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Register a new userOrientation of ground-state orbital in CeCoIn$_5$ and CeRhIn$_5$
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We present core level non-resonant inelastic x-ray scattering (NIXS) data of the heavy fermion compounds CeCoIn$_5$ and CeRhIn$_5$ measured at the Ce $N_{4,5}$-edges. The higher than dipole transitions in NIXS allow determining the orientation of the $Gamma_7$ crystal-field ground-state orbital within the unit cell. The crystal-field parameters of the Ce$M$In$_5$ compounds and related substitution phase diagrams have been investigated in great detail in the past; however, whether the ground-state wavefunction is the $Gamma_7^+$ ($x^2,-,y^2$) or $Gamma_7^-$ ($xy$ orientation) remained undetermined. We show that the $Gamma_7^-$ doublet with lobes along the (110) direction forms the ground state in CeCoIn$_5$ and CeRhIn$_5$. For CeCoIn$_5$, however, we find also some contribution of the first excited state crystal-field state in the ground state due to the stronger hybridization of 4$f$ and conduction electrons, suggesting a smaller $alpha^2$ value than originally anticipated from x-ray absorption. A comparison is made to the results of existing density functional theory plus dynamical mean-field theory calculations.
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The Ce compounds CeCoIn$_5$ and CeRhIn$_5$ are ideal model systems to study the competition of antiferromagnetism (AF) and superconductivity (SC). Here we discuss the pressure--temperature and magnetic field phase diagrams of both compounds. In CeRhIn$_5$ the interesting observation is that in zero magnetic field a coexistence AF+SC phase exist inside the AF phase below the critical pressure $p_{rm c}^star approx 2$ GPa. Above $p_{rm c}^star$ AF is suppressed in zero field but can be re-induced by applying a magnetic field. The collapse of AF under pressure coincides with the abrupt change of the Fermi surface. In CeCoIn$_5$ a new phase appears at low temperatures and high magnetic field (LTHF) which vanishes at the upper critical field $H_{rm c2}$. In both compounds the paramagnetic pair breaking effect dominates at low temperature. We discuss the evolution of the upper critical field under high pressure of both compounds and propose a simple picture of the glue of reentrant magnetism to the upper critical field in order to explain the interplay of antiferromagnetic order and superconductivity.
We discuss recent results on the heavy fermion superconductor CeRhIn$_5$ which presents ideal conditions to study the strong coupling between the suppression of antiferromagnetic order and the appearance of unconventional superconductivity. The appearance of superconductivity as function of pressure is strongly connected to the suppression of the magnetic order. Under magnetic field, the re-entrance of magnetic order inside the superconducting state shows that antiferromagnetism nucleates in the vortex cores. The suppression of antiferromagnetism in CeRhIn$_5$ by Sn doping is compared to that under hydrostatic pressure.
We present linear polarization-dependent soft x-ray absorption spectroscopy data at the Ce $M_{4,5}$ edges of Cd and Sn doped CeCoIn$_5$. The 4$f$ ground state wave functions have been determined for their superconducting, antiferromagnetic and paramagnetic ground states. The absence of changes in the wave functions in CeCo(In$_{1-x}$Cd$_x$)$_5$ suggests the 4$f$,--,conduction electron ($cf$) hybridization is not affected by globally Cd doping, thus supporting the interpretation of magnetic droplets nucleating long range magnetic order. This is contrasted by changes in the wave function due to Sn substitution. Increasing Sn in CeCo(In$_{1-y}$Sn$_y$)$_5$ compresses the 4$f$ orbitals into the tetragonal plane of these materials, suggesting enhanced $cf$ hybridization with the in-plane In(1) atoms and a homogeneous altering of the electronic structure. As these experiments show, the 4$f$ wave functions are a very sensitive probe of small changes in the hybridization of 4$f$ and conduction electrons, even conveying information about direction dependencies.
We have performed $^{59}$Co NMR measurements of CeCoIn$_5$ down to ultralow temperatures. We find that the temperature dependence of the spin-echo intensity provides a good measure of the sample temperature, enabling us to determine a pulse condition not heating up the sample by the NMR pulses down to ultralow temperatures. From the longitudinal relaxation time ($T_1$) measurements at 5 T applied along the $c$ axis, a pronounced peak in $1/T_1T$ is observed at 20 mK, implying an appearance of magnetic order as suggested by the recent quantum oscillation measurements [H. Shishido {it et al.}, Phys. Rev. Lett. {bf 120}, 177201 (2018)]. On the other hand, the NMR spectrum shows no change below 20 mK. Moreover, the peak in $1/T_1 T$ disappears at 6 and 8 T in contrast to the results of the quantum oscillation. We discuss that an antiferromagnetic state with a moment lying in the $a$--$b$ plane can be a possible origin for the peak in $1/T_1 T$ at 5 T.
Magnetization and torque measurements were performed on CeCoIn$_5$ single crystals to study the mixed-state thermodynamics. These measurements allow the determination of both paramagnetic and vortex responses in the mixed-state magnetization. The paramagnetic magnetization is suppressed in the mixed state with the spin susceptibility increasing with increasing magnetic field. The dependence of spin susceptibility on magnetic field is due to the fact that heavy electrons contribute both to superconductivity and paramagnetism and a large Zeeman effect exists in this system. No anomaly in the vortex response was found within the investigated temperature and field range.
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