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We show, by solving Maxwells equations, that an electric charge on the surface of a slab of a linear magnetoelectric material generates an image magnetic monopole below the surface provided that the magnetoelectric has a diagonal component in its magnetoelectric response. The image monopole, in turn, generates an ideal monopolar magnetic field outside of the slab. Using realistic values of the electric- and magnetic- field susceptibilties, we calculate the magnitude of the effect for the prototypical magnetoelectric material Cr$_2$O$_3$. We use low energy muon spin rotation to measure the strength of the magnetic field generated by charged muons as a function of their distance from the surface of a Cr$_2$O$_3$ films, and show that the results are consistent with the existence of the monopole. We discuss other possible routes to detecting the monopolar field, and show that, while the predicted monopolar field generated by Cr$_2$O$_3$ is above the detection limit for standard magnetic force microscopy, detection of the field using this technique is prevented by surface charging effects.
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A general formula for the average vector potential of bulk periodic systems is proposed and shown to set the boundary conditions at magnetic interfaces. For antiferromagnetic materials, the study reveals a unique relation between the macroscopic potential and the orientation-dependent magnetic quadrupole, as a result of the different crystalline and magnetic symmetries. In particular, at surfaces and interfaces of a truncated bulk without inversion and time-reversal symmetries, the average vector potential exhibits a discontinuity, which results in an interfacial magnetic field. In general, however, due to the surface and interface electronic and atomic relaxations, additional magnetization may result. For the experimentally-observed magnetoelectric antiferromagnets, in particular, our symmetry analysis suggest that the relaxation effects could well be a system response to the presence of such a potential discontinuity.
In honor of Igor Dzyaloshinskii on his 90th birthday, we revisit his pioneering work on the linear magnetoelectric effect in light of the modern theory of ferroelectric polarization. We show that the surface magnetic dipole moment associated with magnetoelectric materials is analogous to the bound surface charge in ferroelectrics, in that it can be conveniently described in terms of a bulk magnetoelectric multipolization that is analogous to the ferroelectric polarization. We define the intrinsic surface magnetization to be this surface magnetic dipole moment per unit area, and provide a convenient recipe for extracting it for any surface plane, from knowledge of the bulk magnetic order. We demonstrate the procedure for the prototypical magnetoelectric material, Cr$_2$O$_3$, in which Dzyaloshinskii first identified the linear magnetoelectric effect, and compare the value of the intrinsic surface magnetization to recent experimental measurements. Finally, we argue that non-magnetoelectric antiferromagnets whose multipolization lattices do not contain zero should have an intrinsic surface magnetization, in the same way that non-polar insulators whose polarization lattices do not contain zero have an intrinsic surface charge.
A combined experimental and theoretical study of doping individual Fe atoms into Bi2Se3 is presented. It is shown through a scanning tunneling microscopy study that single Fe atoms initially located at hollow sites on top of the surface (adatoms) can be incorporated into subsurface layers by thermally-activated diffusion. Angle-resolved photoemission spectroscopy in combination with ab-initio calculations suggest that the doping behavior changes from electron donation for the Fe adatom to neutral or electron acceptance for Fe incorporated into substitutional Bi sites. According to first principles calculations within density functional theory, these Fe substitutional impurities retain a large magnetic moment thus presenting an alternative scheme for magnetically doping the topological surface state. For both types of Fe doping, we see no indication of a gap at the Dirac point.
To explore the origin of the Fermi level pinning in germanium we investigate the Ge(001) and Ge(001):H surfaces. The absence of relevant surface states in the case of Ge(001):H should unpin the surface Fermi level. This is not observed. For samples with donors as majority dopants the surface Fermi level appears close to the top of the valence band regardless of the surface structure. Surprisingly, for the passivated surface it is located below the top of the valence band allowing scanning tunneling microscopy imaging within the band gap. We argue that the well known electronic mechanism behind band bending does not apply and a more complicated scenario involving ionic degrees of freedom is therefore necessary. Experimental techniques involve four point probe electric current measurements, scanning tunneling microscopy and spectroscopy.
Using first-principles calculations we predict that the layered-perovskite metal Bi$_5$Mn$_5$O$_{17}$ is a ferromagnet, ferroelectric, and ferrotoroid which may realize the long sought-after goal of a room-temperature ferromagnetic single-phase multiferroic with large, strongly coupled, primary-order polarization and magnetization. Bi$_5$Mn$_5$O$_{17}$ has two nearly energy-degenerate ground states with mutually orthogonal vector order parameters (polarization, magnetization, ferrotoroidicity), which can be rotated globally by switching between ground states. Giant cross-coupling magnetoelectric and magnetotoroidic effects, as well as optical non-reciprocity, are thus expected. Importantly, Bi$_5$Mn$_5$O$_{17}$ should be thermodynamically stable in O-rich growth conditions, and hence experimentally accessible.
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