Dynamical magnetoelectric phenomena of skyrmions in multiferroics

<jats:title>Abstract</jats:title> <jats:p>Magnetic skyrmions, nanoscopic spin vortices carrying a quantized topological number in chiral-lattice magnets, are recently attracting great research interest. Although magnetic skyrmions had been observed only in metallic chiral-lattice magnets such as B20 alloys in the early stage of the research, their realization was discovered in 2012 also in an insulating chiral-lattice magnet <jats:inline-formula id="j_psr-2019-0017_ineq_001"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mtext>Cu</m:mtext> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:msub> <m:mrow> <m:mtext>OSeO</m:mtext> </m:mrow> <m:mn>3</m:mn> </m:msub> </m:math> <jats:tex-math>$\textrm{Cu}_2\textrm{OSeO}_3$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_psr-2019-0017_ineq_001.png" /> </jats:alternatives> </jats:inline-formula>. A characteristic of the insulating skyrmions is that they can host multiferroicity, that is, the noncollinear magnetization alignment of skyrmion induces electric polarizations in insulators with a help of the relativistic spin-orbit interaction. It was experimentally confirmed that the skyrmion phase in <jats:inline-formula id="j_psr-2019-0017_ineq_002"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mtext>Cu</m:mtext> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:msub> <m:mrow> <m:mtext>OSeO</m:mtext> </m:mrow> <m:mn>3</m:mn> </m:msub> </m:math> <jats:tex-math>$\textrm{Cu}_2\textrm{OSeO}_3$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_psr-2019-0017_ineq_002.png" /> </jats:alternatives> </jats:inline-formula> is indeed accompanied by the spin-induced ferroelectricity. The resulting strong magnetoelectric coupling between magnetizations and electric polarizations can provide us with a means to manipulate and activate magnetic skyrmions by application of electric fields. This is in sharp contrast to skyrmions in metallic systems, which are driven through injection of electric currents. The magnetoelectric phenomena specific to the skyrmion-based multiferroics are attracting intensive research interest, and, in particular, those in dynamical regime are widely recognized as an issue of vital importance because their understanding is crucial both for fundamental science and for technical applications. In this article, we review recent studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulating chiral-lattice magnet <jats:inline-formula id="j_psr-2019-0017_ineq_003"> <jats:alternatives> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mtext>Cu</m:mtext> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:msub> <m:mrow> <m:mtext>OSeO</m:mtext> </m:mrow> <m:mn>3</m:mn> </m:msub> </m:math> <jats:tex-math>$\textrm{Cu}_2\textrm{OSeO}_3$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_psr-2019-0017_ineq_003.png" /> </jats:alternatives> </jats:inline-formula>. It is argued that the multiferroic skyrmions show unique resonant excitation modes of coupled magnetizations and polarizations, so-called electromagnon excitations, which can be activated both magnetically with a microwave magnetic field and electrically with a microwave electric field. The interference between thes ...