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The Magnetoelastic Paradox

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

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The Magnetoelastic Paradox

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  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 Martin Rotter,MSL2009

  2. Fundamental interest: • largest spin value in periodic table (S=7/2) • Technical interest: • Giant Magnetocaloric Effect • Giant Magnetostriction STANDARD MODEL OF RARE EARTH MAGNETISM Crystal Field Effect NO Crystal Field Effect Sm,Er, Tm,Yb >0 Ce,Pr,Nd, Tb,Dy,Ho <0 + Gd3+,Eu2+ =0 + e- e- + + L=0 L0 Distortion of 4f – Charge Density Spherical 4f-Charge Density Martin Rotter,MSL2009

  3. T >TN kT >>cf T >TN T <TN T <TN T <TN T <TN H H a STANDARD MODEL OF RARE EARTH MAGNETISM microscopic origin of magnetostriction = strain dependence of magnetic interactions 1) Single ion effects2) Two ion effects  Crystal Field Striction Exchange Striction …spontaneous magnetostriction …forced magnetostriction a kT <cf M. Doerr, M. Rotter, A. Lindbaum, Magnetostriction in Rare Earth based Antiferromagnets Adv. Phys. 54 (2005) 1-66 Martin Rotter,MSL2009

  4. Exchange striction on a Square Lattice J1 J1 Elastic Energy Minimize Free Energy Magnetic Energy Ferromagnet: J1>0 dV/V>0 No distortion (dJ1/de) Martin Rotter,MSL2009

  5. J1 J1 Anti-Ferromagnet With small |J1| J2<0 dV/V=0 J2 J2 Tetragonal Distortion (dJ1/de) !!! J1 J1 Anti-Ferromagnet with NN exchange: J1<0 dV/V<0 No distortion (dJ1/de) Martin Rotter,MSL2009

  6. How to detect a symmetry breaking distortion ? . . . . . . . . J1 . . Anti-Ferromagnet . . J1 Tetragonal Distortion !!! THE MAGNETOELASTIC PARADOX M. Rotter et al. Europhys. lett. 75 (2006) 160-166 Antiferromagnets with L=0 below TN: Symmetry breaking distortions are expected but have NOT been found Intensity 2theta .... ALL Experiments: symmetry breaking distortion  <10-4

  7. 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 by M Rotter 2006 • Optional use in PPMS, VTIs,... • Operated at 14 institutes in A, CH, D, CZ, Brazil, US,UK Martin Rotter,MSL2009

  8. GdNi2B2C ? TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0) small magnetostriction, therefore cap.-dilatometry .... Martin Rotter,MSL2009

  9. 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 Martin Rotter,MSL2009

  10. The Magnetoelastic Paradox .... demonstrated at GdNi2B2CRotter et al. EPL 75 (2006) 160 J2 J1 Orthorhombic Distortion ? Exchange Striction Model Capacitance Dilatometry Standard Model of RE Mag ... McPhase Simulation Martin Rotter,MSL2009

  11. Double Q structure -25 -4 3x10 -20 -4 2x10 -15 -10 -4 1x10 -5 0 0 0 2 4 6 8 10 12 14 e - e < > - < > ~ J J J J + + H H aa bb i i ( 100 ) T , i i ( 010 ) T , Orthorhombic Distortion b T = 2 K Exchange Striction Model Exchange Striction Model b e - a a e Capacitance Dilatometry • Dipolar easy plane anisotropy • Landau Expansion: M4 term stabilizes double q structure ! • The Magnetoelastic Paradox explained !? • J. Jensen&M. Rotter PRB 77 (2008) 134408 • [What if dipolar anisotropy favors moments along c ?] m H (kOe) ||a 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

  12. 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] (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] GdAg2tetr./23 (1/4 2/3 0) [R12] MEP!1.2/0.0 [R19] Gd2Ni2-xIn tetr./20 [R19] 0.8/0.0 [R19]

  13. 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.(<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]

  14. 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

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