Dynamic fingerprint of fractionalized excitations in single-crystalline Cu3Zn(OH)6FBr

Beyond the absence of long-range magnetic orders, the most prominent feature of the elusive quantum spin liquid (QSL) state is the existence of fractionalized spin excitations, i.e., spinons. When the system orders, the spin-wave excitation appears as the bound state of the spinon-antispinon pair. Although scarcely reported, a direct comparison between similar compounds illustrates the evolution from spinon to magnon. Here, we perform the Raman scattering on single crystals of two quantum kagome antiferromagnets, of which one is the kagome QSL candidate Cu3Zn(OH)6FBr, and another is an antiferromagnetically ordered compound EuCu3(OH)6Cl3. In Cu3Zn(OH)6FBr, we identify a unique one spinon-antispinon pair component in the E2g magnetic Raman continuum, providing strong evidence for deconfined spinon excitations. In contrast, a sharp magnon peak emerges from the one-pair spinon continuum in the Eg magnetic Raman response once EuCu3(OH)6Cl3 undergoes the antiferromagnetic order transition. From the comparative Raman studies, we can regard the magnon mode as the spinon-antispinon bound state, and the spinon confinement drives the magnetic ordering.

Dynamic fingerprint of fractionalized excitations in single-crystalline Cu3Zn(OH)6FBr

Beyond the absence of long-range magnetic orders, the most prominent feature of the elusive quantum spin liquid (QSL) state is the existence of fractionalized spin excitations, i.e., spinons. When the system orders, the spin-wave excitation appears as the bound state of the spinon-antispinon pair. Although scarcely reported, a direct comparison between similar compounds illustrates the evolution from spinon to magnon. Here, we perform the Raman scattering on single crystals of two quantum kagome antiferromagnets, of which one is the kagome QSL candidate Cu3Zn(OH)6FBr, and another is an antiferromagnetically ordered compound EuCu3(OH)6Cl3. In Cu3Zn(OH)6FBr, we identify a unique one spinon-antispinon pair component in the E2g magnetic Raman continuum, providing strong evidence for deconfined spinon excitations. In contrast, a sharp magnon peak emerges from the one-pair spinon continuum in the Eg magnetic Raman response once EuCu3(OH)6Cl3 undergoes the antiferromagnetic order transition. From the comparative Raman studies, we can regard the magnon mode as the spinon-antispinon bound state, and the spinon confinement drives the magnetic ordering.

Inessential directed maps and directed homotopy equivalences

A directed space is a topological space $X$ together with a subspace $\vec {P}(X)\subset X^I$ of directed paths on $X$ . A symmetry of a directed space should therefore respect both the topology of the underlying space and the topology of the associated spaces $\vec {P}(X)_-^+$ of directed paths between a source ( $-$ ) and a target ( $+$ )—up to homotopy. If it is, moreover, homotopic to the identity map—in a directed sense—such a symmetry will be called an inessential d-map, and the paper explores the algebra and topology of inessential d-maps. Comparing two d-spaces $X$ and $Y$ ‘up to symmetry’ yields the notion of a directed homotopy equivalence between them. Under appropriate conditions, all directed homotopy equivalences are shown to satisfy a 2-out-of-3 property. Our notion of directed homotopy equivalence does not agree completely with the one defined in Goubault (2017, arxiv:1709:05702v2) and Goubault, Farber and Sagnier (2020, J. Appl. Comput. Topol. 4, 11–27); the deviation is motivated by examples. Nevertheless, directed topological complexity, introduced in Goubault, Farber and Sagnier (2020) is shown to be invariant under our notion of directed homotopy equivalence. Finally, we show that directed homotopy equivalences result in isomorphisms on the pair component categories of directed spaces introduced in Goubault, Farber and Sagnier (2020).

The influence of contemporaneity, genetic variation and herd differences on variation in milk yield and butterfat percentage

1. Paired lactation records of milk yield and fat percentage from experimental twins and commercial twins, full-sisters and half-sisters are used in a study of the influence of contemporaneity, genetic variation and herd differences.2. The design of the investigation was such that members of a pair were alike in:(i) both time of calving and lactation number,(ii) time of calving only,(iii) lactation number only, or(iv) neither time of calving nor lactation number.3. Intra-class correlations between pair members in respect both of yield and fat percentage were highest for contemporary records. Differences in time of calving and in lactation number produced, in aggregate, a decline in correlation of about 20%. However, the separate estimates varied considerably between the different types of pair.4. The within-pair and between-pair variance components independently confirm these effects of contemporaneity. As the degree of contemporaneity of pair members declines the within-pair variance increases in size and the between-pair component decreases.