1. 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

2. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
Magnetostriction Measurements
Magnetostriction in the Standard Model of Rare Earth Magnetism
The Magnetoelastic Paradox (MEP)
Experimental Evidence for the MEP in Gd Compounds
Application of Magnetic Fields - the case of GdNi2B2C
Outlook
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

3. How to measure Magnetostriction ?
Experimental Methods
X-ray Powder Diffraction
Capacitance Dilatometry
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 submitted, optional use in PPMS, VTIs,...
operated at 6 institutes in A, D, CZ, Brazil, US)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

4. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdRu2Si2 Gd Ru Si
(008)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

5. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdRu2Si2
(220)
(202) ? ?
No sign of distortion of the tetragonal plane !
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

6. Spontaneous Magnetostriction
STANDARD MODEL OF RARE EARTH MAGNETISM
Microscopic Origin of Magnetostriction:
Strain dependence of magnetic interactions
Spontaneous Magnetostriction
Crystal Field
Exchange T T
L0
T<TC(N)
L=0, L0 +
T>TC(N)
T<TC(N) e-
„exchange-striction“ +
Gd3+, S=7/2, L=0
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

7. Exchange striction on a Square LatticeJ1 J1
Ferromagnet: J1>0
dV/V<0
No distortion (dJ1/de)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

8. THE MAGNETOELASTIC PARADOX Antiferromagnets with L=0 below TN: J1
THE MAGNETOELASTIC PARADOX
Antiferromagnets with L=0 below TN:
Symmetry breaking distortions are expected
but
have NOT been found J1
Anti-Ferromagnet with
NN exchange: J1<0
dV/V>0
No distortion (dJ1/de) J2 J1 J2 J1
Tetragonal
Distortion (dJ1/de) !!!
Anti-Ferromagnet
With small |J1|
J2<0
dV/V=0
.... but in ALL experiments: distortion  <10-4
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

9. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdCuSn
TN= 24 K q=(0 ½ 0)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

10. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdAg2
TN= 22.7 K
<TR1=21.2K
M||[001]
<TR2=10.8K
M||[110]
GdAu2
TN= 50 K
q=( )
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

11. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
Gd3Ni
Gd3Rh
TN=112 K
TN=100 K
Large magnetostrictive effects on lattice constants – but NO distortion
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

12. Volume Magnetostriction
Spontaneous Magnetoelastic Effects in Gd Compounds
A. Lindbaum, M. Rotter Handbook of Magnetic Materials Vol 14 (Buschow, Elsivier,NL)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

13. Anisotropic Spontaneous Magnetostriction
Ferromagnet
Antiferromagnet ε
TC(N)[K]
Spontaneous Magnetoelastic Effects in Gd Compounds
A. Lindbaum, M. Rotter Handbook of Magnetic Materials Vol 14 (Buschow, Elsivier,NL)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

14. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdNi2B2C
TN= 20 K: M||[010]
<TR= 14 K: M||[0yz]
q = ( ) ?
small magnetostriction, therefore cap.-dilatometry ....
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

15. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdNi2B2C
Forced Magnetostriction
Thermal
Expansion 5 10 15 20 25 0T
2T||a TN
1.5T
0.75T
T (K)
Da/a
Orthorh.
distortion !
TN= 20 K: M||[010]
<TR= 14 K: M||[0yz]
q = ( )
10-4
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

16. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdNi2B2C
.... FWHM determined by fitting ?
At H=0: Domains ?
Powder Xray Diffraction
distortion e=3x10-4
would lead to
FWHM (204)+ 0.1°
FWHM (211)+ 0.05°
at H=0
no distortion
can be found
(magnetoelastic
paradox)
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

17. 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
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

18. The magnetic Hamiltonian
Isotropic exchange (RKKY,...)
Classical Dipole Interaction
Zeeman Energy
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

19. Hmag +
McPhase ?
T=2 K

20. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
Orthorhombic Distortion
The Magnetoelastic Paradox for L= demonstrated at GdNi2B2C Rotter et al. EPL 75 (2006) 160 ?
Exchange Striction Model
Capacitance Dilatometry
Standard Model of RE Mag
... McPhase Simulation
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

21. Status of Research on Magnetostriction in Gd based Antiferromagnets
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 [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 ( ) [29]
GdCu5 hex./26 (1/3 1/3 0.22) [29]
Gd5Ge3 hex./79 [30] work in progress yes work in progress
Gd7Rh3 hex./140 [31, 32]
Gd2PdSi3 hex./21 [33] 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]

22. 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 ( ) [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] work in progress work in progress yes work in progress
GdRu2Ge2 tetr./33 [46] work in progress work in progress
GdNi2Si2 tetr./14.5 ( ) [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.(<818K)/? [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]

23. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
The following compounds are not expected to show a change in lattice symmetry at the transition from the paramagnet to the antiferromagnet, because the propagation vector does not break the symmetry of the lattice and there is only one atom in the primitive crystallographic unit cell. Therefore they cannot exhibit the
magnetoelastic paradox.
Symmetry Magnetic Anisotropic/ Single Forced
/ Propagation isotropic(dV/V) Crystal Magneto-
Neel Spontaneous available -striction
Temp.(K) Magnetostriction (10-3)
GdNi2Ge2 tetr./27 ( ) [67]
GdCo2Ge2 tetr./37.5 [51] ( ) [68]
In the following compounds the propagation does not break the crystal symmetry and there are more than one atom in the primitive crystallographic unit cell. In this case it depends on the relative orientiation of the moments in the unit cell, whether a symmetry breaking distortion is predicted by the exchange striction model or not. Therefore these compounds can in principle exhibit the magnetoelastic paradox although the propagation does not break the crystal symmetry of the lattice.
Gd2Sn2O7 cub./1 (0 0 0) [69] yes
Gd2In hex./100 (0 0 1/6) [70] 0.0/0.0 [R19]
Gd2CuO4 tetr./6.4 (0 0 0) [71]
GdCu2 orth./42 (1/3 0 0) [R21] 4.6/0.6 [72] yes [R22]
Gd5Ge4 orth./130 [11] (0 0 0) [73] ?/<0.1 [74] yes [74]
GdNi0:4Cu0:6 orth./63 (0 0 1/4) [75] 0.0/0.8 [76]
Gd2S3 orth./10 [77] (0 0 0) [78] 0.0/0.0 [79] yes [79]
GdNiSn orth./11 [80] (0 0 0) [81] yes
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

24. Summary and outlook THE MAGNETOELASTIC PARADOX
Antiferromagnets with L=0 below TN:
Symmetry breaking distortions are expected
but
have NOT been found
GdNi2B2C: large distortion at small fields - is this common to all Gd AFM ? ... implication on magnetostrictive technology ?
Magnetoelastic Coupling = long wave length limit of electron phonon interaction ... relevance for superconductivity ?
Note: MnO shows trigonal spontaneous distortion at TN
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

25. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
ToDo
New Methods
Imaging of AFM domains
with XRMS
GdNi2Ge2 ab-plane T = 17 K
Moment direction
200 µm
More Experiments
Powder X-ray Diffraction
Magnetic Neutron / X-ray Scattering
Dilatometry in high Fields
More Theory
Apply Standard model of RE Magnetism
Ab initio Calculation on MEP
Magnetoelastisches Paradoxon = keine Änderung der Symmetrie der Kristallstruktur durch antiferromagnetische Ordnung in Gd-Verbindungen
Viele (ca 7) Fälle untersucht mit großen magnetostriktiven Effekten, aber keine Symmetrieänderung der Struktur bei TN
Gegensatz zu Theorie (Austauschstriktion)
GdNi2B2C:
erstes und einziges Beispiel für Messung der Symmetrieänderung in abh. Magnetfeld
Verzerrung existiert für H>1T
Plan: Untersuchung von magnetismus, magneto-elastischer effekte und Strukturänderungen mit Schwerpunkt auf
Gd-Verbindungen
Anwendung der etablierten Methoden (Dilatometrie, Magnetisierung, ...) und Modellierung
Neue Methoden:
1.) Abbildung antiferromagnetischer Domänen mit XRMS
in GdNi2Ge2-Einkristallen:
• Brechung der tetragonalen Symmetrie in antiferromagnetischer Ordnung durch
Momentausrichung parallel zur a- bzw. b-Achse
• Erstmalige Abbildung mittels ortsaufgelöster resonanter magnetischer Röntgenstreuung
• Ausdehnung von Domänen in Gd-Verbindungen in Größenordnung von 100 µm
• Auflösung momentan 20 µm, jedoch um mind. eine Größenordnung verbesserbar
• Abbildung beliebiger magnetischer Domänen möglich, aber auch Verzerrungs- und kristallographische Domänen
Fortsetzung der Arbeiten:
 Weiterentwicklung dieser neuen Abbildungstechnik für antiferromagnetische Domänen
 Korrelation zu Transporteigenschaften, magnetostriktiven Effekten und resultierenden
Verankerungszentren für supraleitende Fluss-Schläuche
2.) Bestimmung der Anisotropie mit ESR (q=0):
 Beziehung zu B23 – Anwendung der Methode (Bestimmung der Energielücke und daraus Ableitung der Anisotropie)
3.) Transmutation von Gd:
 bereits bestehende Proben sollen durch Bestrahlung mit Neutronenfluss transparent für Neutronen gemacht werden (Isotopenumwandlung)
 erstmalig Messung von niederenergetischen Anregungen (q>0) in Gd verbindungen ...
Anisotropy Measurements
by ESR
Neutron Scattering on
Transparent Gd Compounds
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

26. Magnetostrictive Materials and Magnetic Refrigeration (MMMR)
Workshop
Magnetostrictive Materials and
Magnetic Refrigeration (MMMR)
August 2007,
Vienna, Austria

27. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdRu2Si2 Gd Ru Si
TN=47 K
q=(3/4 0 0)
Note: ε=
ΔFWHM= deg
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

28. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

29. M.Rotter „The Magnetoelastic Paradox“ Lorena 2006
GdSb
Structure NaCl type
Type II AFM order
q=(111)
TN=24.4 K
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

30. Normal thermal Expansion
Anharmonicity of lattice dynamics
anharmonic Potential
Harmonic potential +
Small contribution of band electrons
with Debye function

31. Forced Magnetostriction
Crystal Field
Exchange - Striction
L0
L=0, L0
H <0 H + e- H
>0 +
Gd3+, S=7/2, L=0
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

32. Theory of Magnetostriction
Crystal field
Exchange
with +
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

33. Magnetic Structure from
GdCu2
TN= 42 K M [010]
TR= 10 K q = (2/3 1 0) -7 -7 +7 -7 -7
Magnetic Structure from
Neutron Scattering
Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281
M.Rotter „The Magnetoelastic Paradox“ Lorena 2006