DOCSLIB.ORG

Spectroscopy of Spinons in Coulomb Quantum Spin Liquids

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

MIT-CTP-5122 Spectroscopy of spinons in Coulomb quantum spin liquids Siddhardh C. Morampudi,1 Frank Wilczek,2, 3, 4, 5, 6 and Chris R. Laumann1 1Department of Physics, Boston University, Boston, MA 02215, USA 2Center for Theoretical Physics, MIT, Cambridge MA 02139, USA 3T. D. Lee Institute, Shanghai, China 4Wilczek Quantum Center, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China 5Department of Physics, Stockholm University, Stockholm Sweden 6Department of Physics and Origins Project, Arizona State University, Tempe AZ 25287 USA We calculate the effect of the emergent photon on threshold production of spinons in U(1) Coulomb spin liquids such as quantum spin ice. The emergent Coulomb interaction modifies the threshold production cross- section dramatically, changing the weak turn-on expected from the density of states to an abrupt onset reflecting the basic coupling parameters. The slow photon typical in existing lattice models and materials suppresses the intensity at finite momentum and allows profuse Cerenkov radiation beyond a critical momentum. These features are broadly consistent with recent numerical and experimental results. Quantum spin liquids are low temperature phases of mag- The most dramatic consequence of the Coulomb interaction netic materials in which quantum fluctuations prevent the between the spinons is a universal non-perturbative enhance- establishment of long-range magnetic order. Theoretically, ment of the threshold cross section for spinon pair production these phases support exotic fractionalized spin excitations at small momentum q. In this regime, the dynamic structure (spinons) and emergent gauge fields [1–4]. One of the most factor in the spin-flip sector observed in neutron scattering ex- promising candidate class of these phases are U(1) Coulomb hibits a step discontinuity, quantum spin liquids such as quantum spin ice - these are ex- 1 q 2 q2 pected to realize an emergent quantum electrodynamics [5– S(q;!) ∼ S0 1 − θ(! − 2∆ − ) (1) 11]. Establishing the exotic phenomena in this context would 4 mc 4m provide a foundation for exploring other conjectured phases rather than the naive square root onset predicted by the density of matter. It will also allow us to explore regimes of quan- of states for spinon pairs [12]. Here, m and ∆ are the effective tum electrodynamics which are theoretically interesting, but mass and gap for the spinons and c is the emergent speed of otherwise inaccessible. At present, the main method to diagnose a spin liquid ex- perimentally is through the the absence of distinct features as- sociated with a local order parameter such as Bragg peaks, and instead the presence of a broad continuum in neutron scatter- ing indicative of a multi-particle continuum. However, broad continua can also arise from other causes and one would like to have more specific signatures which highlight the emergent gauge field. Here we identify and study features in the zero- temperature cross-section for spinon production in Coulomb quantum spin liquids which directly reflect central aspects of the underlying theory, including the existence and the unusual nature of the emergent photon. Threshold behavior— The emergent photon in quantum spin ice arises from coherent ring-exchange processes which lift massive degeneracy within the manifold of spin configu- arXiv:1906.01628v1 [cond-mat.str-el] 4 Jun 2019 rations consistent with classical ice rules. As ring-exchange is FIG. 1. Dynamic structure factor S(q; !) in a Coulomb quantum spin typically a weak process, the photon propagates with a small liquid measuring production of two spinons near threshold. Com- speed c and has a small bandwidth set by the Brillouin zone pared to the naive density of states (inset), the threshold intensity is cutoff. On the other hand, the spinons typically propagate due strongly enhanced for small q due to the emergent Coulomb inter- action over an energy range of order the Rydberg scale α2mc2=4 to direct spin exchange interactions, which can be paramet- above threshold 2∆. Bound Rydberg states (not shown) accumulate rically larger than the ring exchange process. This contrast at the Rydberg scale below the threshold. Breit interactions due to the leads to a strongly non-relativistic theory in which spinons transverse photon reduce the threshold enhancement with increasing readily propagate faster than the emergent speed of light. Tak- q. With larger momentum, the spinons exceed the emergent speed of ing into account both the gapless nature of the photon and its light and emit Cerenkov radiation. This causes the threshold to dis- slow speed leads us to predict distinctive features in the cross appear into a diffuse continuum for q > 2mc and a peak in intensity for ! ∼ ( q − mc)2=m. Both plots use the same scales. section. 2 2 2 2 2 light. The threshold intensity jump, S0 / m e = m cα, part comes from pair production of spinons. Neglecting all is proportional to the strength of the Coulomb interaction and interactions, this is given by the bubble diagram provides a measure of the emergent fine structure constant α. The strong onset in Eqn. (1) is analogous to the Sommerfeld χ(0)(q; i!) = (4) enhancement [13, 14] observed in semiconductor exciton pro- duction [15]. However, here the small speed of light means that transverse photon exchange has non-negligible conse- At zero temperature, this produces the usual 3D density of p quences. Indeed, the transverse interaction is responsible for states, S0(q;!) ∼ m3=2 ! − 2∆ − q2=4m. q 2 The effects of interactions can be taken into account with the suppression of the enhancement with mc at finite mo- mentum q. More dramatically, since spinons emits Cerenkov renormalized propagators G(k; iκ) (double lines) and a vertex radiation when their velocity exceeds the speed of light, there Γ(k1; k2; iκ1; iκ2) (triangle). is a finite lifetime for spinons propagating at high energy and momenta. For momenta q > 2mc, even threshold spinons have a finite Cerenkov lifetime, and then the threshold in the χ(q; i!) = (5) dynamic structure factor becomes entirely diffuse. The universality of the threshold behavior follows from Wigner’s insight, according to which the energy depen- where the vertex Γ is defined through an irreducible 2-particle dence of cross sections just above threshold are governed diagram (hatched square) by long distance interactions between the slowly escaping particles[16, 17]. In our case, these are the Coulomb and Breit interactions expressed in Eq. (10), which can be ana- (6) lyzed semiclassically in the long distance region. The short distance scattering wavefunctions are, of course, sensitive to lattice scale effects, but generically those vary smoothly with We work with a renormalized mass m which takes energy near threshold. Thus, the jump at small q and asso- into account the effect of interactions in G(k; iκ) ≡ ciated low energy spectral weight for spinon production are 1 remarkably direct signatures of the emergent gauge theory. and neglect higher-order cor- iκ − k2=2m − i Im Σ(k; iκ) Computation— A minimal model for the spinon dynam- rections to the dispersion. We discuss lifetime effects in the ics is given in an effective mass approximation by the follow- next section and suppress the self-energy Σ until then. All the ing Lagrangian, momenta have a UV cut-off due to the Brillouin zone. There e 2 are higher order corrections to the photon dispersion on a lat- y j(−ir − σ c A) σj L = σ(i@t − σeφ) σ − tice, but they will not affect the effects described below. 2m Among diagrams resulting from interactions, crossed dia- − j j2 − ∆ σ V ( ) (2) grams in the two-particle irreducible vertex Γ can be neglected (ladder approximation) since they are suppressed by products where σ represent the spinon (σ = +1) and anti-spinon (σ = −1) fields, e is the emergent charge, m is the effective of the Bose occupation factor nB which vanish at temper- mass and ∆ is the spinon gap. The higher-order interaction ature well below the spinon gap 2∆. Thus, the dominant potential V ( ) contains all of the short-range interactions be- diagrams in the perturbative expansion are ladder diagrams tween the spinons including those induced by gapped, weakly with Coulomb interactions (dashed line), transverse photon dispersive visons (magnetic monopoles), which we do not oth- exchange (wavy line) and short-range interactions (line with erwise attempt to model. The emergent scalar φ and vector A star) between the spinon and anti-spinon, potentials are governed by the usual Maxwell Lagrangian (in CGS units), (7) 1 2 1 2 2 LEM = (rφ) + (@tA) − (r × A) (3) 8π c2 Just above threshold, we can neglect the frequency depen- dence of the photon propagator as the spinons separate asymp- with emergent speed of light c. We work in Coulomb gauge totically slowly. In this approximation, the vertex Γ is inde- r · A = 0 throughout. (Note that if the system possesses an pendent of the relative frequency between the two spinons, additional global U(1) spin symmetry, as in the XXZ model and Eq. (5) can be reduced to χ(q; i!) = W (0; q; i!) where for quantum spin ice, then the spinon fields must be doubled to account for the fractional assignment of the global charge. X eik:rΓ(q=2 + k; q=2 − k; i!) W (r; q; i!) ≡ (8) That does not change the results presented here qualitatively.) i! − k2=m − q2=4m − 2∆ The neutron scattering cross-section is proportional to the k dynamic structure factor S(q;!), given by the imaginary part We have introduced W for convenience and temporarily ne- of the dynamic spin susceptibility χ(q;!). The interesting glected radiation effects in the propagators. 3 2 Using the Bethe-Salpeter equation (Eq.
Recommended publications
  • Investigation of the Magnetic and Magnetocaloric Properties of Complex Lanthanide Oxides

    Investigation of the Magnetic and Magnetocaloric Properties of Complex Lanthanide Oxides

    Investigation of the magnetic and magnetocaloric properties of complex lanthanide oxides Paromita Mukherjee Department of Physics University of Cambridge This dissertation is submitted for the degree of Doctor of Philosophy King’s College April 2018 This thesis is dedicated to my parents. Declaration I hereby declare that except where specific reference is made to the work of others, the contents of this dissertation are original and have not been submitted in whole or in part for consideration for any other degree or qualification in the University of Cambridge, or any other university. This dissertation is my own work and contains nothing which is the outcome of work done in collaboration, except as specified in the text and Acknowledgements. This dissertation contains fewer than 60,000 words including abstract, tables, footnotes and appendices. Some of the work described herein has been published as follows: Chapter 3 is an expanded version of: P. Mukherjee, A. C. Sackville Hamilton, H. F. J. Glass, S. E. Dutton, Sensitivity of magnetic properties to chemical pressure in lanthanide garnets Ln3A2X3O12, Ln = Gd, Tb, Dy, Ho, A = Ga, Sc, In, Te, X = Ga, Al, Li, Journal of Physics: Condensed Matter 29, 405808 (2017). Chapter 4 contains material from: P. Mukherjee, S. E. Dutton, Enhanced magnetocaloric effect from Cr substitution in Ising lanthanide gallium garnets Ln3CrGa4O12 (Ln = Tb, Dy, Ho), Advanced Functional Materials 27, 1701950 (2017). P. Mukherjee, H. F. J. Glass, E. Suard, and S. E. Dutton, Relieving the frustration through Mn3+ substitution in holmium gallium garnet, Physical Review B 96, 140412(R) (2017). Chapter 5 contains material from: P.
  • A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci- Distorted Artificial Spin Ice

    A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci- Distorted Artificial Spin Ice

    University of Kentucky UKnowledge Physics and Astronomy Faculty Publications Physics and Astronomy 3-8-2021 Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci- Distorted Artificial Spin Ice Loris Giovannini Università di Ferrara, Italy Barry W. Farmer University of Kentucky, [email protected] Justin S. Woods University of Kentucky, [email protected] Ali Frotanpour University of Kentucky, [email protected] Lance E. De Long University of Kentucky, [email protected] Follow this and additional works at: https://uknowledge.uky.edu/physastron_facpub See next page for additional authors Part of the Physics Commons Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Repository Citation Giovannini, Loris; Farmer, Barry W.; Woods, Justin S.; Frotanpour, Ali; De Long, Lance E.; and Montoncello, Federico, "Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice" (2021). Physics and Astronomy Faculty Publications. 673. https://uknowledge.uky.edu/physastron_facpub/673 This Article is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Physics and Astronomy Faculty Publications by an authorized administrator of UKnowledge. For more information, please contact [email protected]. Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice Digital Object Identifier (DOI) https://doi.org/10.3390/magnetochemistry7030034 Notes/Citation Information Published in Magnetochemistry, v.
  • Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets

    Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets

    nanomaterials Article Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets Aniekan Magnus Ukpong Theoretical and Computational Condensed Matter and Materials Physics Group, School of Chemistry and Physics, University of KwaZulu-Natal, Pietermaritzburg 3201, South Africa; [email protected]; Tel.: +27-33-260-5875 Abstract: In this work, first principles ground state calculations are combined with the dynamic evolution of a classical spin Hamiltonian to study the metamagnetic transitions associated with the field dependence of magnetic properties in frustrated van der Waals ferromagnets. Dynamically stabilized spin textures are obtained relative to the direction of spin quantization as stochastic solutions of the Landau–Lifshitz–Gilbert–Slonczewski equation under the flow of the spin current. By explicitly considering the spin signatures that arise from geometrical frustrations at interfaces, we may observe the emergence of a magnetic skyrmion spin texture and characterize the formation under competing internal fields. The analysis of coercivity and magnetic hysteresis reveals a dynamic switch from a soft to hard magnetic configuration when considering the spin Hall effect on the skyrmion. It is found that heavy metals in capped multilayer heterostructure stacks host field-tunable spiral skyrmions that could serve as unique channels for carrier transport. The results are discussed to show the possibility of using dynamically switchable magnetic bits to read and write data without the need for a spin transfer torque. These results offer insight to the spin transport signatures that Citation: Ukpong, A.M. Emergence dynamically arise from metamagnetic transitions in spintronic devices. of Nontrivial Spin Textures in Frustrated Van Der Waals Keywords: spin current; van der Waals ferromagnets; magnetic skyrmion; spin Hall effect Ferromagnets.
  • Quantum Spin-Ice and Dimer Models with Rydberg Atoms

    Quantum Spin-Ice and Dimer Models with Rydberg Atoms

    PHYSICAL REVIEW X 4, 041037 (2014) Quantum Spin-Ice and Dimer Models with Rydberg Atoms A. W. Glaetzle,1,2,* M. Dalmonte,1,2 R. Nath,1,2,3 I. Rousochatzakis,4 R. Moessner,4 and P. Zoller1,2 1Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria 2Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria 3Indian Institute of Science Education and Research, Pune 411 008, India 4Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany (Received 21 April 2014; revised manuscript received 27 August 2014; published 25 November 2014) Quantum spin-ice represents a paradigmatic example of how the physics of frustrated magnets is related to gauge theories. In the present work, we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly laser-admixing Rydberg states to the atomic ground-states, exploiting the strong angular dependence of van der Waals interactions between Rydberg p states together with the possibility of designing steplike potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state-of-the-art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g., on a 4–8 lattice.
  • Magnetic Field-Induced Intermediate Quantum Spin Liquid with a Spinon

    Magnetic Field-Induced Intermediate Quantum Spin Liquid with a Spinon

    Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface Niravkumar D. Patela and Nandini Trivedia,1 aDepartment of Physics, The Ohio State University, Columbus, OH 43210 Edited by Subir Sachdev, Harvard University, Cambridge, MA, and approved April 26, 2019 (received for review December 15, 2018) The Kitaev model with an applied magnetic field in the H k [111] In this article, we theoretically address the following question: direction shows two transitions: from a nonabelian gapped quan- what is the fate of the Kitaev QSL with increasing magnetic field tum spin liquid (QSL) to a gapless QSL at Hc1 ' 0:2K and a second (Eq. 1) beyond the perturbative limit? Previous studies, using a transition at a higher field Hc2 ' 0:35K to a gapped partially variety of numerical methods (30–33), have pushed the Kitaev polarized phase, where K is the strength of the Kitaev exchange model solution to larger magnetic fields outside the perturbative interaction. We identify the intermediate phase to be a gap- regime. At high magnetic fields, one would expect a polarized less U(1) QSL and determine the spin structure function S(k) and phase. What is surprising is the discovery of an intermediate S the Fermi surface F (k) of the gapless spinons using the density phase sandwiched between the gapped QSL at low fields and the matrix renormalization group (DMRG) method for large honey- polarized phase at high fields when a uniform magnetic field is comb clusters. Further calculations of static spin-spin correlations, applied along the [111] direction (Fig. 1C).
  • Phys. Rev. Lett. (1982) Balents - Nature (2010) Savary Et Al.- Rep

    Phys. Rev. Lett. (1982) Balents - Nature (2010) Savary Et Al.- Rep

    Spectroscopy of spinons in Coulomb quantum spin liquids Quantum spin ice Chris R. Laumann (Boston University) Josephson junction arrays Interacting dipoles Work with: Primary Reference: Siddhardh Morampudi Morampudi, Wilzcek, CRL arXiv:1906.01628 Frank Wilzcek Les Houches School: Topology Something Something September 5, 2019 Collaborators Siddhardh Morampudi Frank Wilczek Summary Emergent photon in the Coulomb spin liquid leads to characteristic signatures in neutron scattering Outline 1. Introduction A. Emergent QED in quantum spin ice B. Spectroscopy 2. Results A. Universal enhancement B. Cerenkov radiation C. Comparison to numerics and experiments 3. Summary New phases beyond broken symmetry paradigm Fractional Quantum Hall Effect Quantum Spin Liquids D.C. Tsui; H.L. Stormer; A.C. Gossard - Phys. Rev. Lett. (1982) Balents - Nature (2010) Savary et al.- Rep. Prog. Phys (2017) Knolle et al. - Ann. Rev. Cond. Mat. (2019) Theoretically describing quantum spin liquids • Lack of local order parameters • Topological ground state degeneracy • Fractionalized excitations Interplay in this talk • Emergent gauge fields How do we get a quantum spin liquid? (Emergent gauge theory) Local constraints + quantum fluctuations + Luck Rare earth pyrochlores Classical spin ice 4f rare-earth Non-magnetic Quantum spin ice Gingras and McClarty - Rep. Prog. Phys. (2014) Rau and Gingras (2019) Pseudo-spins in rare-earth pyrochlores Free ion Pseudo-spins in rare-earth pyrochlores Free ion + Spin-orbit ~ eV Pseudo-spins in rare-earth pyrochlores Free ion + Spin-orbit + Crystal field Single-ion anisotropy ~ eV ~ meV Rau and Gingras (2019) Allowed NN microscopic Hamiltonian Doublet = spin-1/2 like Kramers pair Ising + Heisenberg + Dipolar + Dzyaloshinskii-Moriya Ross et al - Phys.
  • Magnetic Monopoles in Spin Ice

    Magnetic Monopoles in Spin Ice

    Master of Science Thesis Magnetic Monopoles in Spin Ice Axel Nordstr¨om Supervisor: Patrik Henelius Department of Theoretical Physics, School of Engineering Sciences Royal Institute of Technology, SE-106 91 Stockholm, Sweden Stockholm, Sweden 2014 Typeset in LATEX Examensarbete inom ¨amnet teoretisk fysik f¨or avl¨aggande av civilingenj¨orsexamen inom utbildningstprogrammet Teknisk fysik. Graduation thesis on the subject Theoretical Physics for the degree of Master of Science in Engineering from the School of Engineering Sciences. TRITA-FYS 2014:26 ISSN 0280-316X ISRN KTH/FYS/{14:26{SE © Axel Nordstr¨om,May 2014 Printed in Sweden by Universitetsservice US AB, Stockholm May 2014 Abstract In this thesis, we investigate the behaviour of magnetic monopoles in spin ice when an external magnetic field is applied. We find that steady state direct currents of magnetic monopoles cannot be maintained for long and consider the possibility of alternating magnetic currents by investigating the alternating current susceptibility using both analytical and Monte Carlo techniques. Moreover, we look at the transition that occurs when a magnetic field is ap- plied in a 111 direction. We show that the transition is a continuous crossover rather thanh a phasei transition in the nearest neighbour model and we study the behaviour of the system during the crossover, especially at the critical field where a temperature independent state appears. Using Monte Carlo methods and analyti- cal methods based on the Bethe approximation, we find that the mean monopole density is 0.4 monopoles per tetrahedron in the temperature independent state at the critical field. Keywords: spin ice, magnetic monopoles, phase transitions.
  • Observing Spinons and Holons in 1D Antiferromagnets Using Resonant

    Observing Spinons and Holons in 1D Antiferromagnets Using Resonant

    Summary on “Observing spinons and holons in 1D antiferromagnets using resonant inelastic x-ray scattering.” Umesh Kumar1,2 1 Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996, USA 2 Joint Institute for Advanced Materials, The University of Tennessee, Knoxville, TN 37996, USA (Dated Jan 30, 2018) We propose a method to observe spinon and anti-holon excitations at the oxygen K-edge of Sr2CuO3 using resonant inelastic x-ray scattering (RIXS). The evaluated RIXS spectra are rich, containing distinct two- and four-spinon excitations, dispersive antiholon excitations, and combinations thereof. Our results further highlight how RIXS complements inelastic neutron scattering experiments by accessing charge and spin components of fractionalized quasiparticles Introduction:- One-dimensional (1D) magnetic systems are an important playground to study the effects of quasiparticle fractionalization [1], defined below. Hamiltonians of 1D models can be solved with high accuracy using analytical and numerical techniques, which is a good starting point to study strongly correlated systems. The fractionalization in 1D is an exotic phenomenon, in which electronic quasiparticle excitation breaks into charge (“(anti)holon”), spin (“spinon”) and orbit (“orbiton”) degree of freedom, and are observed at different characteristic energy scales. Spin-charge and spin-orbit separation have been observed using angle-resolved photoemission spectroscopy (ARPES) [2] and resonant inelastic x-ray spectroscopy (RIXS) [1], respectively. RIXS is a spectroscopy technique that couples to spin, orbit and charge degree of freedom of the materials under study. Unlike spin-orbit, spin-charge separation has not been observed using RIXS to date. In our work, we propose a RIXS experiment that can observe spin-charge separation at the oxygen K-edge of doped Sr2CuO3, a prototype 1D material.
  • Emergent Phenomena in Spin Crossover Systems

    Emergent Phenomena in Spin Crossover Systems

    Emergent Phenomena in Spin Crossover Systems Jace Alex Cruddas B.Sc. (Hons) Candidate’s ORCID A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in Year School of Mathematics and Physics Abstract In general, a spin crossover (SCO) system is any complex, material or framework containing two thermodynamically accessible spin-states: one high-spin (HS) and one low-spin (LS). The transition between spin-states is addressable by temperature, pressure, light irradiation, electric and magnetic fields, and chemical environment. The transition itself can be first-order, exhibiting hysteresis, continuous or a crossover. Typically, accompanied by the ferroelastic ordering of spin-states. It can also be part of an incomplete or multi-step transition accompanied by the antiferroelastic ordering of spin-states. In general, any alterations to the structural characteristics of SCO systems can have an effect on their bulk properties and behaviours. Consequently, constructing structure-property relations has traditionally been an extremely challenging task, and one of both great theoretical and experimental interest. Understanding the mechanisms behind these bulk properties and behaviours could lead to the rational design of SCO systems with enhanced applications and the synthesis of novel properties and behaviours. In this thesis we show that a simple, elastic model of SCO systems hosts almost all experimentally reported SCO properties and behaviours. We demonstrate clear structure-property relations that explain these results, derive the mechanisms of multi-step transitions and explain why and how intermolecular interactions play a role. We also propose that a new exotic state of matter could exist in elastically frustrated SCO materials and frameworks.
  • Neutron Scattering Studies of Spin Ices and Spin Liquids

    Neutron Scattering Studies of Spin Ices and Spin Liquids

    Collection SFN 13, 04001 (2014) DOI: 10.1051/sfn/20141304001 C Owned by the authors, published by EDP Sciences, 2014 Neutron scattering studies of spin ices and spin liquids T. Fennell Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland Abstract. In frustrated magnets, competition between interactions, usually due to incompatible lattice and exchange geometries, produces an extensively degenerate manifold of groundstates. Exploration of these states results in a highly correlated and strongly fluctuating cooperative paramagnet, a broad classification which includes phases such as spin liquids and spin ices. Generally, there is no long range order and associated broken symmetry, so quantities typically measured by neutron scattering such as magnetic Bragg peaks and magnon dispersions are absent. Instead, spin correlations characterized by emergent gauge structure and exotic fractional quasiparticles may emerge. Neutron scattering is still an excellent tool for the investigation these phenomena, and this review outlines examples of frustrated magnets on the pyrochlore and kagome lattices with reference to experiments and quantities of interest for neutron scattering. 1. PREAMBLE In physics, a frustrated system is one in which all interactions cannot be simultaneously minimized, which is also to say that there is competition amongst the interactions. Frustration is most commonly associated with spin systems [1], where its consequences can be particularly well identified, but is by no means limited to magnetism. Frustrated interactions are also relevant in certain structural problems [2–6], colloids and liquid crystals [7], spin glasses [8], stripe phases [9, 10], Josephson junction arrays [11], stellar nuclear matter [12, 13], social dynamics [14], origami [15], and protein folding [16], to name a few.
  • Imaging Spinon Density Modulations in a 2D Quantum Spin Liquid Wei

    Imaging Spinon Density Modulations in a 2D Quantum Spin Liquid Wei

    Imaging spinon density modulations in a 2D quantum spin liquid Wei Ruan1,2,†, Yi Chen1,2,†, Shujie Tang3,4,5,6,7, Jinwoong Hwang5,8, Hsin-Zon Tsai1,10, Ryan Lee1, Meng Wu1,2, Hyejin Ryu5,9, Salman Kahn1, Franklin Liou1, Caihong Jia1,2,11, Andrew Aikawa1, Choongyu Hwang8, Feng Wang1,2,12, Yongseong Choi13, Steven G. Louie1,2, Patrick A. Lee14, Zhi-Xun Shen3,4, Sung-Kwan Mo5, Michael F. Crommie1,2,12,* 1Department of Physics, University of California, Berkeley, California 94720, USA 2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 3Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA 4Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA 5Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 6CAS Center for Excellence in Superconducting Electronics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China 7School of Physical Science and Technology, Shanghai Tech University, Shanghai 200031, China 8Department of Physics, Pusan National University, Busan 46241, Korea 9Center for Spintronics, Korea Institute of Science and Technology, Seoul 02792, Korea 10International Collaborative Laboratory of 2D Materials for Optoelectronic Science & Technology of Ministry of Education, Engineering Technology Research Center for
  • On the Orbiton a Close Reading of the Nature Letter

    On the Orbiton a Close Reading of the Nature Letter

    return to updates More on the Orbiton a close reading of the Nature letter by Miles Mathis In the May 3, 2012 volume of Nature (485, p. 82), Schlappa et al. present a claim of confirmation of the orbiton. I will analyze that claim here. The authors begin like this: When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. As a reader, you should be concerned that they would start off this important paper with a falsehood. I remind you that according to current theory, the electron does not have real spin and real charge. As with angular momentum, it has spin and charge quantum numbers. But all these quantum numbers are physically unassigned. They are mathematical only. The top physicists and journals and books have been telling us for decades that the electron spin is not to be understood as an actual spin, because they can't make that work in their equations. The spin is either understood to be a virtual spin, or it is understood to be nothing more than a place-filler in the equations. We can say the same of charge, which has never been defined physically to this day. What does a charged particle have that an uncharged particle does not, beyond different math and a different sign? The current theory has no answer. Rather than charge and spin and orbit, we could call these quantum numbers red and blue and green, and nothing would change in the theory.