Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu2OSeO3

Laurita, N. J.; Marcus, G. G.; Trump, B. A.; Kindervater, J.; Stone, M. B.; McQueen, T. M.; Broholm, C. L.; Armitage, N. P.

doi:10.1103/PhysRevB.95.235155

Title: Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator ${Cu}_{2} {OSeO}_{3}$

Abstract

In this study, we present a comprehensive study of the low-energy optical magnetic response of the skyrmionic Mott insulator ${Cu}_{2} {OSeO}_{3}$ via high resolution time-domain THz spectroscopy. In zero field, a new magnetic excitation ( $f_{0} = 2.03 THz$ ) which has not been predicted by spin-wave theory is observed and shown, with accompanying time-of-flight neutron scattering experiments, to be a zone folded magnon from the $R$ to $Γ$ points of the Brillouin zone. Highly sensitive polarimetry experiments performed in weak magnetic fields, $μ_{0} H < 200 mT$ , observe Faraday and Kerr rotations which are proportional to the sample magnetization, allowing for optical detection of the skyrmion phase and construction of a magnetic phase diagram. From these measurements, we extract a critical exponent of $β = 0.35 \pm 0.04$ , in good agreement with the expected value for the 3D Heisenberg universality class of $β = 0.367$ . In large magnetic fields, $μ_{0} H > 5 T$ , we observe the magnetically active uniform mode of the ferrimagnetic field polarized phase whose dynamics as a function of field and temperature are studied. In addition to extracting a $g_{eff} = 2.08 \pm 0.03$ , we observe the uniform mode to decay through a non-Gilbert damping mechanism and to possess a finite spontaneous decay rate, $Γ_{0} \approx 25 GHz$ , in the zero temperature limit. Finally, our observations are attributed to Dzyaloshinkii-Moriya interactions, which have been proposed to be exceptionally strong in ${Cu}_{2} {OSeO}_{3}$ and are expected to impact the low-energy magnetic response of such chiral magnets.

Authors:

Laurita, N. J. ^[1]; Marcus, G. G. ^[1]; Trump, B. A. ^[2]; Kindervater, J. ^[1]; Stone, M. B. ^[3]; McQueen, T. M. ^[4]; Broholm, C. L. ^[5]; Armitage, N. P. ^[1]

Johns Hopkins Univ., Baltimore, MD (United States). Inst. for Quantum Matter. Dept. of Physics and Astronomy
Johns Hopkins Univ., Baltimore, MD (United States). Inst. for Quantum Matter. Dept. of Physics and Astronomy. Dept. of Chemistry
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Condensed Matter Division
Johns Hopkins Univ., Baltimore, MD (United States). Inst. for Quantum Matter. Dept. of Physics and Astronomy. Dept. of Chemistry. Dept. of Materials Science and Engineering
Johns Hopkins Univ., Baltimore, MD (United States). Inst. for Quantum Matter. Dept. of Physics and Astronomy. Dept. of Materials Science and Engineering

Publication Date:: Thu Jun 29 00:00:00 EDT 2017

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Johns Hopkins Univ., Baltimore, MD (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); ARCS Foundation (United States)

OSTI Identifier:: 1474719

Alternate Identifier(s):: OSTI ID: 1372525

Grant/Contract Number:: AC05-00OR22725; FG02-08ER46544; DGE-1232825

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 95; Journal Issue: 23; 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; Faraday effect; ferrimagnetism; insulators; Kerr effect; magnetic order parameter; magnetic susceptibility; order parameters; spin waves; topological phases of matter

Citation Formats


                    Laurita, N. J., Marcus, G. G., Trump, B. A., Kindervater, J., Stone, M. B., McQueen, T. M., Broholm, C. L., and Armitage, N. P. Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu2OSeO3.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevB.95.235155.

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                    Laurita, N. J., Marcus, G. G., Trump, B. A., Kindervater, J., Stone, M. B., McQueen, T. M., Broholm, C. L., & Armitage, N. P. Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu2OSeO3.  United States.  https://doi.org/10.1103/PhysRevB.95.235155

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                    Laurita, N. J., Marcus, G. G., Trump, B. A., Kindervater, J., Stone, M. B., McQueen, T. M., Broholm, C. L., and Armitage, N. P. Thu .  
"Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu2OSeO3".  United States.  https://doi.org/10.1103/PhysRevB.95.235155.  https://www.osti.gov/servlets/purl/1474719.

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@article{osti_1474719,

  title        = {Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu2OSeO3},

  author       = {Laurita, N. J. and Marcus, G. G. and Trump, B. A. and Kindervater, J. and Stone, M. B. and McQueen, T. M. and Broholm, C. L. and Armitage, N. P.},

  abstractNote = {In this study, we present a comprehensive study of the low-energy optical magnetic response of the skyrmionic Mott insulator Cu2OSeO3 via high resolution time-domain THz spectroscopy. In zero field, a new magnetic excitation (f0=2.03THz) which has not been predicted by spin-wave theory is observed and shown, with accompanying time-of-flight neutron scattering experiments, to be a zone folded magnon from the R to Γ points of the Brillouin zone. Highly sensitive polarimetry experiments performed in weak magnetic fields, μ0H<200mT, observe Faraday and Kerr rotations which are proportional to the sample magnetization, allowing for optical detection of the skyrmion phase and construction of a magnetic phase diagram. From these measurements, we extract a critical exponent of β=0.35±0.04, in good agreement with the expected value for the 3D Heisenberg universality class of β=0.367. In large magnetic fields, μ0H>5T, we observe the magnetically active uniform mode of the ferrimagnetic field polarized phase whose dynamics as a function of field and temperature are studied. In addition to extracting a geff=2.08±0.03, we observe the uniform mode to decay through a non-Gilbert damping mechanism and to possess a finite spontaneous decay rate, Γ0≈25GHz, in the zero temperature limit. Finally, our observations are attributed to Dzyaloshinkii-Moriya interactions, which have been proposed to be exceptionally strong in Cu2OSeO3 and are expected to impact the low-energy magnetic response of such chiral magnets.},

  doi          = {10.1103/PhysRevB.95.235155},

  journal      = {Physical Review B},

  number       = 23,

  volume       = 95,

  place        = {United States},

  year         = {Thu Jun 29 00:00:00 EDT 2017},

  month        = {Thu Jun 29 00:00:00 EDT 2017}

}

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DOI: 10.48550/arxiv.1311.5556

Magnetoelectric effects in the skyrmion host material Cu2OSeO3
text, January 2015

Ruff, E.; Lunkenheimer, P.; Loidl, A.
arXiv
DOI: 10.48550/arxiv.1504.03918

Microwave magnetochiral effect in Cu2OSeO3
text, January 2015

Mochizuki, Masahito
arXiv
DOI: 10.48550/arxiv.1504.05864

Magnon spectrum of the helimagnetic insulator Cu2OSeO3
text, January 2015

Portnichenko, P. Y.; Romhanyi, J.; Onykiienko, Y. A.
arXiv
DOI: 10.48550/arxiv.1509.02432

HORACE: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments
text, January 2016

Ewings, R. A.; Buts, A.; Le, M. D.
arXiv
DOI: 10.48550/arxiv.1604.05895

Bond electronic polarization induced by spin
text, January 2006

Jia, Chenglong; Onoda, Shigeki; Nagaosa, Naoto
arXiv
DOI: 10.48550/arxiv.cond-mat/0608411

Works referencing / citing this record:

Inelastic light scattering in the spin cluster Mott insulator ${Cu}_{2} {OSeO}_{3}$
journal, December 2019

Versteeg, R. B.; Boguschewski, C.; Becker, P.
Physical Review B, Vol. 100, Issue 22
DOI: 10.1103/physrevb.100.224426

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Title: Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu 2 OSeO 3

Abstract

Citation Formats

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate FeSc 2 S 4 journal, May 2015

Spin Transfer Torques in MnSi at Ultralow Current Densities journal, December 2010

Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets journal, March 2015

A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics journal, January 1958

A New Calculus for the Treatment of Optical SystemsI Description and Discussion of the Calculus journal, January 1941

Mantid—Data analysis and visualization package for neutron scattering and μ SR experiments journal, November 2014

Die Kristallstrukturen der Kupfer(II)-oxo-selenite Cu2O(SeO3) (kubisch und monoklin) und Cu4O(SeO3)3 (monoklin und triklin) journal, January 1986

Theory of coherence in Bose-Einstein condensation phenomena in a microwave-driven interacting magnon gas journal, May 2009

Multiferroics of spin origin journal, July 2014

Ferroelectricity Induced by Proper-Screw Type Magnetic Order journal, July 2007

Microscopic spin-wave theory for yttrium-iron garnet films journal, August 2009

A Modified 8f Geometry with Reduced Optical Aberrations for Improved Time Domain Terahertz Spectroscopy journal, May 2016

Magnetoelectric coupling in the cubic ferrimagnet Cu 2 OSeO 3 journal, September 2008

Magnetoelectric effects in single crystals of the cubic ferrimagnetic helimagnet Cu 2 OSeO 3 journal, June 2012

VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data journal, October 2011

Ferromagnetic Relaxation. I. Theory of the Relaxation of the Uniform Precession and the Degenerate Spectrum in Insulators at Low Temperatures journal, May 1961

Relaxation Process in Ferromagnetism journal, January 1953

A survey of magnetooptic effects journal, June 1968

Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe journal, December 2010

Entangled tetrahedron ground state and excitations of the magnetoelectric skyrmion material Cu 2 OSeO 3 journal, October 2014

μ SR investigation of magnetism and magnetoelectric coupling in Cu 2 OSeO 3 journal, August 2011

Magnetoelectricity in the ferrimagnetic Cu2OSeO3: symmetry analysis and Raman scattering study journal, June 2010

Optically probed symmetry breaking in the chiral magnet Cu 2 OSeO 3 journal, September 2016

Topological properties and dynamics of magnetic skyrmions journal, December 2013

Magnetodielectric coupling of infrared phonons in single-crystal Cu 2 OSeO 3 journal, October 2010

Spin excitations in the skyrmion host Cu 2 OSeO 3 journal, February 2016

Magnetoelectric resonances and predicted microwave diode effect of the skyrmion crystal in a multiferroic chiral-lattice magnet journal, April 2013

Real-space observation of a two-dimensional skyrmion crystal journal, June 2010

The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3 journal, November 2014

Magnon spectrum of the helimagnetic insulator Cu2OSeO3 journal, February 2016

Long-Wavelength Helimagnetic Order and Skyrmion Lattice Phase in Cu 2 OSeO 3 journal, June 2012

Horace : Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments journal, October 2016

Ferrimagnetism of the magnetoelectric compound Cu 2 OSeO 3 probed by S 77 e NMR journal, September 2010

Critical scaling in the cubic helimagnet Cu 2 OSeO 3 journal, February 2014

Exploration of the helimagnetic and skyrmion lattice phase diagram in Cu 2 OSeO 3 using magnetoelectric susceptibility journal, February 2014

Ferromagnetic Relaxation Caused by Interaction with Thermally Excited Magnons journal, March 1961

Interpreting magnetization from Faraday rotation in birefringent magnetic media journal, March 2007

Symmetry conditions for nonreciprocal light propagation in magnetic crystals journal, January 2013

Field dependence of magnon decay in yttrium iron garnet thin films journal, August 2012

Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: Wave vector selective Brillouin light scattering measurements and analysis journal, April 2009

Skyrmion Lattice in a Chiral Magnet journal, February 2009

Theory of Spin-Wave Interactions in Ferro- and Antiferromagnetism journal, January 1960

Dissipation processes in the insulating skyrmion compound Cu 2 OSeO 3 journal, December 2014

Skyrmion lattice in the doped semiconductor Fe 1 − x Co x Si journal, January 2010

Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries journal, July 2014

Spontaneous skyrmion ground states in magnetic metals journal, August 2006

Electric field control of the skyrmion lattice in Cu 2 OSeO 3 journal, October 2012

Colloquium : Spontaneous magnon decays journal, January 2013

Microwave Magnetochiral Effect in Cu 2 OSeO 3 journal, May 2015

Classifying multiferroics: Mechanisms and effects journal, March 2009

Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals journal, January 2012

Magnetoelectric Coupling in Single Crystal Cu 2 OSeO 3 Studied by a Novel Electron Spin Resonance Technique journal, June 2012

An unified view of the spin dynamics in two- and three-dimensional magnetic systems journal, November 1999

Microwave Magnetochiral Dichroism in the Chiral-Lattice Magnet Cu 2 OSeO 3 journal, May 2015

Establishing the Fundamental Magnetic Interactions in the Chiral Skyrmionic Mott Insulator Cu 2 OSeO 3 by Terahertz Electron Spin Resonance journal, October 2014

Magnetoelectric effects in the skyrmion host material Cu2OSeO3 journal, October 2015

A unified field theory of mesons and baryons journal, March 1962

Observation of Skyrmions in a Multiferroic Material journal, April 2012

Bond electronic polarization induced by spin journal, December 2006

Anisotropic Superexchange Interaction and Weak Ferromagnetism journal, October 1960

Strong Dzyaloshinskii-Moriya Interaction and Origin of Ferroelectricity in Cu 2 OSeO 3 journal, September 2012

Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu 2 OSeO 3 journal, June 2012

Polarization modulation time-domain terahertz polarimetry journal, January 2012

Microwave absorption in the frustrated ferrimagnet Cu2OSeO3 journal, February 2010

Emergent electrodynamics of skyrmions in a chiral magnet journal, February 2012

Microscopic theory of spin-polarization coupling in multiferroic transition metal oxides journal, October 2007

Two-step transition in a magnetoelectric ferrimagnet Cu 2 OSeO 3 journal, June 2012

Microscopic description of twisted magnet Cu2OSeO3 journal, May 2015

Lead palladium titanate: A room temperature nanoscale multiferroic thin film journal, February 2020

μSR investigation of magnetism and magnetoelectric coupling in Cu_{2}OSeO_{3} text, January 2011

Polarization modulation time-domain terahertz polarimetry conference, January 2012

Magnetoelectric Coupling in Single Crystal Cu_{2}OSeO_{3} Studied by a Novel Electron Spin Resonance Technique text, January 2012

Skyrmion Lattice in a Chiral Magnet text, January 2009

Theory of coherence in Bose-Einstein condensation phenomena in a microwave driven interacting magnon gas text, January 2009

Skyrmion Lattice in a Doped Semiconductor text, January 2009

Magnetodielectric coupling of infrared phonons in single crystal Cu$_{2}$OSeO$_{3}$ text, January 2010

Spin Transfer Torques in MnSi at Ultra-low Current Densities text, January 2010

Title: Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator ${Cu}_{2} {OSeO}_{3}$

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate ${FeSc}_{2} S_{4}$
journal, May 2015

Spin Transfer Torques in MnSi at Ultralow Current Densities
journal, December 2010

Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets
journal, March 2015

A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics
journal, January 1958

A New Calculus for the Treatment of Optical SystemsI Description and Discussion of the Calculus
journal, January 1941

Mantid—Data analysis and visualization package for neutron scattering and $μ$ SR experiments
journal, November 2014

Die Kristallstrukturen der Kupfer(II)-oxo-selenite Cu2O(SeO3) (kubisch und monoklin) und Cu4O(SeO3)3 (monoklin und triklin)
journal, January 1986

Theory of coherence in Bose-Einstein condensation phenomena in a microwave-driven interacting magnon gas
journal, May 2009

Multiferroics of spin origin
journal, July 2014

Ferroelectricity Induced by Proper-Screw Type Magnetic Order
journal, July 2007

Microscopic spin-wave theory for yttrium-iron garnet films
journal, August 2009

A Modified 8f Geometry with Reduced Optical Aberrations for Improved Time Domain Terahertz Spectroscopy
journal, May 2016

Magnetoelectric coupling in the cubic ferrimagnet ${Cu}_{2} {OSeO}_{3}$
journal, September 2008

Magnetoelectric effects in single crystals of the cubic ferrimagnetic helimagnet Cu $_{2}$ OSeO $_{3}$
journal, June 2012

VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
journal, October 2011

Ferromagnetic Relaxation. I. Theory of the Relaxation of the Uniform Precession and the Degenerate Spectrum in Insulators at Low Temperatures
journal, May 1961

Relaxation Process in Ferromagnetism
journal, January 1953

A survey of magnetooptic effects
journal, June 1968

Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe
journal, December 2010

Entangled tetrahedron ground state and excitations of the magnetoelectric skyrmion material ${Cu}_{2} {OSeO}_{3}$
journal, October 2014

$μ$ SR investigation of magnetism and magnetoelectric coupling in Cu $_{2}$ OSeO $_{3}$
journal, August 2011

Magnetoelectricity in the ferrimagnetic Cu2OSeO3: symmetry analysis and Raman scattering study
journal, June 2010

Optically probed symmetry breaking in the chiral magnet ${Cu}_{2} {OSeO}_{3}$
journal, September 2016

Topological properties and dynamics of magnetic skyrmions
journal, December 2013

Magnetodielectric coupling of infrared phonons in single-crystal ${Cu}_{2} {OSeO}_{3}$
journal, October 2010

Spin excitations in the skyrmion host ${Cu}_{2} {OSeO}_{3}$
journal, February 2016

Magnetoelectric resonances and predicted microwave diode effect of the skyrmion crystal in a multiferroic chiral-lattice magnet
journal, April 2013

Real-space observation of a two-dimensional skyrmion crystal
journal, June 2010

The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3
journal, November 2014

Magnon spectrum of the helimagnetic insulator Cu2OSeO3
journal, February 2016

Long-Wavelength Helimagnetic Order and Skyrmion Lattice Phase in ${Cu}_{2} {OSeO}_{3}$
journal, June 2012

Horace : Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments
journal, October 2016

Ferrimagnetism of the magnetoelectric compound ${Cu}_{2} {OSeO}_{3}$ probed by ${}^{77}S e$ NMR
journal, September 2010

Critical scaling in the cubic helimagnet ${Cu}_{2}$ ${OSeO}_{3}$
journal, February 2014

Exploration of the helimagnetic and skyrmion lattice phase diagram in ${Cu}_{2} {OSeO}_{3}$ using magnetoelectric susceptibility
journal, February 2014

Ferromagnetic Relaxation Caused by Interaction with Thermally Excited Magnons
journal, March 1961

Interpreting magnetization from Faraday rotation in birefringent magnetic media
journal, March 2007

Symmetry conditions for nonreciprocal light propagation in magnetic crystals
journal, January 2013

Field dependence of magnon decay in yttrium iron garnet thin films
journal, August 2012

Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: Wave vector selective Brillouin light scattering measurements and analysis
journal, April 2009

Skyrmion Lattice in a Chiral Magnet
journal, February 2009

Theory of Spin-Wave Interactions in Ferro- and Antiferromagnetism
journal, January 1960

Dissipation processes in the insulating skyrmion compound ${Cu}_{2} {OSeO}_{3}$
journal, December 2014

Skyrmion lattice in the doped semiconductor ${Fe}_{1 - x} {Co}_{x} Si$
journal, January 2010

Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries
journal, July 2014

Spontaneous skyrmion ground states in magnetic metals
journal, August 2006

Electric field control of the skyrmion lattice in Cu ₂ OSeO ₃
journal, October 2012

Colloquium : Spontaneous magnon decays
journal, January 2013

Microwave Magnetochiral Effect in ${Cu}_{2} {OSeO}_{3}$
journal, May 2015

Classifying multiferroics: Mechanisms and effects
journal, March 2009

Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals
journal, January 2012

Magnetoelectric Coupling in Single Crystal ${Cu}_{2} {OSeO}_{3}$ Studied by a Novel Electron Spin Resonance Technique
journal, June 2012

An unified view of the spin dynamics in two- and three-dimensional magnetic systems
journal, November 1999

Microwave Magnetochiral Dichroism in the Chiral-Lattice Magnet ${Cu}_{2} {OSeO}_{3}$
journal, May 2015

Establishing the Fundamental Magnetic Interactions in the Chiral Skyrmionic Mott Insulator ${Cu}_{2} {OSeO}_{3}$ by Terahertz Electron Spin Resonance
journal, October 2014

Magnetoelectric effects in the skyrmion host material Cu2OSeO3
journal, October 2015

A unified field theory of mesons and baryons
journal, March 1962

Observation of Skyrmions in a Multiferroic Material
journal, April 2012

Bond electronic polarization induced by spin
journal, December 2006

Anisotropic Superexchange Interaction and Weak Ferromagnetism
journal, October 1960

Strong Dzyaloshinskii-Moriya Interaction and Origin of Ferroelectricity in ${Cu}_{2} {OSeO}_{3}$
journal, September 2012

Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu $_{2}$ OSeO $_{3}$
journal, June 2012

Polarization modulation time-domain terahertz polarimetry
journal, January 2012

Microwave absorption in the frustrated ferrimagnet Cu2OSeO3
journal, February 2010

Emergent electrodynamics of skyrmions in a chiral magnet
journal, February 2012

Microscopic theory of spin-polarization coupling in multiferroic transition metal oxides
journal, October 2007

Two-step transition in a magnetoelectric ferrimagnet Cu $_{2}$ OSeO $_{3}$
journal, June 2012

Microscopic description of twisted magnet Cu2OSeO3
journal, May 2015

Lead palladium titanate: A room temperature nanoscale multiferroic thin film
journal, February 2020

μSR investigation of magnetism and magnetoelectric coupling in Cu_{2}OSeO_{3}
text, January 2011

Polarization modulation time-domain terahertz polarimetry
conference, January 2012

Magnetoelectric Coupling in Single Crystal Cu_{2}OSeO_{3} Studied by a Novel Electron Spin Resonance Technique
text, January 2012

Skyrmion Lattice in a Chiral Magnet
text, January 2009

Theory of coherence in Bose-Einstein condensation phenomena in a microwave driven interacting magnon gas
text, January 2009

Skyrmion Lattice in a Doped Semiconductor
text, January 2009

Magnetodielectric coupling of infrared phonons in single crystal Cu$_{2}$OSeO$_{3}$
text, January 2010

Spin Transfer Torques in MnSi at Ultra-low Current Densities
text, January 2010

Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals
text, January 2011

Symmetry Conditions for Non-reciprocal Light Propagation in Magnetic Crystals
text, January 2012