Optical gyrotropy in quadrupolar Kondo systems

Abstract

Recent experiments point to a variety of intermetallic systems which exhibit exotic quadrupolar orders driven by the Kondo coupling between conduction electrons and localized quadrupolar degrees of freedom. Using a Luttinger k · p Hamiltonian for the conduction electrons, we study the impact of such quadrupolar order on their energies and wave functions. We discover that such quadrupolar orders can induce a nontrivial Berry curvature for the conduction electron bands, leading to a nonvanishing optical gyrotropic effect. We estimate the magnitude of the gyrotropic response in a candidate quadrupolar material, PrPb3, and discuss the resulting Faraday rotation in thin films.Kondo coupling between conduction electrons and local quadrupolar degrees of freedom is of great interest for realizing the multichannel Kondo lattice model. Candidate materials to realize this physics include Pr-based intermetallic compounds such as PrPb 3 , PrT 2 X 20 (with T =Ir,Rh,Ti,V and X=Zn,Al), PrMg 3 , PrInAg 2 and PrPbBi etc in which the quadrupoles reside on 4f 2 Pr ions.[1-11] These ions possess a non-Kramers Γ 3 doublet ground state due to strong spinorbit coupling and local crystal fields. Matrix elements of the dipole operator, proportional to the total angular momentum, vanish in this doublet Hilbert space. However, matrix elements of quadrupolar operators, rank-2 irreducible tensors formed from the angular momentum, remain nonzero. The Doniach phase diagram suggests that strong hybridization between these quadrupolar doublets and the conduction electrons could lead to unusual heavy Fermi liquids, while weak hybridization could lead to quadrupolar orders driven by Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. [12][13][14][15] Detecting such quadrupolar orders and clarifying the nature of their broken symmetries remain challenging issues due to a dearth of probes which couple directly to the quadrupole moments. In contrast to magnetic dipole order, the ordering of these time-reversal invariant quadrupoles does not directly manifest itself in nuclear magnetic resonance (NMR), muon spin rotation (µSR), or neutron diffraction measurements, necessitating the need for indirect probes. Such probes include: (i) ultrasonic measurements of phonon softening accompanying quadrupolar order, but this is restricted to ferroquadrupolar order; and (ii) magnetic field induced dipolar order, which can be probed by neutron diffraction and whose pattern depends on the underlying quadrupolar state, but this relies on having a field regime strong enough to induce measurable dipolar order while not significantly modifying the underlying quadrupolar order. [6,16] This experimental complexity of probing multipolar orders is also at the heart of the longstanding puzzle of "hidden order" in URu 2 Si 2 . [17,18] In this Letter, we suggest an alternative route -the optical gyrotropic effect [19][20][21][22] -that may provide a sensitive probe of quadrupolar broken symmetries in metals. The optical gyrotropic effect is a certain handedness in the propaga...

Unveiling hidden multipolar orders with magnetostriction

“…Studying the mysterious ordering patterns of higher order multipoles is also often rendered challenging since they typically coexist with conventional dipolar moments. Examples of such symmetry breaking which are of great interest include spin-nematic order 18 in spin S ≥ 1 quantum magnets, quadrupolar charge order in transition metal oxides, and higher multipolar order in actinide dioxides, such as NpO 2 19 , and f -electron heavy fermion materials 20 , such as URu 2 Si 2 21–29 and UBe 13 30–32 . The quest to probe such orders has led to novel experimental techniques, e.g., elasto-resistivity 33–35 to elucidate the quadrupolar order associated with orbital nematicity in the iron pnictides.…”

Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice

“…In fact, the Kitaev model on the hyperhoneycomb lattice had been identified and studied before by Mandal and Surendran [14] who reported the occurrence of a gapless spin liquid with an emergent spinon Fermi surface on a line in momentum space for approximately equal-strength interactions (J x ≈ J y ≈ J z ) as well as the occurrence of a gapped topological spin liquid for anisotropic exchange strength [15]. More recently, extensions to a Heisenberg-Kitaev model [7] have established the stability of this gapless phase in the presence of weak isotropic spin exchange [16][17][18]. This motivated us to ponder alternative three-dimensional lattices that keep the trivalent vertex structure and led us to consider what we call the hyperoctagon lattice [20] illustrated in Fig.…”

Thermal and field-induced transitions in ferroquadrupolar Kondo systems

“…In this framework, weak Kondo coupling leads to two-spin Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions which drive rare-earth local moment ordering and a small FS, while strong Kondo coupling leads to the local moments hybridizing with the conduction electrons resulting in a heavy Fermi liquid with a large FS [1][2][3][4][5][6]. While there has been important work in understanding this physics for materials with local dipole moments [4,5,[7][8][9][10], there is considerably less understanding of higher multipolar orders [11][12][13][14][15][16][17][18].…”