Coexistence of antiferromagnetism and superconductivity inCeRhIn5under high pressure and magnetic field

Abstract

We report on detailed ac calorimetry measurements under high pressure and magnetic field of CeRhIn5. Under hydrostatic pressure the antiferromagnetic order vanishes near p ⋆ c = 2 GPa due to a first order transition. Superconductivity is found for pressures above 1.5 GPa inside the magnetic ordered phase. However, the superconductivity differ from the pure homogeneous superconducting ground state above 2 GPa. The application of an external magnetic field H ab induces a transition inside the superconducting state above p ⋆ c which is strongly related to the re-entrance of the antiferromagnetism with field. This field-induced supplementary state vanishes above the quantum critical point in this system. The analogy to CeCoIn5 is discussed.The discovery of the cerium heavy fermion CeM In 5 (M = Co, Ir, Rh) systems opened a new route to investigate the interplay of magnetic fluctuations, unconventional superconductivity (SC) and antiferromagnetic order (AF) in strongly correlated electron systems in the vicinity of a quantum phase transition (QPT). While CeCoIn 5 and CeIrIn 5 are unconventional superconductors at ambient pressure (p)with most probably d-wave symmetry below T c = 2.2 K and T c = 0.4 K and suited very close to a QPT, CeRhIn 5 offers the possibility to tune a heavy fermion system from AF to SC as function of pressure [1,2,3]. At ambient pressure CeRhIn 5 orders antiferromagnetically below the Néel temperature T N = 3.8 K in an incommensurate helical structure with propagation vector Q = (1/2, 1/2, 0.297) and a staggered moment of about 0.8 µ B [4]. Neutron scattering experiments under pressure showed that this magnetic structure is almost unchanged under pressure up to the highest investigated pressure of 1.7 GPa [5]. SC has been reported for pressures above 0.9 GPa on the basis of resistivity measurements. Nuclear-quadrupole resonance (NQR) measurements in combination with ac susceptibility have shown that SC and AF coexist on a microscopic scale in the pressure range from p = 1.6 − 1.75 GPa [6]. The spin-lattice relaxation rate shows at low temperature an unexpected 1/T 1 ∝ T dependence which gives evidence for a gap-less nature of the low-lying excitations. A pure superconducting ground-state with line nodes in the gap is attained for p > 2 GPa and 1/T 1 ∝ T 3 has been reported [7]. Previous detailed specific heat measurements under hydrostatic pressure give evidence that the magnetic transition disappears by a first order transition at p The application of an external magnetic field H offers a second parameter to influence the competition between AF and SC. Recently it was shown that a magnetic QCP can be achieved in CeCoIn 5 by the application of a magnetic field of the order of the upper critical field H c2 (0) [10,11]. H c2 (T ) in this compound is strongly Pauli limited and the transition becomes first order at low temperatures [12,13,14]. At high magnetic field near H c2 (0) a new superconducting phase was observed which may be the first example of a Fulde-Ferrel-Ovchinnikov-Larkin (FFLO) state...

Controlling superconductivity by tunable quantum critical points

“…Although the contour of r c is influenced by the presence of new broken symmetries at low temperatures, it shows a similar enhancement of r c above T c at the optimal pressure (P c ). Complete suppression of T N near P c provides compelling evidence that the anomalous enhancement of r c in the pressuretemperature plane is a consequence of critical fluctuations from an AFM QCP under the SC dome of Sn-doped CeRhIn 5 . Fig.…”

“…Although there are many cases of superconductors near spindensity-wave QCPs [19][20][21][22][23][24] , superconductivity in a metal whose quantum criticality is unconventional 4 , for example, YbRh 2 Si 2 , CeCu 6 À x Au x and CeRhIn 5 has been rare, raising a question whether the associated critical bosonic and fermionic fluctuations can provide the necessary attractive interaction to form Cooper pairs. Clear identification of the QCP in 4.4% Sn-doped CeRhIn 5 and its sub-T linear temperature dependence of r c in the normal state indicate that unconventional superconductivity is promoted by an unconventional QCP. Recent numerical calculations have found that singlet-pairing correlations are enhanced at such a QCP 25 .…”

“…The dome of pressure-dependent superconductivity T c (P) is a maximum at 2.3 GPa, the pressure where the antiferromagnetic (AFM) QCP is revealed by an applied magnetic field 4 . T N of CeRhIn 5 also is suppressed gradually with Sn substitution for In and reaches 0 K at a critical concentration x c ¼ 0.07, CeRh(In 1 À x Sn x ) 5 (refs 12,13). A gradual enhancement of the electronic Sommerfeld coefficient of specific heat with decreasing temperature and a sub-T linear dependence of the electrical resistivity at x c are consistent with the non-Fermi-liquid behaviours that are observed at the pressureand field-induced QCP of pure CeRhIn 5 , but with less singularity possibly due to effects of disorder from Sn substitution that also prevent the development of superconductivity at x c .…”

“…In the following, we present electrical resistivity measurements of 4.4% Sn-doped CeRhIn 5 under pressure and magnetic field, which reveals that Sn doping shifts the AFM QCP from 2.3 GPa to 1.3 GPa in undoped CeRhIn 5 . This slight Sn substitution leads to a residual impurity scattering that is 300 times larger at atmospheric pressure than that of pure CeRhIn 5 , which should preclude the possibility of superconductivity.…”

“…Unconventional superconductivity is a potential ordered quantum state that subsumes entropy generated by the proliferation of fluctuations emanating from the quantum critical point (QCP) [3][4][5] . In this case, the spectrum of associated quantum fluctuations determines the structure of the superconducting (SC) gap [6][7][8][9] .…”