helimagnetism

{{Short description|Magnetic materials with specific magnetic order}}

File:FeGe magnetic phase diagram2b.png image of helical spin stripes in iron germanide (FeGe) at 90 K]]

Helimagnetism is a form of magnetic ordering where spins of neighbouring magnetic moments arrange themselves in a spiral or helical pattern, with a characteristic turn angle of somewhere between 0 and 180 degrees. It results from the competition between ferromagnetic and antiferromagnetic exchange interactions.{{Cite book |title=Magnetism in condensed matter |date=2001 |publisher=Oxford University Press |isbn=978-0-585-48360-3 |editor-last=Blundell |editor-first=Stephen |series=Oxford master series in condensed matter physics |location=Oxford New York |pages=99–100}} It is possible to view ferromagnetism and antiferromagnetism as helimagnetic structures with characteristic turn angles of 0 and 180 degrees respectively. Helimagnetic order breaks spatial inversion symmetry, as it can be either left-handed or right-handed in nature.

Strictly speaking, helimagnets have no permanent magnetic moment, and as such are sometimes considered a complicated type of antiferromagnet. This distinguishes helimagnets from conical magnets, (e.g. Holmium below 20 K{{cite journal | last1=Perreault | first1=Christopher S. | last2=Vohra | first2=Yogesh K. | last3=dos Santos | first3=Antonio M. | last4=Molaison | first4=Jamie J. | title=Neutron diffraction study of magnetic ordering in high pressure phases of rare earth metal holmium | journal=Journal of Magnetism and Magnetic Materials | publisher=Elsevier BV | volume=507 | year=2020 | doi=10.1016/j.jmmm.2020.166843 | page=166843| bibcode=2020JMMM..50766843P | osti=1607351 | doi-access=free | url=https://www.osti.gov/servlets/purl/1607351 }}) which have spiral modulation in addition to a permanent magnetic moment. Helimagnets can be characterized by the distance it takes for the spiral to complete one turn. In analogy to the pitch of screw thread, the period of repetition is known as the "pitch" of the helimagnet. If the spiral's period is some rational multiple of the crystal's unit cell, the structure is commensurate, like the structure originally proposed for MnO₂. On the other hand, if the multiple is irrational, the magnetism is incommensurate, like the updated MnO₂ structure.

Helimagnetism was first proposed in 1959, as an explanation of the magnetic structure of manganese dioxide.{{cite journal | last=Yoshimori | first=Akio | title=A New Type of Antiferromagnetic Structure in the Rutile Type Crystal | journal=Journal of the Physical Society of Japan | publisher=Physical Society of Japan | volume=14 | issue=6 | date=1959 | doi=10.1143/jpsj.14.807 | pages=807–821| bibcode=1959JPSJ...14..807Y }} Initially applied to neutron diffraction, it has since been observed more directly by Lorentz electron microscopy.{{cite journal | last1=Uchida | first1=Masaya | last2=Onose | first2=Yoshinori | last3=Matsui | first3=Yoshio | last4=Tokura | first4=Yoshinori | title=Real-Space Observation of Helical Spin Order | journal=Science | publisher=American Association for the Advancement of Science (AAAS) | volume=311 | issue=5759 | date=2006 | doi=10.1126/science.1120639 | pages=359–361| pmid=16424334 | bibcode=2006Sci...311..359U | s2cid=37875453 }} Some helimagnetic structures are reported to be stable up to room temperature.{{cite journal | last1=Zhang | first1=S. L. | last2=Stasinopoulos | first2=I. | last3=Lancaster | first3=T. | last4=Xiao | first4=F. | last5=Bauer | first5=A. | last6=Rucker | first6=F. | last7=Baker | first7=A. A. | last8=Figueroa | first8=A. I. | last9=Salman | first9=Z. | last10=Pratt | first10=F. L. | last11=Blundell | first11=S. J. | last12=Prokscha | first12=T. | last13=Suter | first13=A. | last14=Waizner | first14=J. | last15=Garst | first15=M. | last16=Grundler | first16=D. | last17=van der Laan | first17=G. | last18=Pfleiderer | first18=C. | last19=Hesjedal | first19=T. |display-authors=5| title=Room-temperature helimagnetism in FeGe thin films | journal=Scientific Reports | publisher=Springer Science and Business Media LLC | volume=7 | issue=1 | date=2017 | doi=10.1038/s41598-017-00201-z | page=123| pmid=28273923 | pmc=5427977 | bibcode=2017NatSR...7..123Z |doi-access=free}} Like how ordinary ferromagnets have domain walls that separate individual magnetic domains, helimagnets have their own classes of domain walls which are characterized by topological charge.{{cite journal | last1=Schoenherr | first1=P. | last2=Müller | first2=J. | last3=Köhler | first3=L. | last4=Rosch | first4=A. | last5=Kanazawa | first5=N. | last6=Tokura | first6=Y. | last7=Garst | first7=M. | last8=Meier | first8=D. | title=Topological domain walls in helimagnets | journal=Nature Physics | publisher=Springer Science and Business Media LLC | volume=14 | issue=5 | date=2018| doi=10.1038/s41567-018-0056-5 | pages=465–468| arxiv=1704.06288 | bibcode=2018NatPh..14..465S | s2cid=119021621 }}

Many helimagnets have a chiral cubic structure, such as the FeSi (B20) crystal structure type. In these materials, the combination of ferromagnetic exchange and the Dzyaloshinskii–Moriya interaction leads to helixes with relatively long periods. Since the crystal structure is noncentrosymetric even in the paramagnetic state, the magnetic transition to a helimagnetic state does not break inversion symmetry, and the direction of the spiral is locked to the crystal structure.

On the other hand, helimagnetism in other materials can also be based on frustrated magnetism or the RKKY interaction. The result is that centrosymmetric structures like the MnP-type (B31) compounds can also exhibit double-helix type helimagnetism where both left and right handed spirals coexist. For these itinerant helimagnets, the direction of the helicity can be controlled by applied electric currents and magnetic fields.{{cite journal | last1=Jiang | first1=N. | last2=Nii | first2=Y. | last3=Arisawa | first3=H. | last4=Saitoh | first4=E. | last5=Onose | first5=Y. | title=Electric current control of spin helicity in an itinerant helimagnet | journal=Nature Communications | publisher=Springer Science and Business Media LLC | volume=11 | issue=1 | date=2020-03-30 | issn=2041-1723 | doi=10.1038/s41467-020-15380-z | page=1601| pmid=32231211 | pmc=7105454 | doi-access=free }}

class="wikitable" |+Helimagnetic materials
Material ! Temperature range ! Space group
β-MnO2{{cite journal | last1=Regulski | first1=M. | last2=Przeniosło | first2=R. | last3=Sosnowska | first3=I. | last4=Hoffmann | first4=J.-U. | title=Incommensurate magnetic structure of β−MnO2 | journal=Physical Review B | publisher=American Physical Society (APS) | volume=68 | issue=17 | date=2003-11-03 | issn=0163-1829 | doi=10.1103/physrevb.68.172401 | page=172401}} | < 93 K |P42/mnm
FeGe, | < 278 K |P213
MnGe{{cite journal | last1=Martin | first1=N. | last2=Mirebeau | first2=I. | last3=Franz | first3=C. | last4=Chaboussant | first4=G. | last5=Fomicheva | first5=L. N. | last6=Tsvyashchenko | first6=A. V. | title=Partial ordering and phase elasticity in the MnGe short-period helimagnet | journal=Physical Review B | publisher=American Physical Society (APS) | volume=99 | issue=10 | date=2019-03-13 | issn=2469-9950 | doi=10.1103/physrevb.99.100402 | page=100402(R)| bibcode=2019PhRvB..99j0402M | s2cid=128285958 | url=https://hal-cea.archives-ouvertes.fr/cea-02074769/file/2019_PRB-RC_MnGe%20MIEZE.pdf }} | < 170 K |P213
MnSi,{{cite journal | last1=Stishov | first1=Sergei M | last2=Petrova | first2=A E | title=Itinerant helimagnet MnSi | journal=Physics-Uspekhi | publisher=Uspekhi Fizicheskikh Nauk (UFN) Journal | volume=54 | issue=11 | date=2011-11-30 | doi=10.3367/ufne.0181.201111b.1157 | pages=1117–1130| bibcode=2011PhyU...54.1117S | s2cid=122357363 }} | < 29 K |P213
FexCo1−xSi (0.3 ≤ x ≤ 0.85){{cite journal | last1=Watanabe | first1=Hideki | last2=Tazuke | first2=ichi | last3=Nakajima | first3=Haruo | title=Helical Spin Resonance and Magntization Measurement in Itinerant Helimagnet FexCo1−xSi (0.3≤x≤0.85) | journal=Journal of the Physical Society of Japan | publisher=Physical Society of Japan | volume=54 | issue=10 | date=1985| doi=10.1143/jpsj.54.3978 | pages=3978–3986| bibcode=1985JPSJ...54.3978W }}{{cite journal | last1=Bannenberg | first1=L. J. | last2=Kakurai | first2=K. | last3=Falus | first3=P. | last4=Lelièvre-Berna | first4=E. | last5=Dalgliesh | first5=R. | last6=Dewhurst | first6=C. D. | last7=Qian | first7=F. | last8=Onose | first8=Y. | last9=Endoh | first9=Y. | last10=Tokura | first10=Y. | last11=Pappas | first11=C. |display-authors=5| title=Universality of the helimagnetic transition in cubic chiral magnets: Small angle neutron scattering and neutron spin echo spectroscopy studies of FeCoSi | journal=Physical Review B | volume=95 | issue=14 | date=2017 | doi=10.1103/physrevb.95.144433 | page=144433| s2cid=31673243 | url=http://resolver.tudelft.nl/uuid:3611a818-1a52-4be3-aa95-08ba3b78f25f | arxiv=1701.05448 | bibcode=2017PhRvB..95n4433B }} | |P213
Cu2OSeO3{{cite journal | last1=Seki | first1=S. | last2=Yu | first2=X. Z. | last3=Ishiwata | first3=S. | last4=Tokura | first4=Y. | title=Observation of Skyrmions in a Multiferroic Material | journal=Science | publisher=American Association for the Advancement of Science (AAAS) | volume=336 | issue=6078 | date=2012 | doi=10.1126/science.1214143 | pages=198–201| pmid=22499941 | bibcode=2012Sci...336..198S | s2cid=21013909 }} | < 58 K |P213
FeP{{cite journal | last1=Sukhanov | first1=A. S. | last2=Tymoshenko | first2=Y. V. | last3=Kulbakov | first3=A. A. | last4=Cameron | first4=A. S. | last5=Kocsis | first5=V. | last6=Walker | first6=H. C. | last7=Ivanov | first7=A. | last8=Park | first8=J. T. | last9=Pomjakushin | first9=V. | last10=Nikitin | first10=S. E. | last11=Morozov | first11=I. V. | last12=Chernyavskii | first12=I. O. | last13=Aswartham | first13=S. | last14=Wolter | first14=A. U. B. | last15=Yaresko | first15=A. | last16=Büchner | first16=B. | last17=Inosov | first17=D. S. |display-authors=5| title=Frustration model and spin excitations in the helimagnet FeP | journal=Physical Review B | publisher=American Physical Society (APS) | volume=105 | issue=13 | date=2022-04-20 | issn=2469-9950 | doi=10.1103/physrevb.105.134424 | page=134424|arxiv=2201.10358| bibcode=2022PhRvB.105m4424S | s2cid=246276036 }} | < 120 K |Pnma
FeAs{{cite journal | last1=Selte | first1=Kari | last2=Kjekshus | first2=Arne | last3=Andresen | first3=Arne F. | last4=Tricker | first4=M. J. | last5=Svensson | first5=Sigfrid | title=Magnetic Structure and Properties of FeAs. | journal=Acta Chemica Scandinavica | publisher=Danish Chemical Society | volume=26 | year=1972 | issn=0904-213X | doi=10.3891/acta.chem.scand.26-3101 | pages=3101–3113| doi-access=free }} | < 77 K |Pnma
MnP{{cite journal | last1=Forsyth | first1=J B | last2=Pickart | first2=S J | last3=Brown | first3=P J | title=The structure of the metamagnetic phase of MnP | journal=Proceedings of the Physical Society | publisher=IOP Publishing | volume=88 | issue=2 | year=1966 | issn=0370-1328 | doi=10.1088/0370-1328/88/2/308 | pages=333–339| bibcode=1966PPS....88..333F }} | < 50 K | Pnma
CrAs{{cite journal | last1=Selte | first1=Kari | last2=Kjekshus | first2=Arne | last3=Jamison | first3=Warren E. | last4=Andresen | first4=Arne F. | last5=Engebretsen | first5=Jan E. | last6=Ehrenberg | first6=L. | title=Magnetic Structure and Properties of CrAs. | journal=Acta Chemica Scandinavica | publisher=Danish Chemical Society | volume=25 | year=1971 | issn=0904-213X | doi=10.3891/acta.chem.scand.25-1703 | pages=1703–1714| doi-access=free }} | < 261 K | Pnma
CrI2{{cite journal | last1=Schneeloch | first1=John A. | last2=Liu | first2=Shunshun | last3=Balachandran | first3=Prasanna V. | last4=Zhang | first4=Qiang | last5=Louca | first5=Despina|author5-link=Despina Louca | title=Helimagnetism in the candidate ferroelectric CrI 2 | journal=Physical Review B | volume=109 | issue=14 | date=2024-04-03 | issn=2469-9950 | doi=10.1103/PhysRevB.109.144403 | page=144403|arxiv=2310.12120}} | < 17 K | Cmc21
FeCl3{{cite journal | last1=Kang | first1=Byeongki | last2=Kim | first2=Changsoo | last3=Jo | first3=Euna | last4=Kwon | first4=Sangil | last5=Lee | first5=Soonchil | title=Magnetic state of FeCl 3 investigated by NMR | journal=Journal of Magnetism and Magnetic Materials | publisher=Elsevier BV | volume=360 | year=2014 | issn=0304-8853 | doi=10.1016/j.jmmm.2014.01.051 | pages=1–5}} | < 9 K | R{{overline|3}}
NiBr2{{cite journal | last1=Adam | first1=A | last2=Billerey | first2=D | last3=Terrier | first3=C | last4=Katsumata | first4=K | last5=Magariño | first5=J | last6=Tuchendler | first6=J | title=Magnetic resonance experiments in NiBr2 at high frequencies and high magnetic fields | journal=Physics Letters A | publisher=Elsevier BV | volume=79 | issue=4 | year=1980 | issn=0375-9601 | doi=10.1016/0375-9601(80)90369-2 | pages=353–354}} | < 22 K | R{{overline|3}}m
NiI2{{cite journal | last1=Kuindersma | first1=S.R. | last2=Sanchez | first2=J.P. | last3=Haas | first3=C. | title=Magnetic and structural investigations on NiI2 and CoI2 | journal=Physica B+C | publisher=Elsevier BV | volume=111 | issue=2–3 | year=1981 | issn=0378-4363 | doi=10.1016/0378-4363(81)90100-5 | pages=231–248}} | < 75 K | R{{overline|3}}m
Cr1/3NbS2{{cite journal | last1=Miyadai | first1=Tomonao | last2=Kikuchi | first2=Katsuya | last3=Kondo | first3=Hiromitsu | last4=Sakka | first4=Shuzo | last5=Arai | first5=Masatoshi | last6=Ishikawa | first6=Yoshikazu | title=Magnetic Properties of Cr1/3NbS2 | journal=Journal of the Physical Society of Japan | publisher=Physical Society of Japan | volume=52 | issue=4 | date=1983-04-15 | issn=0031-9015 | doi=10.1143/jpsj.52.1394 | pages=1394–1401| bibcode=1983JPSJ...52.1394M }}{{cite journal | last1=Braam | first1=D. | last2=Gomez | first2=C. | last3=Tezok | first3=S. | last4=de Mello | first4=E. V. L. | last5=Li | first5=L. | last6=Mandrus | first6=D. | last7=Kee | first7=Hae-Young | last8=Sonier | first8=J. E. | title=Magnetic properties of the helimagnet Cr1/3NbS2 observed byμSR | journal=Physical Review B | publisher=American Physical Society (APS) | volume=91 | issue=14 | date=2015-04-07 | issn=1098-0121 | doi=10.1103/physrevb.91.144407 | page=144407|arxiv=1501.03094| bibcode=2015PhRvB..91n4407B | s2cid=117648270 }} | < 127 K |P6322
Tb{{cite book | last1=Palmer | first1=S. B. | last2=Baruchel | first2=J. | last3=Farrant | first3=S. | last4=Jones | first4=D. | last5=Schlenker | first5=M. | title=The Rare Earths in Modern Science and Technology | chapter=Observation of Spiral Spin Antiferromagnetic Domains in Single Crystal Terbium | publisher=Springer US | location=Boston, MA | year=1982 | isbn=978-1-4613-3408-8 | doi=10.1007/978-1-4613-3406-4_88 | pages=413–417}} |219–231 K |P63/mmc
Dy{{cite journal | last1=Herz | first1=R. | last2=Kronmüller | first2=H. | title=Field-induced phase transitions in the helical state of dysprosium | journal=Physica Status Solidi A | publisher=Wiley | volume=47 | issue=2 | date=1978 | doi=10.1002/pssa.2210470215 | pages=451–458| bibcode=1978PSSAR..47..451H }} |85–179 K |P63/mmc
Ho{{cite journal | last1=Tindall | first1=D. A. | last2=Steinitz | first2=M. O. | last3=Kahrizi | first3=M. | last4=Noakes | first4=D. R. | last5=Ali | first5=N. | title=Investigation of the helimagnetic phases of holmium in ac-axis magnetic field | journal=Journal of Applied Physics | publisher=AIP Publishing | volume=69 | issue=8 | date=1991| doi=10.1063/1.347913 | pages=5691–5693| bibcode=1991JAP....69.5691T }} |20–132 K |P63/mmc