The%20Magnetoelastic%20Paradox

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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
• 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
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STANDARD MODEL OF RARE EARTH MAGNETISM
Crystal Field Effect
NO Crystal Field Effect
Sm,Er, Tm,Yb ?gt0
Ce,Pr,Nd, Tb,Dy,Ho ?lt0

Gd3,Eu2 ?0

e-
e-


L0
L?0
Spherical 4f-Charge Density
Distortion of 4f Charge Density
Martin Rotter,MSL2009
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STANDARD MODEL OF RARE EARTH MAGNETISM
microscopic origin of magnetostriction
strain dependence of magnetic interactions
1) Single ion effects 2) Two ion
effects ? Crystal Field Striction ?
Exchange Striction
spontaneous magnetostriction
forced magnetostriction
a
kT lt?cf
M. Doerr, M. Rotter, A. Lindbaum,
Magnetostriction in Rare Earth based
Antiferromagnets Adv. Phys. 54 (2005) 1-66
Martin Rotter,MSL2009
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Exchange striction on a Square Lattice
Elastic Energy
Minimize Free Energy
Magnetic Energy
Ferromagnet J1gt0 dV/Vgt0
No distortion (dJ1/de)
Martin Rotter,MSL2009
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Anti-Ferromagnet with NN exchange J1lt0 dV/Vlt0
No distortion (dJ1/de)
Martin Rotter,MSL2009
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How to detect a symmetry breaking distortion ?
THE MAGNETOELASTIC PARADOX M. Rotter et al.
Europhys. lett. 75 (2006) 160-166 Antiferromagnets
with L0 below TN Symmetry breaking
distortions are expected but have NOT been found
Intensity
2theta
.... ALL Experiments symmetry breaking
distortion ? lt10-4
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How to measure Magnetostriction ?
Experimental Methods
Capacitance Dilatometry
X-ray Powder Diffraction

• Anisotropic Effects on
• Polycrystals (Expansion,
• Symmetry-Changes)
• bad resolution (10-4 in dl/l)

• 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

Martin Rotter,MSL2009
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GdNi2B2C
TN 20 K M010 ltTR 14 K M0yz q
(0.55 0 0)
small magnetostriction, therefore
cap.-dilatometry ....
Martin Rotter,MSL2009
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GdNi2B2C
Da/a
TN 20 K M010 ltTR 14 K M0yz q
(0.55 0 0)
10-4
Martin Rotter,MSL2009
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The Magnetoelastic Paradox ....
demonstrated at GdNi2B2CRotter et al. EPL 75
(2006) 160
Orthorhombic Distortion
?
Exchange Striction Model
Capacitance Dilatometry
Standard Model of RE Mag ... McPhase Simulation
Martin Rotter,MSL2009
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Double Q structure
Orthorhombic Distortion
b

T
2 K
Exchange Striction Model
Exchange Striction Model
b
e
-
a

e
a
Capacitance Dilatometry

• Dipolar easy plane anisotropy
• Landau Expansion M4 term stabilizes double q
  structure !
• The Magnetoelastic Paradox explained !?
• J. JensenM. Rotter PRB 77 (2008) 134408
• What if dipolar anisotropy favors moments along
  c ?

m
H
a
(kOe)
0
Standard Model of RE Mag ... McPhase Simulation
Up to now (despite some attempts) no experimental
verification of double q order work in progress !
Martin Rotter,MSL2009
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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
Magneto- Neel Spontaneous available
-striction Temp.(K) Magnetostriction
(10-3) 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 17no MEP ? GdP cub./15 (3/2 3/2 3/2)
17 17 GdSb cub./28 (3/2 3/2 3/2) 20 ?
21, 22no 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 21no 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 Gd2Ni2-xIn
tetr./20 R19 0.8/0.0 R19
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Symmetry Magnetic Anisotropic/ Single
Forced / Propagation isotropic(dV/V)
Crystal Magneto- Neel Spontaneous
available -striction Temp.(K)
Magnetostriction (10-3) Gd2Ni2Cd tetr./65
41 Gd2Ni2Mg tetr./49 42 Gd2Pd2In tetr./21
43 GdNi2B2C tetr./20 (0.55 0 0) 44 MEP!
0.1/0.0 R19, R20 yes R4 GdAu2 tetr./50
(5/6 1/2 1/2) R12 0.0/0.0 R19 GdB4
tetr./42 (1 0 0) 45 GdRu2Si2 tetr./47 46
(0.22 0 0) MEP! -0.6/-0.8 yes in
progress GdRu2Ge2 tetr./33 46 work in
progress 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
19/-2 54 Gd3Rh orth./112 55 MEP ? 6.4/2.1
56 Gd3Ni orth./100 57 MEP ? 4.5/2.9
56 Gd3Co orth./130 58, 59 GdSi2
orth.(lt818K)/? 60 GdSi orth./55 61 work in
progress work in progress yes 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
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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