rare earth and transition metal magnetism ab-initio · 2012-12-07 · rare earth and transition...

Rare earth and transition metal magnetismab-initio

Computational modelling of transition metal and rare earthmaterials’ magnetic properties using ab-initio electronic structure

theory

Julie StauntonUniversity of Warwick, Coventry, United KingdomJulie Staunton University of Warwick, Coventry, United Kingdom Rare earth and transition metal magnetism ab-initio

Magnetic periodic Table

Transition metal d-electrons, rare earth f-electrons.M.Coey and S.Sanvito, Physics World 17,(11), 34, (Nov. 2004)

Julie Staunton University of Warwick, Coventry, United Kingdom Rare earth and transition metal magnetism ab-initio

Materials Modelling and Density Functional Theory

Computational materials modelling must describe ≈ 1024

interacting electrons.

Density functional theory (DFT) makes this problem tractable.It focusses on dependence of the energy of a material onelectronic charge, ρ and magnetisation, ~m, densities.

Many interacting electrons described in terms ofnon-interacting electrons in effective fields (Kohn Sham).

The effective fields have subtle exchange and correlationeffects for nearly bound d- and f-electrons.Temperature dependence.

For T 6= 0K need to identify some electronic attributes whichare slowly varying (Born-Oppenheimer).Separate out these modes and treat their statistical mechanics.

For magnets these are local moments: {ei}

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The effective fields have subtle exchange and correlationeffects for nearly bound d- and f-electrons.

Temperature dependence.For T 6= 0K need to identify some electronic attributes whichare slowly varying (Born-Oppenheimer).Separate out these modes and treat their statistical mechanics.


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The effective fields have subtle exchange and correlationeffects for nearly bound d- and f-electrons.Temperature dependence.

For T 6= 0K need to identify some electronic attributes whichare slowly varying (Born-Oppenheimer).Separate out these modes and treat their statistical mechanics.


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The Heavy Rare Earths Gd,Tb,Dy,Ho, Er,Tm, Yb, Lu

Electronic configurations: 4f76s25d1 for Gd to 4f146s25d1 for Lu.

Hexagonal close packed crystal structures, c,a lattice parameters.

Lanthanide contraction.

Magnetic moments from f-electrons interact via conductionelectrons.


Magnetic order of heavy rare earths from materialsmodelling tested by experiment

blue - ferromagnetic, incommensurate anti-ferromagnetic.Lanthanide Contraction and Magnetism in the Rare Earth Elements, (I. D. Hughes et al, Nature, 446, 650, (2007))

A.Vl. Andrianov, O.A. Saveleva, E. Bauer and J.B.Staunton, PRB 84, 132401, (2011).


Magnetic modulation Q-vectors, transition temperatures

Hughes et al, Nature, 446, 650, (2007)


Magnetic Refrigeration - a promising cooling technology

Magnetic, electronic and lattice entropy interchanging whenmagnetic field is turned on and off.

Need materials that respond strongly to modest magnetic fields.

Large effect when magnetic state changes. Magnetism coupled toanother property.

Rare earth, transition metal magnetic refrigerants.


Ab-initio modelling of the MagnetoCaloric Effect inGadolinium

0 20 40 60 80 100 120Magnetic field change, dH, (kOe)

0

20

40

60

80

100

120

140

Mag

neto

calo

ric e

ffect

, −dS

(dH

,Tc)

, (m

J /c

m^3

K)

Magnetocaloric effect, GdEntropy change with field at Tc

Expt.,(Tc=294K)−>

<− Theory,(Tc=285K)

0 20 40 60 80 100 120Magnetic field change, dH, (kOe)

0

5

10

15

20

Mag

neto

calo

ric e

ffect

, dT_

ad (T

c), (

K)

Magnetocaloric effect, GdTemperature change with field at Tc

<− Theory

Expt. −>

Experimental results from K.Gschneidner Jr. et al., Rep.Prog.Phys. 68, (2005), 1479-1539


Potential rare-earth free magnetic refrigerants- example of CoMnSi

CoMnSi is an metallic helical antiferromagnet.

Magnetic field induced transition from antiferromagnetic toferromagnetic state.

Second order, first order phase transition. Tricriticality, Tt ,Bt .

Magnetic refrigeration. Work near Tt ,Bt .

Material with competing ferromagnetic and anti-ferromagneticinteractions. Linked with magnetostructural effect.

Variations, Co1−xNixMnSi, CoMn1−xCrxSi, CoMnGe1−xPx

Need to control for accessible and useful Tt ,Bt .


Test against experiment

3.06

3.08

3.10

3.12M

n−M

n di

stan

ces

(Å) d1

d2

0 100 200 300 400 500Temperature (K)

3.06

3.08

3.10

3.12CoMnSi

Co0.95Ni0.05MnSi

a

b

c

Z.Gersci et al, PRB,83, 174403, (2011); A.Barcza et al. (2012)); J.B. Staunton et al. arXiv:cond-mat/1206.3394.


Magnetic Anisotropy, K - a crucial property

FePt surface alloys J. Honolka et al. PRL,102, 067207, (2009)

Large K magnetic hardness, permanent magnets.Small K magnetic softness, high permeability.Large K stability of magnetic information, smallermagnetic particles, higher Tb’sFundamental property K links magnetisation direction tostructure via spin-orbit coupling of electrons.K is big for high Z materials with strong T , composition andstructure dependence.Calculation needs to be numerically robust.


Ab-initio modelling of magnetic anisotropy of L10-FePt

0 200 400 600 800 1000Temperature T(K)

0

0.2

0.4

0.6

0.8

1

Mag

netis

atio

n M

(T)

<−−−(0,0,1)

(1,0,0)−−>

M(T) FePt

860 900 9400

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1Magnetisation squared

−2

−1.5

−1

−0.5

0

Mag

netic

ani

sotr

opy

ener

gy (

meV

)

<−−model

MCA FePt

0.5 0.6 0.7 0.8 0.9 1

Order parameter, S

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

MA

E,

Ku (

me

V/a

tom

)

Experiment (bulk)

Theory: c/a=0.98

Theory: c/a=1

Exper.: T=10K [S.Okamoto et al.]

L10−FePt

F(001)−F(100)

J.B. Staunton et al., Phys.Rev.Lett.93, 257204, (2004); J.Phys:CM 16, S5623, (2004), PRB, 74, 144411, (2006)


Atomic scale engineering of K in magnetic nanostructures

S. Ouazi et al., Nature Commun.,in press.


Theoretical modelling of magnetic materials

Summary:Ab-initio materials modelling uses DFT.Slowly varying local moments in sea of ‘fast’ electrons.Strong electron correlations, composition and structure.Magnetism of heavy rare earths, transition metals.Magnetic refrigeration.Including spin-orbit coupling effects describesmagnetic anisotropy K.

Outlook:Find new adaptive magnetic materials,e.g. rare earth replacement materials.Electronic effects, temperature and spintronics.Metamagnetism and improved magnetic refrigeration materials.Nanostructuring magnetic properties.


Acknowledgements

S. Bornemann, H. Ebert et al., LMU Munich, Germany.

K. Sandeman, Z. Gercsi, Imperial College, London, UK.

H. Brune et al., Lausanne, Switzerland.

W. M. Temmerman, Z. Szotek, M. Lueders, L. Petit, STFCDaresbury, UK.

S. Ostanin, A. Ernst et al., MPI Halle, Germany.

A. Vl. Andrianov et al., MSU, Russia.

K. Kern et al., Stuttgart, Germany.

D. Paudyal, K. Gschneidner Jr., V. Pecharsky, Ames Lab.USA.

EPSRC (UK) Grant EP/J006750/1


rare earth and transition metal magnetism ab-initio · 2012-12-07 · rare earth and transition...

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