Scaling and data collapse from local moments in frustrated disordered quantum spin systems

Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common relation -- nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H,T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling $C[H,T]/T \sim H^{-\gamma} F_q[T/H]$ with $F_q[x] = x^{q}$ at small $x$, with $q \in$ (0,1,2) an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a $q$-dependent subdominant term enforced by Maxwell's relations.Comment: v2. Expanded argument in Appendix 2 and revised for clarity. v3. Fixed typo in Fig 3 caption. Main text 4 pages 4 figures, Appendix 6 pages 1 figur

Karola Filng, Herbert Heuss, Frank Sparing, Od „rasne znanosti“ do logora - Romi u II. svjetskom ratu (1. dio), Zagreb: Ibis grafika, 2006., 125 str.

Among oxide compounds with direct metal–metal bonding, the Y₅Mo₂O₁₂ (<i>A</i>₅<i>B</i>₂O₁₂) structural family of compounds has a particularly intriguing low-dimensional structure due to the presence of bioctahedral <i>B</i>₂O₁₀ dimers arranged in one-dimensional edge-sharing chains along the direction of the metal–metal bonds. Furthermore, these compounds can have a local magnetic moment due to the noninteger oxidation state (+4.5) of the transition metal, in contrast to the conspicuous lack of a local moment that is commonly observed when oxide compounds with direct metal–metal bonding have integer oxidation states resulting from the lifting of orbital degeneracy typically induced by the metal–metal bonding. Although a monoclinic <i>C</i>2/<i>m</i> structure has been previously proposed for <i>Ln</i>₅Mo₂O₁₂ (<i>Ln</i> = La–Lu and Y) members of this family based on prior single crystal diffraction data, it is found that this structural model misses many important structural features. On the basis of synchrotron powder diffraction data, it is shown that the <i>C</i>2/<i>m</i> monoclinic unit cell represents a superstructure relative to a previously unrecognized orthorhombic <i>Immm</i> subcell and that the superstructure derives from the ordering of interchangeable Mo₂O₁₀ and LaO₆ building blocks. The superstructure for this reason is typically highly faulted, as evidenced by the increased breadth of superstructure diffraction peaks associated with a coherence length of 1–2 nm in the <i>c</i>* direction. Finally, it is shown that oxygen vacancies can occur when <i>Ln</i> = La, producing an oxygen deficient stoichiometry of La₅Mo₂O_11.55 and an approximately 10-fold reduction in the number of unpaired electrons due to the reduction of the average Mo valence from +4.5 to +4.05, a result confirmed by magnetic susceptibility measurements. This represents the first observation of oxygen vacancies in this family of compounds and provides an important means of continuously tuning the magnetic interactions within the one-dimensional octahedral chains of this system

Site-Specific Structure at Multiple Length Scales in Kagome Quantum Spin Liquid Candidates.

Realizing a quantum spin liquid (QSL) ground state in a real material is a leading issue in condensed matter physics research. In this pursuit, it is crucial to fully characterize the structure and influence of defects, as these can significantly affect the fragile QSL physics. Here, we perform a variety of cutting-edge synchrotron X-ray scattering and spectroscopy techniques, and we advance new methodologies for site-specific diffraction and L-edge Zn absorption spectroscopy. The experimental results along with our first-principles calculations address outstanding questions about the local and long-range structures of the two leading kagome QSL candidates, Zn-substituted barlowite (Cu3Zn x Cu1-x (OH)6FBr) and herbertsmithite (Cu3Zn(OH)6Cl2). On all length scales probed, there is no evidence that Zn substitutes onto the kagome layers, thereby preserving the QSL physics of the kagome lattice. Our calculations show that antisite disorder is not energetically favorable and is even less favorable in Zn-barlowite compared to herbertsmithite. Site-specific X-ray diffraction measurements of Zn-barlowite reveal that Cu2+ and Zn2+ selectively occupy distinct interlayer sites, in contrast to herbertsmithite. Using the first measured Zn L-edge inelastic X-ray absorption spectra combined with calculations, we discover a systematic correlation between the loss of inversion symmetry from pseudo-octahedral (herbertsmithite) to trigonal prismatic coordination (Zn-barlowite) with the emergence of a new peak. Overall, our measurements suggest that Zn-barlowite has structural advantages over herbertsmithite that make its magnetic properties closer to an ideal QSL candidate: its kagome layers are highly resistant to nonmagnetic defects while the interlayers can accommodate a higher amount of Zn substitution

Site-Specific Structure at Multiple Length Scales in Kagome Quantum Spin Liquid Candidates.

Realizing a quantum spin liquid (QSL) ground state in a real material is a leading issue in condensed matter physics research. In this pursuit, it is crucial to fully characterize the structure and influence of defects, as these can significantly affect the fragile QSL physics. Here, we perform a variety of cutting-edge synchrotron X-ray scattering and spectroscopy techniques, and we advance new methodologies for site-specific diffraction and L-edge Zn absorption spectroscopy. The experimental results along with our first-principles calculations address outstanding questions about the local and long-range structures of the two leading kagome QSL candidates, Zn-substituted barlowite (Cu3Zn x Cu1-x (OH)6FBr) and herbertsmithite (Cu3Zn(OH)6Cl2). On all length scales probed, there is no evidence that Zn substitutes onto the kagome layers, thereby preserving the QSL physics of the kagome lattice. Our calculations show that antisite disorder is not energetically favorable and is even less favorable in Zn-barlowite compared to herbertsmithite. Site-specific X-ray diffraction measurements of Zn-barlowite reveal that Cu2+ and Zn2+ selectively occupy distinct interlayer sites, in contrast to herbertsmithite. Using the first measured Zn L-edge inelastic X-ray absorption spectra combined with calculations, we discover a systematic correlation between the loss of inversion symmetry from pseudo-octahedral (herbertsmithite) to trigonal prismatic coordination (Zn-barlowite) with the emergence of a new peak. Overall, our measurements suggest that Zn-barlowite has structural advantages over herbertsmithite that make its magnetic properties closer to an ideal QSL candidate: its kagome layers are highly resistant to nonmagnetic defects while the interlayers can accommodate a higher amount of Zn substitution

Photoinitiated Reactivity of a Thiolate-Ligated, Spin-Crossover Nonheme {FeNO}⁷ Complex with Dioxygen

The nonheme iron complex, [Fe­(NO)­(N3PyS)]­BF₄, is a rare example of an {FeNO}⁷ species that exhibits spin-crossover behavior. The comparison of X-ray crystallographic studies at low and high temperatures and variable-temperature magnetic susceptibility measurements show that a low-spin <i>S</i> = 1/2 ground state is populated at 0–150 K, while both low-spin <i>S</i> = 1/2 and high-spin <i>S</i> = 3/2 states are populated at <i>T</i> > 150 K. These results explain the observation of two N–O vibrational modes at 1737 and 1649 cm^–1 in CD₃CN for [Fe­(NO)­(N3PyS)]­BF₄ at room temperature. This {FeNO}⁷ complex reacts with dioxygen upon photoirradiation with visible light in acetonitrile to generate a thiolate-ligated, nonheme iron­(III)-nitro complex, [Fe^III(NO₂)­(N3PyS)]⁺, which was characterized by EPR, FTIR, UV–vis, and CSI-MS. Isotope labeling studies, coupled with FTIR and CSI-MS, show that one O atom from O₂ is incorporated in the Fe^III–NO₂ product. The O₂ reactivity of [Fe­(NO)­(N3PyS)]­BF₄ in methanol is dramatically different from CH₃CN, leading exclusively to sulfur-based oxidation, as opposed to NO· oxidation. A mechanism is proposed for the NO· oxidation reaction that involves formation of both Fe^III-superoxo and Fe^III-peroxynitrite intermediates and takes into account the experimental observations. The stability of the Fe^III-nitrite complex is limited, and decay of [Fe^III(NO₂)­(N3PyS)]⁺ leads to {FeNO}⁷ species and sulfur oxygenated products. This work demonstrates that a single mononuclear, thiolate-ligated nonheme {FeNO}⁷ complex can exhibit reactivity related to both nitric oxide dioxygenase (NOD) and nitrite reductase (NiR) activity. The presence of the thiolate donor is critical to both pathways, and mechanistic insights into these biologically relevant processes are presented