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 B. Beuneu, LLB – Saclay, France M el Massalami, UFRJ, Brazil

2 M.Rotter „The Magnetoelastic Paradox“ Planneralm 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 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 Experimental Methods 1cm 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 Magnetostriction Measurements

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

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

6 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 Crystal Field TT e- + + L0L0 T<T C(N) Spontaneous Magnetostriction STANDARD MODEL OF RARE EARTH MAGNETISM Microscopic Origin of Magnetostriction: Strain dependence of magnetic interactions Exchange T<T C(N) L=0, L  0 „exchange-striction“ TT Gd 3+, S=7/2, L=0

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

8 M.Rotter „The Magnetoelastic Paradox“ Planneralm 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 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 T N = 24 K q=(0 ½ 0) GdCuSn

10 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 T N = 22.7 K <T R1 =21.2K M||[001] <T R2 =10.8K M||[110] GdAu 2 T N = 50 K GdAg 2 q=( )

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

13 M.Rotter „The Magnetoelastic Paradox“ Planneralm 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 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 T N = 20 K: M||[010] <T R = 14 K: M||[0yz] q = ( ) small magnetostriction, therefore cap.-dilatometry.... GdNi 2 B 2 C ?

15 M.Rotter „The Magnetoelastic Paradox“ Planneralm 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] <T R = 14 K: M||[0yz] q = ( ) GdNi 2 B 2 C

16 M.Rotter „The Magnetoelastic Paradox“ Planneralm 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 GdNi 2 B 2 C Powder Xray Diffraction.... FWHM determined by fitting ?

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

T=2 K H mag + McPhase ?

20 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 Orthorhombic Distortion Standard Model of RE Mag... McPhase Simulation ? The Magnetoelastic Paradox for L=0.... demonstrated at GdNi 2 B 2 C Capacitance Dilatometry Exchange Striction Model

21 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 Transmutation of Gd New Methods Neutron Scattering Imaging of AFM domains with XRMS GdNi 2 Ge 2 ab-plane T = 17 K Moment direction 200 µm Anisotropy Measurements by ESR 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

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

23 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 H  <0 Crystal Field e- + + Exchange - Striction H H  >0 Forced Magnetostriction L0L0L=0, L  0 Gd 3+, S=7/2, L=0

24 M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006 Theory of Magnetostriction Crystal fieldExchange + with