Pressure induced quantum phase transitions in d- and f-electron systems Vladimir A. Sidorov Institute for High Pressure Physics of Russian Academy of Sciences Troitsk - Moscow Workshop “Heavy Fermions and Quantum Phase Transitions”, November 10-12, 2012, IOP CAS, Beijing

Outline Three compounds CePt 2 In 7, CeCoSi and CoS 2 which exhibit quantum phase transition under pressure will be discussed in the presentation. CePt 2 In 7 - a very close analog of CeRhIn 5, where 4f-electrons of Ce play the main role in magnetism, QPT and superconductivity. CeCoSi - a layered antiferromagnet in which Co 3d-electrons become important at high pressure along with Ce 4f-electrons. CoS 2 - a ferromagnet and nearly a half-metal with a high degree of spin polarization. Co 3d-electrons are responsible for magnetism and QPT. A brief review of the experimental technique used in high pressure experiments will be presented.

Collaboration: Los Alamos National Laboratory, USA E. Bauer, P. Tobash, M.Torrez, R.Baumbach, H. Lee, Xin Lu, F. Ronning, J.D. Thompson Sungkyunkwan University, Korea Tuson Park Institute for High Pressure Physics RAS, Russia S.M. Stishov, A.E. Petrova, V.N. Krasnorussky, A.N. Utyuzh Ames Laboratory, USA W. M. Yuhasz, T. A. Lograsso

High pressure apparatus and methods Toroid-type anvil pressure cell 6 GPa at 27 ton, 8 GPa at 34 ton T = 1.2 – 300 K, no magnetic field Before high pressure After 6 GPa The electrical resistivity, magnetic ac-susceptibility and ac-calorimetry measurements can be organized in a single experiment Cylinder-piston (up to 2.2 GPa) and indenter-type (up to 3.2 GPa) cells also were used for some experiments down to 0.1 K and in the magnetic field up to 9 Tesla.

CePt 2 In 7 - pressure induced heavy-fermion superconductivity near QCP Our first measurements on CePt 2 In 7 poly- crystals reveal that it is a close analog of famous CeRhIn 5. Pressure above 3 GPa suppresses magnetism and a broad dome of the heavy-fermion superconductivity appears around quantum critical point. Indium contamination prevents from detailed resistivity measurements in zero magnetic field. The main method was ac-calorimetry. Now In-free single crystals of CePt 2 In 7 became available and we present the new data obtained at high pressure. We constructed P-T diagram based on resistivity and ac-specific heat of single crystals of CePt 2 In 7 and determined some parameters of this heavy-fermion superconductor near QCP.

Resistivity of CePt 2 In 7 single crystals at high pressure The kink on  (T) dependence at T N shift first to higher temperatures And then above ~ 1.5 GPa it shifts to lower temperatures. At 2.47 GPa a signature of a very broad superconducting transition appears at ~2K. At higher pressures it becomes sharp. At 5.3 GPa one can see the onset of a very broad superconducting transition at ~1.7K.. Fits of the low temperature reistivity by the relation  (T) =  0 + AT n give the values of A,  0 and n, which are anomalous near 3.2 GPa. Remarkably, the exponent n is close to 0.5 at this pressure. Similar sublinear behavior of the resistivity was found in CeRhIn5 (T. Park et al., Nature 456(2008) 366).  (T) =  0 + AT n

The upper critical field of CePt 2 In 7 superconductor Resistivity measurements in the indenter cell down to 0.3 K and up to 9 Tesla at 3.1 GPa allow to estimate H c2 (0) and the initial slope dH c2 /dT at T c. The initial slope T/K is close to that -15 T/K observed by Muramatsu et al. (J. Phys. Soc. Japan, 70 (2001) 3362) for CeRhIn 5 heavy- fermion superconductor near pressure-tuned QCP and in the same orientation of the magnetic field. The estimated H c2 (0) ~15 Tesla is lower, than that (~20 Tesla), estimated by Werthamer- Helfand-Hohenberg formula for orbital pair-breaking. So the upper critical field may be limited by Pauli paramagnetic pair breaking as was suggested for CeRhIn 5 by T. Park and J.D. Thompson (New J. Phys. 11 (2009) ).

Specific heat of CePt 2 In 7 single crystals at high pressure The specific heat measurements correlates well with the resistivity measurements. The Neel temperature increases first and then rapidly decreases at high pressure. Above 3.08 GPa the resistive and bulk transitions to the superconducting state take place at the same temperature. But at 2.97 GPa where the resistance of CePt 2 In 7 becomes zero below 2 K, the upturn of the specific heat preceding a peak at the superconducting transition takes place at 1.4 K. This is very similar to CeRhIn 5 (T. Park and J.D. Thompson, New J. Phys. 11 (2009) ). Superconductivity in CePt 2 In 7 emerges from the heave electron normal state, which is due to strong magnetic fluctuations near QCP.

Close analogy between CePt 2 In 7 and CeRhIn 5 P-T diagramEntropy Colossal scattering near QCP  (P)/  (5 GPa) T. Park and J.D. Thompson, New J. Phys. 11 (2009) T. Park et al., Nature 456 (2008) 366

CeCoSi: multiple transitions and quantum criticality at high pressure First synthesis and report of crystal structure: Bodak et al., Zhurnal Struct. Khimii, 11 (1970) 305 Specific heat measurements B. Chevalier et al., Physica B, (2006) 795 AFM transition at 9.2 K (μ eff = 2.8 μ B, Θ p =- 53 K), DOS calculations: B. Chevalier and S.F. Matar, Phys. Rev. B, 70 (2004) Literature data: X-ray absorption spectroscopy: O. Isnard et al., J. Synchrotron Rad., 6 (1999) 701 Single crystals are not available. All experiments were performed on polycrystalline samples.

Properties of arc-melted CeCoSi Single phase material, tetragonal P4/nmm, a = nm, c = nm

Resistivity: pressures up to ~1 GPa. Transformation of the AFM transition related with Ce-sublattice.

Resistivity: pressures up to ~2 GPa. New SDW-like transition.

Resistivity: pressures ~3-4 GPa. Valence transition.

Resistivity: P-T diagram Resistivity measurements at 2 GPa down to 0.1 K Show no signature of superconducrivity near QCP  (T) =  0 + AT n

AC-calorimetry and strain gauge: Possible structural transformation at P ~ 1 GPa. Valence transition at 4.5 GPa.

AC-calorimetry: data. The temperature of AFM transition related with Ce-sublattice does not change much at high pressure, but it splits into two transitions at modest pressure. At ~1.2 GPa the new magnetic transition appear at ~35 K probably related with Co-sublattice and Ce-related transition becomes very broad and is shifted to ~14 K. These big changes in magnetism of CeCoSi are most probably related with a structural transformation at 1.2 GPa. Magnetism is quencehed at ~2 Gpa in the manner of a QCP. The A coefficient of the T 2 term in resistivity and the electronic specific heat coefficient  diverges at 2 GPa. But the enhanced specific heat at 2-3 GPa shows the importance of critical magnetic fluctuations in this pressure range.

AC-calorimetry: P-T diagram. Very complex P-T diagram was found in CeCoSi - structural and valence transitions, two different magnetic transitions, quantum critical point for magnetism and critical end point for valence transition. The structural, valence and magnetic instabilities are probably originate from the effects of hybridization and interplay of Ce 4f and Co 3d-electrons.

First-order-like quantum phase transition in the itinerant ferromagnet CoS 2 C. Utfeld et al., PRL 103 (2009) Below T C = 122 K CoS 2 becomes a ferromagnet with high degree of spin polarization.

T. Goto et al., PRB 56 (1997) Magnetic measurements under pressure reveal metamagnetism and a transformation of a second-order transition to a wekly first-order one at P ~ GPa.

Resistivity measurements of CoS 2 are controversial: in a liquid pressure medium T C decreases faster at high pressure than in a solid medium and the resistive anomaly becomes sharper, whereas it broadens and disappear in a solid pressure medium. S. Yomo, J. Phys. Soc. Japan, 47 (1979) 1486

Resistivity and magnetic ac-susceptibility of CoS 2 at high pressure Compressed helium pressure cell (pressure up to 0.9 Gpa) Compressed liquid toroid-type anvil pressure cell (P up to 6 GPa) V.A. Sidorov et al., Phys. Rev. B, 83 (2011) (R)

Specific heat and magnetic entropy of CoS 2 at high pressure

P-T diagram and nature of the quantum phase transition in CoS 2

Three systems with quantum phase transitions were considered in this presentation: CePt 2 In 7 – a very close analog of CeRhIn 5. The evolution of magnetic entropy through the quantum critical point where one can see the smooth flow of the spin entropy from the magnetic to the superconducting channel gives evidence of the magnetic origin of superconductivity. CeCoSi exhibits a diversity of ground states. The magnetic entropy decreases strongly on approaching the critical pressure (2 GPa) at which quantum critical phenomena usually associated with a QCP are observed. However the residual magnetic anomaly with progressively decreasing magnetic entropy is still visible up to much higher pressures (3 GPa) where the critical end point of the valence transition takes place at low tenperature. These complex phenomena are probably related with the development of magnetism in two different (Ce and Co) magnetic sublattices. CoS 2 exhibits a first-order like quantum phase transition from the ferromagnetic to the paramagnetic state. No quantum critical phenomena are observed and the magnetic entropy decreases to the negligibly small values on approaching the critical pressure. These observations indicate on the progressively increasing itinerancy and the delocalization of the magnetic moment in CoS 2.

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Basics of AC calorimetry in the ideal case If the heater is exited by oscillating power P(t)=P 0 (1-sin  t) then the oscillations of the sample temperature are related with the sample heat capacity (Sullivan and Siedel, 1968) by  T AC = P 0 /  C[1 + (  1 ) -2 + (  2 ) 2 ] -1/2 = (P 0 /  C)F(  ) where  1 = C/K 1 describes the thermal coupling to the bath and  2 describes the thermal coupling sample-heater if (  1 ) 2 >> 1 and (  2 ) 2 << 1 then  T AC = P 0 /  C and F(  )≈1 F(  ) has maximum value [1+2(  2 /  1 )] -1/2 at the optimal frequency  0 =(  1  2 ) -1/2, which is the best for AC calorimetry measurement. Frequency dependence of the product  T AC is to be determined to find  0. It may vary with temperature (and pressure). Appendix

AC calorimetry of Glycerol-water 60/40 at high pressure Frequency dependence of AC calorimetry signal at P=10 kbar The inverse of temperature oscillations (~C) vs T at P=10kbar