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Register a new userStudies on the Magnetic Ground State of a Spin Mobius Strip
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Here we report the synthesis, structure and detailed characterisation of three n-membered oxovanadium rings, Na$_n$[(V=O)$_n$Na$_n$(H$_2$O)$_n$($alpha$, $beta$, or $gamma$-CD)$_2$]$m$H$_2$O (n = 6, 7, or 8), prepared by the reactions of (V=O)SO$_4$$cdot$$x$H$_2$O with $alpha$, $beta$, or $gamma$-cyclodextrins (CDs) and NaOH in water. Their alternating heterometallic vanadium/sodium cyclic core structures were sandwiched between two CD moieties such that O-Na-O groups separated neighbouring vanadyl ions. Antiferromagnetic interactions between the $S$ = 1/2 vanadyl ions led to $S$ = 0 ground states for the even-membered rings, but to two quasi-degenerate $S$ = 1/2 states for the spin-frustrated heptanuclear cluster.
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The anisotropic triangular lattice of the crednerite system Cu(Mn1-xCux)O2 is used as a basic model for studying the influence of spin disorder on the ground state properties of a two-dimensional frustrated antiferromagnet. Neutron diffraction measurements show that the undoped phase (x=0) undergoes a transition to antiferromagnetic long-range order that is stabilized by a frustration-relieving structural distortion. Small deviation from the stoichiometric composition alters the magnetoelastic characteristics and reduces the effective dimensionality of the magnetic lattice. Upon increasing the doping level, the interlayer coupling changes from antiferromagnetic to ferromagnetic. As the structural distortion is suppressed, the long-range magnetic order is gradually transformed into a two-dimensional order.
Integral theorems such as Stokes and Gauss are fundamental in many parts of Physics. For instance, Faradays law allows computing the induced electric current on a closed circuit in terms of the variation of the flux of a magnetic field across the surface spanned by the circuit. The key point for applying Stokes theorem is that this surface must be orientable. Many students wonder what happens to the flux through a surface when this is not orientable, as it happens with a Mobius strip. On an orientable surface one can compute the flux of a solenoidal field using Stokes theorem in terms of the circulation of the vector potential of the field along the oriented boundary of the surface. But this cannot be done if the surface is not orientable, though in principle this quantity could be measured on a laboratory. For instance, checking the induced electric current on a circuit along the boundary of a surface if the field is a variable magnetic field. We shall see that the answer to this puzzle is simple and the problem lies in the question rather than in the answer.
Motivated by the absence of both spin freezing and a cooperative Jahn-Teller effect at the lowest measured temperatures, we study the ground state of Ba3CuSb2O9. We solve a general spin-orbital model on both the honeycomb and the decorated honeycomb lattice, revealing rich phase diagrams. The spin-orbital model on the honeycomb lattice contains an SU(4) point, where previous studies have shown the existence of a spin-orbital liquid with algebraically decaying correlations. For realistic parameters on the decorated honeycomb lattice, we find a phase that consists of clusters of nearest-neighbour spin singlets, which can be understood in terms of dimer coverings of an emergent square lattice. While the experimental situation is complicated by structural disorder, we show qualitative agreement between our theory and a range of experiments.
Capturing the non-collinear magnetic ground state of the spinel vanadates AV$_2$O$_4$ (A= Mn, Fe and Co) remains an outstanding challenge for state-of-the-art ab-initio methods. We demonstrate that both the non-collinear spin texture, as well as the magnitude of local moments, are captured by a single value of the on-site Hubbard $U$ of 2.7~eV in conjunction with the local spin density approximation (LSDA+$U$), provided the source term (i.e., magnetic monopole term) is removed from the exchange-correlation magnetic field ${bf B}_{XC}$. We further demonstrate that the magnetic monopole structure in ${bf B}_{XC}$ is highly sensitive to the value of $U$, to the extent that the interplay between on-site localization and local moment magnitude is qualitatively different depending on whether the source term is removed or not. This suggests that in treating strongly correlated magnetic materials within the LSDA+$U$ formalism, subtraction of the unphysical magnetic monopole term from the exchange-correlation magnetic field is essential to correctly treat the magnetic ground state.
Graphene SU(4) quantum Hall symmetry is extended to SO(8), permitting analytical solutions for graphene in a magnetic field that break SU(4) spontaneously. We recover standard graphene SU(4) physics as one limit, but find new phases and new properties that may be relevant for understanding the ground state. The graphene SO(8) symmetry is found to be isomorphic to one that occurs extensively in nuclear structure physics, and very similar to one that describes high-temperature superconductors, suggesting deep mathematical connections among these physically-different fermionic systems.
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