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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.
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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.
Multiferroics are those materials with more than one ferroic order, and magnetoelectricity refers to the mutual coupling between magnetism and electricity. The discipline of multiferroicity has never been so highly active as that in the first decade of the twenty-first century, and it has become one of the hottest disciplines of condensed matter physics and materials science. A series of milestones and steady progress in the past decade have enabled our understanding of multiferroic physics substantially comprehensive and profound, which is further pushing forward the research frontier of this exciting area. The availability of more multiferroic materials and improved magnetoelectric performance are approaching to make the applications within reach. While seminal review articles covering the major progress before 2010 are available, an updated review addressing the new achievements since that time becomes imperative. In this review, following a concise outline of the basic knowledge of multiferroicity and magnetoelectricity, we summarize the important research activities on multiferroics, especially magnetoelectricity and related physics in the last six years. We consider not only single-phase multiferroics but also multiferroic heterostructures. We address the physical mechanisms regarding magnetoelectric coupling so that the backbone of this divergent discipline can be highlighted. A series of issues on lattice symmetry, magnetic ordering, ferroelectricity generation, electromagnon excitations, multiferroic domain structure and domain wall dynamics, and interfacial coupling in multiferroic heterostructures, will be revisited in an updated framework of physics. In addition, several emergent phenomena and related physics, including magnetic skyrmions and generic topological structures associated with magnetoelectricity will be discussed.
The contribution of bulk and surface to the electrical resistance along crystallographic textit{b}- and textit{c}-axes as a function of crystal thickness gives evidence for a temperature independent surface states in an antiferromagnetic narrow-gap semiconductor CrSb$_{2}$. ARPES shows a clear electron-like pocket at $Gamma$-$Z$ direction which is absent in the bulk band structure. First-principles calculations also confirm the existence of metallic surface states inside the bulk gap. Whereas combined experimental probes point to enhanced surface conduction similar to topological insulators, surface states are trivial since CrSb$_2$ exhibits no band inversion.
We propose a new type of spin-valley locking (SVL), named $textit{C}$-paired SVL, in antiferromagnetic systems, which directly connects the spin/valley space with the real space, and hence enables both static and dynamical controls of spin and valley to realize a multifunctional antiferromagnetic material. The new emergent quantum degree of freedom in the $textit{C}$-paired SVL is comprised of spin-polarized valleys related by a crystal symmetry instead of the time-reversal symmetry. Thus, both spin and valley can be accessed by simply breaking the corresponding crystal symmetry. Typically, one can use a strain field to induce a large net valley polarization/magnetization and use a charge current to generate a large noncollinear spin current. We predict the realization of the $textit{C}$-paired SVL in monolayer V$_2$Se$_2$O, which indeed exhibits giant piezomagnetism and can generate a large transverse spin current. Our findings provide unprecedented opportunities to integrate various controls of spin and valley with nonvolatile information storage in a single material, which is highly desirable for versatile fundamental research and device applications.
Using an electric field instead of an electric current (or a magnetic field) to tailor the electronic properties of magnetic materials is promising for realizing ultralow energy-consuming memory devices because of the suppression of Joule heating, especially when the devices are scaled to the nanoscale. In the review, we summarize recent results on the giant magnetization and resistivity modulation in a metamagnetic intermetallic alloy - FeRh, which is achieved by electric-field-controlled magnetic phase transitions in multiferroic heterostructures. Furthermore, the approach is extended to topological antiferromagnetic spintronics, which is currently receiving attention in the magnetic society, and the antiferromagnetic order parameter has been able to switch back and forth by a small electric field. In the end, we envision the possibility of manipulating exotic physical phenomena in the emerging topological antiferromagnetic spintronics field via the electric-field approach.
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