Quantum Criticality in the Heavy-Fermion Superconductor CeCoIn5 by Johnpierre Paglione A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Physics University of Toronto Copyright °c 2005 by Johnpierre Paglione Abstract Quantum Criticality in the Heavy-Fermion Superconductor CeCoIn5 Johnpierre Paglione Doctor of Philosophy Graduate Department of Physics University of Toronto 2005 The study of quantum phase transitions has received a large amount of attention ow- ing to the fact that a range of anomalous properties appear to be linked to the occurrence of quantum fluctuations. CeCoIn5 is a recently discovered heavy-fermion metal with an unconventional superconducting state below Tc = 2:3 K and a range of properties unex- plained by the conventional Fermi liquid theory of metals. As a member of the CeMIn5 family (where M = Co, Ir or Rh), the anomalous transport, magnetic and thermody- namics properties of CeCoIn5 are thought to arise from an antiferromagnetic instability which has yet to be identi¯ed. This study reports measurements of heat and charge transport in CeCoIn5, as a func- tion of temperature T , magnetic ¯eld H and orientation of current J with respect to the crystal axes, which have unearthed a host of incredible properties. These include the identi¯cation of a ¯eld-tuned quantum critical point (QCP) which coincides with the upper critical ¯eld of the superconducting state at Hc2 = 5 T. As evidenced by divergences of the T 2 coe±cients of both electrical and thermal resistivities in the ¯eld- induced Fermi liquid state, the nature of this QCP is further elucidated by the observed relation between ¢H=T scaling and an anomalous T 2=3 dependence of resistivity in the ii high-¯eld non-Fermi liquid regime of J ? [001] transport. Additional measurements of antiferromagnetic CeRhIn5 were also performed in order to shed light on the similarities and di®erences throughout this series of compounds. As a function of current orientation, qualitatively di®erent behaviour is observed both in temperature and ¯eld dependences of transport. Whereas the temperature dependence of resistivity evolves with ¯eld for J ? [001] transport, it remains linear in temperature for the J k [001] orientation, as observed in both the heat and charge channels. At the critical ¯eld, a test of the Wiedemann-Franz law in the T ! 0 limit has revealed a stunning anisotropy: the Wiedemann-Franz law is obeyed by J ? [001] currents, whereas a 27% violation occurs for J k [001] currents. These observations suggest the existence of two distinct QCPs which influence correspondingly di®erent conduction bands, highlighting the multi-band nature of quantum criticality in CeCoIn5. iii Statement Of Originality The study of heavy-fermion materials has a long history as a popular subject of con- densed matter physics which dates back almost thirty years. Although ¯rst reported in 1979, the presence of unconventional superconductivity in heavy-fermion systems has recently found a resurgence of interest owing to the record-breaking transition tempera- tures discovered in the high-temperature cuprate superconductors in 1986. Since then, the as-yet elusive physics of the cuprates has been suggested to share common ground with that of the heavy-fermion superconductors, since both systems exhibit magnetism closely tied to their superconducting states. In this context, much e®ort has been spent on studying the e®ects of magnetic phase transitions which occur at absolute zero temperature, called quantum phase transitions, since they are often accompanied by the appearance of superconductivity. This thesis is aimed at studying such phenomena in CeMIn5, a system of materials which were discovered only recently in 2000, yet have received a stunning amount of attention owing to a plethora of unconventional normal and superconducting state properties. Although a number of publications have reported a wide range of experimental results on this system, detailed characterizations of heat and charge transport at high magnetic ¯elds and low temperatures have not been reported. Thus the motivation behind the current study is to shed light on the non-Fermi liquid and quantum critical properties of the 115 system by providing a detailed account of the anomalous transport behaviour, thus supplying an important contribution to the study of these subjects in the context of this and other systems. In summary, this thesis presents a comprehensive study of the unconventional physics of the 115 system, in the forms of superconductivity, magnetism and quantum criticality as probed through low temperature transport properties. In the course of this study, a number of unexpected and fascinating observations have been made which ¯nd no counterpart in existing literature. These include: iv 1. a strong e®ect of spin fluctuations on electronic thermal transport, as demonstrated in CeRhIn5; 2. a ¯eld-induced quantum phase transition in CeCoIn5 which exactly coincides with the upper critical ¯eld for superconductivity; 3. both veri¯cation and violation of the Wiedemann-Franz law in CeCoIn5 as a func- tion of current orientation at the quantum critical point - a truly new and eminent discovery. None of these observations have been studied in any detail previous to this work, with the latter two unearthing completely new phenomena which ¯nd no explanation within the current theoretical framework of quantum criticality. As a result of these observations, we were the ¯rst to report the existence of a ¯eld-induced quantum phase transition in CeCoIn5, distinguishing it from the zero-¯eld quantum criticality often cited throughout the current set of publications. The last item, which is the most signi¯cant result of this study, highlights the ¯rst evidence of a \violation anisotropy" of the long-standing law of Wiedemann and Franz. This observation ¯nds no similarity to any previous studies of quantum critical systems or any other material in general. All experimental aspects of this study were performed by myself, primarily with the aid of Makariy Tanatar but also in conjunction of all other members of the research group of Louis Taillefer. Experiments were performed using samples provided by a collabora- tion with Cedomir Petrovic (Brookhaven National Laboratory) and Paul Can¯eld (Ames Laboratory). The various projects presented in and related to this thesis have been sum- marized in a number of manuscripts which have been either submitted or accepted for publication. These are listed: ² "Field-induced quantum critical point in CeCoIn5," Johnpierre Paglione, M.A. Tanatar, D.G. Hawthorn, Etienne Boaknin, R.W. Hill, F. Ronning, M. Suther- land, Louis Taillefer, C. Petrovic, P. C. Can¯eld. Phys. Rev. Lett. 91, 246405 (2003). ² "Field-induced quantum critical point in CeCoIn5," Johnpierre Paglione, M.A. Tanatar, D.G. Hawthorn, Etienne Boaknin, R.W. Hill, F. Ronning, M. Suther- land, Louis Taillefer, C. Petrovic, P. C. Can¯eld. Physica C, 408-410, 705 (2004). v ² "Heat transport as a probe of electron scattering by spin fluctuations: the case of antiferromagnetic CeRhIn5," Johnpierre Paglione, M.A. Tanatar, D.G. Hawthorn, R.W. Hill, F. Ronning, M. Sutherland, Louis Taillefer, C. Petrovic, P.C. Can¯eld. Submitted to Phys. Rev. Lett. (cond-mat/0404269) 2=3 ² "T resistivity and the ¯eld-tuned quantum critical point in CeCoIn5," Johnpierre Paglione, M.A. Tanatar, D.G. Hawthorn, E. Boaknin, R.W. Hill, F. Ronning, M. Sutherland, Louis Taillefer, C. Petrovic, P.C. Can¯eld. Submitted to Phys. Rev. Lett. (cond-mat/0405157) ² "Unpaired electrons in the superconducting state of heavy-fermion CeCoIn5," M.A. Tanatar, Johnpierre Paglione, D.G. Hawthorn, E. Boaknin, R.W. Hill, F. Ronning, M. Sutherland, Louis Taillefer, C. Petrovic, P.C. Can¯eld. (unpublished) All of these papers are a direct result of this study and were written primarily by myself, Makariy Tanatar and Louis Taillefer, together with the participation of all other co- authors. vi Acknowledgements After spending many days (and more nights) compiling this work, there are numerous individuals that deserve an acknowledgement for their contribution to its completion. First and foremost, I would like to thank my supervisor, Louis Taillefer, for providing me with an incredible academic experience that ¯nds no counterpart in any previous endeavours I have followed. His leadership and guidance throughout my graduate career remain unparalleled, and the wealth of experience and knowledge that I have absorbed will aid me in all future directions. Also, my Master's supervisor John Perz provided an excellent welcome to my graduate career. I also would like to acknowledge the continuously evolving research group of Prof. Taillefer that I have been a member of for the past ¯ve years. With a beginning in ultrasound research, I am grateful for the excellent technical guidance and teachings of Andrew MacFarlane, Cyril Proust and Christian Lupien, who helped launch my e®orts at becoming a low temperature experimentalist. Also, the continual aid (and distractions) of Etienne Boaknin, Dave Hawthorn and Mike Sutherland have elevated the joys of graduate life toward the undergraduate level of fun. (I would especially like to thank Etienne for pulling us back to the dock...) Finally, without the professional and technical expertise of Rob Hill, Shiyan Li, Filip Ronning and Makariy Tanatar, I would not have been able to complete this project with such quality and quantity. I especially acknowledge Makariy for continuously \leak-checking" both our experimental equipment and our ideas! He is certainly the main contributor to this project. There are a host of professors, post-docs and students which have greatly enhanced my research experience throughout the years, most notably in the context of the Cana- dian Institute for Advanced Research which has provided numerous opportunities for interaction and collaboration. At the University of Toronto, I have enjoyed many fruitful discussions with Profs. Allan Gri±n, Hae-Young Kee, Yong-Baek Kim, Mike Walker and John Wei, along with many laughs from Prof.