 25 Van Zant St., Norwalk, CT 06855

Colossal MagnetoresistanceWhy the interest?

Fundamental Physics Interest

• The strong coupling of magnetic properties to the lattice structure, spin ordering, angular momentum ordering, and charge ordering.

• Complex phase transitions between metallic, ferromagnetic paramagnetic and insulator phases

• Easily tuned by changing the element concentrations

• Shares complexities with some high temperature superconductors

Colossal MagnetoresistanceWhy the interest?

The theory is still incomplete, however.

Colossal MagnetoresistanceBrief History

1850 1875

1900 1925

1950 1975

2000

Qualitative Discovery of Causal Effect of

Magnetism on Resistance

Quantificationof MR Properties

and Materials

GMR discovered

in Fe/Cr Co/Cu Superlattices

CMR discovered in Superlattice

Manganites

Mn Fe Co Ni Cu Zn Ga Ge As Se Br KrSc Ti V CrK

Tc Ru Rh Pd Ag Cd In Sn Sb Te I XeY Zr Nb MoRb

Re Os Ir Pt Au Hg Tl Pb Bi Po At RnHf Ta WCs

Bh Hs Mt Uun Uuu UubRf Db SgFr

Na

Li

H

ArClSPSiAl

ON NeFCB

He

Am Cm Bk Cf Es Fm Md No Lr Pa U Np PuAc Th

Eu Gd Tb Dy Ho Er Tm Yb LuPr Nd Pm SmLa Ce

Ca

Sr

Ba

Ra

Mg

Be

3d Transition Metal Oxides Mixed-Valence Perovskite Manganese Oxides: R1-xAxMnO3

Colossal Magnetoresistance Materials

Colossal Magnetoresistance Materials

C.M. Resistance

Colossal Magnetoresistance Causal Forces

A little change destroys the effect

Orbital Ordering

Charge Ordering

Spin Ordering

Structural Order

Temperature

Double Exchange

J-T Distortions

La3+

Mn3+

O2-

LaMnO3

Colossal MagnetoresistanceDouble Exchange Mechanism

La1-xSrxMnO3

La+3

Mn+3

O-2

Mn+4

Sr+2

Colossal MagnetoresistanceDouble Exchange Mechanism

La3+

Mn3+

O2-

Mn4+

Sr2+

La1-xSrxMnO3

Colossal MagnetoresistanceDouble Exchange Mechanism

43,2

31

MnOMn

Colossal MagnetoresistanceDouble Exchange Mechanism

La3+

Mn3+

O2-

Mn4+

Sr2+

323,1

4 MnOMn

Colossal MagnetoresistanceDouble Exchange Mechanism

La3+

Mn3+

O2-

Mn4+

Sr2+

Colossal MagnetoresistanceHund’s Rules

• Breaking the Degeneracy– Hund’s Rules for Multi-electron atomic systems

1. Term with maximum multiplicity lies lowest in energy (spin-spin coupling) Typically, the largest total S.

2. For a given multiplicity, the term with the largest value of L lies lowest in energy. (orbit-orbit coupling)

3. For atoms with less than half-filled shells, the level with lowest value of J lies lowest in energy. (spin-orbit Coupling )

SpinSpaceTotal

These rules stem from the overriding constraint of theFermi-Dirac statistics on the total probability density function

SS

SL

JJ

LL

Colossal MagnetoresistanceCoupling Interactions

Breaking the Degeneracy inMany Electron Atomic Systems

Er

e

r

Ze

m

N

i ji ijoioi

1

222

2

442

Central Field Approximation

Attractive Repulsive

10 HHH

EH

ii

ioji ijo

iii

rUr

Ze

r

eH

rUm

hH

)(44

)(2

22

1

22

0

Nucleus

Electrons

Colossal Magnetoresistance

Electrons Reside in Degenerate Energy Levels

Spin-Orbit interactions

i

iii SLrH

)(2

relativistic correction

210 HHHH

Total Hamiltonian

i

i

ii dr

rdV

rcmr

)(1

2

1)(

22

Colossal Magnetoresistance

21 HH (i)

21 HH (ii)

L-S (or Russell-Saunders) coupling case: small and intermediate Z

j-j coupling case: large Z

Breaking the Degeneracy inMany Electron Atomic Systems

1s

2s

3s

4s

2p

3p

3d

1s2 2s2 2p6 3s2 3p6 4s2 3d5

Manganese Z=25

This is the orbital of interest

Colossal MagnetoresistanceEnergy Levels

Colossal Magnetoresistance3d Orbital Types

Orbital surfaces are no longer perfectly symmetric

eg Orbitals

3z2-r2 x2-y2

t2g Orbitals

zx yz xy

3d

Colossal MagnetoresistanceSplitting of the 3d Orbital

t2g

eg

This is still degenerate

Splitting is almost complete

accordance with Hund’s Rules

Colossal MagnetoresistanceJahn-Teller Distortion

The Jahn-Teller Theorem was published in 1937 and states:

"any non-linear molecular system in a degenerate electronic state will be unstable and will undergo distortion to form a system of lower symmetry and lower energy thereby removing the degeneracy"

Colossal MagnetoresistanceJ-T Distortions and Further Splitting

Triplet

Doubleteg

t2g

Jahn – Teller

Mn3+

Hund’sRules

Degeneracy is Split . . . . And with it comes a structural distortion

Colossal MagnetoresistanceOrbital Ordering Resulting from Distortions

The ordering of the overall lattice is magnified by the preferred symmetry and orientation of the individual

electronic orbitals

Charge Ordering

Colossal Magnetoresistance

Spin Ordering

Colossal Magnetoresistance

Colossal MagnetoresistanceImplications for Industry

Smaller Storage Devices

100 GB/inch2 now

EMR promises > 1 TB/inch2

Low Power

Reliable and Sustainable

Companies such as IBM, NEC and NVEhave commercial devices on the market

Extraordinary MR