When simple alloys turn into complicated J.I. Espeso, J.C. Gmez - PowerPoint PPT Presentation

When simple alloys turn into complicated J.I. Espeso, J.C. Gómez Sal, N. Marcano Universidad de Cantabria, INA Zaragoza G.M. Kalvius, D.R. Noakes, A. Amato TU Munich, Virginia State Univ., PSI V. Zlati ć , I. Aviani, M. O č ko Institute of Physics, Zagreb S. Haines, R. Smith, S.S. Saxena Cavendish Laboratory, Cambridge

Acknowledgment to the COST P16 - ECOM action • Three STSM financed by ECOM ■ � Veljko Zlati ć Universidad de Cantabria, Santander, Spain ■ � Jose I. Espeso Institute of Physics, Zagreb, Croatia ■ � Ivica Aviani Cavendish Laboratory, Cambridge, UK

� � Origin of the study Looking for a simple antiferromagnet with FeB-type of structure to study the muon stopping site Candidates: ● CeCu (T N =3.5K) burns spontaneously when powdering ● CeGe (T N =10K) reported as a simple antiferro Buschow et al., Phys. Stat. Sol. 16 (1966) 467

Previous literature on CeGe Study of the CeGe 1-x Si x system Magnetic study of RGe alloys � q = (0 , 1 / 2 , 0) Buschow et al., Phys. Stat. Sol. 16 (1966) 467 Schobinger-Papamantellos et al., Physica B 349 (2004) 100 Tipical of a simple AF

� � Obtaining the sample ● Polycrystalline sample prepared at an arc furnace ● Perfect agreement with the FeB-type of structure ( Pnma space group) a = 8.350 Å � b = 4.078 Å � c = 6.022 Å 1500 CeGe Cu K α λ = 1.5418 Å 1000 Intensity 500 0 20 30 40 50 60 70 2 θ (degrees)

Heat capacity results � T θ D � 3 � ( e x − 1) 2 dx + R � ∆ 2 x 4 e x i � − � ∆ i � 2 T C p = γ T + 9 nR T 2 θ D 0 60 CeGe 50 θ D = 240 ± 5 K 40 6 p (J/K mol) 5 γ = 10.3 ± 2 mJ/K 2 mol 30 Δ 2 4 mag (J/K mol) ∆ 1 = 53.0 ± 0.4 K 3 C 20 Δ 1 ∆ 2 = 137 ± 1 K 2 C 1 10 0 0 50 100 150 200 250 300 Temperature (K) 0 0 50 100 150 200 250 300 Temperature (K)

Low T Heat capacity 10 7 1.2 6 R ln2 1 8 CeGe 5 0.8 mag (J/K mol) S 2 mol) mag (J/K 6 4 p /T (J/K 0.6 3 2 mol) 4 C 0.4 C 2 2 0.2 1 CeGe 0 0 0 0 50 100 150 200 2 4 6 8 10 12 14 2 (K 2 ) Temperature (K) T ● The ordering temperature is in agreement with that previously reported (T N = 10.8 K) ● Δ C mag = 6.7 J/K mol ⇒ µ Ce ≈ 1.1 µ B , in agreement with neutron data ● The Sommerfeld coefficient at low T is not much enhanced ● S mag at T N is not much reduced with regard to R · ln2 Classical antiferromagnet (till now ...)

First surprising results Muon spectroscopy ● Three different precession frequencies in the µ SR response Ratio of frequencies and intensities is T-independent All three converge at T N 35 30 CeGe 25 Frequency (Hz) 20 15 10 T N 5 0 4 6 8 10 12 T(K)

ac and dc magnetic susceptibility CeGe CeGe 0.14 0.08 FC M/H (emu/mol Oe) 0.12 1000 Hz 0.07 ZFC χ ' (emu/mol) 100 Hz 0.1 0.06 0.08 0.05 h ac = 1 Oe 0.06 0.04 200 Oe 0.04 0.03 0.02 FC M/H (emu/mol Oe) ZFC 0.06 1000 Hz 0.0015 100 Hz 0.05 χ '' (emu/mol) 0.001 1000 Oe 0.04 0.0005 0 FC 0.06 M/H (emu/mol Oe) ZFC 0 10 20 30 40 50 0.05 Temperature (K) • χ ac must be taken with caution 3000 Oe 0.04 • Ferromagnetic contribution in M/H 0 5 10 15 20 • Strong irreversibility associated to Temperature (K) this FM contribution

Isothermal magnetization 1 • Saturation far to be reached CeGe 0.8 ⇓ 9.8K strong anisotropy 8.3K 0.6 M( µ B /Ce) 4.8K 14K 1.8K 0.4 24K • Broad metamagnetic 49K transitions 0.2 ⇓ 98K not so simple magnetic 147K 0 structure 0 20 40 60 80 Magnetic Field (kOe)

Heat capacity under field 12 0 T CeGe 1 T 10 3.5 T 5 T 8 • The applied magnetic field P (J/K mol) 7 T unveils two transitions 9 T 6 • Both of them have 4 C antiferromagnetic character 2 0 0 5 10 15 20 Temperature (K)

Electrical resistivity ● Increase of the resistivity at T N ● Two possible explanations: gap opening at the magnetic superzone (Tb, Dy, Ho, Er, Tm) electron scattering by substitutional spin disorder (HoMn 12-x Fe x ) 800 CeGe 700 600 ρ ( µ Ω cm) 300 500 290 ρ ( µ Ω cm) 280 270 400 260 250 300 240 0 2 4 6 8 10 12 14 16 18 Temperature (K) 200 0 50 100 150 200 250 300 Temperature (K)

How to distinguish Gap opening at the magnetic superzone Substitutional spin disorder Strong effect of magnetic field No effect of magnetic field Thulium 140 (b) HoMn 12-x Fe x x=4 130 x=3 120 T N T (K) 110 Ellerby et al., Phys. Rev. B 57 (1998) 8416 T N x=2 100 Our results (d) 140 x=8 280 120 CeGe T N 260 ρ ( µ Ω cm ) x=9 100 0 T 240 3 T 5 T HoMn 12-x Fe 7 T x 220 80 9 T 0 100 200 300 400 200 T(K) 0 4 8 12 16 20 Stankiewicz et al., Phys. Rev. Lett. 89 (2002) 106602 Temperature (K)

� � � � Model for the resistivity R.J. Elliott and F.A. Wedgwood, Proc. Phys. Soc. Lond. 81 (1963) 846 � T � 5 � θ D /T z 5 ρ phon ∝ sinh 2 ( z/ 2) dz θ D 0 ρ = α + β T + γ (1 − 1 2 M 2 ) 1 − Γ M 310 α = 120.6 ± 0.7 300 β = 110 ± 1 CeGe 290 ρ ( µ Ω cm) γ = 90.8 ± 0.8 280 270 Γ = 0.321 ± 0.001 ρ fit 260 fit residual • Smaller coupling than the 250 heavy rare-earths: 240 Dy ---> Γ = 0.68 Ho ---> Γ = 0.65 0 5 10 15 20 Er ---> Γ = 0.66 Temperature (K) Tm ---> Γ = 0.73 Elliot63 and Ellerby98

Thermopower results Thermopower of Thulium 0 CeGe -1 Ce 0.9 La 0.1 Ge -2 -3 S ( µ V/K) -4 -5 -6 -7 Edwards et al., Phys. Rev. 176 (1968) 753 -8 10 100 Temperature (K) • Confirm the gap opening at the magnetic superzone • Effect of dilution on the Ce site

Measurements under pressure 0.1 70 CeGe P = 15 kbar P = 11 kbar 60 0.09 H = 10 kOe ρ (P,T)- ρ (P,0)( µ Ω cm) CeGe 50 M ( µ B /Ce) 0.08 40 30 0.07 P = 0 kbar 20 P = 9 kbar P = 1 kbar 10 0.06 P = 12 kbar P = 4.5 kbar 0 0 5 10 15 20 0 2 4 6 8 10 12 14 T(K) T(K) • T N does not change with pressure • Small influence of the Kondo effect

Back to neutron diffraction Schobinger-Papamantellos et al., Physica B 349 (2004) 100

Back to neutron diffraction 5000 CeGe 4000 D1B λ = 2.52 Å Commensurate structure 15 K - 2.4 K 3000 Magnetic Intensity 5000 CeGe 2000 Pattern matching 4000 D1B λ = 2.52 Å 1000 Incommensurate structure 15 K - 2.4 K 3000 0 Magnetic Intensity 2000 1000 10 20 30 40 50 60 70 2 θ (degrees) 0 � q = (0 , 1 / 2 , 0) 10 20 30 40 50 60 70 2 θ (degrees) q = (0 , 0 . 51 , 0) � Schobinger-Papamantellos et al., Physica B 349 (2004) 100

Conclusions • Partial studies may lead to unsound conclusions 1/ χ or C p ⇒ CeGe is a simple AFM • The magnetic structure of CeGe is incommensurate ■ � Three frequencies in μ SR ■ � Different contributions in M/H and C p (T,H) ■ � Gap opening at the magnetic superzone ( ρ , S) ■ � Neutron diffraction ⇒ q = (0, 0.51, 0) • Small influence of the Kondo hybridization