Compact merons and skyrmions in thin chiral magnetic films

A meron is a controversial topological excitation because i t carries just one half of the topological charge unit. It is believed that it is tightly binded to another mero n and cannot be observed by isolating it. We present a counter example, investigating the 2-dimensional nonlinear sigma model together with the DzyaloshinskiiMoriya interaction, where topological excitations are mer ons, bimerons and skyrmions. They behave as if they were free particles since they are electrically neutral. A p rominent feature is that the topological charge density is strictly confined within compact domains. We propose an an alytic approach for these compact excitations, and construct a phase diagram. It is comprised of the helix, meron, skyrmion-crystal, skyrmion-gas and ferromagnet phases. It explains quite well the experimental data recent ly performed in chiral magnets such as MnSi and FeCoSi thin films, as verifies that merons are surely basic top ological excitations in the system. Topological excitations are endlessly fascinating. They a re constantly under investigations in all branches of physics . Well known examples are vortices and skyrmions[1]. A fantastic topological object is a meron: It cannot exist by itse lf since it carries only one half of the topological charge unit . A meron was originally invented as a half-instanton in the context of quark confinement in particle physics[2]. Later it wa s introduced as a half-skyrmion in order to account for a certain anomalous behavior in bilayer quantum Hall effects[3]. Though the meron is a theoretically useful concept, it remains to be a long-standing problem whether it exists in reality. There is no clear evidence for its existence in spite o f experimental endeavors[1]. Magnetic thin films are ideal systems to investigate and test various intriguing ideas on topological excitations. Inde ed, a skyrmion crystal[4] as well as a single skyrmion[5] have been observed in chiral magnets such as MnSi and FeCoSi thin films. Furthermore, magnetic domains observed in ferro magnets such as a TbFeCo thin film[6] are shown to be giant skyrmions[7] as large as ∼ 1�m . In this paper we point out that merons are also detectable as almost isolated objects. The ground state of a chiral magnet is a helical state in the absence of external magnetic field. The spin texture of the helical state has a stripe-domain structure, where the widt h of a stripe has a fixed value determined by sample parameters. A stripe breaks into pieces as the magnetic field increases. By calculating the topological charge density, we show that the endpoint of a broken stripe has the topological charge Qsky = 1/2. It is natural to identify them as merons. Finite-length stripes are bimerons [Fig.1], among which the shortest ones are skyrmions. When we talk about skyrmions in the 2-dimensional space, it is implicit to assume a Belavin-Polyakov skyrmion. Its spin texture approaches the ground-state value only polynomially at large distance. On the contrary, a skyrmion must be strict ly compact in the chiral magnet since it is embedded within a stripe-domain structure. We propose an analytic scheme to explore compact skyrmions, merons and bimerons. Being electrically neutral excitations, they behave as if they were fr ee particles. Based on this observation we construct a phase di agram of the chiral ferromagnet. It explains quite well the