Movement of Atoms [Sound, Phonons]

Brockhouse 1950 ...

E

Q

π/a

The Nobel Prize in Physics 1994

Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays

Movement of Spins - Magnons

ij

jiijJH SS)(2

1

153

T=1.3 KMF - Zeeman Ansatz (for S=1/2)

Movement of Spins - Magnons

ij

jiijJH SS)(2

1

Bohn et. al. PRB 22 (1980) 5447

T=1.3 K

153

Movement of Spins - Magnons

ij

jiijJH SS)(2

1

Bohn et. al. PRB 22 (1980) 5447

T=1.3 Ka

153

                                                                                                   

                   

Measured spin wave dispersion relations for x=0.35 and x=0.40. Solid lines show the best fits for the Heisenberg ferromagnet Hamiltonian with nearest neighbour exchange only. Dashed lines show the best fit including second neighbour interactions as well (i.e. hopping along Mn-O-Mn- O-Mn).

(a) Crystal structure of La2-

2xSr1+2xMn2O7. The Mn ions are at

the centre of the MnO6 octahedra.

Circles denote La and Sr. (b) Expanded view of MnO6 octahedra

in a single bilayer, showing the Mn d3z2 -r2  and dx2-y2  orbitals.

UO2:Spin wave dispersion curves measured at 16.5 K along the principal crystallographic directions. Dashed lines and crosses correspond to acoustic phonon branches. Open symbols indicate qualitatively smaller magnon intensity than the filled points. The non-spin-flip cross-section was always found to be negligible.

Movement of Charges - the Crystal Field Concept

+

+

+

+

+

+

+

+

+

+

Hamiltonian ilm

iml

mlcf OBH

,

)(JE

Q

4f –charge density

NdCu2 – Crystal Field Excitations

orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ion

Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297

T=10 KT=40 KT=100 K

NdCu2 - 4f Charge Density)()(|)(|)(ˆ

,...,06,4,2,0

24

nmT

nmn

mnnnmf ZOecrR Jr

Magnetische Anregungen

'''

'

'

)('2

121

21

''

)(

''2

121

'

'

''

''

1

1

)()}({)}({

)0()(

)()(1

2

1),(

dkk

i

g

d

kdk

i

g

d

ddAB

WWiddN

TjjTjj

WWi

jjjj

tiinelmag

JeN

A

JeN

B

SeegFgF

JJJtJ

eegFgFN

dteS

k

k

dd

dddd

b

jjjj

Gκ

Gκ

BBκ

RRκκ

),('

),()ˆˆ('

'

2

2

22

κκκκ nucmag S

k

kNS

mc

e

k

kN

dEd

d

)(1

12)( ''

/ BAkTBA e

S

1

00 )()(1)(),(

κκ J

*)()(2

1)('' zz

iz ABBABA

Calculate Magnetic Excitations and the Neutron Scattering Cross Section

),()ˆˆ('

'

2

2

22

QQQ

magS

mc

e

k

kN

dEd

d

''/1

12 kTe

S

'

')(

'21

21

21 ),()}({)}({),( ''

dddd

WWiddN

inelmag SeeQgFQgFS dddd

b

QQ BBκ

*)()(2

1)('' ''' zz

iz dddddd

)(

||||)(

)()(1)(),(

,,0

1

00

jiij ij

THTH nniJJjjJJi

J

QQ Linear Response Theory, MF-RPA

ij

jii

iBJiilm

iml

ml ijJgOBH JJHJJ )(

2

1)(

,

Kristallfeld – übergänge

,

2

212

2

2

22

)(||||)ˆˆ(

)('

'

EEnJJ

gFemc

e

k

kN

dEd

d W

κκ

Mittelung über Polykristall

,32

2

212

2

2

22

)(||||

)('

'

EEnJJ

gFemc

e

k

kN

dEd

d W

0 2 4 6 80

2

4

F2

AF2 AF3

FM

F1

AF1

0H (

T)

T (K)

NdCu2 Magnetic Phasediagram(Field along b-direction)

Complex Structures

AF1

Q=

Complex Structures

F1

Q=

Complex Structures

F2

Q=

NdCu2 Magnetic PhasediagramH||b

F3

AF1

F1

ab

c

F1

Lines=ExperimentColors=Theory

Magnetische Anregungen– NdCu2

H=3T||b

τ

NdCu2F3

AF1

F1

F3: measured dispersion was fitted to get exchange constants J(ij)

1950 Movements of Atoms [Sound, Phonons]

a

τorbiton

lmij

jmli

mlQ OOijCH

,

)()()( JJDescription: quadrupolar (+higher order) interactions

a

τorbiton

1970 Movement of Spins [Magnons]

? Movement of Orbitals [Orbitons]

M. Rotter, Institut für physikalische Chemie, Universität Wien

McPhase - the World of Rare Earth MagnetismMcPhase is a program package for the calculation of

magnetic properties of rare earth based systems.          Magnetization                       Magnetic Phasediagrams

    Magnetic Structures            Elastic/Inelastic/Diffuse                                               Neutron Scattering

                                             Cross Section

and much more....

Magnetostriction 

Crystal Field/Magnetic/Orbital Excitations

McPhase runs on Linux and Windows and is available as freeware.

McPhase is being developed by   M. Rotter, Institut für Physikalische Chemie, Universität Wien, Austria

  M. Doerr, Technische Universität Dresden, Germany R. Schedler, Hahn Meitner Institut, Berlin, Germany

  P. Fabi né Hoffmann, Forschungszentrum Jülich, Germany   S. Rotter, Wien, Austria

M. Banks, Max Planck Institute, Stuttgart, GermanyDuc Manh Le, University of London, U.K.

Important Publications referencing McPhase:

• M. Rotter, S. Kramp, M. Loewenhaupt, E. Gratz, W. Schmidt, N. M. Pyka, B. Hennion, R. v.d.Kamp Magnetic Excitations in the antiferromagnetic phase of NdCu2 Appl. Phys. A74

(2002) S751     • M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu2

Compounds using McPhase J. of Applied Physics 91 (2002) 8885• M. Rotter Using McPhase to calculate Magnetic Phase Diagrams of Rare Earth Compounds J. Magn. Magn. Mat. 272-276 (2004) 481

• M. Rotter High Speed Algorithm for the calculation of Magnetic and Orbital Excitations in Rare Earth based Systems  Computational Materials Science38 (2006) 400