Normal modes of a spin cycloid or helix

Fishman, Randy S.; Rõõm, Toomas; de Sousa, Rogério

doi:10.1103/PhysRevB.99.064414

Title: Normal modes of a spin cycloid or helix

Abstract

Although spin cycloids and helices are quite common, remarkably little is known about the normal modes of a spin cycloid or helix with finite length on a discrete lattice. Based on simple one-dimensional lattice models, we numerically evaluate the normal modes of a spin cycloid or helix produced by either Dzyaloshinskii-Moriya (DM) or competing exchange (CE) interactions. The normal modes depend on the type of interaction and on whether the nearest-neighbor exchange is antiferromagnetic (AF) or ferromagnetic (FM). In the AF/DM and FM/DM cases, there is only a single Goldstone mode; in the AF/CE and FM/CE cases, there are three. For FM exchange, the spin oscillations produced by non-Goldstone modes contain a mixture of tangential and transverse components. For the DM cases, we compare our numerical results with analytic results in the continuum limit. Examples are given of materials that fall into all four cases.

Authors:

^[1]; Rõõm, Toomas ^[2]; de Sousa, Rogério ^[3]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division
National Inst. of Chemical Physics and Biophysics, Tallinn (Estonia)
Univ. of Victoria, BC (Canada)

Publication Date:: Wed Feb 13 00:00:00 EST 2019

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1559728

Alternate Identifier(s):: OSTI ID: 1494655

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 99; Journal Issue: 6; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Fishman, Randy S., Rõõm, Toomas, and de Sousa, Rogério. Normal modes of a spin cycloid or helix.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevB.99.064414.

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                    Fishman, Randy S., Rõõm, Toomas, & de Sousa, Rogério. Normal modes of a spin cycloid or helix.  United States.  https://doi.org/10.1103/PhysRevB.99.064414

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                    Fishman, Randy S., Rõõm, Toomas, and de Sousa, Rogério. Wed .  
"Normal modes of a spin cycloid or helix".  United States.  https://doi.org/10.1103/PhysRevB.99.064414.  https://www.osti.gov/servlets/purl/1559728.

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@article{osti_1559728,

  title        = {Normal modes of a spin cycloid or helix},

  author       = {Fishman, Randy S. and Rõõm, Toomas and de Sousa, Rogério},

  abstractNote = {Although spin cycloids and helices are quite common, remarkably little is known about the normal modes of a spin cycloid or helix with finite length on a discrete lattice. Based on simple one-dimensional lattice models, we numerically evaluate the normal modes of a spin cycloid or helix produced by either Dzyaloshinskii-Moriya (DM) or competing exchange (CE) interactions. The normal modes depend on the type of interaction and on whether the nearest-neighbor exchange is antiferromagnetic (AF) or ferromagnetic (FM). In the AF/DM and FM/DM cases, there is only a single Goldstone mode; in the AF/CE and FM/CE cases, there are three. For FM exchange, the spin oscillations produced by non-Goldstone modes contain a mixture of tangential and transverse components. For the DM cases, we compare our numerical results with analytic results in the continuum limit. Examples are given of materials that fall into all four cases.},

  doi          = {10.1103/PhysRevB.99.064414},

  journal      = {Physical Review B},

  number       = 6,

  volume       = 99,

  place        = {United States},

  year         = {Wed Feb 13 00:00:00 EST 2019},

  month        = {Wed Feb 13 00:00:00 EST 2019}

}

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Title: Normal modes of a spin cycloid or helix

Abstract

Citation Formats

Phenomenological Discussion of Magnetic Ordering in the Heavy Rare-Earth Metals journal, October 1961

Moriya Interaction and the Problem of the Spin Arrangements in β MnS journal, May 1962

Incommensurability and spin dynamics in the low-temperature phases of Ni 3 V 2 O 8 journal, June 2013

Space-time parity violation and magnetoelectric interactions in antiferromagnets journal, June 2004

Ferroelectricity in Spiral Magnets journal, February 2006

Multiferroics of spin origin journal, July 2014

Magnetic ordering in EuRh 2 As 2 studied by x-ray resonant magnetic scattering journal, March 2009

Correlated band theory of spin and orbital contributions to Dzyaloshinskii-Moriya interactions journal, September 2010

Possible Observation of Cycloidal Electromagnons in BiFeO 3 journal, July 2008

Magnetically Driven Ferroelectric Order in Ni 3 V 2 O 8 journal, August 2005

Evidence for spiral magnetic order in the heavy fermion material CeRhIn 5 journal, September 2000

Spin rotation technique for non-collinear magnetic systems: application to the generalized Villain model journal, April 2009

Spin state and spectroscopic modes of multiferroic BiFeO 3 journal, April 2013

Ferroelectricity in the cycloidal spiral magnetic phase of Mn W O 4 journal, November 2006

Terahertz Spectroscopy of Spin Waves in Multiferroic BiFeO 3 in High Magnetic Fields journal, June 2013

Origin of the long period magnetic ordering in BiFeO3 journal, February 1995

Spiral phase and spin waves in the quasi-two-dimensional antiferromagnet Ba 2 Cu Ge 2 O 7 journal, December 1996

Long-wavelength magnetic and magnetoelectric excitations in the ferroelectric antiferromagnet BiFeO 3 journal, March 2011

Helical spin structure in manganese silicide MnSi journal, July 1976

Electronic structure and the origin of the Dzyaloshinskii-Moriya interaction in MnSi journal, May 2016

Magnetic order and spin-flop transitions in the cobalt-doped multiferroic Mn 1 − x Co x WO 4 journal, September 2012

Cubic magnets with Dzyaloshinskii-Moriya interaction at low temperature journal, May 2006

Multishell contribution to the Dzyaloshinskii-Moriya spiraling in MnSi-type crystals journal, December 2013

Multiferroics progress and prospects in thin films journal, January 2007

Multiferroics: a magnetic twist for ferroelectricity journal, January 2007

Theory of helical magnetic structures and phase transitions in MnSi and FeGe journal, November 1980

Anisotropic Superexchange Interaction and Weak Ferromagnetism journal, October 1960

Identifying the spectroscopic modes of multiferroic BiFeO 3 journal, December 2012

Magnetic order and crystal structure in the superconducting RNi 2 B 2 C materials journal, March 1997

Band Structure of Helimagnons in MnSi Resolved by Inelastic Neutron Scattering journal, August 2015

Optical coupling to spin waves in the cycloidal multiferroic Bi Fe O 3 journal, January 2008

Tunable ( δ π , δ π )-Type Antiferromagnetic Order in α -Fe(Te,Se) Superconductors journal, June 2009

Phenomenological Discussion of Magnetic Ordering in the Heavy Rare-Earth Metals
journal, October 1961

Moriya Interaction and the Problem of the Spin Arrangements in $β MnS$
journal, May 1962

Incommensurability and spin dynamics in the low-temperature phases of Ni $_{3}$ V $_{2}$ O $_{8}$
journal, June 2013

Space-time parity violation and magnetoelectric interactions in antiferromagnets
journal, June 2004

Ferroelectricity in Spiral Magnets
journal, February 2006

Multiferroics of spin origin
journal, July 2014

Magnetic ordering in ${EuRh}_{2} {As}_{2}$ studied by x-ray resonant magnetic scattering
journal, March 2009

Correlated band theory of spin and orbital contributions to Dzyaloshinskii-Moriya interactions
journal, September 2010

Possible Observation of Cycloidal Electromagnons in ${BiFeO}_{3}$
journal, July 2008

Magnetically Driven Ferroelectric Order in ${Ni}_{3} V_{2} O_{8}$
journal, August 2005

Evidence for spiral magnetic order in the heavy fermion material ${CeRhIn}_{5}$
journal, September 2000

Spin rotation technique for non-collinear magnetic systems: application to the generalized Villain model
journal, April 2009

Spin state and spectroscopic modes of multiferroic BiFeO $_{3}$
journal, April 2013

Ferroelectricity in the cycloidal spiral magnetic phase of $Mn W O_{4}$
journal, November 2006

Terahertz Spectroscopy of Spin Waves in Multiferroic ${BiFeO}_{3}$ in High Magnetic Fields
journal, June 2013

Origin of the long period magnetic ordering in BiFeO3
journal, February 1995

Spiral phase and spin waves in the quasi-two-dimensional antiferromagnet ${Ba}_{2}$ Cu ${Ge}_{2}$ $O_{7}$
journal, December 1996

Long-wavelength magnetic and magnetoelectric excitations in the ferroelectric antiferromagnet BiFeO $_{3}$
journal, March 2011

Helical spin structure in manganese silicide MnSi
journal, July 1976

Electronic structure and the origin of the Dzyaloshinskii-Moriya interaction in MnSi
journal, May 2016

Magnetic order and spin-flop transitions in the cobalt-doped multiferroic Mn $_{1 - x}$ Co $_{x}$ WO $_{4}$
journal, September 2012

Cubic magnets with Dzyaloshinskii-Moriya interaction at low temperature
journal, May 2006

Multishell contribution to the Dzyaloshinskii-Moriya spiraling in MnSi-type crystals
journal, December 2013

Multiferroics progress and prospects in thin films
journal, January 2007

Multiferroics: a magnetic twist for ferroelectricity
journal, January 2007

Theory of helical magnetic structures and phase transitions in MnSi and FeGe
journal, November 1980

Anisotropic Superexchange Interaction and Weak Ferromagnetism
journal, October 1960

Identifying the spectroscopic modes of multiferroic BiFeO $_{3}$
journal, December 2012

Magnetic order and crystal structure in the superconducting ${RNi}_{2}$ $B_{2}$ C materials
journal, March 1997

Band Structure of Helimagnons in MnSi Resolved by Inelastic Neutron Scattering
journal, August 2015

Optical coupling to spin waves in the cycloidal multiferroic $Bi Fe O_{3}$
journal, January 2008

Tunable ( $δ π$ , $δ π$ )-Type Antiferromagnetic Order in $α$ -Fe(Te,Se) Superconductors
journal, June 2009