A composition theorem for the Fourier Entropy-Influence conjecture

The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96] seeks to relate two fundamental measures of Boolean function complexity: it states that $H[f] \leq C Inf[f]$ holds for every Boolean function $f$, where $H[f]$ denotes the spectral entropy of $f$, $Inf[f]$ is its total influence, and $C > 0$ is a universal constant. Despite significant interest in the conjecture it has only been shown to hold for a few classes of Boolean functions. Our main result is a composition theorem for the FEI conjecture. We show that if $g_1,...,g_k$ are functions over disjoint sets of variables satisfying the conjecture, and if the Fourier transform of $F$ taken with respect to the product distribution with biases $E[g_1],...,E[g_k]$ satisfies the conjecture, then their composition $F(g_1(x^1),...,g_k(x^k))$ satisfies the conjecture. As an application we show that the FEI conjecture holds for read-once formulas over arbitrary gates of bounded arity, extending a recent result [OWZ11] which proved it for read-once decision trees. Our techniques also yield an explicit function with the largest known ratio of $C \geq 6.278$ between $H[f]$ and $Inf[f]$, improving on the previous lower bound of 4.615

Antiferromagnetic phase of the gapless semiconductor V3Al

Discovering new antiferromagnetic compounds is at the forefront of developing future spintronic devices without fringing magnetic fields. The antiferromagnetic gapless semiconducting D03 phase of V3Al was successfully synthesized via arc-melting and annealing. The antiferromagnetic properties were established through synchrotron measurements of the atom-specific magnetic moments, where the magnetic dichroism reveals large and oppositely-oriented moments on individual V atoms. Density functional theory calculations confirmed the stability of a type G antiferromagnetism involving only two-third of the V atoms, while the remaining V atoms are nonmagnetic. Magnetization, x-ray diffraction and transport measurements also support the antiferromagnetism. This archetypal gapless semiconductor may be considered as a cornerstone for future spintronic devices containing antiferromagnetic elements.Comment: Accepted to Physics Review B on 02/23/1

Magnetic properties of Fe/Dy multilayers: a Monte Carlo investigation

We investigate the magnetic properties of a Heisenberg ferrimagnetic multilayer by using Monte Carlo simulations. The aim of this work is to study the local structural anisotropy model which is a possible origin of the perpendicular magnetic anisotropy in transition metal/rare earth amorphous multilayers. We have considered a face centered cubic lattice where each site is occupied by a classical Heisenberg spin. We have introduced in our model of amorphous multilayers a small fraction of crystallized Fe-Dy nanoclusters with a mean anisotropy axis along the deposition direction. We show that a competition in the energy terms takes place between the mean uniaxial anisotropy of the Dy atoms in the nanoclusters and the random anisotropy of the Dy atoms in the matrix.Comment: accepte pour publication - Proceeding of the Joint European Magnetic Symposia (JEMS 06) - Journal of Magnetism and Magnetic Material

Proximity Driven Enhanced Magnetic Order at Ferromagnetic Insulator / Magnetic Topological Insulator Interface

Magnetic exchange driven proximity effect at a magnetic insulator / topological insulator (MI/TI) interface provides a rich playground for novel phenomena as well as a way to realize low energy dissipation quantum devices. Here we report a dramatic enhancement of proximity exchange coupling in the MI / magnetic-TI EuS / Sb$_{2-x}$V$_x$Te$_3$ hybrid heterostructure, where V doping is used to drive the TI (Sb$_{2}$Te$_3$) magnetic. We observe an artificial antiferromagnetic-like structure near the MI/TI interface, which may account for the enhanced proximity coupling. The interplay between the proximity effect and doping provides insights into controllable engineering of magnetic order using a hybrid heterostructure.Comment: 5 pages, 4 figure

Monte Carlo investigation of the magnetic anisotropy in Fe/Dy multilayers

By Monte Carlo simulations in the canonical ensemble, we have studied the magnetic anisotropy in Fe/Dy amorphous multilayers. This work has been motivated by experimental results which show a clear correlation between the magnetic perpendicular anisotropy and the substrate temperature during elaboration of the samples. Our aim is to relate macroscopic magnetic properties of the multilayers to their structure, more precisely their concentration profile. Our model is based on concentration dependent exchange interactions and spin values, on random magnetic anisotropy and on the existence of locally ordered clusters that leads to a perpendicular magnetisation. Our results evidence that a compensation point occurs in the case of an abrupt concentration profile. Moreover, an increase of the noncollinearity of the atomic moments has been evidenced when the Dy anisotropy constant value grows. We have also shown the existence of inhomogeneous magnetisation profiles along the samples which are related to the concentration profiles

Prediction of Ferromagnetic Ground State of NaCl-type FeN

Ab-initio results for structural and electronic properties of NaCl-type FeN are presented in a framework of plane-wave and ultrasoft pseudopotentials. Competition among different magnetic ordering is examined. We find the ferromagnetic phase stable overall. Stabilization over the unpolarized phase is obtained by splitting one flat t_2g-type band crossing the Fermi energy. A comparison with CrN is considered. We find large differences in the properties of the two systems that can be addressed to the smaller ionicity and magnetization of FeN.Comment: 5 pages, 4 figures, twocolumn latex style Sentence changed in Section III line 1