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Chen, X. Zhou, H. Liu, J. Li, and J. Guo, "A swallow-tailed wideband planar monopole antenna with semi-elliptical base," Journal of Electromagnetic Waves and Applications , Vol. Brown, G.

Woodward Jr. Wong, K. Lin, "Stripline-fed printed triangular monopole," Electron. Lee, J. Park, and S. Lee, "Bow-tie wideband monopole antenna with the novel impedance-bandwidth technique," Microwave Opt. Johnson, J. Verbiest, J. Evans, J.

Design Of Monopole Antenna Essay

Ammann, "Planar trapezoidal and pentagonal monopoles with impedance bandwidths in excess of ," Proc. Chen, Z.

Chia, "Impedance characteristics of trapezoidal planar monopole antennas," Microwave Opt. CO;2-D Ali, M. Okoniewski, M. Stuckly, and S. Rahman, M. Stuchly, and M. Okoniewski, "Dual-band strip-sleeve monopole for handheld telephones," Microwave Opt.


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CO;2-F Chen, H. Chen, and W. Abstract Abstract. Subjects considered include the fermion-monopole scattering processes, charge conservation in the fermion-monopole system and its relationship to gauge invariance, and monopole catalysis resulting from monopoles with charges larger than a Dirac charge and from monopoles with a different topology than those of the SU 5 grand unified theory.

Special emphasis is placed on the conservation laws which determine the allowed monopole-fermion interactions and on catalysis as a probe of the structure of a grand unified theory.

High pressure route to generate magnetic monopole dimers in spin ice.

Stone, J. Country of publication. United States. Descriptors DEI. Descriptors DEC. Publication Year Publication Year. In the present case of MnGe, the elastic response is an order of magnitude larger than the conventional case for example, in MnSi , showing up as the critical elastic softening around the topological phase transition for H k and also as the fine structure in the magnetization process for H k. It is noteworthy that there is no distinct or discontinuous anomaly in the corresponding magnetization curve see Fig.

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The above experimental results are consistent with theoretical predictions of unique features associated with the monopole dynamics in MnGe. To clarify the role of emergent magnetic field, we extract the unusual contributions and compare them with theoretical calculations taking account of emergent-field effect and its spatial and temporal variations via spin-wave excitations see Methods for detail. Theoretical counterparts are shown in Fig. As shown in Fig. This continuity also ensures that the topological phase transition due to the pair annihilation is of the second order; indeed, no hysteretic or discontinuous behaviour is experimentally observed The large, positive MR reaching the maximum around the magnetic phase boundary is ascribed to the fluctuations of emergent magnetic field that is critically enhanced around the monopole—antimonopole annihilation point, as represented in Fig.

Although in general various mechanisms can simultaneously contribute to MR see Supplementary Note 2 and Supplementary Fig. The calculated exhibits an anisotropy and gets larger towards the upsurge at the phase transition see Supplementary Fig. Spin-wave excitations in the monopole—antimonopole crystal, which are composed of three modes linear, quadratic and gapped dispersions as functions of momentum , have much lower energies than the temperature and play a key role in a microscopic process of the inelastic scattering of conduction electrons by monopole fluctuations see Methods.

In line with this model, modification of magnetic interactions due to the sound-wave-induced strain is responsible for the observed elastic anomalies Fig. In reality, mixing up the three-mode magnon spectrum and the acoustic phonon spectrum results in a dramatic elastic softening around the phase transition for the parallel H k case as well as a multi-peak-and-trench elastic response for the orthogonal H k case, as shown Fig.

See Methods, Supplementary Fig. Figure 3 shows the data sets of the monopole-related transport properties at various temperatures. However, those that remain unexplained may originate from emergent monopoles as well, given their close ties to the critical magnetic-field points; the corresponding magnetic fields H c2 and for the additional anomalies in MR and elastic constant are later presented in Fig.

Magnetic-field dependences of topological Hall resistivity a , longitudinal MR b and change in elastic constant with propagation directions parallel to the magnetic field c. Contour mappings of topological Hall resistivity a , positive contribution to longitudinal MR b and elastic constant with propagation directions parallel to the magnetic field c in T — H plane.

The critical fields H c are defined as inflection points in M — H curves. The magnetic field where the topological Hall resistivity shows its extremum H THE:peak and other characteristic magnetic fields H c1 , H c2 , and are also indicated in the corresponding panels. With this reservation, we can separately assess these characteristic features from static and dynamic responses of emergent magnetic monopoles. The observed critical behaviours in MR and elastic property are well accounted for by the theoretical models, considering fluctuations of emergent monopoles, and hence represent the topological phase transition associated with the pair annihilation of the real-space hedgehog spin singularities in MnGe.

The topology of spin structure, guaranteed by the three-mode helical magnetic ordering, enables the topological phase transition to survive even at finite temperatures, which can realize versatile unique phenomena based on the dynamics of emergent magnetic monopoles. Polycrystalline MnGe samples were synthesized with a cubic-anvil-type high-pressure apparatus. The material was confirmed to be single phase of Btype chiral cubic structure at room temperature by powder X-ray analyses. A phase comparison method 31 was used for measurements of relative change in elastic constant.

The sample has a cuboid shape with dimensions of 3. The imaginary-time spin-wave Lagrangian density for hedgehog—antihedgehog lattice takes the form,. The emergent magnetic field b i are spatially averaged within a magnetic cell, as we are interested in the long-wavelength behaviour. The first two terms originate from the spin Berry phase and the last two manifest the rigidity gained after symmetry breaking on the formation of hedgehog—antihedgehog lattice.

The key feature consists in a three-mode magnon spectrum linear, quadratic in momentum k and gapped, respectively of this theory see also Supplementary Fig. The interaction with spin-wave fluctuations enters via the spatial and temporal dependence of the emergent vector potential a and a potential V on the spin configurations.

Moreover, equal-time finite temperature correlation functions of the emergent magnetic fields can be calculated as well, so as to compare the fluctuations as stated in the main text. Together with and a standard longitudinal phonon theory, by integrating out the spin-wave fields, we can attain an effective phonon theory that well describes the new phonon excitations under the hybridization with magnon modes. A new renormalized k -linear phonon mode as identified by examining the spectral function takes direct charge of the elastic responses.

Detailed calculation results of the MR and the ultrasonic responses for more general cases with the use of a broader range of parameter values can be found in the papers in preparation by Zhang et al. How to cite this article: Kanazawa, N. Critical phenomena of emergent magnetic monopoles in a chiral magnet. Anderson, P. Wen, X. Press Qi, X. Topological insulators and superconductors. Nagaosa, N. Emergent electromagnetism in solids. T , Berry, M. Quantal phase factors accompanying adiabatic changes.

A , 45—57 Volovik, G. Linear momentum in ferromagnets.

Please note:

C Solid State Phys. Kotiuga, P. The algebraic topology of Bloch points. IEEE Trans. Feldtkeller, E.

References

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Critical phenomena of emergent magnetic monopoles in a chiral magnet | Nature Communications

Unwinding of a skyrmion lattice by magnetic monopoles. Science , — Kanazawa, N. Large topological Hall effect in a short-period helimagnet MnGe. Possible skyrmion-lattice ground state in the B20 chiral-lattice magnet MnGe as seen via small-angle neutron scattering. B 86 , Tanigaki, T. Real-space observation of short-period cubic lattice of skyrmions in MnGe.

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Nano Lett. Binz, B. Chirality induced anomalous-Hall effect in helical spin crystals. B , — Skyrmion lattice in a chiral magnet.