PrologPrologNumerical Modeling in MagnetismNumerical Modeling in MagnetismMacro-Magnetism: Solution of Maxwells Equations –
Engineering of (electro)magnetic devices
Atomic Magnetism: Instrinsic Magnetic Properties
Micromagnetism: Domain Dynamics, Hysteresis
MFM image
Micromagnetic simulation.
Atomic Magnetism-Atomic Magnetism- Modeling Instrinsic Magnetic Properties Modeling Instrinsic Magnetic Properties
Band Models• Spin Polarized First Principle Methods: restricted to simple Magnetic Structures, T=0, no dynamics, no rare earth
elements ... there are attempts to overcome these restrictions
Localized Moment Models Ising-, Heisenberg-, xy-, Standard Model of RE-Magnetism)• Exact Methods: e.g. branch and bound algorithm, transfer
matrix algorithm• Monte Carlo Methods• Selfconsistent Mean Field Method
Atomic Magnetism-Atomic Magnetism- Modeling Instrinsic Magnetic Properties Modeling Instrinsic Magnetic Properties
McPhase 2.4.lnk
Band Models• Spin Polarized First Principle Methods: restricted to simple Magnetic Structures, T=0, no dynamics, no rare earth
elements ... there are attempts to overcome these restrictions
Localized Moment Models Ising-, Heisenberg-, xy-, Standard Model of RE-Magnetism)• Exact Methods: e.g. branch and bound algorithm, transfer
matrix algorithm• Monte Carlo Methods• Selfconsistent Mean Field Method
M. Rotter, Institut für physikalische Chemie, Universität Wien
Martin Rotter - McPhase Course TU Dresden 2005
McPhase - the World of Rare Earth Magnetism
The Standard Model of RE Magnetism - The Standard Model of RE Magnetism - the Crystal Field Conceptthe Crystal Field Concept
+
+
+
+
+
+
+
+
+
+
Hamiltonian ilm
iml
mlcf OBH
,
)(JE
Q
4f –charge density
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Example: NdCuExample: NdCu2 2
ab
c
Crystal Structure of RCu2
Imma (orthorhombic)
... 9 nonzero CF Parameters9 nonzero CF Parameters
you can use module pointc to calculate CF parameters by the pointcharge model+
++
+
++
+++
+
++
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
NdCuNdCu2 2 – Crystal Field Excitations– Crystal Field Excitations
orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ion
Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297
McPhase can• solve CF Model• Calculate Intensities and Energies• Calculate and Plot Charge Density• ...
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Make a Crystal Field ModelMake a Crystal Field Modelusing McPhase Module using McPhase Module CfieldCfield
CF Hamiltonian ilm
iml
mlcf OBH
,
)(J
Example files in directory /mcphas/examples/ndcu2b_new/cf
• Edit file Bkq.parameter and enter CF parameters Blm
• Start module cfield - type: cfield –r -B• View output file cfield.out: CF - energies, eigenstates,
transition-matrixelements and corresponding neutron intensities
• Use module convolute to convolute energy vs intensity results with spectrometer resolution function
Module simmannfit can do this again and again for youto fit the result of the calculation to your spectrum by variation of the CF-parameters
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Magnetism would be boring Magnetism would be boring without a magnetic fieldwithout a magnetic field
Hamiltonian
i
iBJilm
iml
ml gOBH HJJ
,
)(
Use module cfieldto calculate magnetization
type: cfield –m
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Specific HeatSpecific Heat
Use module cpcalc to calculate specific heat
type: cpcalc 5 30 1
Tmin=5 Tmax=30 dT=1
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
T=10 KT=40 KT=100 K
Use modules chrgplot+javaview to plot 4f charge density
)()(|)(|)(ˆ
,...,06,4,2,0
24
nmT
nmn
mnnnmf ZOecrR Jr
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Use modules pointc+chrgplot+javaview
T=2KH=0Same CEF
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Module Module mcphasmcphas
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Input files for module mcphas: mcphas.j (structure), mcphas.cf (single ion properties), mcphas.tst (table of initial values), mcphas.ini (H,T-range, ...)
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Do you really want to see the MF Do you really want to see the MF equations ?equations ?
ij
jii
iBJiilm
iml
ml ijJgOBH JJHJJ )(
2
1)(
,
))((
jjii
ijjijiji
JJJJ
JJJJJJJJ
ij
jii
effiiBJi
ilmi
ml
ml ijJgOBH JJHJJ )(
2
1)(
,
j
jBJi
effi g
ijJJHH
)(
Cfield can calculate
effiTiBJi
effiii g
HJHMM
,
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Bulk Properties Calculated by Bulk Properties Calculated by module module mcphasmcphas
Magnetization output file: mcphas.fum
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
NdCuNdCu22 Specific Heat Specific Heat
output file: mcphas.fum
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Crystal field
T
e-
+
+
L0
T<TC(N)
Spontaneous MagnetostrictionSpontaneous Magnetostriction
Microscopic Source of Magneostriction: Strain dependence of magnetic interactions
Exchange
T<TC(N) L=0, L0
„exchange-striction“
.... Symmetry decreases
T
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
H <0
Crystal Field
e-
+
+
Exchange Striction
H
H>0
Forced MagnetostrictionForced Magnetostriction
L0 L=0, L0
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Calculation of MagnetostrictionCalculation of Magnetostriction
lmi
iml
mlcf OBH
,
)()( J ij
jiex ijJH JJ),(2
1
Crystal Field Exchange
k
T k i i
k i i JH J J,
) , (
lm
Tml
ml B
H J O, ) (
+
...)0()0()(
excf HH
excfel HHEH
cEel 2
1mit
}{ / TkH BeTrZ ZTkF B ln 0
F
Output file: mcphas.jj*Output file: mcphas.xyt
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
NdCuNdCu2 2 Magnetostriction Magnetostriction
H cfH
cfH )0(
Crystal Field
)0( exH
exH
Exchange - Striction
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
NdCuNdCu22 Magnetic Phase Diagram Magnetic Phase Diagram
F3
AF1
F1
output file: mcphas.xytUse module phased or displaycontour for color plot of phasediagram
ab
c
F1
lines=experiment
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
output file: mcphas.hkl
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Dispersive Magnetic Excitations
ij
jiijJH SS)(2
1
153
T=1.3 KMF - Zeeman Ansatz
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
... Spinwaves (Magnons)
ij
jiijJH SS)(2
1
Bohn et. al. PRB 22 (1980) 5447
T=1.3 K
153
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Spinwaves (Magnons)
ij
jiijJH SS)(2
1
Bohn et. al. PRB 22 (1980) 5447
T=1.3 Ka
153
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Module Module Mcdisp Mcdisp – Calculate Magnetic – Calculate Magnetic Excitation Energies and the Neutron Excitation Energies and the Neutron
Scattering Cross Section Scattering Cross Section
),()ˆˆ('
'
2
2
22
κκκ magS
mc
e
k
kN
dEd
d
''/1
12 kTe
S
'
')(
'21
21
21 ),()}({)}({),( ''
dddd
WWiddN
inelmag SeegFgFS dddd
b
κκ BBκ
*)()(2
1)('' ''' zz
iz dddddd
)(
||||)(
)()(1)(),(
,,0
1
00
jiij ij
THTH nniJJjjJJi
J
κκ MF-RPA
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Module Module Mcdisp Mcdisp – a novel fast – a novel fast algorithm for magnetic algorithm for magnetic
excitations – Rotter 2005excitations – Rotter 2005
s
ss
s
s
ss
s
s
s
s
s UUUUMM 1**
10 )(
)(),()()(1 00 κκJ
*
'''
''
'''*'''''
'''
),(),(
ss
ssssss UU κ
κTransformation:
''
''''*''
'' )()( ssssss UJUL κκ
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
),()()( '''11
''
*
''''
11''' κκ ss
ss
ssssssss L
all other components of Ψ are zero
with definition:
0 if 1
0 if 1
s
s''''
ssss
with definition: *
''''
11'''' )( sss
ssssss LA κ
Generalized eigenvalue problem (analogue to dynmical matrix in the case of phonons!!)
ttA
Solution gives eigenvalues r and eigenvectors ,...),( 21 tt
(1)
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
(1) may then be inverted to give the following expression for Ψ
'
*''
1'11 )(),(
rrsrrrrsr
ss κ
r
srsrsr
sss
ss UU '*1
*'1
*
'' ))((),('' κκ
using Diracs formula: )(11
lim0
r
rr
iPi
r
ssssss
ss UU '*1
'111
*
'' ),(),( κκback transformation...
*)()(2
1)('' ''' zz
iz ssssss +calculation of absorptive part...
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
McDisp - fast algorithm - Cookbook
ss
s UM , ... lize...diagona *
''''1
''*1'''' )( s
ssssssssss UJUA
κ...setup Matrix
,... rttA
...solve generalized EV Problem
r
srsrsr
sss
ss UU '*1
*'1
*
'' ))((),('' κκ
),()ˆˆ('
'
2
2
22
κκκ magS
mc
e
k
kN
dEd
d
''/1
12 kTe
S
'
')(
'21
21
21 ),()}({)}({),( ''
dddd
WWiddN
inelmag SeegFgFS dddd
b
κκ BBκ
)(||||: ,, jiTHTHs nniJJjjJJiMijs 1)
2)
3)
4)
5)
NdCuNdCu22F3
AF1
F1
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Diffuse ScatteringDiffuse Scattering
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
McPhase ModulesMcPhase Modules
Symmetry - CFSymmetry - CFLocal Point Symmetry limits the number of nonzero
Crystal Field Parameters(mind: local symmetry at rare earth position may be lower than lattice symmetry, i.e. The
lattice may be cubic, but the local symmetry tetragonal)
Point Group / Latt. Symmetry
Coordinate Orientation Nonzero Blm
O cubic xyz||abc B40,B44,B60,B64
O cubic z||111 B40,B43,B60,B63,B66
D6h hexagonal xyz||abc B20,B40,B60,B66
D4h tetragonal xyz||abc B20,B40,B44,B60,B64
C3v (no lattice) B20,B40,B43,B60,B63
C2h monoclinic B20,B40,B60,B66,B66s
D3d (quasicubic in dhcp)
xyz||abc B20,B40,B43,B60,B63,B66
D2 orthorh. xyz||abc B20,B22,B40,B42,B44,B60,B62,B64,B66
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Example: 2nd order CF terms for point symmetry mm2=C2v
We choose here the basis of Racah instead of Stevensoperators for the Crystal field, because these transformlike the spherical harmonic functions
02
02
12
22
22
~
228
3~
28
3~
OO
PiPO
PiOO
yzxz
xy
C2v 1E 1C2 1σy 1σx
A1 1 1 1 1
B1 1 -1 -1 1
A2 1 1 -1 -1
B2 1 -1 1 -1These operators form a reducable representation T2(G) of the point group
Irr.Repr.
Group elements G
'
'2
2'2 )(
~)()'(
~
m
mmm
m OGTO JJCharacter table of mm2
Group Theory basics taken from: Elliott&Dawber Symmetry in Physics, McMillan Press, 1979
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The representation T2(G) can be decomposed into irreducibleRepresentations (i.e. „the Olm can be linear combined to another Basis so that in this basis the representation T2 bas block diagonal form with each block corresponding to a irreducible representation“)
222211112 )( BmAmBmAmGT BABA The m‘s tell, how often a representation occurs. mA1 tells, how often the unit representation occurs in the decomposition, i.e. how many different independent basis vectors span this subspace, i.e. how many independent crystal field parameters will occur.
p
pAppA c
gm *1
1
1Cp... Number of members of class p g.... Number of group elements χ.... Character of class
m
lmmp a
alGT
)2/sin(
))2/1sin(()(
a... Angle of rotation
Class p a χp
E 0 5
C2 π 1
σy π 1
σx π 1
2)1115(4
11 Am
i.e. We expect 2 independent 2nd order CF parameters
A little group theoretical trick for calculating m
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The basis of the 2 A1 representation occuring in the decomposition of T2(G) can be found using the projection operator
G
AA GTGg
P )()(1 211
In order to calculate it, we have to epxlicitely write down the reducable representation T2:
02
02
12
22
22
~
228
3~
28
3~
OO
PiPO
PiOO
yzxz
xy
',2
'
',2
'
'22
'
'2
'
)(
)1()(
)1()(
)(
mmxmm
mmm
ymm
mmm
mm
mmmm
T
T
CT
ET
Jx‘=-Jx, Jy‘=-Jy
Jy‘=-Jy
Jx‘=-Jx
',',''1
' )1()1(4
1mmmm
mmm
mmm
AmmP
02
02
112
1
22
22
22
22
1
~~,0
~8
3~~
2
1~
OOPOP
OOOOP
AA
A
B20 and B22 are nonzero.
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Symmetry – Bilinear InteractionSymmetry – Bilinear Interaction
ij
jiex ijJH JJ )(2
1
Anisotropic Interaction (J(ij) is a tensor)
ij
jiex ijJH JJ )(2
1
Isotropic interaction (J(ij) is a scalar)
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
CeCu2 Structure
Ce
Cu
(quasi)hexagonal types of neighbors
M. Rotter et al., Eur. Phys. J. B 14, 29 (2000)M. Rotter et al., JMMM. 214, 281 (2000)
neighbors related by symmetry must have related interaction constants J(ij)
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
ij
jiex ijJH JJ )(2
1
Anisotropic Interaction –Symmetry Considerations
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
ETC...
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Example: bc mirror plane
0
1
cccb
bcbb
aa
JJ
JJ
J
SJSJ
S
JJH
0
0
00
100
010
001
'
''2
1
2
11010
JJJ
JJJJ
a
b
Symmetry – Quadrupolar Symmetry – Quadrupolar InteractionInteraction
Isotropic Quadrupolar Interaction
dhcp –lattice: between hexagonal sites
dhcp –lattice: between quasicubic sites
Derivation similar to CF operator using representation T(G)=T2(G)xT2 (G)
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Example for quadrupolar Example for quadrupolar interactions: PrCuinteractions: PrCu22
+
+
+
+
+
+
+
+
+
+
+
+
H
M
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
PrCuPrCu22
+
+
+
+
+
+
+
+
+
+
+
+
ij
jiijQ OOCH )()( 22
22 JJ
Ferroquadrupolarer (Cij>0) Austausch (durch CF-Phonon WW)
www.mcphase.de
Settai et. al. JPSJ 67 (1998) 636 012
TO
022
TO02
2 T
O
GMS
Settai et. al. JPSJ 67 (1998) 636
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
PrCuPrCu22
ij
jiijQ OOCH )()( 22
22 JJ
Ferroquadrupolar (Cij>0) Interaction
Settai et. al. JPSJ 67 (1998) 636
The Model describes well:• the quadrupolar phasen diagram• the magnetisation• the magnetostriction• die temperature dependence of elastic constants
Whats about the Dynamics ?
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Orbital Excitations (Orbitonen)Orbital Excitations (Orbitonen)
ij
jiQ OOCH )()( 22
22 JJ
+Antiferroquadrupolar (C<0) Interaction
+
+
+
+
+
+
+
+
+
+
Crystal field ilm
iml
mlcf OBH
,
)(JE
Q
4f – charge density
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
PrCuPrCu22
+
+
+
+
+
+
+
+
+
+
+
+
ij
jiijQ OOCH )()( 22
22 JJ
Ferroquadrupolar (Cij>0) Interaction (via CF-Phonon coupling)
Settai et. al. JPSJ 67 (1998) 636
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
McPhase: www.mcphase.de Rotter, JMMM 272-276 (2003) 481
Г
00L
Ene
rgy
(meV
)
2.5
01 2
Experiment
Kawarazaki et. al., J. Phys. Cond. Mat. 7 (1995) 4051
PrCuPrCu2 2
Orbital Modes T=5 K, H=0 TOrbital Modes T=5 K, H=0 T
MF-RPA Model
?
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
[Interpretation von Kawarazaki et. al., J. Phys. Cond. Mat. 7 (1995) 4051]
Könnte nicht auch die Austauschwechselwirkungzu der beobachteten Dispersion führen ?
PrCuPrCu22
Г
00L
Ene
rgy
(meV
)
2.5
Nur Quadrupolaustausch
01 2
Magnetic ExcitationsRotter et. al., Europ. Phys. J. B 14 (2000) 29
NdCu2NdCu2
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
PrCuPrCu22
Nur Quadrupolaustausch
00L
Ene
rgy
(meV
)
2.5
+ magnetic Interactions
ij
jiex ijJH SS)(2
1
01 2
ij
jiQ OOCH )()( 22
22 JJ
Г
00L
Ene
rgy
(meV
)
2.5
Quadruplar Interaction only
01 2
nurmagnetischer
Austausch
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Messung
PrCuPrCu2 2 Orbital modes in Magnetic field Orbital modes in Magnetic field
T=2 K, H||a T=2 K, H||a
McPhase: www.mcphase.de Rotter, JMMM 272-276 (2003) 481
IN12(ILL) März 2004(15 Tesla cryomagnet)
Rechnung
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The model describes well:• macroscopic properties and quadrupolar Phase diagram• Magnitude of dispersion of orbital modes
Quadrupolar Effects Neutrons can be scattered by 4f - Orbitons – Orbiton spectroscopy:
- Determination of multipolar Interactions- Modeling of GMS
ij
jiijQ OOCH )()( 22
22 JJ
Crystal field + Ferroquadrupolar (Cij>0) InteractionsSettai et. al. JPSJ 67 (1998) 636
PrCu2
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
How to start – the story of NdCuHow to start – the story of NdCu22 Suszeptibility: 1/χ(T) at high T
... Crystal Field Parameters B20, B2
2
Specific Heat Cp ... first info about CF levels Magnetisation || a,b,c on single crystals in the paramagnetic state, ... ground state matrix elements Neutron TOF spectroscopy – CF levels
... All Crystal Field Parameters Blm
Thermal expansion in paramagnetic state – CF influence
... Magnetoelastic parameters (dBlm/dε)
Neutron diffraction: magnetic structure in fields || easy axis ... phase diagram H||b - model
... Jbb Neutron spectroscopy on single crystals in H||b=3T
... Anisotropy of Jij - determination of Jaa=Jcc
Magnetostriction ... Confirmation of phase diagram models H||a,b,c, dJ(ij)/dε
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The story of NdCuThe story of NdCu22
Inverse suszeptibility at high T
... B20=0.8 K, B2
2=1.1 K Hashimoto, Journal of Science of the
Hiroshima University A43, 157 (1979)
)(10
)32)(12()0()1(
3
15
)32)(12()0()1(
3
1
)(10
)32)(12()0()1(
3
1
22
02
02
22
02
BBJJ
qJJJk
BJJ
qJJJk
BBJJ
qJJJk
c
b
a
Θabc
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The story of NdCuThe story of NdCu22
Specific haet Cp and entropy – first info about levels
Rln2
Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
How to start analysis – the story of How to start analysis – the story of NdCuNdCu22
Magnetization: Kramers ground state doublet |+-> matrix elements
Module cfield can also calculate magnetization using a full set of CF parameters
P. Svoboda et al. JMMM 104 (1992) 1329
5.1/
8.2/
1.2/
,,
))2/()(tanh(
xJc
zJb
yJa
BB
Jgg
Jgg
Jgg
cba
kTMHggM
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
How to start analysis – the story of How to start analysis – the story of NdCuNdCu22
Neutron TOF spectroscopy – CF levels
... Blm
Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297
B20=1.35 K
B22=1.56 K
B40=0.0223 K
B42=0.0101 K
B44=0.0196 K
B60=4.89x10-4 K
B62=1.35x10-4 K
B64=4.89x10-4 K
B66=4.25 x10-3 K
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The story of NdCuThe story of NdCu22 Thermal expansion – cf influence
... Magnetoelastic parameters (A=dB20/dε, B=dB2
2/dε)
E. Gratz et al., J. Phys.: Condens. Matter 5, 567 (1993)
Neutron diffraction+ magnetization: magstruc, phasediag H||b-> model
... Jbb
The story of NdCuThe story of NdCu22
f(B) [arb.units] T=0K
B
F1
F2
F3
BcAF1 F3
Bc1
Bc2
Bc3
AF1
n(k)=sum of Jbb(ij) with ij being of bc plane k
M. Loewenhaupt et al., Z. Phys. B: Condens. Matter 101, 499 (1996)
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
NdCuNdCu22 Magnetic Phase Diagram Magnetic Phase Diagram
F3
AF1
F1
output file: mcphas.xytUse module phased or displaycontour for color plot of phasediagram
ab
c
F1
lines=experiment
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
The story of NdCuThe story of NdCu22
Neutron spectroscopy on single crystals in H||b=3T
... Anisotropy of J(ij) - determination of Jaa=Jcc
F3
M. Rotter et al., Eur. Phys. J. B 14, 29 (2000)
Jaa=Jcc(R)
NdCuNdCu22F3
AF1
F1
M. Rotter, et al. Applied Phys. A 74 (2002) s751
How to start analysis – the story of How to start analysis – the story of NdCuNdCu22
Magnetostriction ... Confirmation of phasediagram model for H||a,b,c, and determination of dJ(ij)/dε
M. Rotter, et al. J. of Appl. Physics 91 10(2002) 8885
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
„„The Standard Model of Rare Earth Magnetism has been well The Standard Model of Rare Earth Magnetism has been well established and can describe the magnetic properties of Rare earth established and can describe the magnetic properties of Rare earth
compounds. There is no need for a program like McPhase.“compounds. There is no need for a program like McPhase.“
Nonsense !• In very few RE systems a large number of results of the SM have been
compared to experimental data: e.g. the full magneto-striction tensor has been analysed only in 1 case (NdCu2)
• Quadrupolar Excitations have not been compared to the SM
• There is a number of wrong predictions of the SM: e.g. -magnetoelastic paradoxon in L=0 AF-systems-extra magnetic modes or no modes (CeCu2, CeNi9Ge4,
Nd2CuO4),-wrong saturation moments, e.g. in Eu-Skutterudite- ...
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
Exchange-Striction
Orthorhombic Distortion
Standard Model of RE Mag... McPhase SimulationHH JJJJ
JJJJ
JJJJ
,)100(,)010(
)100()010(
)100()010(
~
))((
))((
TiiTiibbaa
iiiibbaa
iiiiibbaa
elex
B
A
EHH
?
The magnetoelasticThe magnetoelastic Paradoxon Paradoxon
for L=0for L=0demonstrateddemonstrated at at GdNi2B2C
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
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
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
and much more....
Magnetostriction
Crystal Field/Magnetic/Orbital Excitations
McPhase - the World of Rare Earth MagnetismMartin Rotter - McPhase Course TU Dresden 2005
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, R. Schedler, Institut für Festkörperphysik, Technische Universität Dresden, Germany
P. Fabi né Hoffmann, Forschungszentrum Jülich, Germany S. Rotter, Wien, Austria
M.Banks, Max Planck Institute Stuttgart, Germany
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
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