Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products

Cheong, Sang-Wook; Huang, Fei-Ting; Kim, Minhyong

doi:10.1088/1361-6633/ac97aa

Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products

Journal Article · 22 November 2022 · Reports on Progress in Physics

DOI:https://doi.org/10.1088/1361-6633/ac97aa· OSTI ID:2419198

^[1]; ; Kim, Minhyong

OSTI

Abstract

The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vector-like, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z₂× Z₂× Z₂group with Abelian additive operation, and the cross products form a Z₂× Z₂group with Abelian additive operation or Q₈, a non-Abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has symmetry operational similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.

Research Organization:: Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: FG02-07ER46382;

OSTI ID:: 2419198

Journal Information:: Reports on Progress in Physics, Journal Name: Reports on Progress in Physics Journal Issue: 12 Vol. 85; ISSN 0034-4885

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

References (64)

Ueber die durch Bewegung eines im homogenen electrischen Felde befindlichen Dielectricums hervorgerufene electrodynamische Kraft Röntgen, W. C. Annalen der Physik und Chemie, Vol. 271, Issue 10 https://doi.org/10.1002/andp.18882711003	journal	January 1888
The interpretation of the new particles as displaced charge multiplets Gell-Mann, M. Il Nuovo Cimento, Vol. 4, Issue S2 https://doi.org/10.1007/bf02748000	journal	April 1956
A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics Dzyaloshinsky, I. Journal of Physics and Chemistry of Solids, Vol. 4, Issue 4 https://doi.org/10.1016/0022-3697(58)90076-3	journal	January 1958
Helical magnetic structure in CrB2 Funahashi, S.; Hamaguchi, Y.; Tanaka, T. Solid State Communications, Vol. 23, Issue 11 https://doi.org/10.1016/0038-1098(77)90969-3	journal	September 1977
Neutron diffraction study of the layered compounds MnPSe3 and FePSe3 Wiedenmann, A.; Rossat-Mignod, J.; Louisy, A. Solid State Communications, Vol. 40, Issue 12 https://doi.org/10.1016/0038-1098(81)90253-2	journal	December 1981
Evidence for the helical spin structure due to antisymmetric exchange interaction in Cr13NbS2 Moriya, T.; Miyadai, T. Solid State Communications, Vol. 42, Issue 3 https://doi.org/10.1016/0038-1098(82)91006-7	journal	April 1982
Synthesis and magnetic structure of the YbMn2Sb2 compound Morozkin, A. V.; Isnard, O.; Henry, P. Journal of Alloys and Compounds, Vol. 420, Issue 1-2 https://doi.org/10.1016/j.jallcom.2005.10.051	journal	August 2006
Magnetic order in CaMn2Sb2 studied via powder neutron diffraction Bridges, C. A.; Krishnamurthy, V. V.; Poulton, S. Journal of Magnetism and Magnetic Materials, Vol. 321, Issue 22 https://doi.org/10.1016/j.jmmm.2009.07.015	journal	November 2009
Magnetic ordering and spin structure in Ca-bearing clinopyroxenes CaM2+(Si, Ge)2O6, M=Fe, Ni, Co, Mn Redhammer, Günther J.; Roth, Georg; Treutmann, Werner Journal of Solid State Chemistry, Vol. 181, Issue 11 https://doi.org/10.1016/j.jssc.2008.08.014	journal	November 2008
Real-Space Observation of Short-Period Cubic Lattice of Skyrmions in MnGe Tanigaki, Toshiaki; Shibata, Kiyou; Kanazawa, Naoya Nano Letters, Vol. 15, Issue 8 https://doi.org/10.1021/acs.nanolett.5b02653	journal	July 2015
Observation of Quasi-Two-Dimensional Polar Domains and Ferroelastic Switching in a Metal, Ca ₃ Ru ₂ O ₇ Lei, Shiming; Gu, Mingqiang; Puggioni, Danilo Nano Letters, Vol. 18, Issue 5 https://doi.org/10.1021/acs.nanolett.8b00633	journal	April 2018
Noncentrosymmetric Oxides Halasyamani, P. Shiv; Poeppelmeier, Kenneth R. Chemistry of Materials, Vol. 10, Issue 10 https://doi.org/10.1021/cm980140w	journal	October 1998
Inverting polar domains via electrical pulsing in metallic germanium telluride Nukala, Pavan; Ren, Mingliang; Agarwal, Rahul Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15033	journal	April 2017
Ferroic nature of magnetic toroidal order Zimmermann, Anne S.; Meier, Dennis; Fiebig, Manfred Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5796	journal	September 2014
Valley magnetoelectricity in single-layer MoS2 Lee, Jieun; Wang, Zefang; Xie, Hongchao Nature Materials, Vol. 16, Issue 9 https://doi.org/10.1038/nmat4931	journal	July 2017
Electric current control of spin helicity in an itinerant helimagnet Jiang, N.; Nii, Y.; Arisawa, H. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-15380-z	journal	March 2020
Visualization of ferroaxial domains in an order-disorder type ferroaxial crystal Hayashida, T.; Uemura, Y.; Kimura, K. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-18408-6	journal	September 2020
Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface Ding, Xinqiang; Lin, Xingcheng; Zhang, Bin Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-21377-z	journal	February 2021
SOS: symmetry-operational similarity Cheong, Sang-Wook npj Quantum Materials, Vol. 4, Issue 1 https://doi.org/10.1038/s41535-019-0193-9	journal	October 2019
Trompe L’oeil Ferromagnetism Cheong, Sang-Wook npj Quantum Materials, Vol. 5, Issue 1 https://doi.org/10.1038/s41535-020-0235-3	journal	June 2020
Frustration-driven magnetic fluctuations as the origin of the low-temperature skyrmion phase in Co7Zn7Mn6 Ukleev, V.; Karube, K.; Derlet, P. M. npj Quantum Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41535-021-00342-5	journal	April 2021
Permutable SOS (symmetry operational similarity) Cheong, Sang-Wook; Lim, Seongjoon; Du, Kai npj Quantum Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41535-021-00346-1	journal	June 2021
Crystal-chirality-dependent control of magnetic domains in a time-reversal-broken antiferromagnet Kimura, Kenta; Kato, Yasuyuki; Kimura, Shojiro npj Quantum Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41535-021-00355-0	journal	May 2021
Observation of a ferro-rotational order coupled with second-order nonlinear optical fields Jin, Wencan; Drueke, Elizabeth; Li, Siwen Nature Physics, Vol. 16, Issue 1 https://doi.org/10.1038/s41567-019-0695-1	journal	November 2019
Observation of the nonlinear Hall effect under time-reversal-symmetric conditions Ma, Qiong; Xu, Su-Yang; Shen, Huitao Nature, Vol. 565, Issue 7739 https://doi.org/10.1038/s41586-018-0807-6	journal	December 2018
Structural and magnetic properties of the ordered perovskite Pb2CoTeO6 Ivanov, S. A.; Nordblad, P.; Mathieu, R. Dalton Transactions, Vol. 39, Issue 46 https://doi.org/10.1039/c0dt00558d	journal	January 2010
Observation of Antisymmetric Exchange Interaction in Yttrium Orthoferrite Treves, D.; Alexander, S. Journal of Applied Physics, Vol. 33, Issue 3 https://doi.org/10.1063/1.1728631	journal	March 1962
Magnetoelectric Effects in TbPO[sub 4] Rado, G. T.; Ferrari, J. M.; Wolfe, Hugh C. AIP Conference Proceedings https://doi.org/10.1063/1.2946809	conference	January 1973
Magnetic-field-induced dielectric anomaly and electric polarization in Mn ₄ Nb ₂ O ₉ Fang, Y.; Zhou, W. P.; Yan, S. M. Journal of Applied Physics, Vol. 117, Issue 17 https://doi.org/10.1063/1.4913815	journal	May 2015
Improper ferroelectrics Dvořák, V. Ferroelectrics, Vol. 7, Issue 1 https://doi.org/10.1080/00150197408237942	journal	January 1974
Coupled order parameters in the Landau theory of phase transitions in solids Stokes, H. T.; Hatch, D. M. Phase Transitions, Vol. 34, Issue 1-4 https://doi.org/10.1080/01411599108205192	journal	June 1991
Ordering, metastability and phase transitions in two-dimensional systems Kosterlitz, J M; Thouless, D J Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203 https://doi.org/10.1088/0022-3719/6/7/010	journal	April 1973
Determination of the magnetization distribution in Cr ₂ O ₃ using spherical neutron polarimetry Brown, P. J.; Forsyth, J. B.; Lelièvre-Berna, E. Journal of Physics: Condensed Matter, Vol. 14, Issue 8 https://doi.org/10.1088/0953-8984/14/8/323	journal	February 2002
Some symmetry aspects of ferroics and single phase multiferroics ^* Schmid, Hans Journal of Physics: Condensed Matter, Vol. 20, Issue 43 https://doi.org/10.1088/0953-8984/20/43/434201	journal	October 2008
The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect Spaldin, Nicola A.; Fiebig, Manfred; Mostovoy, Maxim Journal of Physics: Condensed Matter, Vol. 20, Issue 43 https://doi.org/10.1088/0953-8984/20/43/434203	journal	October 2008
Spontaneous non-reciprocal reflection of light from antiferromagnetic Cr ₂ O ₃ Krichevtsov, B. B.; Pavlov, V. V.; Pisarev, R. V. Journal of Physics: Condensed Matter, Vol. 5, Issue 44 https://doi.org/10.1088/0953-8984/5/44/014	journal	November 1993
Field-induced topological Hall effect and double-fan spin structure with a c -axis component in the metallic kagome antiferromagnetic compound Y Mn 6 Sn 6 Wang, Qi; Neubauer, Kelly J.; Duan, Chunruo Physical Review B, Vol. 103, Issue 1 https://doi.org/10.1103/PhysRevB.103.014416	journal	January 2021
BaNi 2 V 2 O 8 : A two-dimensional honeycomb antiferromagnet Rogado, N.; Huang, Q.; Lynn, J. W. Physical Review B, Vol. 65, Issue 14 https://doi.org/10.1103/PhysRevB.65.144443	journal	April 2002
Skyrmion lattice in the doped semiconductor Fe 1 − x Co x Si Münzer, W.; Neubauer, A.; Adams, T. Physical Review B, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevB.81.041203	journal	January 2010
Magnetic properties of the geometrically frustrated S = 1 2 antiferromagnets, La 2 LiMoO 6 and Ba 2 YMoO 6 , with the B-site ordered double perovskite structure: Evidence for a collective spin-singlet ground state Aharen, Tomoko; Greedan, John E.; Bridges, Craig A. Physical Review B, Vol. 81, Issue 22 https://doi.org/10.1103/PhysRevB.81.224409	journal	June 2010
Correlation between Spin Helicity and an Electric Polarization Vector in Quantum-Spin Chain Magnet LiCu 2 O 2 Seki, S.; Yamasaki, Y.; Soda, M. Physical Review Letters, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevLett.100.127201	journal	March 2008
Cu 3 Nb 2 O 8 : A Multiferroic with Chiral Coupling to the Crystal Structure Johnson, R. D.; Nair, Sunil; Chapon, L. C. Physical Review Letters, Vol. 107, Issue 13 https://doi.org/10.1103/PhysRevLett.107.137205	journal	September 2011
Giant Improper Ferroelectricity in the Ferroaxial Magnet CaMn 7 O 12 Johnson, R. D.; Chapon, L. C.; Khalyavin, D. D. Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.067201	journal	February 2012
Magnetic Inversion Symmetry Breaking and Ferroelectricity in TbMnO 3 Kenzelmann, M.; Harris, A. B.; Jonas, S. Physical Review Letters, Vol. 95, Issue 8 https://doi.org/10.1103/PhysRevLett.95.087206	journal	August 2005
Local-Ising-type magnetic order and metamagnetism in the rare-earth pyrogermanate Er 2 Ge 2 O 7 Taddei, K. M.; Sanjeewa, L.; Kolis, J. W. Physical Review Materials, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevMaterials.3.014405	journal	January 2019
Magnetic Structures of Holmium. I. The Virgin State Koehler, W. C.; Cable, J. W.; Wilkinson, M. K. Physical Review, Vol. 151, Issue 2 https://doi.org/10.1103/physrev.151.414	journal	November 1966
Structural distortions in the low-temperature phase of NbO 2 Pynn, R.; Axe, J. D.; Thomas, R. Physical Review B, Vol. 13, Issue 7 https://doi.org/10.1103/physrevb.13.2965	journal	April 1976
First-principles study of two- and one-dimensional honeycomb structures of boron nitride Topsakal, M.; Aktürk, E.; Ciraci, S. Physical Review B, Vol. 79, Issue 11 https://doi.org/10.1103/physrevb.79.115442	journal	March 2009
Group-theory analysis of electrons and phonons in N -layer graphene systems Malard, L. M.; Guimarães, M. H. D.; Mafra, D. L. Physical Review B, Vol. 79, Issue 12 https://doi.org/10.1103/physrevb.79.125426	journal	March 2009
Ferroelectricity from spin supercurrents in LiCuVO 4 Mourigal, M.; Enderle, M.; Kremer, R. K. Physical Review B, Vol. 83, Issue 10 https://doi.org/10.1103/physrevb.83.100409	journal	March 2011
Group theory analysis of phonons in two-dimensional transition metal dichalcogenides Ribeiro-Soares, J.; Almeida, R. M.; Barros, E. B. Physical Review B, Vol. 90, Issue 11 https://doi.org/10.1103/physrevb.90.115438	journal	September 2014
Group theory for structural analysis and lattice vibrations in phosphorene systems Ribeiro-Soares, J.; Almeida, R. M.; Cançado, L. G. Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/physrevb.91.205421	journal	May 2015
Revisiting spin cycloids in multiferroic BiFeO 3 Xu, Bin; Dupé, Bertrand; Xu, Changsong Physical Review B, Vol. 98, Issue 18 https://doi.org/10.1103/physrevb.98.184420	journal	November 2018
Eight Types of Symmetrically Distinct Vectorlike Physical Quantities Hlinka, J. Physical Review Letters, Vol. 113, Issue 16 https://doi.org/10.1103/physrevlett.113.165502	journal	October 2014
Strain Engineering of the Berry Curvature Dipole and Valley Magnetization in Monolayer MoS 2 Son, Joolee; Kim, Kyung-Han; Ahn, Y. H. Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/physrevlett.123.036806	journal	July 2019
Formation Mechanism of the Helical Q Structure in Gd-Based Skyrmion Materials Nomoto, Takuya; Koretsune, Takashi; Arita, Ryotaro Physical Review Letters, Vol. 125, Issue 11 https://doi.org/10.1103/physrevlett.125.117204	journal	September 2020
Spin-Wave Dispersion Relation for Er Metal at 4.5° K Nicklow, R. M.; Wakabayashi, N.; Wilkinson, M. K. Physical Review Letters, Vol. 27, Issue 6 https://doi.org/10.1103/physrevlett.27.334	journal	August 1971
Skyrmion lattice structural transition in MnSi Nakajima, Taro; Oike, Hiroshi; Kikkawa, Akiko Science Advances, Vol. 3, Issue 6 https://doi.org/10.1126/sciadv.1602562	journal	June 2017
New magnetic phase of the chiral skyrmion material Cu ₂ OSeO ₃ Qian, Fengjiao; Bannenberg, Lars J.; Wilhelm, Heribert Science Advances, Vol. 4, Issue 9 https://doi.org/10.1126/sciadv.aat7323	journal	September 2018
Ultrafast manipulation of mirror domain walls in a charge density wave Zong, Alfred; Shen, Xiaozhe; Kogar, Anshul Science Advances, Vol. 4, Issue 10 https://doi.org/10.1126/sciadv.aau5501	journal	October 2018
Observation of chiral phonons Zhu, Hanyu; Yi, Jun; Li, Ming-Yang Science, Vol. 359, Issue 6375 https://doi.org/10.1126/science.aar2711	journal	February 2018
Electric field control of natural optical activity in a multiferroic helimagnet Masuda, Ryoji; Kaneko, Yoshio; Tokura, Yoshinori Science, Vol. 372, Issue 6541 https://doi.org/10.1126/science.aaz4312	journal	April 2021
Magnetic-field-induced toroidal moment in the magnetoelectric Cr2O3 Popov, Yu. F.; Kadomtseva, A. M.; Belov, D. V. Journal of Experimental and Theoretical Physics Letters, Vol. 69, Issue 4 https://doi.org/10.1134/1.568032	journal	February 1999
Analogy between the Magnetic Dipole Moment at the Surface of a Magnetoelectric and the Electric Charge at the Surface of a Ferroelectric Spaldin, N. A. Journal of Experimental and Theoretical Physics, Vol. 132, Issue 4 https://doi.org/10.1134/s1063776121040208	journal	April 2021

Similar Records

Permutable SOS (symmetry operational similarity)

Journal Article · 2021 · npj Quantum Materials · OSTI ID:1849747

Permutable SOS (symmetry operational similarity)

Journal Article · 2021 · npj Quantum Materials · OSTI ID:1787893

Exact and broken symmetries in a hydrodynamical description of chiral spin states

Journal Article · 1993 · Physical Review, B: Condensed Matter; (United States) · OSTI ID:5751541

Related Subjects

Physics

Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products

Citation Formats

References (64)

Similar Records

Related Subjects