Anomalous Hall effect in NiPt thin films

We study Hall effect in sputtered NixPt1-x thin films with different Ni concentrations. Temperature, magnetic field and angular dependencies are analyzed and the phase diagram of NiPt thin films is obtained. It is found that films with sub-critical Ni concentration exhibit cluster-glass behavior at low temperatures with a perpendicular magnetic anisotropy below the freezing temperature. Films with over-critical Ni concentration are ferromagnetic with parallel anisotropy. At the critical concentration the state of the film is strongly frustrated. Such films demonstrate canted magnetization with the easy axis rotating as a function of temperature. The magnetism appears via consecutive paramagnetic - cluster glass - ferromagnetic transitions, rather than a single second-order phase transition. But most remarkably, the extraordinary Hall effect changes sign at the critical concentration. We suggest that this is associated with a reconstruction of the electronic structure of the alloy at the normal metal - ferromagnet quantum phase transition.Comment: 12 pages, 17 figure

Applications of p-deficiency and p-largeness

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich for the remaining primes. We also generalise a result of Grigorchuk on Coxeter groups to odd primes.Comment: 23 page

(Contravariant) Koszul duality for DG algebras

A DG algebras $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op} \equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories of DG modules with degreewise finite-dimensional homology. It induces an equivalences of $D^{df}_{b}(A)^{op}$ and the category of perfect DG $RHom_A(K,K)$-modules, and vice-versa. Corresponding statements are proved also when $H(A)$ is simply connected and $H^{<0}(A)=0$.Comment: 33 page

Schreier rewriting beyond the classical setting

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving the ranks of actions and the ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish the generalization of the Schreier formula to the case of subgroups of infinite index. We also study and apply large modules over free associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V., Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008), 753 - 759.Comment: 17 page