Temperature Dependence of the Magnetic Hyperfine Field of 181 Ta

1. Temperature Dependence of the Magnetic Hyperfine Field of 181Ta in Rare Earth-Cobalt Laves Phases RCo2 H. Saitovitch, P. R. J. Silva, J. Th. Cavalcante, Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil P. de la Presa, M. Forker Helmholtz Institut für Strahlen- und Kernphysik, Universität Bonn, Germany Support:

2. MOTIVATION • Rare Earth-Cobalt Laves Phases RCo2 may be a very suitable series of compounds to study magnetic interactions • well known compounds • Interesting interaction of 3d - 4f electrons • Easy to prepare • Easy doping • Good theoretical knowledge • Here we will focus on the nature of magnetic transition order

3. The C15 lattice structure of RCo2 Co – non-cubic point symmetry, combined magnetic and electric hfi Rare earth – cubic point symmetry, pure magnetic interaction

4. 181Hf 111In 42.5 d 2.81 d β- EC 1/2+ 7/2+ Q = 2.53(10) b µ = 3.34 µN γ1 133 keV γ1 172 keV Q = 0.83(13) b µ = -0.77 µN t1/2 = 10.8 ns 5/2+ t1/2 =84 ns 5/2+ γ2 247 keV γ2 482 keV 1/2+ 111Cd 7/2+ 181Ta Experimental detail Probe isotopes Sources preparations PAC equipment Temperature variation

5. The temperature dependence of the magnetic hyperfine field of 111Cd in RCo2 Previous measured spectra PrCo2 GdCo2 DyCo2 Second-order transition First-order transition

6. FM a1> 0,a3 < 0, a5 >0 H = 0 M(TC)‏ a1> 0, a3 < 0, a5 >0 H > 0 Md -Md H Theory of itinerant electron magnetism Wohlfarth and Rhodes , 1962: Landau expansion of the free energy a1 < 0 , a3 > 0 a1 < 0 , a3 < 0 One minimum: Continuous, second order phase transition (SOT)‏ Two minima: Discontinuous, first order phase transition (FOT)‏

7. a3(T) = a3(0)(1-T/T0) ; a3(0) < 0 a3 To ~ 150 K T FOT SOT Temperature dependence of the Landau coefficients a1 and a3 Based on the analysis of the susceptibility of YCo2 Bloch et al. predict a change of sign of a3 at T0 ~ 150 K Consequence: The order of the transition depends on the order temperature TC TC < T0 First-order transition (FOT), TC < T0 : Second-order transition (SOT)

8. HR LR SOT FOT Curie temperatures of RCo2

9. The order of the magnetic phase transitions of RCo2 deduced from the magnetic hyperfine field at 111Cd SOT FOT First results of these studies M. Forker et al., PHYS. REV. B 68, 014409 (2003)‏

10. PAC spectra of TbCo2 111Cd:TbCo2 181Ta:TbCo2

11. The temperature dependence of the magnetic hyperfine field of the probe nuclei 111Cd and 181Ta in TbCo2

12. PAC spectra of HoCo2 181Ta:HoCo2 111Cd:HoCo2

13. The temperature dependence of the magnetic hyperfine field of the probe nuclei 111Cd and 181Ta in HoCo2

14. SUMMARY / REMARKS • For T/Tc ≥ 0.5 the MHF of 181Ta decreases much faster with temperature than that of 111Cd, both in SOT compounds (TbCo2) and FOT compounds (HoCo2); probably because 111Cd is closed shells, so MHF is mainly caused by the spin polarization of the s-conduction electrons. • In contrast, 181Ta has an open 5d-shell with a finite 5d spin which may produce a core polarization contribution to the MHF. It is conceivable that the expectation values of this core polarization depends on coupling of the 5d spin to the host magnetization. • If the coupling is weak, the 5d spin possibly fluctuates, resulting in a decrease of the time averaged core polarization part of the field which should be stronger the closer one comes to Tc. • Probe isotope 140La/140Ce

16. Magnetic elements 3d elements: Mn…Ni - unclosed 3d shell : (Ar) 3dm Rare earth (4f)elements : (Xe) 4fn 5d2 6s1 ; in solids: mostly R3+ - (Xe) 4fn except Ce, Eu, Yb n: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

17. magnetization magnetic field H T. Goto et al. Solid State Commun.72, 945 (1989)‏ Itinerant electron metamagnetism

18. Russel-Saunders Coupling L J (g-1)J S Magnetic properties of trivalent rare earth (R) ions

19. RCo2: metamagnetism driven by the 4f-exchange field ~ (g-1)J