arXiv subjects

N. B. Perkins

Publications and source records attributed to N. B. Perkins.

At least 19 recordsLinked to original sources

arXiv2019

Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality

Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $α$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $ω$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $ω$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low $T$. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-$T$ properties of putative spin liquids.

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arXiv2016

Classical spin liquid instability driven by off-diagonal exchange in strong spin-orbit magnets

We show that the off-diagonal exchange anisotropy drives Mott insulators with strong spin-orbit coupling to a classical spin liquid regime, characterized by an infinite number of ground states and Ising variables living on closed or open strings. Depending on the sign of the anisotropy, quantum fluctuations either fail to lift the degeneracy down to very low temperatures, or select non-collinear magnetic states with unconventional spin correlations. The results apply to all 2D and 3D tri-coordinated materials with bond-directional anisotropy, and provide a consistent interpretation of the suppression of the x-ray magnetic circular dichroism signal reported recently for $β$-Li$_2$IrO$_3$ under pressure.

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arXiv2015

Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet

We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na$_2$IrO$_3$, and may also play a role in $α$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.

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arXiv2014

A structural distortion induced magneto-elastic locking in Sr$_2$IrO$_4$ revealed through nonlinear optical harmonic generation

We report a global structural distortion in Sr$_2$IrO$_4$ using spatially resolved optical second and third harmonic generation rotational anisotropy measurements. A symmetry lowering from an $I4_{1}/acd$ to $I4_{1}/a$ space group is observed both above and below the Néel temperature that arises from a staggered tetragonal distortion of the oxygen octahedra. By studying an effective super-exchange Hamiltonian that accounts for this lowered symmetry, we find that perfect locking between the octahedral rotation and magnetic moment canting angles can persist even in the presence of large non-cubic local distortions. Our results explain the origin of the forbidden Bragg peaks recently observed in neutron diffraction experiments and reconcile the observations of strong tetragonal distortion and perfect magneto-elastic locking in Sr$_2$IrO$_4$.

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arXiv2014

Raman Scattering Signatures of Kitaev Spin Liquids in A$_2$ IrO$_3$ Iridates

We study theoretically the Raman scattering response $I(ω)$ in the gapless quantum spin liquid phase of the Kitaev-Heisenberg model. The dominant polarization-independent contribution $I_K (ω)$ reflects the density of states of the emergent Majorana fermions in the ground-state flux-sector. The integrability-breaking Heisenberg exchange generates a second contribution, whose dominant part $I_H (ω)$ has the form of a quantum quench corresponding to an abrupt insertion of four $Z_2$ gauge fluxes. This results in a weakly polarization dependent response with a sharp peak at the energy of the flux excitation accompanied by broad features, which can be related to Majorana fermions in the presence of the perturbed gauge field. We discuss the experimental situation and explore more generally the influence of integrability breaking for Kitaev spin liquid response functions.

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arXiv2011

Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction

We study quantum phase transitions induced by the on-site spin-orbit interaction lambda(L.S) in a toy model of vanadium chains. In the lambda->0 limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, which can be viewed as an orbital liquid. Using a combination of analytical arguments and density-matrix renormalization group calculation, we show that an intermediate phase, where the ferro-orbital state is accompanied by a spin Neel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds CaV2O4 and ZnV2O4 are also discussed.

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arXiv2010

Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds

Magnetic properties of uranium and neptunium compounds showing the coexistence of Kondo screening effect and ferromagnetic order are investigated within the Anderson lattice Hamiltonian with a two-fold degenerate $f$-level in each site, corresponding to $5f^2$ electronic configuration with $S=1$ spins. A derivation of the Schrieffer-Wolff transformation is presented and the resulting Hamiltonian has an effective $f$-band term, in addition to the regular exchange Kondo interaction between the $S=1$ $f$-spins and the $s=1/2$ spins of the conduction electrons. The obtained effective Kondo lattice model can describe both the Kondo regime and a weak delocalization of $5f$-electron. Within this model we compute the Kondo and Curie temperatures as a function of model parameters, namely the Kondo exchange interaction constant $J_K$, the magnetic intersite exchange interaction $J_H$ and the effective $f$-bandwidth. We deduce, therefore, a phase diagram of the model which yields the coexistence of Kondo effect and ferromagnetic ordering and also accounts for the pressure dependence of the Curie temperature of uranium compounds such as UTe.

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arXiv2009

Variational study of the antiferromagnetic insulating phase of V2O3 based on Nth order Muffin-Tin-Orbitals

Motivated by recent results of $N$th order muffin-tin orbital (NMTO) implementation of the density functional theory (DFT), we re-examine low-temperature ground-state properties of the anti-ferromagnetic insulating phase of vanadium sesquioxide V$_2$O$_3$. The hopping matrix elements obtained by the NMTO-downfolding procedure differ significantly from those previously obtained in electronic structure calculations and imply that the in-plane hopping integrals are as important as the out-of-plane ones. We use the NMTO hopping matrix elements as input and perform a variational study of the ground state. We show that the formation of stable molecules throughout the crystal is not favorable in this case and that the experimentally observed magnetic structure can still be obtained in the atomic variational regime. However the resulting ground state (two $t_{2g}$ electrons occupying the degenerate $e_g$ doublet) is in contrast with many well established experimental observations. We discuss the implications of this finding in the light of the non-local electronic correlations certainly present in this compound.

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arXiv2007

The underscreened Kondo lattice model applied to heavy fermion uranium compounds

We present theoretical results for the underscreened Kondo lattice model with localized S=1 spins coupled to a conduction band through a Kondo coupling, $J_K$, and interacting among them ferromagnetically. We use a fermionic representation for the spin operators and expand the Hamiltonian in terms of bosonic fields. For large values of $J_K$, we obtain a ferromagnetically ordered solution and a Kondo regime with a Kondo temperature, $T_K$, larger than the Curie temperature, $T_C$. This finding suggests a scenario for a coexistence of Kondo effect and ferromagnetic order. In some uranium compounds, like $UTe$ or $UCu_{0.9}Sb_{2}$, this kind of coexistence has been experimentally observed: they order ferromagnetically with a Curie temperature of order $T_C \sim 100K$ and exhibit a Kondo behavior for $T > T_C$. The proposed underscreened Kondo lattice model accounts well for the coexistence between magnetic order and Kondo behavior and yields to a new ``ferromagnetic Doniach diagram''.

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arXiv2007

Magnetic excitations in vanadium spinels

We study magnetic excitations in vanadium spinel oxides AV$_2$O$_4$ (A=Zn, Mg, Cd) using two models: first one is a superexchange model for vanadium S=1 spins, second one includes in addition spin-orbit coupling, and crystal anisotropy. We show that the experimentally observed magnetic ordering can be obtained in both models, however the orbital ordering is different with and without spin-orbit coupling and crystal anisotropy. We demonstrate that this difference strongly affects the spin-wave excitation spectrum above the magnetically ordered state, and argue that the neutron measurement of such dispersion is a way to distinguish between the two possible orbital orderings in AV$_2$O$_4$.

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arXiv2007

Doniach diagram for ordered, disordered and underscreened Kondo lattices

The Doniach's diagram has been originally proposed to describe the competition between the local Kondo effect and the intersite RKKY interactions in cerium compounds. Here we discuss the extension of this diagram to different variations of Kondo lattice model. We consider a) ordered cerium compounds where the competition between magnetic order and Kondo effect plays an important role, as $CeRh_2Si_2$, b) disordered cerium systems with competing spin glass phase, magnetic ordered phases and a Kondo phase, as the heavy fermion cerium alloy $CeCu_xNi_{1-x}$ and, c) uranium compounds where a coexistence between Kondo effect and ferromagnetic order has been observed, as UTe. We show that all these cases can be described by a generalized Doniach phase diagram.

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arXiv2006

Coexistence of ferromagnetism and Kondo effect in uranium compounds

Coexistence between ferromagnetic order and Kondo behavior has been observed in some uranium compounds. The underscreened Kondo lattice model can provide a possible description of this coexistence. Here we present a model of a lattice of S=1 spins coupled to the conduction electrons through an intra-site exchange interaction $J_{K}$ and an inter-site ferromagnetic exchange $f-f$ interaction $J_{H}$. Finite temperature results show that the Kondo temperature is larger than the Curie ordering temperature, $T_{C}$, providing a possible scenario for the coexistence of Kondo effect and magnetic order. Also, the Kondo behavior disappears abruptly for low values of $J_{K}$ and smoothly when changing the band occupation. These results are in qualitative agreement with the experimental situation for the above mentioned uranium compounds.

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arXiv2005

Orbital order in vanadium spinels

Motivated by recent theoretical and experimental controversy, we present a theoretical study to clarify the orbital symmetry of the ground state of vanadium spinel oxides AV$_2$O$_4$ (A=Zn, Mg, Cd). The study is based on an effective Hamiltonian with spin-orbital superexchange interaction and a local spin-orbit coupling term. We construct a classical phase-diagram and prove the complex orbital nature of the ground state. Remarkably, with our new analysis we predict correctly also the coherent tetragonal flattening of oxygen octahedra. Finally, through analytical considerations as well as numerical ab-initio simulations, we propose how to detect the predicted complex orbital ordering through vanadium K edge resonant x-ray scattering.

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arXiv2005

Valence-Bond Crystal, and Lattice Distortions in a Pyrochlore Antiferromagnet with Orbital Degeneracy

We discuss the ground state properties of a spin 1/2 magnetic ion with threefold $t_{2g}$ orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti$^{3+}$ ion in B-spinel MgTi$_2$O$_4$. We formulate an effective spin-orbital Hamiltonian and study its low energy sector by constructing several exact-eigenstates in the limit of vanishing Hund's coupling. We find that orbital degrees of freedom modulate the spin-exchange energies, release the infinite spin-degeneracy of pyrochlore structure, and drive the system to a non-magnetic spin-singlet manifold. The latter is a collection of spin-singlet dimers and is, however, highly degenerate with respect of dimer orientations. This ``orientational'' degeneracy is then lifted by a magneto-elastic interaction that optimizes the previous energy gain by distorting the bonds in suitable directions and leading to a tetragonal phase. In this way a valence bond crystal state is formed, through the condensation of dimers along helical chains running around the tetragonal c-axis, as actually observed in MgTi$_2$O$_4$. The orbitally ordered pattern in the dimerized phase is predicted to be of ferro-type along the helices and of antiferro-type between them. Finally, through analytical considerations as well as numerical ab-initio simulations, we predict a possible experimental tool for the observation of such an orbital ordering, through resonant x-ray scattering.

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arXiv2004

Valence bond crystal in a pyrochlore antiferromagnet with orbital degeneracy

We discuss the ground state of a pyrochlore lattice of threefold-orbitally-degenerate $S=1/2$ magnetic ions. We derive an effective spin-orbital Hamiltonian and show that the orbital degrees of freedom can modulate the spin exchange, removing the infinite spin-degeneracy characteristic of pyrochlore structures. The resulting state is a collection of spin-singlet dimers, with a residual degeneracy due to their relative orientation. This latter is lifted by a magneto-elastic interaction, induced in the spin-singlet phase-space, that forces a tetragonal distortion. Such a theory provides an explanation for the helical spin-singlet pattern observed in the B-spinel MgTi$_2$O$_4$.

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arXiv2003

An effective spin-orbital Hamiltonian for the double perovskite Sr$_2$FeW O$_6$: Derivation of the phase diagram

We formulate a superexchange theory of insulating double-perovskite compounds such as Sr$_2$FeWO$_6$. An effective spin-orbital Hamiltonian is derived in the strong coupling limit of Hubbard model for d-electrons on Fe and W ions. The relevant degrees of freedom are the spins S=2 and the three-fold orbital degeneracy of Fe$^{2+}$-ions. W-sites are integrated out by means of a fourth-order perturbative expansion. The magnetically and orbitally ordered ground states of the effective Hamiltonia n are discussed as a function of the model parameters. We show that for realistic values of such parameters the ground state is antiferromagnetic, as experimentally observed. The order found is of type-II, consisting of \{111\} ferromagnetic planes stac ked antiferromagnetically. The orbital order energy scale found is one order of magnitude less than the spi n one.

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arXiv2002

Doping dependence of the exchange energies in bilayer manganites: Role of orbital degrees of freedom

Recently, an intriguing doping dependence of the exchange energies in the bilayer manganites $La_{2-2x}Sr_{1+2x}Mn_2O_7$ has been observed in the neutron scattering experiments. The intra-layer exchange only weakly changed with doping while the inter-layer one drastically decreased. Here we propose a theory which accounts for these experimental findings. We argue, that the observed striking doping dependence of the exchange energies can be attributed to the evaluation of the orbital level splitting with doping. The latter is handled by the interplay between Jahn-Teller effect (supporting an axial orbital) and the orbital anisotropy of the electronic band in the bilayer structure (promoting an in-plane orbital), which is monitored by the Coulomb repulsion. The presented theory, while being a mean-field type, describes well the experimental data and also gives the estimates of the several interesting energy scales involved in the problem.

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arXiv2001

Spin-1 effective Hamiltonian with three degenerate orbitals: An application to the case of V$_2$O$_3$

Motivated by recent neutron and x-ray observations in V$_2$O$_3$, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t_{2g} states containing two electrons coupled to spin S = 1, and use it to re-examine the low-temperature ground-state properties of this compound. An axial trigonal distortion of the cubic states is also taken into account. Since there are no assumptions about the symmetry properties of the hopping integrals involved, the resulting spin-orbital Hamiltonian can be generally applied to any crystallographic configuration of the transition metal ion giving rise to degenerate t_{2g} orbitals. Specializing to the case of V$_2$O$_3$ we consider the antiferromagnetic insulating phase. We find two variational regimes, depending on the relative size of the correlation energy of the vertical pairs and the in-plane interaction energy. The former favors the formation of stable molecules throughout the crystal, while the latter tends to break this correlated state. We determine in both cases the minimizing orbital solutions for various spin configurations, and draw the corresponding phase diagrams. We find that none of the symmetry-breaking stable phases with the real spin structure presents an orbital ordering compatible with the magnetic space group indicated by very recent observations of non-reciprocal x-ray gyrotropy in V$_2$O$_3$. We do however find a compatible solution with very small excitation energy in two distinct regions of the phase space, which might turn into the true ground state of V$_2$O$_3$ due to the favorable coupling with the lattice. We illustrate merits and drawbacks of the various solutions and discuss them in relation to the present experimental evidence.

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