Orbital-exchange and fractional quantum number excitations in an f-electron metal, Yb ₂ Pt ₂ Pb

Abstract

It is generally believed that fractional quantum excitations such as spinons in one-dimensional (1D) spin chains only proliferate and govern magnetism in systems with small and isotropic atomic magnetic moments, such as spin−1/2 Cu 2+ . In contrast, large and anisotropic orbital-dominated moments, such as those produced by strong spin-orbit coupling in the rare earths, are considered to be classical, becoming static as T → 0 since the conventional Heisenberg-Dirac exchange interaction [1, 2] cannot reverse their directions. We present here the results of neutron scattering measurements on Yb 2 Pt 2 Pb that completely negate this common wisdom. A diffuse continuum of magnetic excitations is observed in Yb 2 Pt 2 Pb, direct evidence that the elementary excitations carry a fractional spin quantum number, S = 1/2. The excitations disperse in only one direction, showing that the Yb moments form spin chains that are embedded in, but effectively decoupled from the three-dimensional conduction electron bands in metallic Yb 2 Pt 2 Pb. The spectrum of magnetic excitations strongly resembles the spinon continuum found in S = 1/2 Heisenberg spin chains, and indeed comparison to the 1D XXZ Hamiltonian indicates only a moderate exchange anisotropy, ∆ = J zz /J xx ∼ 3. Here we show how the orbital physics of 4f -electron exchange interactions can reconcile this moderately-anisotropic quantum Hamiltonian with the extreme anisotropy of the putatively classical Yb (J = 7/2) magnetic moments with respect to magnetic fields. We find that the unexpected quantum behavior emerges at low energies from the competition of interactions that act on much higher energy scales, i.e. the strong on-site Coulomb and spin-orbit interactions, as well as the crystal fields, and the inter-site hopping. Our findings thus provide a unique and a hitherto unforeseen manifestation of emergence [3] of quantum physics in the system of semi-classical electronic orbitals.The unusual properties of Yb 2 Pt 2 Pb derive in part from its crystal structure (Fig. 1A,B), where the Yb 3+ ions form ladders along the c−axis, with rungs on the orthogonal bonds of the ShastrySutherland Lattice (SSL) [5] in the ab-planes. Equally important is the strong spin-orbit coupling, which combines spin and orbital degrees of freedom into a large, J = 7/2 Yb moment.The absence of a Kondo effect indicates minimal coupling of Yb to the conduction electrons of this excellent metal [6, 7]. A point-charge model (Supplementary Information) indicates that the crystal electric field (CEF) lifts the eightfold degeneracy of the Yb 3+ moments, producing a Kramers doublet ground state that is a nearly pure state of the total angular momentum, J , |J, m J = |7/2, ±7/2 . The estimated anisotropy of the Landé g-factor is in good agreement with that of the measured magnetization, g /g ⊥ = 7.5(4) [6][7][8], implying strong Ising anisotropy in Yb 2 Pt 2 Pb, which confines the individual Yb moments to two orthogonal sublattices in the The reality is, in fact, completely different.The neutron scatt...

Spinon confinement and a sharp longitudinal mode in Yb2Pt2Pb in magnetic fields

“…1(C)], the continuum is entirely flat, indicating that the spinons are completely incoherent between the chains.In zero field, our measurements agree well with time-dependent density matrix renormalization group (tDMRG) calculations [28] for the XXZ model (1) [ Fig. 1(D)], although experiment indicates that the spectral weight is spread throughout the spinon Brillouin zone (BZ) more evenly and to higher energies than these calculations predict, suggesting non-negligible next-neighbor coupling [26]. Comparisons of our data to theory indicate only a modest anisotropy, ∆ ∼ 2 − 3.…”

“…It is clear that the XXZ Hamiltonian (1) is an appropriate description for Yb 2 Pt 2 Pb despite the large and orbitally dominated moment of the Yb ions. Due to their Kramers doublet ground state of almost pure |J, m J = |7/2, ±7/2 , the Yb moments have a pseudospin S = 1/2 character [26,29]. Rather than quenching the quantum spin dynamics, the strong Ising magnetic anisotropy imposed by the crystal electric field acting on the f −orbital wave function instead singles out the longitudinal excitation channel in two orthogonal sublattices of 1D chains with moments oriented along the (110) and (110) crystal directions.The essential features of the quantum continuum can be understood by noting that each spinon carries spin 1/2, and so the angular momentum selection rules dictate that neutron scattering in Yb 2 Pt 2 Pb measures two-spinon states where the total spin is zero, with one spinon in each spin state, ±1/2.…”

“…In order to describe the boundaries of the two-spinon continuum, it is convenient to adopt the language of particles and holes occupying the fermionic spinon dispersion along the chain direction, E p,h = ± I 2 sin 2 (πq L ) + ∆ 2 S cos 2 (πq L ) 1/2 , 0 ≤ q L < 1 rlu, where ∆ S is an energy gap brought on by the XXZ anisotropy ∆ > 1, and I defines the dispersion bandwidth and encodes the 3 coupling J [ Fig. 1(E)] [1,26,30,31]. In place of electric charge, these particles and holes each carry a half unit of spin angular momentum.…”

“…The saturation field in Yb 2 Pt 2 Pb is 2.3 T, precisely the field needed for µ = 0.485 meV, the value of I when ∆ = 2.6, the number obtained by requiring that Eqn. (1) provides best description of the entire µ 0 H = 0 excitation spectrum [26]. The comparison is less favorable when ∆ is taken to be 3.46, the value derived directly from fitting the lower boundary of the continuum.…”

Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides

“…More broadly, our study offers a new approach to a central question in frustrated magnetic systems, i.e., the nature of their elementary excitations. Yb 2 Pt 2 Pb is a metal recently identified as an anomalous quasi-1D quantum magnet in which electronic transport may be a probe of spinon dynamics [35]. Further application to systems with novel excitations such as monopoles in spin ice [36], spinons in spin liquids [37], and quasi-1D quantum magnets [38] could offer new insights into these phenomena.…”