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The Magnetoelastic Paradox
M. Rotter, A. Barcza, IPC, Universität Wien, Austria
H. Michor, TU-Wien, Austria
A. Lindbaum, FH-Linz, Austria
M. Doerr, M. Loewenhaupt, IFP TU-Dresden, Germany
B. Beuneu, LLB – Saclay, France
M el Massalami, UFRJ, Brazil
2M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
1. Magnetostriction Measurements
2. Magnetostriction in the Standard
Model of Rare Earth Magnetism
3. The Magnetoelastic Paradox (MEP)
4. Experimental Evidence for the MEP
in Gd Compounds
5. Application of Magnetic Fields - the
case of GdNi2B2C
6. Outlook
3M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Experimental Methods1cm
Capacitance Dilatometry
X-ray Powder Diffraction
• Good resolution (10-9 in dl/l)• 45 T Magnetic Fields - forced magnetostriction
• requires single crystals
• Anisotropic Effects on Polycrystals (Expansion, Symmetry-Changes)• bad resolution (10-4 in dl/l)
Rotter et.al. Rev. Sci. Instr. 69 (1998) 2742
Magnetostriction Measurements
4M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
X Axis
0 30 60 90 120 150 180 210 240 270
a [Å
]
4,154
4,156
4,158
4,160
4,162
T(K)
0 30 60 90 120 150 180 210 240 270
c [Å
]
9,600
9,604
9,608
9,612
9,616
9,620
Debye fit for T > 47 K
Debye fit for T > 47 K
TN=47 KGdRu2Si2
95,7 96,0 96,3 96,6 96,9
50
100
150
200
250
300
Inte
nsi
ty (
cou
nts
)
2*Theta(deg)
60K 10K(008)
GdRuSi
5M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
55,6 55,8 56,0 56,2
25
50
75
100
125
150
Inte
nsi
ty (
cou
nts
)2*Theta(deg)
60K 10K
(202)
74,4 74,7 75,0 75,3 75,6
50
100
150
200
250
300
Inte
nsi
ty (
cou
nts
)
2*Theta(deg)
60K 10K(220)
GdRu2Si2
? ?
No sign of distortion of the tetragonal plane !
6M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Crystal Field
T
e-
+
+
L0
T<TC(N)
Spontaneous Magnetostriction
STANDARD MODEL OF RARE EARTH MAGNETISMMicroscopic Origin of Magnetostriction:
Strain dependence of magnetic interactions
Exchange
T<TC(N) L=0, L0
„exchange-striction“
T
Gd3+, S=7/2, L=0
7M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
No distortion (dJ1/d)
ij
jimag ijJH JJ),(2
1
kT k i i
k i i JH J J,
) , (
...)0()(
magH
magel HEH
cEel 2
1
}{ / TkH BeTrZ ZTkF B ln 0
F
Ferromagnet: J1>0dV/V<0
J1J1
Exchange striction on a Square Lattice
8M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
No distortion (dJ1/d)
Anti-Ferromagnet withNN exchange: J1<0dV/V>0
Tetragonal Distortion (dJ1/d) !!!
Anti-FerromagnetWith small |J1|J2<0dV/V=0
J1J1
J2
J1
J2
J1
THE MAGNETOELASTIC PARADOX
Antiferromagnets with L=0 below TN:
Symmetry breaking distortions are expectedbut
have NOT been found
.... but in ALL experiments: distortion <10-4
9M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
TN= 24 K q=(0 ½ 0)
GdCuSn
10M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
TN= 22.7 K
<TR1=21.2K M||[001]<TR2=10.8K M||[110]
GdAu2
TN= 50 K
GdAg2
q=(0.362 0 1)
11M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Gd3Rh TN=112 K
Large magnetostrictive effects on lattice constants – but NO distortion
Gd3NiTN=100 K
12M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Spontaneous Magnetoelastic Effects in Gd Compounds A. Lindbaum, M. Rotter Handbook of Magnetic Materials Vol 14 (Buschow, Elsivier,NL)
Volume Magnetostriction
13M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Spontaneous Magnetoelastic Effects in Gd Compounds A. Lindbaum, M. Rotter Handbook of Magnetic Materials Vol 14 (Buschow, Elsivier,NL)
Anisotropic Spontaneous Magnetostriction
FerromagnetAntiferromagnetε
TC(N)[K]
cbas V
dV
s
ds
,,
|3
|
14M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0)
small magnetostriction, therefore cap.-dilatometry ....
GdNi2B2C
?
15M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Thermal Expansion
5 10 15 20 25
0T
2T||a
TN
1.5T
0.75T
T (K)
Forced Magnetostriction
Orthorh.distortion !
10-4
a/a
TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0)
GdNi2B2C
16M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
At H=0: Domains ?
distortion =3x10-4 would lead to FWHM (204)+ 0.1° FWHM (211)+ 0.05°
at H=0 no distortioncan be found
GdNi2B2C
Powder Xray Diffraction
.... FWHM determined by fitting
?
17M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
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
www.mcphase.de
18M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
iiBJ
ijji
ijjimag
g
ijJ
ijJH
CD
HJ
JJ
JJ
)(2
1
),(2
1
The magnetic Hamiltonian
Isotropic exchange (RKKY,...)
Classical Dipole Interaction
Zeeman Energy
5
22
||
||))((3)()(
ji
jijijiBJ
RRRRgijJ
CD RR
RR
0 5 10 15 20 25 30
0,0
0,5
1,0
1,5 Experiment McPhase Calc. GdNi
2B
2C
c P/T
(J/m
olK
2 )
T(K)
Angle 2(°)
4 6 8 10 12 14 16 18 20
Inte
nsi
ty (
co
un
ts)
-2000
0
2000
4000 T=2.2K
nuc
(0.4
55 1
2)
(0.5
45 1
2)
(0.4
55 0
3)
(0.5
45 0
2)
(0.6
36 0
1)(0
.455
0 1
)(0
.545
0 0
)
magT=2 K0 2 4 6 8 10 12 14
0
1x10-4
2x10-4
3x10-4
0
-5
-10
-15
-20
-25
T = 2 K
a- b
0H||a (T)
Hmag
+McPhase
?
20M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
0 2 4 6 8 10 12 14
0
1x10-4
2x10-4
3x10-4
0
-5
-10
-15
-20
-25
T = 2 K
a- b
0H||a (T)
Orthorhombic Distortion
Standard Model of RE Mag... McPhase Simulation
HH JJJJ
JJJJ
JJJJ
,)010(,)100(
)010()100(
)010()100(
~
))((
))((
TiiTiibbaa
iiiibbaa
iiiiibbaa
elmag
B
A
EHH
?
The Magnetoelastic Paradox for L=0
.... demonstrated at GdNi2B2C
Capacitance D
ilatometry
Exchange Striction Model
21M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
• Transmutation of Gd
New Methods
Neutron Scattering
• Imaging of AFM domains with XRMS
GdNi2Ge2 ab-plane T = 17 K
Mom
ent d
irect
ion
200 µm
• Anisotropy Measurements by ESR
More Experiments• Powder X-ray Diffraction• Magnetic Neutron / X-ray
Scattering• Dilatometry in high
Fields
ToDo
More Theory• Apply Standard model
of RE Magnetism• Ab initio Calculation on
MEP
Anharmonicity of lattice dynamics
+ Small contribution of band electrons
anharmonic Potential
Harmonic potential
with Debye function
)/(22
1 TTDKTK Dphonel
z
xe
dxx
zzD
0
3
3 1
3)(
Normal thermal Expansion
23M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
H <0
Crystal Field
e-
+
+
Exchange - Striction
H
H>0
Forced Magnetostriction
L0 L=0, L0
Gd3+, S=7/2, L=0
24M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006
Theory 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
1with
}{ / TkH BeTrZ ZTkF B ln 0
F