Spin Hamiltonians in Magnets: Theories and Computations

Li, Xueyang; Yu, Hongyu; Liu, Feng; Feng, Junsheng; Whangbo, Myung‐Hwan; Xiang, Hongjun

doi:10.3390/molecules26040803

Cited by 47 publications

(37 citation statements)

References 164 publications

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“…However, our work showed that each kagomé layer of Cu 2+ ions consists of very-weakly interacting two-leg spin ladders, so the seemingly exotic magnetic properties previously attributed to magnetic frustration are simply explained by a well-studied S = 1/2 antiferromagnetic uniform Heisenberg chain model. To find a correct spin lattice for any given magnetic material, it is necessary to evaluate the relative strengths of various possible spin exchanges of a given magnetic system by using an unbiased and straightforward method such as the energy-mapping analysis, based on first principles DFT calculations [3,4,19,33].…”

Section: Discussionmentioning

confidence: 99%

Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2·2H2O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

et al. 2022

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We determined the spin exchanges between the Cu2+ ions in the kagomé layers of volborthite, Cu3V2O7(OH)2·2H2O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagomé layers of Cu2+ ions are hardly spin-frustrated, and the magnetic properties of volborthite below ~75 K should be described by very weakly interacting antiferromagnetic uniform chains made up of effective S = 1/2 pseudospin units. This conclusion was verified by synthesizing single crystals of not only Cu3V2O7(OH)2·2H2O but also its deuterated analogue Cu3V2O7(OD)2·2D2O and then by investigating their magnetic susceptibilities and specific heats. Each kagomé layer consists of intertwined two-leg spin ladders with rungs of linear spin trimers. With the latter acting as S = 1/2 pseudospin units, each two-leg spin ladder behaves as a chain of S = 1/2 pseudospins. Adjacent two-leg spin ladders in each kagomé layer interact very weakly, so it is required that all nearest-neighbor spin exchange paths of every two-leg spin ladder remain antiferromagnetically coupled in all spin ladder arrangements of a kagomé layer. This constraint imposes three sets of entropy spectra with which each kagomé layer can exchange energy with the surrounding on lowering the temperature below ~1.5 K and on raising the external magnetic field B. We discovered that the specific heat anomalies of volborthite observed below ~1.5 K at B = 0 are suppressed by raising the magnetic field B to ~4.2 T, that a new specific heat anomaly occurs when B is increased above ~5.5 T, and that the imposed three sets of entropy spectra are responsible for the field-dependence of the specific heat anomalies.

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Section: Discussionmentioning

confidence: 99%

Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2·2H2O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

et al. 2022

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“…To evaluate the Dzyaloshinskii-Moriya and asymmetric spin exchanges, the energy-mapping analysis employs the four-state method [2,13], in which non-collinearly ordered broken-symmetry states are used. A further generalization of this energy-mapping method was developed to enable the evaluation of other energy terms that one might include in a model spin Hamiltonian [14].…”

Section: Energy Mappingmentioning

confidence: 99%

Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals

2021

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In this review on spin exchanges, written to provide guidelines useful for finding the spin lattice relevant for any given magnetic solid, we discuss how the values of spin exchanges in transition metal magnetic compounds are quantitatively determined from electronic structure calculations, which electronic factors control whether a spin exchange is antiferromagnetic or ferromagnetic, and how these factors are related to the geometrical parameters of the spin exchange path. In an extended solid containing transition metal magnetic ions, each metal ion M is surrounded with main-group ligands L to form an MLn polyhedron (typically, n = 3–6), and the unpaired spins of M are represented by the singly-occupied d-states (i.e., the magnetic orbitals) of MLn. Each magnetic orbital has the metal d-orbital combined out-of-phase with the ligand p-orbitals; therefore, the spin exchanges between adjacent metal ions M lead not only to the M–L–M-type exchanges, but also to the M–L…L–M-type exchanges in which the two metal ions do not share a common ligand. The latter can be further modified by d0 cations A such as V5+ and W6+ to bridge the L…L contact generating M–L…A…L–M-type exchanges. We describe several qualitative rules for predicting whether the M–L…L–M and M–L…A…L–M-type exchanges are antiferromagnetic or ferromagnetic by analyzing how the ligand p-orbitals in their magnetic orbitals (the ligand p-orbital tails, for short) are arranged in the exchange paths. Finally, we illustrate how these rules work by analyzing the crystal structures and magnetic properties of four cuprates of current interest: α-CuV2O6, LiCuVO4, (CuCl)LaNb2O7, and Cu3(CO3)2(OH)2.

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“…In this circumstance, there is a chance to stabilize a multiple-Q state by taking into account additional other interactions to the model in (1), such as the magnetic anisotropy [57,58,59,115,116,24,25,117], bond-dependent interactions in the form of compass and Kitaev type [118,119,120,121,122,123,124,125], and higher-order multiple-spin interactions derived by higher-order exchange processes beyond the Heisenberg one [126,127,60,128,129,130]. Also, thermal fluctuations [131,56,132], quantum fluctuations [133,134,135,136], and disorder by impurities [137,138,139,140,141] play a role in stabilizing such multiple-Q states.…”

Section: Frustration In Insulating Magnetsmentioning

confidence: 99%

Topological spin crystals by itinerant frustration

Hayami,

Motome

2021

Preprint

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Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

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Spin Hamiltonians in Magnets: Theories and Computations

Cited by 47 publications

References 164 publications

Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2·2H2O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2·2H2O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

Spin Exchanges between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals

Topological spin crystals by itinerant frustration

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