The Magnetoelastic Paradox

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

5. GdRu2Si2 (202) (220) ? ? 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 Crystal Field Exchange T T L0 L=0, L0 T<TC(N) + 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 Lattice J1 J1 Ferromagnet: J1>0 dV/V<0 No distortion (dJ1/de) M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

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

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

10. GdAg2 TN= 22.7 K <TR1=21.2K M||[001] <TR2=10.8K M||[110] GdAu2 TN= 50 K q=(0.362 0 1) M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

11. 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. GdNi2B2C ? TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0) small magnetostriction, therefore cap.-dilatometry .... M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

15. GdNi2B2C 2T||a 1.5T TN Orthorh. distortion ! 0.75T 0T 5 10 15 20 25 T (K) Thermal Expansion Forced Magnetostriction Da/a TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0) 10-4 M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

16. 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-theWorldofRareEarthMagnetism 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 www.mcphase.de 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. The Magnetoelastic Paradox for L=0.... demonstrated at GdNi2B2CRotter et al. EPL 75 (2006) 160 Orthorhombic Distortion ? 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. Systems witha symmetry breaking magnetic propagation vector and large spontaneous magnetostriction demonstratethe 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] [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] 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] GdAg2tetr./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 (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] work in progress work in progress yes work 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.(<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. The followingcompounds are not expected to show a change in lattice symmetry at the transition from the paramagnetto the antiferromagnet, because the propagation vector does not break the symmetry of the lattice andthere 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 (0 0 0.79) [67] GdCo2Ge2 tetr./37.5 [51] (0 0 0.93) [68] In the followingcompounds the propagation does not break the crystal symmetry and there are more than one atom inthe primitive crystallographic unit cell. In this case it depends on the relative orientiation of the momentsin the unit cell, whether a symmetry breaking distortion is predicted by the exchange striction modelor not. Therefore these compounds can in principle exhibit the magnetoelastic paradox although thepropagation does not break the crystal symmetry of the lattice. Symmetry Magnetic Anisotropic/ Single Forced / Propagation isotropic(dV/V) Crystal Magneto- Neel Spontaneous available -striction Temp.(K)Magnetostriction (10-3) 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] Gd2S3orth./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. ToDo GdNi2Ge2ab-plane T = 17 K 200 µm Moment direction New Methods • Imaging of AFM domains • with XRMS • 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 • Anisotropy Measurements • by ESR • Neutron Scattering on • Transparent Gd Compounds M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

26. Workshop Magnetostrictive Materials and Magnetic Refrigeration (MMMR) 13.-15. August 2007, Vienna, Austria http://www.univie.ac.at/MMMR/

27. GdRu2Si2 Gd Ru Si TN=47 K q=(3/4 0 0) Note: ε=4.10-5 ... ΔFWHM=0.0015 deg M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

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

29. 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 anharmonicPotential Harmonic potential with Debye function + Small contribution of band electrons

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