scholarly journals Gauge fields in real and momentum spaces in magnets: monopoles and skyrmions

2012 ◽  
Vol 370 (1981) ◽  
pp. 5806-5819 ◽  
Author(s):  
N. Nagaosa ◽  
X. Z. Yu ◽  
Y. Tokura
Keyword(s):  
Hall Effect ◽  
Gauge Field ◽  
Berry Phase ◽  
Solid Angle ◽  
Spontaneous Magnetization ◽  
Anomalous Hall Effect ◽  
Magnetic Monopoles ◽  
Real Space ◽  
Gauge Fields ◽  
Quantum Mechanical

Electronic states in magnets are characterized by the quantum mechanical Berry phase defined in both the real and momentum spaces. This Berry phase constitutes the gauge fields, i.e. the emergent electromagnetic fields in solids, and affects the motion of the electrons. In momentum space, the band crossings act as the magnetic monopoles, i.e. the sources or sinks of the gauge flux. In real space, the spin textures with non-coplanar spin configurations produce the gauge field by the solid angle leading to the spin chirality. Skyrmion is the representative structure supporting this gauge field. A typical phenomenon reflecting this gauge field is the anomalous Hall effect, i.e. the Hall effect produced by the spontaneous magnetization combined with the relativistic spin–orbit interaction. We discuss a few examples recently studied related to these issues with some new results on skyrmion formation.

scholarly journals Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Fei Wang ◽  
Xuepeng Wang ◽  
Yi-Fan Zhao ◽  
Di Xiao ◽  
Ling-Jie Zhou ◽  
...  
Keyword(s):  
Hall Effect ◽  
Electric Fields ◽  
First Principles ◽  
Berry Phase ◽  
Condensed Matter ◽  
Anomalous Hall Effect ◽  
First Principles Calculations ◽  
Sign Reversal ◽  
Berry Curvature ◽  
Topological Materials

AbstractThe Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

scholarly journals The Berry phase in ferromagnetic spin systems and the anomalous Hall effect

2007 ◽  
Vol 75 (4) ◽  
pp. 448-450
Author(s):  
B Basu ◽  
P Bandyopadhyay
Keyword(s):  
Hall Effect ◽  
Berry Phase ◽  
Anomalous Hall Effect ◽  
Spin Systems

scholarly journals Synthesis and observation of non-Abelian gauge fields in real space

Science ◽  
2019 ◽  
Vol 365 (6457) ◽  
pp. 1021-1025 ◽  
Author(s):  
Yi Yang ◽  
Chao Peng ◽  
Di Zhu ◽  
Hrvoje Buljan ◽  
John D. Joannopoulos ◽  
...  
Keyword(s):  
Gauge Field ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Final States ◽  
Abelian Gauge ◽  
Classical Waves ◽  
Break Time ◽  
Bohm Effect ◽  
Aharonov Bohm

Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES

1990 ◽  
Vol 05 (03) ◽  
pp. 175-182 ◽  
Author(s):  
T. D. KIEU
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Berry Phase ◽  
Integral Functional ◽  
Gauge Fields ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Normal Ordering ◽  
Schwinger Model ◽  
Holomorphic Representation

The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.

CHIRAL SPIN LIQUID STATES IN 3-SPACE DIMENSIONS AND TOPOLOGICAL ASPECTS OF MONOPOLE SUPERCONDUCTIVITY

1993 ◽  
Vol 07 (13n14) ◽  
pp. 913-919
Author(s):  
B. BASU ◽  
P. BANDYOPADHYAY
Keyword(s):  
Magnetic Flux ◽  
Gauge Field ◽  
Spin System ◽  
Berry Phase ◽  
Gauge Fields ◽  
Spin Liquid ◽  
Abelian Gauge ◽  
Heisenberg Spin ◽  
Pair Condensation ◽  
Liquid States

We have studied here the topological aspects of monopole superconductivity in 3+1 dimensions. It is pointed out that Heisenberg spin system may be associated with non-Abelian gauge fields. When the spin and charge become separated, spinons and holons emerge and holons interacting with such a gauge field associate a magnetic flux giving rise to nonzero Berry phase and causes the existence of chiral spin liquid. This also suggests that these holons are much heavier than their free counterpart and the pair of such holons forms a bosonic state respecting rotational invariance. Superconductivity arises out of this pair condensation.

scholarly journals Anomalous Hall effect and Berry phase in two-dimensional magnetic structures

2008 ◽  
Vol 104 ◽  
pp. 012018 ◽  
Author(s):  
V K Dugaev ◽  
J Barnaś ◽  
M Taillefumier ◽  
B Canals ◽  
C Lacroix ◽  
...  
Keyword(s):  
Hall Effect ◽  
Berry Phase ◽  
Anomalous Hall Effect ◽  
Two Dimensional ◽  
Magnetic Structures
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