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
M. Zschintzsch, ISP TU-Dresden, Germany
B. Beuneu, LLB – Saclay, France
M el Massalami, UFRJ, Brazil
J. Prokleska, Charles University, Prague, CZ
A. Kreyssig, IOWA State University, Ames, US
Martin Rotter,MSL2009
STANDARD MODEL OF RARE EARTH MAGNETISM
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
Crystal Field Effect
Fundamental
interest:
• largest spinCe,Pr,Nd,
value in
Sm,Er,
+ table
Tm,Yb
Tb,Dy,Ho
periodic
(S=7/2)
>0
<0
Technical interest:
• Giant Magnetocaloric
eEffect
• Giant Magnetostriction
+
L0
Distortion of 4f – Charge Density
Martin Rotter,MSL2009
NO Crystal Field Effect
+
Gd3+,Eu2+
=0
e-
+
L=0
Spherical 4f-Charge Density
STANDARD MODEL OF RARE EARTH MAGNETISM
microscopic origin of magnetostriction =
strain dependence of magnetic interactions
1) Single ion effects
cos(2 k
 ij
| ri  r j |)

3
 Crystal Field
Striction
| ri  r j |
RKKY
F
kT >>cf
T >TN
 Exchange Striction
a
kT <cf
T >TN
T <TN
T <TN
2) Two ion effects
H
…spontaneous
magnetostriction
T <TN
…forced
magnetostriction
T <TN
H
M. Doerr, M. Rotter, A. Lindbaum,
in Rare Earth based Antiferromagnets
| ri  r jMagnetostriction
|
a
Adv. Phys. 54 (2005) 1-66
Martin Rotter,MSL2009
Exchange striction on a Square Lattice
H  E H
(e  0 )   e
 ...
  ( H ma g )
el
e
mag

Elastic Energy
E el 
1
2
 c e

e
Minimize Free Energy

F   k B T ln Z

Magnetic Energy
H mag  
1
2

 J ( ij , e ) J
i
J
F
j
e

Z  Tr {e
 H / k BT
 0
ij
e



k
 J (i , i  k )
e

 J i J i  k  T ,H
Ferromagnet: J1>0
dV/V>0
No distortion (dJ1/de)
J11
Martin Rotter,MSL2009
}
Anti-Ferromagnet with
NN exchange: J1<0
dV/V<0
No distortion (dJ1/de)
JJ11
JJ22
J11
Martin Rotter,MSL2009
Anti-Ferromagnet
With small |J1|
J2<0
dV/V=0
Tetragonal
Distortion (dJ1/de) !!!
How to detect a
symmetry breaking distortion ?
.
.THE MAGNETOELASTIC
PARADOX
.
.
Anti-Ferromagnet
M. Rotter et al. Europhys. lett. 75 (2006) 160-166
Antiferromagnets with L=0 below TN:
Intensity
..
. .
Symmetry breaking distortions are expected
but
Tetragonal
have
NOT been found
Distortion !!!
.
. .
J
.
J11
  2 d sin 
2theta
.... ALL Experiments: symmetry breaking distortion e <10-4
How to measure
Magnetostriction
?
Experimental
Methods
X-ray Powder
Diffraction
• Anisotropic Effects on
Polycrystals (Expansion,
Symmetry-Changes)
• bad resolution (10-4 in dl/l)
Martin Rotter,MSL2009
•
•
•
•
Capacitance
Dilatometry
• Good resolution (10-9 in dl/l)
• 45 T Magnetic Fields - forced
magnetostriction
• requires single crystals
Rotter et.al. Rev. Sci. Instr. 69 (1998) 2742
Patent by M Rotter 2006
Optional use in PPMS, VTIs,...
Operated at 14 institutes in A, CH, D, CZ, Brazil, US,UK
GdNi2B2C
TN= 20 K: M||[010]
<TR= 14 K: M||[0yz]
q = (0.55 0 0)
?
small magnetostriction, therefore cap.-dilatometry ....
Martin Rotter,MSL2009
GdNi2B2C
TN= 20 K: M||[010]
<TR= 14 K: M||[0yz]
q = (0.55 0 0)
2T||a
a/a
10-4
1.5T
TN
Orthorh.
distortion !
0.75T
0T
5
10
15
20
25
T (K)
Thermal
Expansion
Forced Magnetostriction
Martin Rotter,MSL2009
The Magnetoelastic
Paradox
Orthorhombic Distortion
-25
J1
.... demonstrated
at GdNi2B2C
ea-eb
J2
3x10
-4
2x10
-4
1x10
-4
T=2K
-20
?
-15
-10
-5
0
Rotter et al. EPL 75 (2006) 160
0
2
4
6
8 10 12 14
0
0H||a (T)
H  H mag  Eel 
  A(e aa  e bb )( J i J i  (100)  J i J i  ( 010) ) 
i
 B (e aa  e bb )( J i J i  (100)  J i J i  ( 010) )

Standard Model of RE Mag
... McPhase Simulation
e aa  e bb ~  J i J i  (100) T ,H   J i J i  ( 010) T ,H
Martin Rotter,MSL2009
Double Q structure
Orthorhombic Distortion
b
-25
T=2K
-4
3x10
-20
-4
ea-eb
2x10
a
-15
-4
-10
1x10
• Dipolar easy plane
anisotropy
• Landau Expansion: M4
term stabilizes double q
structure !
The Magnetoelastic
Paradox explained !?
-5
0
0
2
4
6
8 10 12 14
0H||a (kOe)
Standard Model of RE Mag
... McPhase Simulation
J. Jensen&M. Rotter PRB 77 (2008) 134408
[What if dipolar anisotropy favors
moments along c ?]
0
e aa  e bb ~  J i J i  (100 ) T , H   J i J i  ( 010 ) T ,H
Up
to now (despite some attempts) no experimental
Martin Rotter,MSL2009
verification of double q order– work in progress !
Status of Research on Magnetostriction in Gd based Antiferromagnets. Systems with a
symmetry breaking magnetic propagation vector and large spontaneous magnetostriction demonstrate
the existence of the magnetoelastic paradox and are marked by "MEP".
Symmetry Magnetic
Anisotropic/
Single
Forced
/
Propagation
isotropic(dV/V)
Crystal
MagnetoNeel
Spontaneous
available
-striction
-3)
Temp.(K)
Magnetostriction (10
GdIn3
cub./43 [12] (1/2 1/2 0) [13] MEP!
0.0/~-0.3 [14]
yes
GdCu2In
cub./10
(1/3 1 0) [R18]
0.0/-0.1 [15]
GdPd2In
cub./10 [16]
0.0/0.0 [15]
GdAs
cub./25
(3/2 3/2 3/2) [17, 18, 19] [17]no MEP ?
GdP
cub./15
(3/2 3/2 3/2) [17] [17]
GdSb
cub./28
(3/2 3/2 3/2) [20]
? [21, 22]no MEP?
Yes
work in progress
GdSe
cub./60
(3/2 3/2 3/2) [20]
GdBi
cub./32
(3/2 3/2 3/2) [20]
[21]no MEP ?
GdS
cub./50
(3/2 3/2 3/2) [20]
EuTe
cub./9.8
(3/2 3/2 3/2) [23]
[23]
GdTe
cub./80
(3/2 3/2 3/2) [20]
GdAg
cub./133
(1/2 1/2 0) [24]
GdBe13
cub./27
(0 0 1/3) [25]
Gd2Ti2O7 cub./1
(1/2 1/2 1/2) [26]
yes
GdB6
cub./16
(1/4 1/4 1/2) [27]
yes
Gd2CuGe3 hex./12 [28]
GdGa2
hex./23.7
(0.39 0.39 0) [29]
GdCu5
hex./26
(1/3 1/3 0.22) [29]
Gd5Ge3
hex./79 [30] (0.35 0 0)
work in progress
yes
work in progress
Gd7Rh3
hex./140 [31, 32]
Gd2PdSi3 hex./21 [33]
work in progress
yes
GdCuSn
hex./24
(0 1/2 0) [34] MEP!
1.9/-0.5 [35]
GdAuSn
hex./35 [34] (0 1/2 0) [36]
GdAuGe
hex./16.9 [37]
GdAgGe
hex./14.8 [38]
GdAuIn
hex./12.2 [38]
GdAuMg
hex./81 [39]
GdAuCd
hex./66.5 [40] (1/2 0 1/2) [40]
GdAg2
tetr./23
(1/4 2/3 0) [R12] MEP!
1.2/0.0 [R19]
/
Propagation
Neel
Temp.(K)
Gd2Ni2Cd tetr./65 [41]
Gd2Ni2Mg tetr./49 [42]
Gd2Pd2In tetr./21 [43]
GdNi2B2C tetr./20
(0.55 0 0) [44] MEP!
GdAu2
tetr./50
(5/6 1/2 1/2) [R12]
GdB4
tetr./42
(1 0 0) [45]
GdRu2Si2 tetr./47 [46] (0.22 0 0)
MEP!
GdRu2Ge2 tetr./33 [46] work in progress
GdNi2Si2
tetr./14.5
(0.21 0 0.9) [47]
GdNi2Sn2 tetr./7 [48]
GdPt2Ge2 tetr./7 [48]
GdCo2Si2 tetr./45 [48]
GdAu2Si2 tetr./12
(1/2 0 1/2) [R12]
GdPd2Ge2 tetr./18 [48]
GdPd2Si2 tetr./16.5 [49]
GdIr2Si2
tetr./82.4 [49]
GdPt2Si2
tetr./9.3 [49] (1/3 1/3 1/2) [50]
GdOs2Si2 tetr./28.5 [49]
GdAg2Si2 tetr./10 [48]
GdFe2Ge2 tetr./9.3 [51, 52]
GdCu2Ge2 tetr./15 [51]
GdRh2Ge2 tetr./95.4 [51]
GdRh2Si2 tetr./106 [49]
GdCu2Si2 tetr./12.5
(1/2 0 1/2) [47]
GdPt3Si
tetr./7.5 [53] work in progress
GdCu(FeB) orth./45
(0 1/4 1/4) [54]
Gd3Rh
orth./112 [55]
Gd3Ni
orth./100 [57]
Gd3Co
orth./130 [58, 59]
GdSi2
orth.(<818K)/? [60]
GdSi
orth./55 [61] work in progress
GdCu6
orth./16 [62] work in progress
GdAlO3
orth./3.9 [63]
GdBa2Cu3O7 orth./2.2
(1/2 1/2 1/2) [64] [65]
GdPd2Si
orth./13 [66]
isotropic(dV/V)
Spontaneous
Magnetostriction (10-3)
Crystal
available
Magneto-striction
0.1/0.0 [R19, R20]
0.0/0.0 [R19]
yes
[R4]
-0.6/-0.8
work in progress
yes
in progress
yes
work in progress
19/-2 [54]
MEP ? 6.4/2.1 [56]
MEP ? 4.5/2.9 [56]
work in progress
Summary on the MEP
 prevalence of double-q structures might explain the
magnetoelastic Paradox – experimental verification by
scattering techniques ?
 GdNi2B2C: large distortion at small fields - is this common to
other high spin value AFM ? ... implication on magnetostrictive
technology ?
 Magnetoelastic Coupling = long wave length limit of electron
phonon interaction ... relevance for superconductivity ?
Martin Rotter,MSL2009