Abstract
We study the spontaneous magnetization and the magnetic hysteresis using the gauge/gravity duality. We first propose a novel and general formula to compute the magnetization in a large class of holographic models. By using this formula, we compute the spontaneous magnetization in a model like a holographic superconductor. Furthermore, we turn on the external magnetic field and build the hysteresis curve of magnetization and charge density. To our knowledge, this is the first holographic model realizing the hysteresis accompanied with spontaneous symmetry breaking.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [Adv. Theor. Math. Phys.2 (1998) 231] [hep-th/9711200] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev.D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].
S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev.B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
T. Albash and C.V. Johnson, A Holographic Superconductor in an External Magnetic Field, JHEP09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Parity-Violating Hydrodynamics in 2 + 1 Dimensions, JHEP05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
K.K. Kim, N. Kim and Y.-L. Zhang, Composite-particle hydrodynamics from dyonic black branes, J. Korean Phys. Soc.65 (2014) 973 [arXiv:1307.0428] [INSPIRE].
M. Blake and A. Donos, Quantum Critical Transport and the Hall Angle, Phys. Rev. Lett.114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].
A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP03 (2013) 108 [arXiv:1212.0871] [INSPIRE].
Y. Seo, K.-Y. Kim, K.K. Kim and S.-J. Sin, Character of matter in holography: Spin-orbit interaction, Phys. Lett.B 759 (2016) 104 [arXiv:1512.08916] [INSPIRE].
M. Blake, Momentum relaxation from the fluid/gravity correspondence, JHEP09 (2015) 010 [arXiv:1505.06992] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Thermoelectric Conductivities at Finite Magnetic Field and the Nernst Effect, JHEP07 (2015) 027 [arXiv:1502.05386] [INSPIRE].
M. Blake, Magnetotransport from the fluid/gravity correspondence, JHEP10 (2015) 078 [arXiv:1507.04870] [INSPIRE].
M. Blake, A. Donos and N. Lohitsiri, Magnetothermoelectric Response from Holography, JHEP08 (2015) 124 [arXiv:1502.03789] [INSPIRE].
R.-G. Cai and R.-Q. Yang, Antisymmetric tensor field and spontaneous magnetization in holographic duality, Phys. Rev.D 92 (2015) 046001 [arXiv:1504.00855] [INSPIRE].
R.-G. Cai, R.-Q. Yang and F.V. Kusmartsev, Holographic antiferromganetic quantum criticality and AdS 2scaling limit, Phys. Rev.D 92 (2015) 046005 [arXiv:1505.03405] [INSPIRE].
R.-G. Cai, R.-Q. Yang, Y.-B. Wu and C.-Y. Zhang, Massive 2-form field and holographic ferromagnetic phase transition, JHEP11 (2015) 021 [arXiv:1507.00546] [INSPIRE].
A. Donos, J.P. Gauntlett, T. Griffin, N. Lohitsiri and L. Melgar, Holographic DC conductivity and Onsager relations, JHEP07 (2017) 006 [arXiv:1704.05141] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].
C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev.D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev.D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett.101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett.103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys.A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
M. Bañados and S. Theisen, Scale invariant hairy black holes, Phys. Rev.D 72 (2005) 064019 [hep-th/0506025] [INSPIRE].
B. Ahn, S. Hyun, K.K. Kim, S.-A. Park and S.-H. Yi, Holography without counter terms, Phys. Rev.D 94 (2016) 024043 [arXiv:1512.09319] [INSPIRE].
B. Ahn, S. Hyun, S.-A. Park and S.-H. Yi, Scaling symmetry and scalar hairy rotating AdS 3black holes, Phys. Rev.D 93 (2016) 024041 [arXiv:1508.06484] [INSPIRE].
N. Evans, T. Kalaydzhyan, K.-Y. Kim and I. Kirsch, Non-equilibrium physics at a holographic chiral phase transition, JHEP01 (2011) 050 [arXiv:1011.2519] [INSPIRE].
S. Hyun, J. Jeong, S.-A. Park and S.-H. Yi, Scaling symmetry and scalar hairy Lifshitz black holes, JHEP10 (2015) 105 [arXiv:1507.03574] [INSPIRE].
S. Hyun, S.-A. Park and S.-H. Yi, Revisiting the thermodynamic relations in AdS/CMT models, Phys. Rev.D 95 (2017) 066012 [arXiv:1609.04351] [INSPIRE].
S. Hyun, J. Jeong, S.-A. Park and S.-H. Yi, Thermodynamic Volume and the Extended Smarr Relation, JHEP04 (2017) 048 [arXiv:1702.06629] [INSPIRE].
K.-Y. Kim, K.K. Kim and M. Park, A Simple Holographic Superconductor with Momentum Relaxation, JHEP04 (2015) 152 [arXiv:1501.00446] [INSPIRE].
G. Bertotti, Hysteresis in Magnetism, Academic Press (1998).
L. Bao et al., Quantum Corrections Crossover and Ferromagnetism in Magnetic Topological Insulators, Sci. Rep.3 (2013) 2391.
J. Barzola-Quiquia et al., Quantum oscillations and ferromagnetic hysteresis observed in iron filled multiwall carbon nanotubes, Nanotechnology23 (2012) 015707.
C. Chang et al., Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator, Science340 (2013) 167.
K. Kim and Y. Seo, work in progress.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1902.10929
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kim, K.K., Kim, KY., Seo, Y. et al. Building magnetic hysteresis in holography. J. High Energ. Phys. 2019, 158 (2019). https://doi.org/10.1007/JHEP07(2019)158
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2019)158