Topological insulators are insulating materials that display conducting surface states protected by time-reversal symmetry, wherein electron spins are locked to their momentum. This unique property opens up new opportunities for creating next-generation electronic, spintronic and quantum computation devices. Introducing ferromagnetic order into a topological insulator system without compromising its distinctive quantum coherent features could lead to the realization of several predicted physical phenomena. In particular, achieving robust long-range magnetic order at the surface of the topological insulator at specific locations without introducing spin-scattering centres could open up new possibilities for devices. Here we use spin-polarized neutron reflectivity experiments to demonstrate topologically enhanced interface magnetism by coupling a ferromagnetic insulator (EuS) to a topological insulator (Bi2Se3) in a bilayer system. This interfacial ferromagnetism persists up to room temperature, even though the ferromagnetic insulator is known to order ferromagnetically only at low temperatures (<17 K). The magnetism induced at the interface resulting from the large spin-orbit interaction and the spin-momentum locking of the topological insulator surface greatly enhances the magnetic ordering (Curie) temperature of this bilayer system. The ferromagnetism extends ~2 nm into the Bi2Se3 from the interface. Owing to the short-range nature of the ferromagnetic exchange interaction, the time-reversal symmetry is broken only near the surface of a topological insulator, while leaving its bulk states unaffected. The topological magneto-electric response originating in such an engineered topological insulator could allow efficient manipulation of the magnetization dynamics by an electric field, providing an energy-efficient topological control mechanism for future spin-based technologies.

It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This is a consequence of a non-trivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge-fields, which form a gas of magnetic monopoles. In the presence of logarithmic interactions, the original electric charges are unconfined . The confined phase, which is permanent in the absence of matter fields, is reached at a critical electric charge, where the interaction between magnetic charges is screened by a pair unbinding transition in a Kosterlitz-Thouless type of phase-transition.

PACS. 72.25.-b -Spin polarized transport. PACS. 72.25.Mk -Spin transport through interfaces. PACS. 74.50.+r -Tunneling phenomena; point contacts, weak links, Josephson effects.Abstract. -We consider the tunnel current between two ferromagnetic metals from a perspective similar to the one used in superconductor/superconductor tunnel junctions. We use fundamental arguments to derive a Josephson-like tunnel spin current I spin J ∝ sin(θ1 − θ2).Here the phases are associated with the planar contribution to the magnetization, c † ↑ c ↓ ∼ e iθ . The crucial step in our analysis is the fact that the z-component of the spin is canonically conjugate to the phase of the planar contribution: [θ, S z ] = i. This is the counterpart to the commutation relation [ϕ, N ] = i in superconductors, where ϕ is the phase associated with the superconducting order parameter and N is the Cooper pair number operator. We briefly discuss the experimental consequences of our theoretical analysis.

Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so-called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1/2 quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry-phase term that projects out the S=1/2 sector. The result is a first-order phase transition, thus contradicting the conjecture.

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if N is large enough. We argue that nonperturbatively this result should persist down to N = 2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent η for the decay of the two-spin correlation function to first-order in ǫ = 4 − d. We also note the scaling relation η = d + 2(1 − ϕ/ν) connecting the exponent η for the decay to the correlation length exponent ν and the crossover exponent ϕ. The most remarkable incarnation of the LandauGinzburg theory of phase transitions is the one embodied by Wilson's renormalization group (RG) [1]. According to this point of view, the Landau-Ginzburg theory is uniquely determined by the effective coupling constants obtained by integrating out high-energy modes. In this way, the large distance scaling behavior of different physical quantities is governed by the fixed points in the space of coupling constants. This is the so called LandauGinzburg-Wilson (LGW) paradigm of phase transitions [2]. The LGW paradigm is known to fail in a number of quantum phase transitions. One prominent example is the transition between the Néel state to a valence bond solid (VBS) state in a two-dimensional Mott insulator [3]. This transition features a quantum critical point (QCP), which is at odds with the LGW scenario that would predict a first-order phase transition. The crucial observation in this context is that both phases break symmetries in distinct spaces: the Néel state breaks the SU(2) symmetry of the Hamiltonian, while the paramagnetic VBS state breaks lattice symmetries. A continuous such order-order phase transition would not be captured by a LGW-like point of view [4].For an SU(2) Heisenberg antiferromagnet the spinons z α are the elementary constituents of the spin orientation field n. We have n a = z † σ a z, a = 1, 2, 3, where z = (z 1 , z 2 ) and σ a are the Pauli matrices. This is the so called CP 1 representation of the SU(2) spins. There is an inherent local gauge invariance in this representation, since n remains invariant when the spinon fields change by a local phase factor, i.e., z α → e iθ(x) z α . Thus, it seems to be natural to effectively describe a Mott insulator through a gauge theory coupled to "spinon matter". The gauge field here is an emergent photon: it is dynamically generated as a consequence of the local gauge invariance of n in terms of the spinon fields. Note that only expectation values of gauge-invariant operators can be nonzero, in agreement with Elitzur's theorem [5]. The VB...