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

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

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

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

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

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

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

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

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

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=(0.362 0 1) M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

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

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

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

M.Rotter „The Magnetoelastic Paradox“ Lorena 2006 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

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 = (0.55 0 0) 10-4 M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

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

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 www.mcphase.de M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

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

Hmag + McPhase ? T=2 K

M.Rotter „The Magnetoelastic Paradox“ Lorena 2006 Orthorhombic Distortion The Magnetoelastic Paradox for L=0 .... 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

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] 0.0/0.0 [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] 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]

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]

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 (0 0 0.79) [67] GdCo2Ge2 tetr./37.5 [51] (0 0 0.93) [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

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

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

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

M.Rotter „The Magnetoelastic Paradox“ Lorena 2006 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

M.Rotter „The Magnetoelastic Paradox“ Lorena 2006

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

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

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

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

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