Movement of Atoms [Sound, Phonons]
Brockhouse 1950 ...
The Nobel Prize in
Physics 1994
E
Phonon Spectroscopy: 1) neutrons
2) high resolution X-rays
π/a
Q
Movement of Spins - Magnons
153
1
H    J (ij )Si  S j
2 ij
MF - Zeeman Ansatz
(for S=1/2)
T=1.3 K
Movement of Spins - Magnons
153
1
H    J (ij )Si  S j
2 ij
T=1.3 K
Bohn et. al.
PRB 22 (1980) 5447
Movement of Spins - Magnons
1
H    J (ij )Si  S j
2 ij
153
a
T=1.3 K
Bohn et. al.
PRB 22 (1980) 5447
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 La22xSr1+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
+
+
+
+
+
4f –charge density
+
+
+
E
+
+
Hamiltonian H cf 
m m
B
 l Ol (J i )
lm,i
Q
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
NdCu2 - 4f Charge Density
 ˆ (r ) | R4 f (r ) |2
m
ec


O
 nm n n (J) T Z nm ()
n 0, 2, 4, 6
m 0 ,..., n
T=100
T=40
T=10 K
K
K
Magnetische Anregungen
d 
k '  e
 N 
ddE'
k  m c2
2
S  mag
2




inel
2
 (  κˆ  κˆ  )S  mag (κ, )  N

1
it 1
(κ ,  ) 
dte
2 
N
k'
S nuc (κ ,  )
k
iκ ( R  R
1
1




gF
(

)
gF
(

)
e
2
j 2
j'
j
j' )
e
 W j W j '

jj '
  J j (t ) J j ' (0) T   J j  J j ' T  

1
2N b
iκ ( B d  B d ' ) Wd Wd '
1
1
{
gF
(

)}
{
gF
(

)}
e
e
S Bd Ad ' ( )
2
d 2
d'
dd '
Bd 
Ad ' 
1
Ng
e
1
Ng
iκ G k ' 
e
 J k 'd '
iκ G k

J kd
k
k'
S BA ( )  2
1
1  e  / kT
''
 BA
( )
1
 BA ' ' ( z )   BA ( z )   AB ( z*)
2i

 (κ,  )   0 ( ) 1   0 ( ) J (κ )

1
Calculate Magnetic Excitations and the Neutron
Scattering Cross Section
1
m m
H   Bl Ol ( J i )   g Ji  B J i H   J i J (ij )J j
2 ij
lm,i
i
d 
k '  e
 N 
ddE'
k  m c2
2
S

2
inel
mag



2
( 




ˆ
ˆ
 Q Q  )S mag (Q,  )


iκ( Bd Bd ' ) Wd Wd ' 
1
1
1
(Q, )  2Nb { 2 gF(Q)}d { 2 gF(Q)}d ' e
e
Sdd ' (Q, )
dd '


1 
 dd ' ' ' ( z ) 
 dd ' ( z )   d'd ( z*)
2i



S  2
1
1  e  / kT
 ''

 1
 (Q,  )   0 ( ) 1   0 ( ) J (Q) Linear Response Theory, MF-RPA
 0 ( )  

ij
 i | J   J  H ,T | j  j | J    J   H ,T | i 
 j   i  
(ni  n j )
Kristallfeld – übergänge
2
d 
k '  e  2W 1
2
 N  2  e
2 gF ( ) 
ddE'
k  mc 
  (   κˆ  κˆ  )   | J |    | J  |   n  ( E  E   )
2
2
 ,
Mittelung über Polykristall
2
d
k '  e  2W 1
2
 N  2  e
2 gF ( ) 
ddE'
k  mc 
  23   | J |    | J |   n  ( E  E   )
2
 ,
2
NdCu2 Magnetic Phasediagram
(Field along b-direction)
4
FM
0H (T)
F2
2
F1
AF3
AF1 AF2
0
0
2
4
T (K)
6
8
Complex Structures
AF1
Q=
Complex Structures
F1
Q=
Complex Structures
F2
Q=
NdCu2 Magnetic Phasediagram
H||b
F1   
F3 
c
F1 
a
b
AF1 
Lines=Experiment
Colors=Theory
Magnetische Anregungen–
NdCu2
H=3T||b
τ
F3 
F3: measured
dispersion was
fitted to get
exchange
constants J(ij)
NdCu2
F1 
AF1 
1950
Movements of Atoms [Sound, Phonons]
1970
Movement of Spins [Magnons]
?
Movement of Orbitals [Orbitons]
aa
ττorbiton
orbiton
Description: quadrupolar
(+higher order) interactions
H Q    C (ij )  Olm (J i )  Olm (J j )
ij ,lm
M. Rotter, Institut für physikalische Chemie, Universität Wien
McPhase - the World of Rare Earth Magnetism
McPhase 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
Crystal Field/Magnetic/Orbital Excitations
Magnetostriction
and much more....
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, Germany
Duc 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