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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.

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Presentation on theme: "The Magnetoelastic Paradox M. Rotter, A. Barcza, IPC, Universität Wien, Austria H. Michor, TU-Wien, Austria A. Lindbaum, FH-Linz, Austria M. Doerr, M."— Presentation transcript:

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 2 M.Rotter The Magnetoelastic Paradox Lorena 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 GdNi 2 B 2 C 6.Outlook

3 3 M.Rotter The Magnetoelastic Paradox Lorena 2006 Experimental Methods 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 (patent submitted, optional use in PPMS, VTIs,... operated at 6 institutes in A, D, CZ, Brazil, US) How to measure Magnetostriction ?

4 4 M.Rotter The Magnetoelastic Paradox Lorena 2006 GdRu 2 Si 2 (008) Gd Ru Si

5 5 M.Rotter The Magnetoelastic Paradox Lorena 2006 (202) (220) GdRu 2 Si 2 ? ? No sign of distortion of the tetragonal plane !

6 6 M.Rotter The Magnetoelastic Paradox Lorena 2006 Crystal Field T e- + + L 0 T

7 7 M.Rotter The Magnetoelastic Paradox Lorena 2006 No distortion (dJ 1 /d ) Ferromagnet: J 1 >0 dV/V<0 J1J1 J1J1 Exchange striction on a Square Lattice

8 8 M.Rotter The Magnetoelastic Paradox Lorena 2006 No distortion (dJ 1 /d ) Anti-Ferromagnet with NN exchange: J 1 <0 dV/V>0 Tetragonal Distortion (dJ 1 /d ) !!! Anti-Ferromagnet With small |J 1 | J 2 <0 dV/V=0 J1J1 J1J1 J2J2 J1J1 J2J2 J1J1 THE MAGNETOELASTIC PARADOX Antiferromagnets with L=0 below T N : Symmetry breaking distortions are expected but have NOT been found.... but in ALL experiments: distortion <10 -4

9 9 M.Rotter The Magnetoelastic Paradox Lorena 2006 T N = 24 K q=(0 ½ 0) GdCuSn

10 10 M.Rotter The Magnetoelastic Paradox Lorena 2006 T N = 22.7 K

11 11 M.Rotter The Magnetoelastic Paradox Lorena 2006 Gd 3 Rh T N =112 K Large magnetostrictive effects on lattice constants – but NO distortion Gd 3 Ni T N =100 K

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

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

14 14 M.Rotter The Magnetoelastic Paradox Lorena 2006 T N = 20 K: M||[010]

15 15 M.Rotter The Magnetoelastic Paradox Lorena 2006 Thermal Expansion T 2T||a TNTN 1.5T 0.75T T (K) Forced Magnetostriction Orthorh. distortion ! a/a T N = 20 K: M||[010]

16 16 M.Rotter The Magnetoelastic Paradox Lorena 2006 At H=0: Domains ? distortion =3x10 -4 would lead to FWHM (204)+ 0.1° FWHM (211)+ 0.05° at H=0 no distortion can be found (magnetoelastic paradox) GdNi 2 B 2 C Powder Xray Diffraction.... FWHM determined by fitting ?

17 17 M.Rotter The Magnetoelastic Paradox Lorena 2006 McPhase - the World of Rare Earth MagnetismMcPhase - 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

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

19 T=2 K H mag + McPhase ?

20 20 M.Rotter The Magnetoelastic Paradox Lorena 2006 Orthorhombic Distortion Standard Model of RE Mag... McPhase Simulation ? The Magnetoelastic Paradox for L=0.... demonstrated at GdNi 2 B 2 C Rotter et al. EPL 75 (2006) 160 Capacitance Dilatometry Exchange Striction Model

21 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] [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] 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 ( ) [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 progressyes 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 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. 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

24 24 M.Rotter The Magnetoelastic Paradox Lorena 2006 THE MAGNETOELASTIC PARADOX Antiferromagnets with L=0 below T N : Symmetry breaking distortions are expected but have NOT been found GdNi 2 B 2 C: 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 T N Summary and outlook

25 25 M.Rotter The Magnetoelastic Paradox Lorena 2006 New Methods Imaging of AFM domains with XRMS GdNi 2 Ge 2 ab-plane T = 17 K Moment direction 200 µm Anisotropy Measurements by ESR Neutron Scattering on Transparent Gd Compounds 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

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

27 27 M.Rotter The Magnetoelastic Paradox Lorena 2006 Gd Ru Si GdRu 2 Si 2 T N =47 K q=(3/4 0 0) Note: ε= ΔFWHM= deg

28 28 M.Rotter The Magnetoelastic Paradox Lorena 2006

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

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

31 31 M.Rotter The Magnetoelastic Paradox Lorena 2006 H <0 Crystal Field e- + + Exchange - Striction H H >0 Forced Magnetostriction L 0L=0, L 0 Gd 3+, S=7/2, L=0

32 32 M.Rotter The Magnetoelastic Paradox Lorena 2006 Theory of Magnetostriction Crystal fieldExchange + with

33 33 M.Rotter The Magnetoelastic Paradox Lorena 2006 T N = 42 K M [010] T R = 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000)


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