Quadrupolar Ordered Phases in Pr-based Superconductors PrT 2 Zn 20 (T = Rh and Ir)

Transcription

1 NHSCP214 ISSP, University of Tokyo, Kashiwa Quadrupolar Ordered Phases in Pr-based Superconductors PrT 2 Zn 2 (T = Rh and Ir) Takahiro Onimaru 1 K. T. Matsumoto 1, N. Nagasawa 1, K. Wakiya 1, K. Umeo 2, S. Kittaka 3, T. Sakakibara 3, and T. Takabatake 1,4 1 AdSM, 2 N-BARD, 3 IAMR, Hiroshima University 4 ISSP, University of Tokyo 1

2 Outline Multipoles of non-kramers Pr 3+ ion with 4f 2 configuration PrT 2 Zn 2 (T=Rh and Ir)! Crystal electric field (CEF) effect Non-Kramers doublet ground state! Quadrupole order and superconducting transition! Further topic: Non-Fermi liquid behavior, Multi-channel Kondo effect, etc. Summary 2

3 Multipoles of 4f electrons Electric Monopole, e - Quadruples of 4f electrons Strong spin-orbit interaction " J =L±S Magnetic Dipole J x, J y, J z Electric Quadrupole O 2 ( = 2J z2 -J x2 -J y 2 ) : Γ 3 O 2 2 ( = J x2 -J y 2 ) O yz, O zx, O xy : Γ 5 (O αβ = J α J β +J β J α ) Magnetic Octupole T xa, T ya, T z a ( Γ 4 ) T xb, T yb, T z b ( Γ 5 ) T xyz ( Γ 2 ) Pr 3+ : 4f 2 configuration (J=4) (Cubic CEF: Oh ) 3 H 4 (9) Γ 5 Γ 4 Γ 3 Γ 1 Dipole Quadru -pole Octupole Γ 5 Γ 4 Γ 3 Γ 1 How to remove the entropy of the degenerated state? 3

4 Cubic Pr-based compounds Crystal Structure Point group CEF GS PrSn 3 AuCu 3 O h Γ 1 - Γ 4 Magnetic order AFM T N =8.6 K PrPb 3 AuCu 3 O h Γ 3 PrPtBi MgAgAs O h Γ 3 Multipole order SC transition T Q =.4 K FQ T Q =1.35 K PrInAg 2 BiF 3 O h Γ 3 PrMg 3 Fe 3 Al O h Γ 3 Pr 3 Pd 2 Ge 6 C 6 Cr 23 O h, T d Γ 5, Γ 3 Pr 3 Pd 2 Si 6 C 6 Cr 23 O h, T d Γ 5, Γ 3 AFM T N =.14 K PrOs 4 Sb 12 AT 4 X 12 T h Γ 1 - Γ 4 (1) PrRu 4 P 12 AT 4 X 12 T h Γ 1, Γ 4 (2) (T<T co =63 K) PrFe 4 P 12 AT 4 X 12 T h Γ 1 - Γ 4 (1) T Q =.26 K T Q =.21 K (B>2 T) T Q =.11 K Scalar-type T M =6.5 K T c =1.85 K PrPt 4 Ge 12 AT 4 X 12 T h Γ 1 T c =8 K 4

5 Non-Kramers Pr 3+ ions in crystals Pr 3+ ion: 4f 2 configuration (L=5, S=1, J=4) 3 H 4 (J =4) (9) Cubic CEF (O h ) Γ K Γ K Γ K Γ 3 In the Γ 3 doublet, there is no magnetic dipole, but quadrupoles O 2 and O 2, and octupole T xyz. (O 2 >) Quadrupoles of 4f electrons PrPb 3 Simple cubic structure order Antiferro-quadrupole () order at T Q =.4 K E. Bucher et al., J. Low. Temp. 2 (1974) 322. (O 2 <) Pr Pb Incommensurate quadrupole structures Indirect RKKY-type interaction. Quadrupoles are partially quenched. T. Onimaru et al., Phys. Rev. Lett. 94 (25) Quadrupole Magne*c dipole Crystal structure of PrPb 3 PrInAg 2, PrMg 3 : No ordering, Quadrupole Kondo effect A. Yatskar et al., Phys. Rev. Lett. 77 (1996) 3637., H. Tanida et al., J. Phys. Soc. Jpn. 75 (26) Composite order in two-channel Kondo lattice S. Hoshino et al., J. Phys. Soc. Jpn. 82, 4477 (213.) Incommensurate quadrupole structure in PrPb 3. (T. Onimaru et al., PRL, 25.) 5

6 Crystal structure of PrT 2 Zn 2 (T=Ru, Rh, Ir) Cubic CeCr 2 Al 2 -type (Space group: Fd3m) T Pr PrT 2 Zn 2 T=Ru Rh Ir T. Nasch et al., Z. Naturforsch. B 52 (1997) 123. T. Onimaru et al, J. Phys. Soc. Jpn. 79 (21) The Pr ions are encapsulated into highly symmetric Zn-cages. Pr site : Cubic T d point group Pr Zn(16c) Zn(96g) Zn a=14.3 Å Zn(16c) atoms insides Pr and Zn(96g) cage Non-Kramers Γ 3 doublet for Pr 3+ ion Quadrupole moments are active. Strong hybridization of the 4f electrons with conduction electrons Heavy fermion state and Kondo effect Anharmonic atomic vibrations couple with 4f and conduction electrons. 6

7 Magnetic susceptibility: PrT 2 Zn 2 (T=Ru, Rh, Ir) T. Onimaru et al., J. Phys.: Condens. Matter 24 (212) χ obeys the Curie-Weiss law above 3 K. Effective magnetic moment µ eff 3.5(2) µ B /f.u. for T=Ru 3.54(2) µ B /f.u. for T=Rh 3.49(2) µ B /f.u. for T=Ir Pr ions are trivalent. The CEF effect is weak. The small negative θ P s indicate weak magnetic interaction between the Pr-ions. Van-Vleck paramagnetic behavior. The CEF ground states is non-magnetic Γ 1 or Γ 3. 7

8 Magnetic specific heat T. Onimaru et al., J. Phys.: Condens. Matter 24 (212) Γ 4 Γ 3 32 K Γ 3 1 K Schottky-type peaks appear at 12 K. # CEF ground state: Γ 3 doublets PrRu 2 Zn 2 : Structural transition at T S =138 K Shoulder-like anomaly # Splitting of Γ 3 doublet by the lattice modulation. T. Onimaru et al, Phys. Rev. LeJ. 16 (211) T. Onimaru et al, Phys. Rev. B 86 (212) I. Ishii, et al., J. Phys. Soc. Jpn. 8, 9361 (211). 8

9 Inelastic neutron scattering K. Iwasa et al., J. Phys. Soc. Jpn. 82 (213) PrRh 2 Zn 2 PrIr 2 Zn 2 Γ 1 79 K Γ 4 (2) 68 K Γ 5 68 K Γ 1 66 K Γ 4 (1) 31 K Γ 4 28 K Γ 23 Γ 3 Cubic T Cubic T d cf. Structural transition at 17~47 K. Spectra are well reproduced by the CEF level schemes with the nonmagnetic doublet ground state. 9

10 PrT 2 X 2 (T: Transition metal, X: Al, Zn) Lattice parameter (Å) Structural transition PrRu 2 Zn (4) T S =138 K PrRh 2 Zn (3) T S =17 ~47 K CEF ground state Singlet (T < T S ) Γ 23 doublet (T) (T < T S ) PrOs 2 Zn (5) T S =87 K? PrIr 2 Zn (2) Γ 3 doublet PrTi 2 Al (7) Γ 3 doublet PrV 2 Al (2) Γ 3 doublet Quadrupole order T Q =.6 K (>.4 K) T Q =.11 K FQ T Q =2 K T Q =.6 K SC transition (>.4 K) T c =.6 K (>.4 K) T c =.5 K T c =.2 K (a. p.) T c =1 K (~8 GPa) PrNb 2 Al (3) Γ 3 doublet T. Onimaru et al., JPSJ 79 (21) T. Onimaru et al., PRL 16 (211) T. Onimaru et al., PRB 86 (212) K. Wakiya et al., JKPS 62 (213) A. Sakai and S. Nakatsuji, JPSJ 8 (211) R. Higashinaka et al., JPSJ 8 (211) SA48. A. Sakai et al., JPSJ 81 (212) K. Matsubayashi et al., PRL 19 (212)

11 Magnetic specific heat T. Onimaru et al., Phys. Rev. Lett. 16 (211) T. Onimaru et al., Phys. Rev. B 86 (212) Γ 4 Γ 3 32 K Elastic modulus (C 11 -C 12 )/2 Sharp peaks appear at low temperatures. I. Ishii et al., J. Phys. Soc. Jpn. 8 (211) PrRh 2 Zn 2 Antiferroquadrupole () ordering at T Q =.6 K. I. Ishii et al., Phys. Rev. B 87 (213) PrIr 2 Zn 2 ordering at T Q =.11 K. I. Ishii et al., J. Phys. Soc. Jpn. 8 (211)

12 PrRh 2 Zn 2 i. Anisotropic behavior of T Q. T Q : [1] < [11] < [111] ii. T Q increases with increasing B for [11] and [111]. ordering occurs at T Q =.6 K. 12

13 I H A(B) ordered state: PrRh 2 Zn 2 Two-sublattice mean-field model ( ) J K Γ 3 O 2 = H CEF g J µ B JH K 1 J B(A) + K 2 J A(B) T. Onimaru et al., Phys. Rev. B 86 (212) ( O + O 2 O ) 2 B(A) 2 2 B(A) 2 Two sub-lattice mean-field calculation well reproduces the anisotropic B-T phase diagrams. Antiferromagnetic interaction between the field-induced magnetic moments of the Pr 3+ ions stabilizes the ordered state. 13

14 Metamagnetic behavior in B [1] Two-sublattice mean-field model I H A(B) ( ) J = H CEF g J µ B JH K 1 J B(A) + K 2 J A(B) K Γ 3 O 2 ( O + O 2 O ) 2 B(A) 2 2 B(A) 2 T=.1 K Metamagnetic behavior was observed at around B=5 T. In mean-field model calculation, order parameter is changed in B, where metamagnetic behavior is found, resulting from level-crossing. # Switching of the OP possibly changes the conduction band? 14

15 Order parameter of the phase Mean-field calculation K. Hattori and H. Tsunetsugu, JPSJ 83, 3479 (213). Phase I: O small O 2 FQ Phase II: Collinear O 2 Phase III: Canted Phase IV: Paramagnetic state I. Ishii et al., JPSJ. 8 (211) Gapless spin-wave excitation at the boarder of the O 2 2 phases. Unusual singularities of χ Q at T=T Q for H= and the critical field for [111]. 15

16 Simultaneous Superconducting and transitions in PrRh 2 Zn 2 ρ (µω cm) 8 5. mt 1.5 mt 4 B= T C B [111] V AC (a. u.) T C.1.2 T (K) T. Onimaru et al., Phys. Rev. B 86 (212) PrRh 2 Zn 2 LaIr 2 Zn 2 C mag / T (J / K 2 mol) 3 T Q =.6 K Rln5 Rln T (K) S (J / Kmol) Superconducting transition occurs at T c =.6 K. The magnetic entropy at T Q is only.1rln2 which is much smaller than Rln2 expected for an order of the nonmagnetic doublet ground state. The quadrupole fluctuations remain active below T Q? 16

17 Ferroquadrupole order and heavy-fermion superconductivity in the isostructural PrTi 2 Al 2 FQ transition at T Q =2 K. Magnetic entorpy at T Q is.9rln2. Superconducting transition at T c =.2 K. m*=16m A. Sakai et al., J. Phys. Soc. Jpn. 81 (212) T c is increased up to T c =1 K at 8 GPa Heavy-fermion superconductor A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 8 (211) K. Matsubabashi et al., Phys. Rev. LeJ. 19 (212)

18 Anomalous temperature dependence of ρ(t) and C(T) PrIr 2 Zn 2 S/T ~.31 µv/k 2 (T. Ikeura and K. Izawa) # Weak hybridization between the 4f and conduction electrons?! Entropy of the Γ 3 doublet is released by dynamic Jahn- Teller distor*on in PrMg 3. K. Araki et al., J. Phys. Soc. Jpn. 81 (212) 2371.

19 Summary PrT 2 Zn 2 (T = Ru, Rh, and Ir) For T=Rh and Ir, the CEF ground state are the non-magnetic Γ 3 doublet with quadrupolar degrees of freedom. Antiferro-quadrupolar () ordering at T Q was confirmed. $ To determine the structure and order parameters, microscopic measurements are in progress. Non-Fermi liquid behavior was observed above T Q. $ Hybridization effect must play an important role in forming the ground state. PrT 2 X 2 (X=Al and Zn) family is appropriate for revealing characteristics of the quadrupoles such as quadrupole order, multi-channel Kondo effect, exotic superconductivity. 19