Magnetic Order with Fractionalized Excitations in Pyrochlore Magnets with Strong Spin-Orbit Coupling

Abstract

A recent inelastic neutron scattering experiment on the pyrochlore magnet Yb 2 Ti 2 O 7 uncovers an unusual scattering continuum in the spin excitation spectrum despite the splayed ferromagnetic order in the ground state. While there exist well defined spin wave excitations at high magnetic fields, the one magnon modes and the two magnon continuum start to strongly overlap upon decreasing the field, and eventually they become the scattering continuum at zero field. Motivated by these observations, we investigate the possible emergence of a magnetically ordered ground state with fractionalized excitations in the spin model with the exchange parameters determined from two previous experiments. Using the fermionic parton mean field theory, we show that the magnetically ordered state with fractionalized excitations can arise as a stable mean field ground state in the presence of sufficiently strong quantum fluctuations. The spin excitation spectrum in such a ground state is computed and shown to have the scattering continuum. Upon increasing the field, the fractionalized magnetically ordered state is suppressed, and is eventually replaced by the conventional magnetically ordered phase at high fields, which is consistent with the experimental data. We discuss further implications of these results to the experiments and possible improvements on the theoretical analysis.

Beyond magnons in Nd2ScNbO7: An Ising pyrochlore antiferromagnet with all in all out order and random fields

“…The quantum fluctuating state supports emergent topological quasiparticles with unusual properties, like magnetic charge, fractionalized values of electron spin, and non-locality [3][4][5][6]. Although the quest for a definitive 3D quantum spin liquid has been unsuccessful so far [3,4], there are proposals that the features of interest-exotic quasiparticles-appear even in materials which have long-range magnetic order but magnetic exchange Hamiltonians close to a quantum spin liquid (called "proximate" or "condensed" quantum spin liquids) [7][8][9][10]. Such behavior has been observed in 1D spin chains [11,12], and is theorized to exist for higher dimensional materials as well.…”

“…The pyrochlore lattice, with its magnetically frustrating geometry of corner-sharing tetrahedra, features prominently in proposals for spin-liquids [5,6,[13][14][15][16][17] and proximate spin liquids [9,10]. A recent class of compounds that has received much attention is pyrochlore magnets based on the Nd 3+ ion [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Competing $U(1)$ and $\mathbb{Z}_2$ dipolar-octupolar quantum spin liquids on the pyrochlore lattice: application to Ce$_2$Zr$_2$O$_7$

“…( 5) leads to a quartic Hamiltonian in bosonic operators. Applying standard MF decoupling procedure [40], every quartic term in the Hamiltonian is first rewritten in the form…”

Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet

“…An interesting possibility is that a QSL coexists with a conventional order. So far, theoretical understandings of such an exotic coexistence are mainly based on mean-field analyses [33][34][35][36][37], and no example has been found by numerical calculation. In some recent experiments, the evidence of fractionalized excitations is found in the materials with magnetically ordered ground states, such as the scattering continuum in the pyrochlore magnet Yb 2 Ti 2 O 7 [38], which demands further theoretical understanding of the possible coexistence of QSL and magnetic order.…”