Model of magnetostriction Magnetoelastic behavior of rare earth based intermetallics in high magnetic fields up to 33 T M. Doerr a, M. Rotter b, J. Brooks c,d, E. Jobiliong d, A. Lindbaum b, R. Vasic d, and M. Loewenhaupt a a Institute of Solid State Physics (IFP), TU Dresden, D Dresden, GERMANY b Institute of Physical Chemistry, University Vienna, Währingerstr. 42, A-1090 Vienna, AUSTRIA c Department of Physics, Florida State University, Tallahassee, FL , USA d National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL , USA Magnetostriction measurements are a powefull tool to study the magnetoelastic interactions and magnetic phase transitions. The magnetoelastic behavior can be calculated using a theoretical model which takes into account the crystal field striction as well as the exchange striction. Magnetostrictive measurements in resistive. water cooled high field magnets give good results. The resolution is still limited to by mechanical vibrations. Summary We acknowledge support by the Austrian Science Foundation (FWF) within the projects P16957 and P17226 and by the Deutsche Forschungsgemeinschaft (DFG) within the Sonderforschungsbereich 463. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement No. DMR , by the State of Florida, and by the DOE. Magnetostriction in high magnetic fields The capacitive miniature-dilatometer.... measures thermal expansion at H=const. and magnetostriction at T=const. with a resolution of (in supercond. magnets)....uses a tilted plate capacitor made from Ag....has small dimensions: diameter d=22mm, height h=40mm [1] M.Rotter et al., Rev.Sci.Instrum. 69 (1998) Magnets The dilatometer was successfully used in a superconducting 17 T-magnet (Oxford Instruments) with a 4 He-gas flow cryostat or a 3 He insert (T = K).....water-cooled resistive magnets with 4 He bath cryostats Rare earth intermetallics... RCu 2 Sample stick with the capacitive miniature dilatometer (Ag-cell, right) (installation at NHMFL) 33T-BITTER-magnet NHMFL Tallahassee Magnetostriction Phase diagram (easy direction) Miniature dilatometer [1] (a,p....shielding electrodes, b,o....capacitor plates, c...screen, d...distance piece, e...sample, f...sapphire rings, q,r....holder) Experimental methods X-ray or neutron diffraction (spontaneous effects, H=const., sensitivity ) Extensometers (using strain gauges, spontaneous and field induced effects, successfully tested in pused fields, sensitivityf ) Interferometry (spontaneous effects H=0, sensitivity ) Capacitive dilatometry (spontaneous and field induced effects, sensitivity but practically only ) The RCu 2 compounds magnetostriction result from...  the single ion crystal field (CEF) contribution and  the two ion exchange interaction. The mean field – Monte Carlo simulation program McPhase ( allows to model the magnetostriction. The elastic constants – important for applications - can be calculated. [2] M.Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda: J. Appl. Phys. 91 (2002) [3] M. Doerr, A. Lindbaum, M. Rotter: Adv. Phys. 54 (2005) 1. 23T-BITTER-magnet GHMFL Grenoble Sample stick with the capacitive miniature dilatometer (Ag-cell, right) (installation at GHMFL) 4f R = Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Noise levels in BITTER-magnets Technical precautions to avoid electrical or mechanical noise Noise level in  l/l before the improvement Electrical isolation between dilatometer and cryostat / magnet / pump 5x10 -5 Ground free power lines 1x10 -5 Short and loop free wiring in the dilatometer cell 3x10 -6 Damping the dilatometer mechanically to avoid vibrations caused by strong water flow 1x10 -6 Possible resolution in BITTER-magnets <1x10 -6 Magnetostriction measurements on RCu 2 were performed up to the highest available steady magnetic fields. They show the transitions between different magnetically ordered phases clearly. Together with magnetization measurements the allow to construct the magnetic phase diagrams. Especially, the influence of magnetic transitions on the crystalline structures via magnetoelastic interaction can be studied. It may result in lattice distortions, giant magnetostrictive effects = GMS [3] and symmetry changes or low dimensional lattice expansion. NHMFL