Physics and Astronomy › Condensed Matter Physics

Advanced Condensed Matter Physics

Works Count: 38387

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Description

This cluster of papers explores the properties and behavior of quantum spin liquids in frustrated magnets, with a focus on topics such as spin-orbit coupling, Kitaev model, Mott insulators, spin dynamics, superconductivity, geometric frustration, magnetic monopoles, and topological order.

Keywords

Quantum Spin Liquids; Frustrated Magnets; Spin-Orbit Coupling; Kitaev Model; Mott Insulators; Spin Dynamics; Superconductivity; Geometric Frustration; Magnetic Monopoles; Topological Order

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates

2011-05-02

Xiangang Wan , Ari M. Turner , Ashvin Vishwanath +1 more

We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, … We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, and argue that it may be realized in a class of pyrochlore iridates (such as ${\mathrm{Y}}_{2}$Ir${}_{2}$O${}_{7}$) based on calculations using the $\text{LDA}+U$ method. This state is a three-dimensional analog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. For intermediate correlation strengths, we find this to be the ground state of the pyrochlore iridates, coexisting with noncollinear magnetic order. A narrow window of magnetic ``axion'' insulator may also be present. An applied magnetic field is found to induce a metallic ground state.

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Zero-point entropy in ‘spin ice’

1999-05-01

A. P. Ramirez , A. Hayashi , R. J. Cava +2 more

Time-reversal symmetry-breaking superconductivity in Sr2RuO4

1998-08-01

G. M. Luke , Y. Fudamoto , Kenji Kojima +7 more

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Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift

1998-12-01

K. Ishida , Hidekazu Mukuda , Y. Kitaoka +4 more

Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>IrO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

2012-03-20

Yogesh Singh , Soham Manni , Johannes Reuther +5 more

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates ${A}_{2}{\mathrm{IrO}}_{3}$ ($A=\mathrm{Na}$, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital $S=1/2$ moments can be … Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates ${A}_{2}{\mathrm{IrO}}_{3}$ ($A=\mathrm{Na}$, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital $S=1/2$ moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from $\ensuremath{\theta}\ensuremath{\approx}\ensuremath{-}125\text{ }\text{ }\mathrm{K}$ for ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ to $\ensuremath{\theta}\ensuremath{\approx}\ensuremath{-}33\text{ }\text{ }\mathrm{K}$ for ${\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, while the ordering temperature remains roughly the same ${T}_{N}\ensuremath{\approx}15\text{ }\text{ }\mathrm{K}$. Using functional renormalization group calculations we show that this evolution of $\ensuremath{\theta}$ and ${T}_{N}$ as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ is deep in a magnetically ordered regime, while ${\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ appears to be close to a spin-liquid regime.

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Band theory and Mott insulators: HubbardUinstead of StonerI

1991-07-15

В. И. Анисимов , Jan Zaanen , O. K. Andersen

We propose a form for the exchange-correlation potential in local-density band theory, appropriate for Mott insulators. The idea is to use the ``constrained-local-density-approximation'' Hubbard parameter U as the quantity relating … We propose a form for the exchange-correlation potential in local-density band theory, appropriate for Mott insulators. The idea is to use the ``constrained-local-density-approximation'' Hubbard parameter U as the quantity relating the single-particle potentials to the magnetic- (and orbital-) order parameters. Our energy functional is that of the local-density approximation plus the mean-field approximation to the remaining part of the U term. We argue that such a method should make sense, if one accepts the Hubbard model and the success of constrained-local-density-approximation parameter calculations. Using this ab initio scheme, we find that all late-3d-transition-metal monoxides, as well as the parent compounds of the high-${\mathit{T}}_{\mathit{c}}$ compounds, are large-gap magnetic insulators of the charge-transfer type. Further, the method predicts that ${\mathrm{LiNiO}}_{2}$ is a low-spin ferromagnet and NiS a local-moment p-type metal. The present version of the scheme fails for the early-3d-transition-metal monoxides and for the late 3d transition metals.

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On the ground state properties of the anisotropic triangular antiferromagnet

1974-08-01

P. Fazekas , P. W. Anderson

Abstract Our aim is to present further evidence supporting a recent suggestion by Anderson (1973) that the ground state of the triangular antiferromagnet is different from the conventional three-sublattice Néel … Abstract Our aim is to present further evidence supporting a recent suggestion by Anderson (1973) that the ground state of the triangular antiferromagnet is different from the conventional three-sublattice Néel state. The anisotropic Heisenberg model is investigated. Near the Ising limit a peculiar, possibly liquid-like state is found to be energetically more favourable than the Néel-state. It seems to be probable that this type of ground state prevails in the anisotropy region between the Ising model and the isotropic Heisenberg model. The implications for the applicability of the resonating valence bond picture to the S = ½ antiferromagnets are also discussed.

Geometrical Frustration in the Ferromagnetic Pyrochlore<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>Ho</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Ti</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:…

1997-09-29

Mark Harris , S. T. Bramwell , D. F. McMorrow +2 more

We report a detailed study of the pyrochlore ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, in which the magnetic ions $({\mathrm{Ho}}^{3+})$ are ferromagnetically coupled with $J\ensuremath{\sim}1\mathrm{K}$. We show that the presence of local Ising anisotropy leads … We report a detailed study of the pyrochlore ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, in which the magnetic ions $({\mathrm{Ho}}^{3+})$ are ferromagnetically coupled with $J\ensuremath{\sim}1\mathrm{K}$. We show that the presence of local Ising anisotropy leads to a geometrically frustrated ground state, preventing long-range magnetic order down to at least 0.05 K. However, unlike in the case of a frustrated antiferromagnet, this disorder is principally static. In a magnetic field, the ground-state degeneracy is broken and ordered magnetic phases are formed which display an unusual history dependence due to the slow dynamics of the system. These results represent the first experimental evidence for geometrical frustration in a ferromagnetic system.

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Oxide pyrochlores — A review

1983-01-01

M. A. Subramanian , G. Aravamudan , G. V. Subba Rao

Novel<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>J</mml:mi><mml:mi>eff</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Mott State Induced by Relativistic Spin-Orbit Coupling in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>IrO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>

2008-08-15

Beom Joon Kim , Hosub Jin , S. J. Moon +7 more

We investigated the electronic structure of 5d transition-metal oxide Sr2IrO4 using angle-resolved photoemission, optical conductivity, x-ray absorption measurements, and first-principles band calculations. The system was found to be well described … We investigated the electronic structure of 5d transition-metal oxide Sr2IrO4 using angle-resolved photoemission, optical conductivity, x-ray absorption measurements, and first-principles band calculations. The system was found to be well described by novel effective total angular momentum Jeff states, in which the relativistic spin-orbit coupling is fully taken into account under a large crystal field. Despite delocalized Ir 5d states, the Jeff states form such narrow bands that even a small correlation energy leads to the Jeff=1/2 Mott ground state with unique electronic and magnetic behaviors, suggesting a new class of Jeff quantum spin driven correlated-electron phenomena.

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Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

2006-01-19

Ruifang Wang , Cristiano Nisoli , R. S. Freitas +7 more

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Synthesis, Structure, and Bonding in Polyiodide and Metal Iodide−Iodine Systems

2003-03-22

Per H. Svensson , Lars Kloo

ADVERTISEMENT RETURN TO ISSUEArticleNEXTSynthesis, Structure, and Bonding in Polyiodide and Metal Iodide−Iodine SystemsPer H. Svensson and Lars KlooView Author Information Inorganic Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden … ADVERTISEMENT RETURN TO ISSUEArticleNEXTSynthesis, Structure, and Bonding in Polyiodide and Metal Iodide−Iodine SystemsPer H. Svensson and Lars KlooView Author Information Inorganic Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden Cite this: Chem. Rev. 2003, 103, 5, 1649–1684Publication Date (Web):March 22, 2003Publication History Received10 July 2002Published online22 March 2003Published inissue 1 May 2003https://pubs.acs.org/doi/10.1021/cr0204101https://doi.org/10.1021/cr0204101research-articleACS PublicationsCopyright © 2003 American Chemical SocietyRequest reuse permissionsArticle Views11035Altmetric-Citations727LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Anions,Chemical structure,Iodine,Ions,Molecules Get e-Alerts

Interaction between the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-Shells in the Transition Metals. II. Ferromagnetic Compounds of Manganese with Perovskite Structure

1951-05-01

Clarence Zener

Recently, Jonker and Van Santen have found an empirical correlation between electrical conduction and ferromagnetism in certain compounds of manganese with perovskite structure. This observed correlation is herein interpreted in … Recently, Jonker and Van Santen have found an empirical correlation between electrical conduction and ferromagnetism in certain compounds of manganese with perovskite structure. This observed correlation is herein interpreted in terms of those principles governing the interaction of the $d$-shells of the transition metals which were enunciated in the first paper of this series. Both electrical conduction and ferromagnetic coupling in these compounds are found to arise from a double exchange process, and a quantitative relation is developed between electrical conductivity and the ferromagnetic Curie temperature.

Mott physics and band topology in materials with strong spin–orbit interaction

2010-03-21

D. A. Pesin , Leon Balents

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Spin Dynamics of the Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Kagome Lattice Antiferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ZnCu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>OH</mml:mi><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mi>Cl</mml:mi><mml:mn>2</…

2007-03-09

Joel S. Helton , K. Matan , Matthew P. Shores +7 more

We have performed thermodynamic and neutron scattering measurements on the S=1/2 kagome lattice antiferromagnet Zn Cu_3 (OH)_6 Cl_2. The susceptibility indicates a Curie-Weiss temperature of ~ -300 K; however, no … We have performed thermodynamic and neutron scattering measurements on the S=1/2 kagome lattice antiferromagnet Zn Cu_3 (OH)_6 Cl_2. The susceptibility indicates a Curie-Weiss temperature of ~ -300 K; however, no magnetic order is observed down to 50 mK. Inelastic neutron scattering reveals a spectrum of low energy spin excitations with no observable gap down to 0.1 meV. The specific heat at low-T follows a power law with exponent less than or equal to 1. These results suggest that an unusual spin-liquid state with essentially gapless excitations is realized in this kagome lattice system.

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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">RuCl</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:math>: A spin-orbit assisted Mott insulator on a honeycomb lattice

2014-07-29

K. W. Plumb , J. P. Clancy , Luke J. Sandilands +5 more

We examine the role of spin-orbit coupling in the electronic structure of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, in which Ru ions in $4{d}^{5}$ configuration form a honeycomb lattice. Our x-ray absorption spectroscopy measurements at … We examine the role of spin-orbit coupling in the electronic structure of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, in which Ru ions in $4{d}^{5}$ configuration form a honeycomb lattice. Our x-ray absorption spectroscopy measurements at the Ru $L$ edges exhibit distinct spectral features associated with the presence of substantial spin-orbit coupling, as well as an anomalously large branching ratio. Furthermore the measured optical spectra can be described very well with first-principles electronic structure calculations obtained by taking into account both spin-orbit coupling and electron correlations. We propose that $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ is a spin-orbit assisted Mott insulator, and that the bond-dependent Kitaev interaction may be important for understanding magnetism of this compound.

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Theory of the First-Order Magnetic Phase Change in U<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

1966-01-14

M. Blume

A simple model accounts semiquantitatively for the first-order magnetic phase change observed recently in U${\mathrm{O}}_{2}$ by Frazer, Shirane, Cox, and Olsen. The model assumes that the electronic structure of the … A simple model accounts semiquantitatively for the first-order magnetic phase change observed recently in U${\mathrm{O}}_{2}$ by Frazer, Shirane, Cox, and Olsen. The model assumes that the electronic structure of the paramagnetic ${\mathrm{U}}^{4+}$ ion consists of a nonmagnetic singlet ground state and a low-lying magnetic triplet, and that only bilinear isotropic exchange interactions are present. In a molecular-field theory the triplet is split by an internal field proportional to the magnetization. If the molecular field is sufficiently strong, one of the components of the triplet will lie, in the magnetic state, below the singlet, and a self-consistent magnetic solution is obtained at $T=0$. Increasing the temperature causes the magnetization to be reduced, and the low-lying component of the triplet is raised in energy. It is shown that a "catastrophe" may occur at some critical temperature so that the magnetization is reduced discontinuously to zero. It is also found that, depending on the ratio of the singlet-triplet energy difference to the molecular-field splitting of the triplet, one obtains either no magnetic ordering, a first-order phase change, or a second-order transition.

A spin triplet supercurrent through the half-metallic ferromagnet CrO2

2006-02-01

R. S. Keizer , Sebastian T. B. Goennenwein , T. M. Klapwijk +3 more

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Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet

2012-12-01

Tianheng Han , Joel S. Helton , Shaoyan Chu +4 more

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Calculation of Coulomb-interaction parameters for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:…

1989-05-01

Mark S. Hybertsen , Michael Schlüter , N. E. Christensen

The constrained-density-functional approach is used to calculate the energy surface as a function of local charge fluctuations in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. This energy surface is then mapped onto a self-consistent mean-field solution … The constrained-density-functional approach is used to calculate the energy surface as a function of local charge fluctuations in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. This energy surface is then mapped onto a self-consistent mean-field solution of the Hubbard model which allows extraction of the Coulomb interaction parameters when combined with one-electron parameters derived from band-structure results. Variations in the local Cu d charges and in-plane O p charge are considered for the prototypical high-${T}_{c}$ parent oxide ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. To isolate the charge fluctuations, the calculations are done in a supercell of size up to 2\ifmmode\times\else\texttimes\fi{}2 in the basal plane. The local density-functional calculations are done using the linear muffin-tin orbital approach with the atomic sphere approximation. In the Hubbard Hamiltonian, the Cu d(${x}^{2}$-${y}^{2}$) and O p(x,y) orbitals are included in the pd\ensuremath{\sigma} configuration. The one-electron parameters consist of bare on-site energies (${\ensuremath{\varepsilon}}_{p}$,${\ensuremath{\varepsilon}}_{d}$) and first-neighbor hopping from Cu to O (${t}_{\mathrm{pd}}$) and from O to O (${t}_{\mathrm{pp}}$) while the Coulomb-interaction parameters include on-site (${U}_{d}$,${U}_{p}$) and intersite (${U}_{\mathrm{pd}}$,${U}_{\mathrm{pp}}$) terms. Results of the present calculation indicate that ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ is intermediate between the extreme spin or charge fluctuation regimes. This places strong constraints on the available parameter space for theories of high-${T}_{c}$ superconductivity based on the extended Hubbard model.

Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure

1987-03-02

Meiying Wu , J. R. Ashburn , C. J. Torng +6 more

A stable and reproducible superconductivity transition between 80 and 93 K has been unambiguously observed both resistively and magnetically in a new Y-Ba-Cu-O compound system at ambient pressure. An estimated … A stable and reproducible superconductivity transition between 80 and 93 K has been unambiguously observed both resistively and magnetically in a new Y-Ba-Cu-O compound system at ambient pressure. An estimated upper critical field ${\mathrm{H}}_{\mathrm{c}2}$(0) between 80 and 180 T was obtained.

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Exact Dimer Ground State and Quantized Magnetization Plateaus in the Two-Dimensional Spin System<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>SrCu</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>BO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi /></mml:…

1999-04-12

Hiroshi Kageyama , Kazuyoshi Yoshimura , Raivo Stern +7 more

Magnetic susceptibility, Cu NQR, and high-filed magnetization have been measured in polycrystalline $\mathrm{SrCu}{}_{2}(\mathrm{BO}{}_{3}{)}_{2}$ having a two-dimensional (2D) orthogonal network of Cu dimers. This cuprate provides a new class of 2D … Magnetic susceptibility, Cu NQR, and high-filed magnetization have been measured in polycrystalline $\mathrm{SrCu}{}_{2}(\mathrm{BO}{}_{3}{)}_{2}$ having a two-dimensional (2D) orthogonal network of Cu dimers. This cuprate provides a new class of 2D spin-gap system $(\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}30\mathrm{K})$ in which the ground state can be solved ``exactly.'' Furthermore, in the magnetization, two plateaus corresponding to $\frac{1}{4}$ and $\frac{1}{8}$ of the full Cu moment were first observed for 2D quantum spin systems.

Geometrically frustrated magnetic materials

2001-01-01

John E. Greedan

The current state of efforts to understand the phenomenon of geometric magnetic frustration is described in the context of several key materials. All are transition metal oxides which crystallize with … The current state of efforts to understand the phenomenon of geometric magnetic frustration is described in the context of several key materials. All are transition metal oxides which crystallize with magnetic lattices which are geometrically or topologically prone to frustration such as those based on triangles or tetrahedra which share corners, edges or faces. These include the anhydrous alums, jarosites, pyrochlores, spinels, magnetoplumbites, garnets, ordered NaCl and other structure types. Special attention is paid to materials which do not undergo long range ordering at the lowest temperatures but instead form exotic ground states such as spin glasses, spin liquids and spin ices, and to S = 1/2 based materials.

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

2011-08-09

Kaiyu Yang , Yuan-Ming Lu , Ying Ran

There have been lots of interest in pyrochlore Iridates A2Ir2O7 where both strong spin-orbital coupling and strong correlation are present. A recent LDA calculation suggests that the system is likely … There have been lots of interest in pyrochlore Iridates A2Ir2O7 where both strong spin-orbital coupling and strong correlation are present. A recent LDA calculation suggests that the system is likely in a novel three dimensional topological semi-metallic phase: a Weyl semi-metal. Such a system has zero carrier density and arrives at the quantum limit even in a weak magnetic field. In this paper we discuss two novel quantum effects of this system in a magnetic field: a pressure-induced anomalous Hall effect and a magnetic field induced charge density wave at the pinned wavevector connecting Weyl nodes with opposite chiralities. A general formula of the anomalous hall coefficients in a Weyl semi-metal is also given. Both proposed effects can be probed by experiments in the near future, and can be used to detect the Weyl semi-metal phase.

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The superconductivity of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">RuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and the physics of spin-triplet pairing

2003-05-01

A. P. Mackenzie , Y. Maeno

This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the … This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

Electrical and Optical Properties of Narrow-Band Materials

1970-10-15

David Adler , J. Feinleib

The electrical and optical properties of materials which are characterized by narrow bands in the vicinity of the Fermi energy are discussed. For such materials, electronic correlations and the electron-phonon … The electrical and optical properties of materials which are characterized by narrow bands in the vicinity of the Fermi energy are discussed. For such materials, electronic correlations and the electron-phonon coupling must be considered explicitly. Correlations in $f$ bands and in extremely narrow $d$ bands can be handled in the ionic limit of the Hubbard Hamiltonian. It is shown that free carriers in such bands form small polarons which contribute to conduction only by means of thermally activated hopping. Wider bands may also exist near the Fermi energy. Carriers in these bands may form large polarons and give a bandlike contribution to conductivity. A model is proposed for determining the density of states of pure stoichiometric crystals, beginning with the free-ion energy levels, and taking into account the Madelung potential, screening and covalency effects, crystalline-field stabilizations, and overlap effects. Exciton states are considered explicitly. The Franck-Condon principle necessitates the construction of different densities of states for electrical conductivity and optical absorption. Because of the bulk of experimental data presently available, the model is applied primarily to NiO. The many-particle density of states of pure stoichiometric NiO is calculated and is shown to be in agreement with the available experimental data. When impurities are present or nonstoichiometry exists, additional transitions must be discussed from first principles. The case of Li-doped NiO is discussed in detail. The calculations are consistent with the large mass of experimental information on this material. It is concluded that the predominant mechanism for conduction between 200 and 1000 \ifmmode^\circ\else\textdegree\fi{}K is the transport of hole-like large polarons in the oxygen $2p$ band. A method for representing the many-particle density of states on an effective one-electron diagram is discussed. It is shown that if correlations are important, donor or acceptor levels cannot be drawn as localized levels in the energy gap when multiple conduction or valence bands are present. This result comes about because extrinsic ionization energies of two correlated bands differ by an energy which bears no simple relation to the difference in energies of the intrinsic excitations, which are conventionally used to determine the relative positions of the bands.

Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>IrO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

2010-07-09

Jiří Chaloupka , George Jackeli , Giniyat Khaliullin

We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between ${\mathrm{Ir}}^{4+}$ ions in a family of layered iridates ${A}_{2}{\mathrm{IrO}}_{3}$ ($A=\mathrm{Li},\mathrm{Na}$). Depending on the … We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between ${\mathrm{Ir}}^{4+}$ ions in a family of layered iridates ${A}_{2}{\mathrm{IrO}}_{3}$ ($A=\mathrm{Li},\mathrm{Na}$). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional N\'eel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

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A Structurally Perfect S = 1/2 Kagomé Antiferromagnet

2005-09-09

Matthew P. Shores , Emily A. Nytko , Bart M. Bartlett +1 more

The syntheses and magnetic susceptibilities of a pure series of rare copper minerals from the atacamite family with general formula ZnxCu4-x(OH)6Cl2 (0 </= x </= 1) are reported. The structure … The syntheses and magnetic susceptibilities of a pure series of rare copper minerals from the atacamite family with general formula ZnxCu4-x(OH)6Cl2 (0 </= x </= 1) are reported. The structure of these compounds features a corner-sharing triangular kagomé lattice of antiferromagnetically coupled Cu(II) ions. We correlate the onset of magnetic ordering with the mole fraction of paramagnetic Cu(II) ions located between kagomé layers and demonstrate that the fully Zn-substituted compound shows no magnetic ordering down to 2 K, resulting in a highly spin-frustrated S = 1/2 lattice.

Coulomb gap and low temperature conductivity of disordered systems

1975-02-21

A. L. Efros , B. I. Shklovskiǐ

The Coulomb interaction between localized electrons is shown to create a 'soft' gap in the density of states near the Fermi level. The new temperature dependence of the hopping DC … The Coulomb interaction between localized electrons is shown to create a 'soft' gap in the density of states near the Fermi level. The new temperature dependence of the hopping DC conductivity is the most important manifestation of the gap. The form of the density of states within the gap is discussed.

Spin Chirality, Berry Phase, and Anomalous Hall Effect in a Frustrated Ferromagnet

2001-03-30

Y. Taguchi , Yasuaki Oohara , H. Yoshizawa +2 more

An electron hopping on non-coplanar spin sites with spin chirality obtains a complex phase factor (Berry phase) in its quantum mechanical amplitude that acts as an internal magnetic field, and … An electron hopping on non-coplanar spin sites with spin chirality obtains a complex phase factor (Berry phase) in its quantum mechanical amplitude that acts as an internal magnetic field, and is predicted to manifest itself in the Hall effect when it is not cancelled. The present combined work of transport measurement, neutron scattering, and theoretical calculation provides evidence that the gigantic anomalous Hall effect observed in Nd2Mo2O7, a pyrochlore ferromagnet with geometrically frustrated lattice structure, is mostly due to the spin chirality and the associated Berry phase originating from the Mo spin tilting.

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models

2009-01-06

George Jackeli , Giniyat Khaliullin

We study the magnetic interactions in Mott-Hubbard systems with partially filled ${t}_{2g}$ levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a … We study the magnetic interactions in Mott-Hubbard systems with partially filled ${t}_{2g}$ levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to ``engineer'' in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain ``weak'' ferromagnetism, with an anomalously large ferromagnetic moment, in ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$.

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Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

2011-04-29

Simeng Yan , David A. Huse , Steven R. White

We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We … We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.

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The Verwey transition - a topical review

2002-03-15

F. Walz

This review encompasses the story of the Verwey transition in magnetite over a period of about 90 years, from its discovery up to the present. Despite this long period of … This review encompasses the story of the Verwey transition in magnetite over a period of about 90 years, from its discovery up to the present. Despite this long period of thorough investigation, the intricate multi-particle system Fe3O4 with its various magneto-electronic interactions is not completely understood, as yet - although considerable progress has been achieved, especially during the last two decades. It therefore appeared appropriate to subdivide this retrospect into three eras: (I) from the detection of the effect to the Verwey model (1913-1947), being followed by a period of: (II) checking, questioning and modification of Verwey's original concepts (1947-1979). Owing to prevailing under-estimation of the role of crystal preparation and qualitiy control, this period is also characterized by a series of uncertainties and erroneous statements concerning the reaction order (one or two) and type of the transition (multi-stage or single stage). These latter problems, beyond others, could definitely be solved within era (III) (1979 to the present) - in favour of a first-order, single-stage transition near 125 K - on the basis of experimental and theoretical standards established in the course of a most inspiring conference organized in 1979 by Sir Nevill Mott in Cambridge and solely devoted to the present topic. Regarding the experimental field of further research, the remarkable efficiency of magnetic after-effect (MAE) spectroscopy as a sensitive probe for quality control and investigation of low-temperature (4 K<T<Tv) charge transport mechanisms is pointed out. Under theoretical aspects two concepts, going back to Mott and Ihle-Lorenz, presently appear most promising. Mott's view of the Verwey transition, as corresponding to the phase changing of a Wigner glass (T>Tv) into a Wigner crystal (T<Tv), describes most adequately the various low-temperature mechanisms in Fe3O4 in terms of tunnelling and variable range hopping of small polarons. On the other hand, the well-elaborated Ihle-Lorenz model, assuming a superposition of polaron-band and -hopping conductivity, is in better agreement with the high-temperature data (Tv<T<600 K).

Finite Size Effects in Antiferromagnetic NiO Nanoparticles

1997-08-18

R. H. Kodama , Salah A. Makhlouf , A. E. Berkowitz

Antiferromagnetic NiO nanoparticles exhibit anomalous magnetic properties, such as large moments, and coercivities and loop shifts of up to 10 kOe. This behavior is difficult to understand in terms of … Antiferromagnetic NiO nanoparticles exhibit anomalous magnetic properties, such as large moments, and coercivities and loop shifts of up to 10 kOe. This behavior is difficult to understand in terms of 2-sublattice antiferromagnetic ordering which is accepted for bulk NiO. Numerical modeling of spin configurations in these nanoparticles yields 8-, 6-, or 4-sublattice configurations, indicating a new finite size effect, in which the reduced coordination of surface spins causes a fundamental change in the magnetic order throughout the particle. The relatively weak coupling between the sublattices allows a variety of reversal paths for the spins upon cycling the applied field, resulting in large coercivities and loop shifts.

Raman and x-ray studies of Ce1−xRExO2−y, where RE=La, Pr, Nd, Eu, Gd, and Tb

1994-08-15

J. R. McBride , K. C. Hass , B. D. Poindexter +1 more

Powdered samples of the type Ce1−xRExO2−y, where RE=La, Pr, Nd, Eu, Gd, and Tb, are synthesized over the range 0≤x≤0.5 starting from nitrate solutions of the rare earths. X-ray diffraction … Powdered samples of the type Ce1−xRExO2−y, where RE=La, Pr, Nd, Eu, Gd, and Tb, are synthesized over the range 0≤x≤0.5 starting from nitrate solutions of the rare earths. X-ray diffraction and Raman scattering are used to analyze the samples. These compounds, at least in the low doping regime and for strictly trivalent dopants, form solid solutions that maintain the fluorite structure of CeO2 with a change in lattice constant that is approximately proportional to the dopant ionic radius. The single allowed Raman mode, which occurs at 465 cm−1 in pure CeO2, is observed to shift to lower frequency with increasing doping level for all the rare earths. However, after correcting for the Grüneisen shift from the lattice expansion, the frequency shift is actually positive for all the strictly trivalent ions. In addition, the Raman line broadens and becomes asymmetric with a low frequency tail, and a new broad feature appears in the spectrum at ∼570 cm−1. These changes in the Raman spectrum are attributed to O vacancies, which are introduced into the lattice whenever a trivalent RE is substituted for Ce4+. This conclusion is supported by a simple model calculation of the effects of O vacancies on the Raman spectrum. The model uses a Green’s function technique with the vacancies treated as point defects with zero mass.

Phase-Sensitive Observation of a Spin-Orbital Mott State in Sr 2 IrO 4

2009-03-06

Beomjoon Kim , H. Ohsumi , Takashi Komesu +4 more

Measurement of the quantum-mechanical phase in quantum matter provides the most direct manifestation of the underlying abstract physics. We used resonant x-ray scattering to probe the relative phases of constituent … Measurement of the quantum-mechanical phase in quantum matter provides the most direct manifestation of the underlying abstract physics. We used resonant x-ray scattering to probe the relative phases of constituent atomic orbitals in an electronic wave function, which uncovers the unconventional Mott insulating state induced by relativistic spin-orbit coupling in the layered 5 d transition metal oxide Sr 2 IrO 4 . A selection rule based on intra-atomic interference effects establishes a complex spin-orbital state represented by an effective total angular momentum = 1/2 quantum number, the phase of which can lead to a quantum topological state of matter.

Spin liquids in frustrated magnets

2010-03-09

Leon Balents

Magnetic monopoles in spin ice

2008-01-01

Claudio Castelnovo , R. Moessner , S. L. Sondhi

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Spin Ice State in Frustrated Magnetic Pyrochlore Materials

2001-11-16

S. T. Bramwell , Michel J. P. Gingras

A frustrated system is one whose symmetry precludes the possibility that every pairwise interaction ("bond") in the system can be satisfied at the same time. Such systems are common in … A frustrated system is one whose symmetry precludes the possibility that every pairwise interaction ("bond") in the system can be satisfied at the same time. Such systems are common in all areas of physical and biological science. In the most extreme cases, they can have a disordered ground state with "macroscopic" degeneracy; that is, one that comprises a huge number of equivalent states of the same energy. Pauling's description of the low-temperature proton disorder in water ice was perhaps the first recognition of this phenomenon and remains the paradigm. In recent years, a new class of magnetic substance has been characterized, in which the disorder of the magnetic moments at low temperatures is precisely analogous to the proton disorder in water ice. These substances, known as spin ice materials, are perhaps the "cleanest" examples of such highly frustrated systems yet discovered. They offer an unparalleled opportunity for the study of frustration in magnetic systems at both an experimental and a theoretical level. This article describes the essential physics of spin ice, as it is currently understood, and identifies new avenues for future research on related materials and models.

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Magnetic pyrochlore oxides

2010-01-26

J. S. Gardner , Michel J. P. Gingras , John E. Greedan

Within the past $20\phantom{\rule{0.3em}{0ex}}\text{years}$ or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type ${{A}_{2}}^{3+}{{B}_{2}}^{4+}{\mathrm{O}}_{7}$, where $A$ is a rare-earth ion … Within the past $20\phantom{\rule{0.3em}{0ex}}\text{years}$ or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type ${{A}_{2}}^{3+}{{B}_{2}}^{4+}{\mathrm{O}}_{7}$, where $A$ is a rare-earth ion and $B$ is usually a transition metal. Both the $A$ and $B$ sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long-range ordered ground states in accord with the third law of thermodynamics is frustrated, resulting in some novel short-range ordered alternatives, such as spin glasses, spin ices, and spin liquids, and much new physics. This article attempts to review the myriad of properties found in pyrochlore oxides, mainly from a materials perspective, but with an appropriate theoretical context.

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Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature

2015-10-28

Satoru Nakatsuji , Naoki Kiyohara , Tomoya Higo

Quantum spin liquid states

2017-04-18

Yi Zhou , Kazushi Kanoda , Tai-Kai Ng

This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states … This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin $1/2$ systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin ($S>1/2$) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems ($\kappa$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[(Pd(dmit)$_{2}$]$_{2}$), kagome lattice systems (ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$) and hyperkagome lattice systems (Na$_{4}$Ir$_{3}$O$_{8}$), is reviewed and compared against the corresponding theories.

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Large thermoelectric power in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">NaCo</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>single crystals

1997-11-15

Ichiro Terasaki , Y. Sasago , K. Uchinokura

We measured and analyzed the transport properties of single-crystal ${\mathrm{NaCo}}_{2}{\mathrm{O}}_{4}$, which is a metallic transition-metal oxide consisting of a two-dimensional triangle lattice of Co. Reflecting the crystal structure, the resistivity … We measured and analyzed the transport properties of single-crystal ${\mathrm{NaCo}}_{2}{\mathrm{O}}_{4}$, which is a metallic transition-metal oxide consisting of a two-dimensional triangle lattice of Co. Reflecting the crystal structure, the resistivity is highly anisotropic between in- and out-of-plane directions, and the in-plane resistivity is as low as 200 $\ensuremath{\mu}\ensuremath{\Omega}$ cm at 300 K. Most strikingly, the in-plane thermoelectric power of ${\mathrm{NaCo}}_{2}{\mathrm{O}}_{4}$ is about 100 $\ensuremath{\mu}$V/K at 300 K, which is nearly ten times larger than that of typical metals. The large thermoelectric power and the low resistivity suggest that ${\mathrm{NaCo}}_{2}{\mathrm{O}}_{4}$ is a potential thermoelectric material.

Introduction to frustrated magnetism : materials, experiments, theory

2011-01-01

C. Lacroix , P. Mendels , Frédéric Mila

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Concept and realization of Kitaev quantum spin liquids

2019-03-25

H. Takagi , T. Takayama , George Jackeli +2 more

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Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices

2020-03-18

Yanhao Tang , Lizhong Li , Tingxin Li +7 more

Quantum spin liquids: a review

2016-11-08

L. Savary , Leon Balents

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More … Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.

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Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator

2010-06-30

Xiangang Wan , Ari M. Turner , Ashvin Vishwanath +1 more

In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, … In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y$_{2}$Ir$_{2}$O$_{7}$ and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter $\theta=\pi$, may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.

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Introduction to Frustrated Magnetism

2011-01-01

C. Lacroix , P. Mendels , Frédéric Mila

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Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

2016-04-04

Arnab Banerjee , Craig A. Bridges , Jiaqiang Yan +7 more

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Effect of Ti-doping on the dimer transition in Lithium Ruthenate

2025-06-25

Sheetal Jain , Zhengbang Zhou , Ezekiel Horsley +7 more | Physical Review Materials

Recent advances in quantum spin liquids in two-dimensional kagome system YCu3(OH)6+x X 3-x (X = Cl, Br)

2025-06-25

Shiliang Li | Chinese Physics Letters

Abstract The two-dimensional kagome lattice serves as a prototypical platform for exploring quantum spin liquids owing to its pronounced geometric frustration. Substantial advancements have been achieved in herbertsmithite and its … Abstract The two-dimensional kagome lattice serves as a prototypical platform for exploring quantum spin liquids owing to its pronounced geometric frustration. Substantial advancements have been achieved in herbertsmithite and its structural analogs. These quantum-spin-liquid candidates exhibit large superexchange interactions yet resist magnetic ordering down to the lowest measurable temperatures, which are typically three or four orders of magnitude below the energy scale of the primary exchange energies. Nevertheless, the existence of unavoidable intrinsic interlayer magnetic impurities leads to persistent debates on their ground states. A breakthrough emerged with the discovery of YCu 3 (OH) 6+ x X 3- x ( X = Cl, Br), a novel material family rigorously verified to eliminate magnetic impurity interference. This short review highlights critical advances in these materials, emphasizing experimental signatures consistent with a Dirac quantum spin liquid and the observation of a one-ninth magnetization plateau and possible quantum oscillations. Local structural characteristics play a crucial role in clarifying the complex emergent quantum phenomena of these materials. Collectively, these findings establish this material class as an promising platform for investigating quantum spin liquid behavior in two-dimensional kagome lattices.

Disorder-induced spin excitation continuum and spin-glass ground state in the inverse spinel CuGa <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>2</mml:mn></mml:msub></mml:math> O <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>4</mml:mn></mml:msub></mml:math>

2025-06-24

NULL AUTHOR_ID | Physical review. B./Physical review. B

Magnetic Phases and Zone-Folded Phonons in a Frustrated van der Waals Magnet

2025-06-23

Amit Pawbake , Florian Petot , F. Le Mardelé +7 more | ACS Nano

2D magnetic materials have attracted extensive research interest due to their potential application in nanospintronics, optospintronics, and magnonics. Ferromagnetic- and antiferromagnetic-layered materials have been demonstrated and successfully inserted into van … 2D magnetic materials have attracted extensive research interest due to their potential application in nanospintronics, optospintronics, and magnonics. Ferromagnetic- and antiferromagnetic-layered materials have been demonstrated and successfully inserted into van der Waals heterostructures. However, the effects of magnetic frustration in van der Waals materials and the possibilities offered by spin configurations characterized by nonlinear spin arrangements have not been fully considered yet. Herein, we establish the magnetic phase diagram of bulk CrOCl, a frustrated van der Waals magnet, using magnetization and magneto-optical spectroscopy techniques. In particular, we use the magnetic superstructures relative to the crystallographic unit cell and the associated rich zone-folded phonon series to describe the magnetic-field-induced phases. Theoretical calculations taking into account the competing nearest neighbors' magnetic exchange interactions provide insight into the lattice vibrations of this class of magnetic system. This study expands the scope of 2D magnetic materials and provides a methodology to characterize frustrated van der Waals magnets.

Crystal structure and thermodynamic properties of post-spinel-type CaV2O4 at high temperatures (298.15–1373 K)

2025-06-21

Dapeng Zhong , Jie Yu , Xin Jin +6 more | Calphad

Cation Exchange as a Route to Introduce Magnetism to Hybrid-Improper Polar Phases

2025-06-20

Rachel Conway , Fabio Orlandi , Pascal Manuel +3 more | Inorganic Chemistry

The pseudo Ruddlesden-Popper phase Li2CaTa2O7 is converted to ZnCaTa2O7, FeCaTa2O7, or CoCaTa2O7 by reaction with the corresponding transition-metal dichloride. Diffraction data reveal that ZnCaTa2O7 adopts a polar crystal structure (P2cm) … The pseudo Ruddlesden-Popper phase Li2CaTa2O7 is converted to ZnCaTa2O7, FeCaTa2O7, or CoCaTa2O7 by reaction with the corresponding transition-metal dichloride. Diffraction data reveal that ZnCaTa2O7 adopts a polar crystal structure (P2cm) with the Zn2+cations ordered into stripes within the interlayer coordination sites, and the TaO6 units adopt an a-b-c+/-(a-b-)c+ tilting pattern. In contrast, FeCaTa2O7 and CoCaTa2O7 adopt polar structures (P21nm) with the transition-metal cations ordered in a checkerboard pattern within the interlayer coordination sites, and the TaO6 units adopt an a-b-c+/ b-a-c+ tilting pattern. The different polar structures adopted are rationalized on the basis of the size of the interlayer transition-metal cation. On cooling, FeCaTa2O7 (TN = 40 K) and CoCaTa2O7 (TN = 25 K) adopt antiferromagnetically ordered states with spins aligned parallel to the crystallographic stacking axis and arranged in a G-type manner. Close inspection of the NPD data collected from FeCaTa2O7 at low temperature reveals a diffuse component to the magnetic scattering, which, in combination with magnetization data, suggest a glassy component to the low-temperature magnetic state. Neither FeCaTa2O7 nor CoCaTa2O7 shows significant lattice parameter anomalies around their respective Néel temperatures, in contrast to the previously reported manganese analogue MnCaTa2O7.

Block Copolymer Self-Assembly-Directed Mesoporous Gyroidal Strontium Titanate with Room-Temperature Ferromagnetism

2025-06-20

William Moore , Nengli Yang , Abigail K. Nason +5 more | ACS Applied Materials & Interfaces

Block copolymer structure direction has been demonstrated as a technique to impart nanostructure and mesoporosity with enhanced properties to a variety of metal oxides for applications including catalysis, energy conversion … Block copolymer structure direction has been demonstrated as a technique to impart nanostructure and mesoporosity with enhanced properties to a variety of metal oxides for applications including catalysis, energy conversion and storage, as well as superconductivity. Such approaches require polymer-compatible solution synthesis routes toward oxide nanoclusters, which are not generally available for a broad range of functional materials. Here, we report an acetic acid-based sol-gel-derived method for the synthesis of mesoporous ternary strontium titanate with a morphology consistent with alternating gyroid. In-depth structural characterization suggests a periodic gyroidal structure and phase purity of the resultant perovskite. Magnetometry reveals that these normally diamagnetic oxide materials are ferromagnetic at room temperature. This magnetism is significantly enhanced by mild vacuum annealing, suggesting oxygen vacancies as the source of ferromagnetism. Block copolymer self-assembly-directed mesoporous ternary perovskites may provide a rich platform for studying surface and interfacial effects in surface-dominated systems by enhancing normally dilute surface phenomena.

Intermediate phases in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math> -RuCl <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>3</mml:mn></mml:msub></mml:math> under in-plane magnetic field via interlayer spin interactions

2025-06-20

NULL AUTHOR_ID | Physical review. B./Physical review. B

Probing loop currents and collective modes of charge density waves in Kagome materials with NV centers

2025-06-20

Ying-Ming Xie , Naoto Nagaosa | npj Quantum Materials

Symmetry-Constrained Anomalous Transport in the Altermagnetic Material CuX2 (X = F, Cl)

2025-06-19

Zhengxuan Wang , Ruqian Wu , Chunlan Ma +6 more | Chinese Physics Letters

Abstract Altermagnetism, a recently identified class of collinear magnetism, combines key features of antiferromagnets and ferromagnets. Despite having zero net magnetization, altermagnetic materials exhibit anomalous transport effects, including the anomalous … Abstract Altermagnetism, a recently identified class of collinear magnetism, combines key features of antiferromagnets and ferromagnets. Despite having zero net magnetization, altermagnetic materials exhibit anomalous transport effects, including the anomalous Hall, Nernst, and thermal Hall effects, as well as magneto-optical Kerr and Faraday effects. These phenomena, previously thought unique to ferromagnets, are dictated by symmetry, as confirmed by density functional theory (DFT) calculations. However, an effective model-based approach to verify these symmetry constraints remains unavailable. In this Letter, we construct a k · p model for d-wave altermagnets CuX 2 (X = F, Cl) using spin space group representations and apply it to calculate the anomalous Hall effect. The symmetry-imposed transport properties predicted by the model are in agreement with the DFT results, providing a foundation for further investigation into symmetry-restricted transport phenomena in altermagnetic materials.

Lattice Distortion Engineering: Manipulation of Electrochemical Properties for Pyrochlore Ruthenates as Electrocatalysts in Water Splitting

2025-06-19

Hengyu Guo , Yanzong Huang , Chenfen Long +5 more | Small

Abstract Pyrochlores ruthenates, owing to their D 3d symmetric configurations of [RuO 6 ] octahedra to efficiently avoid the Ru dissolution during the oxygen evolution reaction (OER) process, have been … Abstract Pyrochlores ruthenates, owing to their D 3d symmetric configurations of [RuO 6 ] octahedra to efficiently avoid the Ru dissolution during the oxygen evolution reaction (OER) process, have been promising as non‐iridium electrocatalysts for proton exchange membrane water electrolysis (PEMWE). In this work, a lattice‐distortion strategy is proposed, by using a series of lanthanides (from Gd to Lu) as the dominant A sites and a series of alkalines (from Mg to Ba) as the A‐site substitutions, to investigate the geometric effect on the pyrochlores for OER. It is found that the larger radii difference between the A sites and the A‐site substitutions, the larger lattice expansion of these alloyed pyrochlore ruthenates, accompanied by the shortened Ru─O bonding, the enlarged Ru─O─Ru bond angle, and the enhanced covalency of [RuO 6 ] octahedra. The large lattice expansion also leads a rapid A‐site leaching and the formation of protective RuO x reconstruction layers, which suppress the progressive metal dissolution, the lattice contraction, and the resulting insulated OER deactivation. On account of the synergistic effect from the lattice distortion, the most distorted LuBa pyrochlores exhibit the highest OER performance and the greatest enhancement in either electrochemical testing or PEMWE operation, demonstrating their considerable potential for practical applications.

Neutron scattering and thermodynamic evidence for emergent photons and fractionalization in a pyrochlore spin ice

2025-06-19

Bin Gao , Félix Desrochers , David W. Tam +7 more | Nature Physics

Near Room‐Temperature Ferromagnetic Phase Achieved in 4d Ruthenate via Interfacial Ferrimagnetic Coupling and Octahedral Rotation Engineering

2025-06-19

Mengqin Wang , Qinghua Zhang , Xiao Deng +7 more | Advanced Science

Abstract Transition metal oxides (TMOs) simultaneously possessing strong spin‐orbit coupling, near room‐temperature ferromagnetism, and excellent conductivity are scarce while they show great potential applications in oxide spintronics. Here, a TMO … Abstract Transition metal oxides (TMOs) simultaneously possessing strong spin‐orbit coupling, near room‐temperature ferromagnetism, and excellent conductivity are scarce while they show great potential applications in oxide spintronics. Here, a TMO with all these features is reported, existing as an interfacial phase in the 4 d Ca 0.5 Sr 0.5 RuO 3 layer sandwiched by two LaMnO 3 layers. This phase is well conductive and ferromagnetic in a wide temperature range, with the highest Curie temperature of ≈275 K among the 4 d /5 d ‐TMOs. Particularly, this interfacial phase shows a considerably improved saturation magnetization (≈2 µ B /Ru, twice that of the bulk counterpart), and a greatly reduced coercive force. All these features are highly desired by the application of spin‐orbit torque. Due to the presence of strong spin‐orbit coupling, such a Ca 0.5 Sr 0.5 RuO 3 interfacial phase exhibits a significantly larger anomalous Hall conductivity than the typical 3 d oxide ferromagnet La 2/3 Sr 1/3 MnO 3 near room temperature. Analyses based on the techniques of X‐ray magnetic circular dichroism, polarized‐neutron reflectometry, and scanning transmission electron microscopy reveal a magnetic exchange interaction between the interfacial phases of Ca 0.5 Sr 0.5 RuO 3 and LaMnO 3 and an obvious expansion of the interfacial Mn─O─Mn bond angle, stabilizing the high‐temperature ferromagnetic state of the CSRO/LMO interface.

Synthesis of inter‐lanthanide sesquioxides LnLn'O3 by polymeric steric entrapment

2025-06-18

Brooke K. Downing , Steven M. Hnatko , Tinsley Elizabeth DeForest +6 more | Journal of the American Ceramic Society

Abstract Lanthanide oxides are well known in the fields of optical, electronic, and magnetic materials. Even so, there are many application spaces yet to be explored. Previous modeling of inter‐lanthanide … Abstract Lanthanide oxides are well known in the fields of optical, electronic, and magnetic materials. Even so, there are many application spaces yet to be explored. Previous modeling of inter‐lanthanide sesquioxides, in which the compound contains two lanthanide cations, predicts the lowest level energy structure as a function of chemistry, which this work seeks to verify. Three materials of interest, ErLuO 3 , LaLuO 3 , and SmLuO 3 , were synthesized for the first time by the polymeric steric entrapment (PSE) method. X‐ray diffraction confirms the stable state predictions of ErLuO 3 and SmLuO 3 forming a bixbyite type structure and LaLuO 3 forming a perovskite type structure. This work demonstrates PSE as a viable and reliable route toward the synthesis of these unique materials.

Emergent exchange-driven giant magnetoelastic coupling in a correlated itinerant ferromagnet

2025-06-17

Carolina A. Marques , Luke C. Rhodes , Weronika Osmolska +7 more | Nature Physics

First-principles Hubbard parameters with automated and reproducible workflows

2025-06-16

Lorenzo Bastonero , Cristiano Malica , Eric Macke +4 more | npj Computational Materials

Abstract We introduce an automated, flexible framework (aiida-hubbard) to self-consistently calculate Hubbard U and V parameters from first-principles. By leveraging density-functional perturbation theory, the computation of the Hubbard parameters is … Abstract We introduce an automated, flexible framework (aiida-hubbard) to self-consistently calculate Hubbard U and V parameters from first-principles. By leveraging density-functional perturbation theory, the computation of the Hubbard parameters is efficiently parallelized using multiple concurrent and inexpensive primitive cell calculations. Furthermore, the intersite V parameters are defined on-the-fly during the iterative procedure to account for atomic relaxations and diverse coordination environments. We devise a novel, code-agnostic data structure to store Hubbard related information together with the atomistic structure, to enhance the reproducibility of Hubbard-corrected calculations. We demonstrate the scalability and reliability of the framework by computing in high-throughput fashion the self-consistent onsite U and intersite V parameters for 115 Li-containing bulk solids with up to 32 atoms in the unit cell. Our analysis of the Hubbard parameters calculated reveals a significant correlation of the onsite U values on the oxidation state and coordination environment of the atom on which the Hubbard manifold is centered, while intersite V values exhibit a general decay with increasing interatomic distance. We find, e.g., that the numerical values of U for the 3d orbitals of Fe and Mn can vary up to 3 eV and 6 eV, respectively; their distribution is characterized by typical shifts of about 0.5 eV and 1.0 eV upon change in oxidation state, or local coordination environment. For the intersite V a narrower spread is found, with values ranging between 0.2 eV and 1.6 eV when considering transition metal and oxygen interactions. This framework paves the way for the exploration of redox materials chemistry and high-throughput screening of d and f compounds across diverse research areas, including the discovery and design of novel energy storage materials, as well as other technologically-relevant applications.

Accessing the Magnetic Morphology of Ferromagnetic Molecular-Based Nanoparticles from Polarized Small-Angle Neutron Scattering

2025-06-16

G. Chaboussant | Inorganics

Polarized Small-Angle Neutron Scattering is a versatile low-energy neutron scattering technique that allows for the access of magnetic information on nanosize objects of size 2–100 nm, from individual properties like … Polarized Small-Angle Neutron Scattering is a versatile low-energy neutron scattering technique that allows for the access of magnetic information on nanosize objects of size 2–100 nm, from individual properties like the magnetization distribution inside the object to the collective behaviors, e.g., spin-glass effects or long-range magnetic ordering. The multi-scale possibilities of this technique is particularly relevant to encompass simultaneously the individual and collective many-body phenomena. In this article, we report the direct measurement of the magnetic form factor of “Prussian Blue Analog” molecular-based Ferromagnetic nanoparticles CsxINiII[CrIII(CN)6] embedded in a polymer matrix with use of Polarized Small-Angle Neutron Scattering. We show that PSANS is particularly adapted to evaluate the internal magnetization distribution in nanoparticles and determine their magnetic morphology.

Magnetic excitations from the hexagonal spin clusters in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math> = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> distorted honeycomb lattice antiferromagnet Cu <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>2</mml:mn></mml:msub></mml:math> (pymca…

2025-06-16

NULL AUTHOR_ID | Physical review. B./Physical review. B

Effect of anisotropic parameters on some properties of the vHs superconductor in kagome materials

2025-06-16

R. Thaninworapak , Pongkaew Udomsamuthirun , Arpapong Changjan +3 more | Solid State Communications

Frustrated kagome-lattice bilayer quantum Heisenberg antiferromagnet

2025-06-16

NULL AUTHOR_ID | Physical review. B./Physical review. B

Effect of nonmagnetic dilution in Ba2CoTeO6: A composite system of spin-1/2 triangular Heisenberg-like and honeycomb Ising-like antiferromagnets

2025-06-16

Xueqin Zhao , Jinou Dong , Lingfeng Xie +5 more | EPL (Europhysics Letters)

Abstract We report the evolution of the magnetic state in Ba 2 CoTeO 6 with magnetic Co 2+ substituted by non-magnetic Zn 2+ . Ba 2 CoTeO 6 , a … Abstract We report the evolution of the magnetic state in Ba 2 CoTeO 6 with magnetic Co 2+ substituted by non-magnetic Zn 2+ . Ba 2 CoTeO 6 , a strongly frustrated antiferromagnet which consists of two highly frustrated subsystems, undergoes two antiferromagnetic transitions at T N1 ∼ 12 K and T N2 ∼ 3 K, respectively. The magnetization and specific heat measurements demonstrate that the antiferromagnetic transition at T N1 in the parent compound Ba 2 CoTeO 6 is drastically suppressed with Zn/Co substitution. On the other hand, with the increasing of Zn doping level x , the antiferromagnetic ordering below T N2 in Ba 2 CoTeO 6 firstly become a spin glass state, and eventually transforms into a spin disordered state at higher Zn concentration x = 0.6. Our results indicates that magnetic site dilution by Zn/Co substitution is an effective approach to induce the novel disordered state in Ba 2 CoTeO 6 .

Probing chiral Kitaev spin liquids via dangling boundary fermions

2025-06-14

Shang-Shun Zhang , Gábor B. Halász , Cristian D. Batista | npj Quantum Materials

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X-ray diffraction study of the magnetization plateau above 40 T in the frustrated helimagnet CuGaCr <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>4</mml:mn></mml:msub></mml:math> S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>8</mml:mn></mml:msub></mml:math>

2025-06-13

NULL AUTHOR_ID | Physical review. B./Physical review. B

Magnetic and thermodynamic studies on the distorted kagome magnet Pr <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>3</mml:mn></mml:msub></mml:math> BWO <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>9</mml:mn></mml:msub></mml:math>

2025-06-13

NULL AUTHOR_ID | Physical review. B./Physical review. B

Electronic anisotropy and rotational symmetry breaking at a Weyl semimetal/spin ice interface

2025-06-13

Tsung-Chi Wu , Yueqing Chang , Ang-Kun Wu +7 more | Science Advances

In magnetic pyrochlore materials, the interplay of spin-orbit coupling, electronic correlations, and geometrical frustration gives rise to exotic quantum phases, including topological semimetals and spin ice. While these phases have … In magnetic pyrochlore materials, the interplay of spin-orbit coupling, electronic correlations, and geometrical frustration gives rise to exotic quantum phases, including topological semimetals and spin ice. While these phases have been observed in isolation, the interface-driven phenomena emerging from their interaction have never been realized previously. Here, we report on the discovery of interfacial electronic anisotropy and rotational symmetry breaking at a heterostructure consisting of the Weyl semimetal Eu 2 Ir 2 O 7 and spin ice Dy 2 Ti 2 O 7 . Subjected to magnetic fields, we unveil a sixfold anisotropic transport response that is theoretically accounted by a Kondo-coupled heterointerface, where the spin ice’s field-tuned magnetism induces electron scattering in the Weyl semimetal’s topological Fermi-arc states. Furthermore, at elevated magnetic fields, we reveal a twofold anisotropic response indicative of the emergence of a symmetry-broken many-body state. This discovery showcases the potential of pyrochlore frustrated magnet/topological semimetal heterostructures in search of emergent interfacial phenomena.

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Spin models and cluster multipole method: Application to kagome magnets

2025-06-12

NULL AUTHOR_ID | Physical review. B./Physical review. B

Chiral symmetry and magnetism in a three-dimensional kagome lattice: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math> Pt <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>2</mml:mn></mml:msub></mml:math> B prototype crystals ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math> = La and Nd)

2025-06-12

NULL AUTHOR_ID | Physical review. B./Physical review. B

Multiple Magnetic Phases, Spin-Phonon Coupling, and Magnetocaloric Effect in the Non-centrosymmetric Antiferromagnet Ni1.8Co0.2InSbO6

2025-06-12

Neha Patel , Srishti Dixit , Swayangsiddha Ghosh +7 more | Journal of Physics D Applied Physics

Abstract Non-centrosymmetric helical magnets are renowned for their exotic magnetic properties and their association with complex physical behaviors. Here, we investigate the trigonal Ni 1.8 Co 0.2 InSbO 6 system … Abstract Non-centrosymmetric helical magnets are renowned for their exotic magnetic properties and their association with complex physical behaviors. Here, we investigate the trigonal Ni 1.8 Co 0.2 InSbO 6 system (space group R3), revealing multiple fascinating characteristics. Magnetic studies demonstrate a long-range antiferromagnetic (AFM) transition at T N ∼ 80 K, a spin-glass state at T SG ∼ 25 K, and a non-Griffith phase above T N . A metamagnetic transition is observed at various fields, with the phase transition from a first-order to second-order with the increase of temperature. This transition is attributed to the interplay between ferromagnetic (FM) and AFM phases. Raman spectroscopy indicates spin-phonon coupling below T N , reflecting the impact of magnetic ordering on lattice dynamics. Magnetocaloric effect measurements further reveal AFM-to-FM phase transitions above critical magnetic fields. These findings emphasize the significance of spin-lattice interactions and metamagnetic behavior in this system.

Successive metamagnetic transitions and magnetoelectric switching in the spin-1/2 chain antiferromagnet CoSe <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>2</mml:mn></mml:msub></mml:math> O <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi/><mml:mn>5</mml:mn></mml:msub></mml:math>

2025-06-11

NULL AUTHOR_ID | Physical review. B./Physical review. B