From Ferromagnetism to Spin-Density Wave: Magnetism in the Two Channel Periodic Anderson Model

Abstract

The magnetic properties of the two channel periodic Anderson model for uranium ions, comprised of a quadrupolar and a magnetic doublet are investigated through the crossover from the mixedvalent to the stable moment regime using dynamical mean field theory. In the mixed-valent regime ferromagnetism is found for low carrier concentration on a hypercubic lattice. The Kondo regime is governed by band magnetism with small effective moments and an ordering vector q close to the nesting vector Q p͑1, 1, . . .͒. In the stable moment regime nearest neighbor antiferromagnetism dominates for less than half band filling and a spin-density wave transition for larger than half filling. PACS numbers: 75.20.Hr, 71.27. + a, 75.30.Mb Heavy Fermion (HF) materials [1] have drawn much attention since the discovery of superconductivity in CeCu 2 Si 2 [2] which is characterized by an anisotropic order parameter with symmetry yet to be determined. Over the years, it became clear that the heavy Fermi liquid is not the ground state: almost all HF materials show magnetic or superconducting phase transitions, which either compete with each other in Ce based compounds or coexist in uranium based materials. Additionally, doubts were cast on whether the Fermi-liquid picture is even applicable for the normal state properties in some U-based [3] or doped compounds [4].In this paper, new results on magnetism in the two channel periodic Anderson model (TCPAM) [5] are presented. In the TCPAM, the restricted local Hilbert space, consisting of a quadrupolar and a magnetic ground state doublet for two different valence configurations, models a uranium ion in a cubic environment, which can fluctuate between 5f 2 ͞5f 3 or 5f 1 ͞5f 2 ground state configurations. On symmetry grounds, the coupling of the ion to the itinerant electrons via hybridization can be characterized by an orbital and a spin label generating an effective two band model [3].It has been shown that the paramagnetic phase exhibits non-Fermi-liquid properties, as manifest in a large residual resistivity [5]. They are caused by the overcompensated effective impurity on each uranium site acting as an incoherent scatterer. The predicted absence of a Drude peak in the optical conductivity [5] has been found experimentally in UBe 13 [6]. On a lattice, however, the residual entropy [7] is expected to be quenched by a phase transition. Candidates are magnetic, channel ordering, or superconducting transitions, which all have to bind the residual magnetic or quadrupolar spin. In the periodic two channel Kondo model, antiferromagnetic and charge ordering phase transitions have been reported in the strong coupling limit of the model jJjr 0 ͑0͒ . 0.5 [8], r 0 ͑e͒ being the noninteracting density of states. Additionally, the authors interpret a sign change in the pair susceptibility for a spin/channel singlet sector as a superconducting transition. The absence of a divergence is viewed as indicator of a first order transition.In this paper, I focus on possible spin transitions. I have calculated t...

Cubic hastatic order in the two-channel Kondo-Heisenberg model

“…The infinite dimensional two-channel Kondo lattice model was studied with dynamical mean-field theory (DMFT) early on by Cox, Jarrell and collaborators, where they found non-Fermi liquid behavior at high temperatures 14,15 , and both odd-frequency superconducting and antiferromagnetic ground states at low temperatures 16,92 ; however, channel symmetry breaking was not examined in these early studies. Recently, Hoshino and collaborators have studied this problem extensively in the infinite-dimensional limit using continuous time quantum Monte Carlo (CTQMC) and DMFT to treat the hypercubic two-channel Kondo lattice 31,67,93,94 .…”

Transport properties of heavy-fermion systems

“…15, S(T ) is plotted for ε f − ε c = −U/2 and fixed total filling for a variety of different values of U [for the low-temperature scale T 0 see Eq. (9) and Sec. VI].…”

Influence of disorder on the transport properties of heavy-fermion systems

“…As a consequence, phase transitions remain mean-field-like in DMFT since k-dependent fluctuations are not included in a local approximation. 20,57,58 The following exact relations for the conduction electron Green function G c ( k, z) and the f -electron Green function G f ( k, z) can be obtained for the PAM (1):…”