MAGNETORESISTIVITY and QUANTUM CRITICALITY in HEAVY FERMION SUPERCONDUCTOR Ce1−Xybxcoin5
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MAGNETORESISTIVITY AND QUANTUM CRITICALITY IN HEAVY FERMION SUPERCONDUCTOR Ce1−xYbxCoIn5 A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Derek J. Haney August, 2016 Dissertation written by Derek J. Haney B.S., University of Akron, Akron, OH, 2010 M.A., Kent State University, Kent, OH, 2013 Approved by Carmen Almasan, Ph.D., Chair, Doctoral Dissertation Committee James Gleeson, Ph.D., Members, Doctoral Dissertation Committee Almut Schroeder, Ph.D., Robin Selinger, Ph.D. Accepted by James Gleeson, Ph.D., Chair, Department of Physics James L. Blank, Ph.D., Dean, College of Arts and Sciences ii TABLE OF CONTENTS LIST OF FIGURES . v LIST OF TABLES . xiv Acknowledgments . xv 1 Introduction . 1 1.1 Heavy Fermions . 1 1.1.1 Kondo Effect . 3 1.1.2 Ruderman-Kittel-Kasuya-Yosida Interaction . 7 1.2 Quantum Criticality . 9 1.2.1 Fermi Liquid Theory . 11 1.2.2 Non-Fermi Liquid Behavior Due to Quantum Criticality . 13 1.3 Magnetoresistivity in Heavy Fermions . 15 1.4 CeCoIn5 .................................. 16 1.4.1 CeIn3 and CeM In5 ........................ 16 1.4.2 Ce1−xYbxCoIn5 .......................... 26 2 Experimental Details . 32 2.1 Sample Growth and Preparation . 32 2.2 Physical Property Measurement System . 33 2.3 Helium-3 Option . 36 2.4 Electrical Transport Measurement . 38 iii 2.5 Pressure . 40 2.6 Magnetoresistivity . 45 2.7 Heat Capacity Measurement . 46 3 Pressure Studies of the Quantum Critical Alloy Ce0:93Yb0:07CoIn5 . 49 3.1 Introduction . 49 3.2 Experimental results and discussion . 51 3.3 Conclusions . 64 4 Quantum Criticality and Gap Structure in Ce1−xYbxCoIn5 . 67 4.1 Introduction . 67 4.2 Experimental results and discussion . 69 4.3 Conclusions . 79 5 Magnetoresistivity Study of the Kondo Impurity to Kondo Lattice Crossover in Ce1−xYbxCoIn5 .......................... 80 5.1 Introduction . 80 5.2 Experimental results and discussion . 81 5.3 Conclusions . 93 6 Summary and Outlook . 94 BIBLIOGRAPHY . 99 iv LIST OF FIGURES 1.1 Magnetic resistivity per mole cerium of CexLa1−xCu6 for different dop- ings. Data per Onuki and Komatsubara (1987) [5]. 5 1.2 Indirect exchange interaction J at interatomic spacing a between local moments due to Friedel oscillations of the conduction electron spin density. 8 1.3 Doniach phase diagram, showing TK and TRKKY with changing ex- change interaction J, and illustrating the resulting phases of magnetic order, Fermi liquid, and (possible) superconductivity around a critical Jc. ..................................... 10 1.4 (a) Low temperature T − g phase diagram of typical quantum crit- ical system where g is a tuning parameter, such as field H, pres- sure P , or doping x. (b) Exponent value " of temperature depen- " dence of ρ(T ) / T for YbRh2Si2 for different temperatures and fields. Applied field B is parallel to the c-axis of the crystal. Graph from Custers, et al. 2003) [33]. 14 1.5 Unit cell crystal structure of CeM In5 (M = Co, Rh, or Ir). Figure from Ref. [43]. 18 v 1.6 Figure compiled from Ref. [14]. (a) Temperature dependent resistiv- ity ρ and magnetic susceptibility χ = M=H of CeCoIn5. Open circles represent χ with H k c and open squares represent χ with H ? c. The inset to (a) shows zero-field-cooled χ (circles, left axis) measured in 10 Oe and resistivity (triangles, right axis) in the vicinity of the super- conducting transition. (b) Specific heat C=T for CeCoIn5 at applied fields of H = 0 and H = 50 kOe. The nuclear Schottky contribution (due to a large nuclear quadrupole of In) has been subtracted. The inset to (b) shows the resulting entropy as a function of temperature. 20 1.7 An H − T phase diagram of CeCoIn5 from Ref. [49] showing the ex- istence of a QCP at approximately HQCP = 5:1 T. The solid squares show the temperature/field at which ρ crossed over from NFL ρ / T to FL ρ / T 2. The filled circles show the location of a peak in the field dependence of the magnetoresistance of CeCoIn5. The inset shows the divergence of A, which is from the low-temperature, high-field Fermi 2 liquid resistivity ρ(T ) = ρ0 + AT ..................... 23 vi 1.8 From Ref. [53]. Phase diagram for CeCoIn5 at low temperatures, dis- playing the superconducting phase and the antiferromagnetic phase within the vortex cores. (a) T − P phase diagram at zero field. Nega- tive pressure measurements from Ref. [54], where a negative chemical pressure was obtained by doping CeCoIn5 with cadmium on the in- dium sites. (b) H − P phase diagram at zero temperature, illustrating the quantum critical line. The red line is from Hu and collaborator's calculations [53], and the dotted yellow line is the result of applying theory from Ref. [55] and using parameters derived by Hu et al. (c) H − T phase diagram at zero pressure showing the superconducting dome with the AFM region within it. The inset shows the same at chemically negative pressure (due to cadmium doping), showing that at negative pressures, the superconducting dome is contained within the AFM region rather than the other way around. 25 1.9 From Ref. [59]. Superconducting transition temperature Tc and coher- ence temperature Tcoh plotted as a function of residual resistivity ρ0 for different doping levels of Ce1−xRxCoIn5. Closed symbols represent Tc and open symbols represent Tcoh. The grey upward-pointing tri- angles on the left represent x = 0, i.e., pure CeCoIn5. Regardless of the nature of the dopant, Tc and Tcoh are each suppressed to zero with increasing x (with x / ρ0). 27 vii 1.10 From Ref. [62]. (a) Field dependence of transverse magnetoresistance of CeCoIn5 for different temperatures. Inset shows that of (nominal) Ce0:6Yb0:4CoIn5, which lacks the strong coherent behavior at low field that CeCoIn5 displays. (b) Temperature dependence of Hmax, which is the field value of the peaks in (a), which is where coherent behavior gives way to single-ion behavior. (c) H − x phase diagram illustrating the behavior of HQCP vs. doping. Inset shows Tc and Tcoh at different doping levels of Ce1−xYbxCoIn5 and Ce1−xLaxCoIn5. 28 2.1 (a) A cross-sectional view of the PPMS sample chamber showing its components. (b) A cutaway view of the sample chamber showing the puck with sample at the bottom of the sample chamber. 35 2.2 A schematic showing the use of the T-shaped platform in order to align the c axis of the sample parallel to the applied magnetic field. 37 2.3 (a) A schematic of the four-terminal sensing method. (b) A photograph of a sample in our lab in which we are applying the four-terminal sensing method. 39 2.4 A photograph of a half-assembled pressure cell. 41 2.5 Photographs of a wired feedthrough. (a) Image of the feedthrough, showing the wires coming out of the back. (b) Close-up of the sample on top of the platform. (c) Side view of the platform with the tin manometer on the left and the sample on the right. 44 2.6 A side view of the heat capacity setup. 47 viii 3.1 (a) Resistivity ρa of Ce0:93Yb0:07CoIn5 as a function of temperature T for different pressures P (0, 2.7, 5.1, 7.4, and 8:7 kbar). The arrow at the maximum of the resistivity data marks the coherence temperature Tcoh. (b) Evolution of Tcoh as a function of pressure P . Inset: Super- conducting critical temperature Tc as a function of pressure P . The solid lines are guides to the eye. 53 p 3.2 (a) Fits of the resistivity ρa(P; T ) = ρa0(P ) + A(P )T + B(P ) T for different pressures on Ce0:93Yb0:07CoIn5 over the temperature range 3 K ≤ T ≤ 15 K. (b) Pressure P dependence of the linear T contribu- p tion A and T contribution B, obtained from fits of the resistivity data shown in panel (a). (c) Pressure P dependence of the residual resistivity ρa0, obtained from the fits. 56 p 3.3 (a) Resistivity ρa of Ce0:93Yb0:07CoIn5 as a function of T , in the temperature range 1:8 K ≤ T ≤ 5 K. The solid lines are linear fits of p ∗ the data with ρa(P; T ) = ρa0(P ) + B (P ) T for 1:8 K ≤ T ≤ 5 K. In- p ∗ set: Pressure P dependence of the coefficient B . (b) ρa vs T of Ce0:92Yb0:08CoIn5 measured in zero magnetic field and at 4 T. The 4 T data has been offset upwards by 5 µΩ cm for visual clarity. 58 ix 3.4 Magnetic field H dependence (plotted as function of H2) of magne- toresistivity (MR) ∆ρa/ρa(H = 0) ≡ [ρa(H) − ρa(H = 0)]/ρa(H = 0)] of Ce0:93Yb0:07CoIn5 measured at two different temperatures and am- bient pressure. The dashed line in the main figures marks Hmax, cor- responding to the coherence giving way to single-ion Kondo behavior. Inset: MR data vs H2 measured under 5:1 kbar. The red line shows the quadratic regime of MR. 61 3.5 Temperature T dependence of the maximum in magnetoresistivity Hmax for different pressures P . The solid lines below 10 K are linear fits to the data. 63 3.6 Pressure P dependence of residual resistivity ρa0 (obtained through the fitting of the resistivity data as discussed in the text), normalized to its value at zero pressure (right vertical axis) and P dependence of inverse slope of Hmax(T ) normalized to its value at zero pressure (left vertical axis). 65 4.1 (a) Normalized resistivity ρ(T )/ρ(300 K) of Ce1−xYbxCoIn5 (x = 0:09 and 0:16) as a function of temperature T .