Electronic structure and magnetism in the frustrated antiferromagnet LiCrO2

LiCrO2 is a 2D triangular antiferromagnet, isostructural with the common battery material LiCoO2 and a well-known Jahn-Teller antiferromagnet NaNiO2. As opposed to the latter, LiCrO2 exibits antiferromagnetic exchange in Cr planes, which has been ascribed to direct Cr-Cr d-d overlap. Using LDA and LDA+U first principles calculations I confirm this conjecture and show that (a) direct d-d overlap is indeed enhanced compared to isostructural Ni and Cr compounds, (b) p-d charge transfer gap is also enhanced, thus suppressing the ferromagnetic superexchange, (c) the calculated magnetic Hamiltonian maps well onto the nearest neighbors Heisenberg exchange model and (d) interplanar inteaction is antiferromagnetic.Comment: 5 pages, 4 figure

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On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP