Skyrmion Mass Research Articles

Anisotropic Mass of a Magnetic Skyrmion due to Its Interaction with Conduction Electrons: A Schwinger–Keldysh Field Theory Approach

Anisotropic Mass of a Magnetic Skyrmion due to Its Interaction with Conduction Electrons: A Schwinger–Keldysh Field Theory Approach

Skyrmion mass from spin-phonon interaction

The inertial mass of a skyrmion arising from spin-phonon interaction is computed exactly within a toy model of the magnetoelastic coupling in a ferromagnetic film. The mass scales as the square of the strength of the magnetoelastic coupling, as the square of the film thickness, and as the first power of the lateral size of the skyrmion. For nanometer skyrmions it is in the ballpark of a few electron masses but may be significantly greater in materials with large magnetostriction. These findings are expected to stand for any complex structure of spin-phonon interaction in real materials. They must be taken into account when addressing the speed of information processing based upon skyrmions.

Skyrmion stability at finite isospin chemical potential and temperature * * Supported in part by Natural Science Foundation of China (NSFC) (11805097, 11535005, 11690030), and the Jiangsu Provincial Natural Science Foundation of China (BK20180323)

The skyrmion stability at finite isospin chemical potential is studied using the Skyrme Lagrangian with a finite pion mass . A critical value , above which a stable soliton does not exist, is found. We also explore some properties of the skyrmion as function of , i.e., the isoscalar rms radius and the isoscalar magnetic rms radius. Finally, considering the finite temperature effect on the skyrmion mass, we obtain a critical temperature , using the profile function of the skyrmion, above which the skyrmion mass does not have a minimum, which can be interpreted as the occurrence of the deconfinement phase transition.

Direct search constraints on very heavy dark skyrmions

In the standard dark matter creation scenario, dark matter arises from freeze-out due to decoupling from the thermal heat bath in the early universe. On the other hand, topological solitons can also emerge during phase transitions through the Kibble–Zurek mechanism or through bubble nucleation. In particular, Murayama and Shu found that the Kibble–Zurek mechanism can produce topological defects up to about 10 PeV, and Bramante et al. had recently pointed out that direct search constraints can be extrapolated to very large masses. Motivated by these observations, we examine direct search constraints for PeV scale dark skyrmions with a Higgs portal coupling to baryons. We find abundance constraints on the combination g_V^2M_S of Skyrme coupling g_V and skyrmion mass M_S. We also find that extrapolation of the direct search constraints from XENON1T to very high masses constrains the combination g_{wh}/g_V^4 as a function of M_S, where g_{wh} is the Higgs portal coupling of the dark skyrmions.

Edge states in a two-dimensional honeycomb lattice of massive magnetic skyrmions

We study the collective dynamics of a two-dimensional honeycomb lattice of magnetic skyrmions. By performing large-scale micromagnetic simulations, we find multiple chiral and non-chiral edge modes of skyrmion oscillations in the lattice. The non-chiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handednesses depending on the mode frequency. To interpret the emerging multiband nature of the chiral edge states, we generalize the massless Thiele's equation by including a second-order inertial term of skyrmion mass as well as a third-order non-Newtonian gyroscopic term, which allows us to model the band structure of skrymion oscillations. Theoretical results compare well with numerical simulations. Our findings uncover the importance of high order effects in strongly coupled skyrmions and are helpful for designing novel topological devices.

Quantum Dynamics of Skyrmions in Chiral Magnets

We study the quantum propagation of a Skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finite-temperature path integral formalism, using field theoretic tools. Promoting the center of the Skyrmion to a dynamic quantity, the fluctuations around the Skyrmionic configuration give rise to a time-dependent damping of the Skyrmion motion. From the frequency dependence of the damping kernel, we are able to identify the Skyrmion mass, thus providing a microscopic description of the kinematic properties of Skyrmions. When defects are present or a magnetic trap is applied, the Skyrmion mass acquires a finite value proportional to the effective spin, even at vanishingly small temperature. We demonstrate that a Skyrmion in a confined geometry provided by a magnetic trap behaves as a massive particle owing to its quasi-one-dimensional confinement. An additional quantum mass term is predicted, independent of the effective spin, with an explicit temperature dependence which remains finite even at zero temperature.

Brownian motion of massive skyrmions in magnetic thin films

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.

The little skyrmion: new dark matter for little Higgs models

We study skyrmions in the littlest Higgs model and discuss their possible role as dark matter candidates. Stable massive skyrmions can exist in the littlest Higgs model also in absence of an exact parity symmetry, since they carry a conserved topological charge due to the non-trivial third homotopy group of the SU(5)/SO(5) coset. We find a spherically symmetric skyrmion solution in this coset. The effects of gauge fields on the skyrmion solutions are analyzed and found to lead to an upper bound on the skyrmion mass. The relic abundance is in agreement with the observed dark matter density for reasonable parameter choices.

Hadrons as Skyrmions in the presence of isospin chemical potential

The stability of the Skyrmion solution in the presence of finite isospin chemical potential $\mu $ is considered, showing the existence of a critical value $\mu_{c} = 222.8$ MeV where the Skyrmion mass vanishes. Using the Hamiltonian formulation, in terms of collective variables, we discuss the behavior of different skyrmionic parameters as function of the isospin chemical potential ($\mu$), such as the energy density, the isoscalar radius and the isoscalar magnetic radius. We found that the radii start to grow very fast for $\mu \geq 140$ MeV, suggesting the occurrence of a phase transition.

Skyrmions in the presence of isospin chemical potential

We analyze the existence of localized finite energy topological excitations on top of the perturbative pion vacuum within the Skyrme model at finite isospin chemical potential and finite pion mass. We show that there is a critical isospin chemical potential μIc above which such solutions cease to exist. We find that μIc is closely related to the value of the pion mass. In particular for vanishing pion mass we obtain μIc=0 in contradiction with some results recently reported in the literature. We also find that below μIc the skyrmion mass and baryon radius show, at least for the case of the hedgehog ansatz, only a mild dependence on the isospin chemical potential.

Skyrme model and isospin chemical potential

We discuss the stability of the skyrmion solution in the presence of a finite isospin chemical potential μ. Solving numerically the mass of the skyrmion as function of μ, we find a critical value μc=222.8MeV where the skyrmion mass vanishes. We compare the exact numerical treatment with an analytical discussion based on a special shape for the profile of the skyrmion due to Atiyah and Manton. The extension of this ansatz for finite μ works quite well for μ<121MeV. Then, for small values of μ, where the analytical approach is valid, we consider the possibility of having an angular deformation for the skyrmionic profile, which is possible for finite values of μ. This is, however, a small effect. Finally we introduce finite temperature corrections, which strength the instability induced by the chemical potential, finding the dependence of the critical temperature on μ.

Massive Skyrmions in quantum Hall ferromagnets

We apply the theory of elasticity to study the effects of skyrmion mass on lattice dynamics in quantum Hall systems. We find that massive Skyrme lattices behave like a Wigner crystal in the presence of a uniform perpendicular magnetic field. We make a comparison with the microscopic Hartree-Fock results to characterize the mass of quantum Hall skyrmions at $\nu=1$ and investigate how the low temperature phase of Skyrme lattices may be affected by the skyrmion mass.

Quantized skyrmion fields in 2+1 dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.

Casimir corrections in the bound state soliton model

We consider the one-loop corrections to the SU(3) skyrmion mass within the bound state soliton approach. We show that the standard SU(3) renormalization scheme is not appropiate within this framework and propose to use an alternative one based on SU(2). For physical meson masses and decay constants the resulting Casimir correction turns out to be rather scale-independent and leads to an acceptable estimate of the nucleon mass.

Skyrmion mass and a new kind of cyclotron resonance for the 2D electron gas

The skyrmionic mass is calculated using a gradient expansion method. A special cyclotron resonance is predicted, with a frequency determined by the exchange energy. The possibility of an extra bound electron is discussed.

Skyrmion quantization and the decay of the Delta.

We present the complete solution to the so-called ``Yukawa problem'' of the Skyrme model. This refers to the perceived difficulty of reproducing, purely from soliton physics, the usual pseudovector pion-nucleon coupling, echoed by pion coupling to the higher-spin/isospin baryons (I=J=3/2, 5) / 2 ,. . .,${\mathit{N}}_{\mathit{c}}$/2) in a manner fixed by large-${\mathit{N}}_{\mathit{c}}$ group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration: the rotationally improved Skyrmion. This is the near-hedgehog solution obtained by minimizing the usual Skyrmion mass functional augmented by an all-important (iso)rotational kinetic term. The numerics are pleasing: a \ensuremath{\Delta} decay width within a few MeV of its measured value, and, furthermore, the higher-spin baryons (I=J\ensuremath{\ge}5/2) with widths so large (\ensuremath{\Gamma}&gt;800 MeV) that these undesirable large-${\mathit{N}}_{\mathit{c}}$ artifacts effectively drop out of the spectrum, and pose no phenomenological problem. Beyond these specific results, we ground the Skyrme model in the Feynman path integral, and set up a transparent collective coordinate formalism that makes maximal use of the 1/${\mathit{N}}_{\mathit{c}}$ expansion. This approach elucidates the connection between Skyrmions on the one hand, and Feynman diagrams in an effective field theory on the other.

Chiral Expansion, Large N C Expansion, and the Skyrmion Mass

The chiral lagrangian determined in the framework of ChPT could be compatible with stable soliton solutions. We address the question of performing a consistent semi-classical expansion in the soliton sector. The chiral and large N c expansions are found not to be independent. The one-loop contribution to the soliton mass is completely evaluated using ζ-function techniques. We show that an accurate estimate is possible despite an incomplete knowledge of the counterterms, because of dominating indirect zero-mode contributions. It turns out that the chiral and large N c expansions both fail in the soliton sector if the lagrangian is truncated at order four. A minimal extension to chiral order six is proposed, for which both expansions are found to become consistent. Sensible values of the nucleon and delta masses are predicted without adjusting any parameter.

Virtual-pion fluctuations around the bare skyrmion

Pion fluctuations around the skyrmion are quantized by Dirac's method. In the large- N c limit, where N c is the number of colors, the O( N c 0) quantum correction to the skyrmion mass that comes from the virtual-pion fluctuations is shown to be negative. A perturbative expansion using the usual Feynman-Dyson technique but with noncovariant pion propagators is developed to evaluate the quantum correction. As a result of delicate cancellations, it is a good approximation to keep just the leading-order terms in the perturbation series. This approximation gives rise to the pion decay constant F π = 172 MeV, to be compared with the experimental value of 186 MeV. The axial coupling constant g A is also improved considerably. An application of the method to the (1 + 1)-dimensional kink model and sine-Gordon model supports our results.

Recoil effects in a quantum theory of the Skyrmion

The purpose of this work is to illustrate how the Kerman-Klein method of quantization, introduced originally for the restoration of broken symmetries in the non-relativistic many-body problem and later utilized by Goldstone and Jackiw (1975) for a one-dimensional soliton, can be applied to the study of Skyrmion physics. In this method, one replaces the piecemeal quantization of collective coordinates by a formal canonical quantization of a full classical Hamiltonian, collectivity arising from the structure of the associated Hilbert space. In this first account, the restoration of translational invariance is studied using a quantized form of the original Skyrme Hamiltonian. This involves the study of matrix elements of the Heisenberg equations of motion by means of the completeness relation in a restricted Hilbert space consisting of all possible momentum eigenstates of the Skyrmion. In the limit in which the ratio of the Compton wavelength of the Skyrmion to its size is negligible (corresponding to the large Nc limit of QCD), the resulting classical field equation properly describes a boosted hedgehog. Higher order terms in this ratio describe quantum recoil corrections to the Skyrmion mass. In contrast to (1+1)-dimensional field theories studied previously, a gradient expansion for the calculation of these corrections diverges. In a more careful evaluation, there is a finite but large contribution from the Skyrme term. The dependence of the result on the ordering ambiguities that occur in the quantization of the field kinetic energy is also described.

On the Casimir energy of a skyrmion

We evaluate the leading correction to the classical skyrmion mass, that is, the Casimir energy. We use a method which is well defined in the chiral limit. The main ultraviolet divergence is cancelled by the counterterms of Gasser and Leutwyler. We show that the result is controlled by the low energy behavior of the phase-shifts which are large and positive due to the presence of two normalizable zero-modes. As a consequence, the sign and order of magnitude do not depend on the truncation of the chiral lagrangian. The correction is found to be negative and rather large, of the order of 1 GeV.