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Coupling between Magnon and Phonon: Personal perspective
Je-Geun ParkCenter for Correlated Electron Systems, Institute for Basic Science
Dept. Physics & Astronomy
Seoul National UniversityPOSTECH Colloquium 12 April 2017
Outline
What is magnon-phonon coupling?
Part 1: Magnon-magnon coupling
Part 2: Magnon-phonon coupling
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Linearized Model & Quasiparticles
Quasiparticle decay superfluid 4He
M. B. Stone et al., Nature 440, 187 (2006)
The notion of a renormalized and stable quasiparticle is fundamental to modern theories of condensed matter physics.
D>1: Magnon
T. Huberman et al., PRB 72, 014413 (2005)
Nonlinear Phonon & Lifetime
Decay process Silicon at RT
At 0 K
T. R. Hart et al., PRB 1, 638 (1970)
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Magnon lifetime
Decay process Magnon linewidth
Crazy atoms: phonon & magnon
Phonon
Magnon
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Magnon phonon coupling New hybrid quasi-particle [C. Kittel, Phys. Rev. 110, 836 (1958)] Related to many fundamental physical properties of solids e.g. pintronics & multiferroics: possible new functionality
Photo induced magnetic domain in YIG
N. Ogawa et al., PNAS 112, 8977 (2015)G. Laurence et al., RRB 8, 2130 (1973)
Thermal conductivity of FeCl2
Kab
Kc
Magnon phonon hybridization FeF2 (S. Lovesey, “Theory of Neutron Scattering from Condensed
Matter systems,” sect. 9.8) Magnon-phonon hybridization: Lattice vibrations may modulate the
orbital properties. The modulation is transmitted to the spin by the spin-orbit interaction
·Magnetic Hamiltonian
Still the effect is small. Large K/J≃2 in FeF2, uncommon in 3d
ions
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Magnon-Phonon: CMR ManganitesLa0.70Ca0.30MnO3P. Dai et al., PRB (2000)
J. A. Fernandez-BacaPINS workshop, BNL April 6-7, 2006
Taste for Materials: Metal Physics
Prof. Bryan R. Coles, FRS (1926-1997)
My first foolish & expensive attempt to spin-lattice: Invar Problem
Do you smell the material?
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Invar Problem I met in 1990
My Personal Journey to Spin-Lattice
Prof. Duk Joo Kim (1934 ~ 1997)
금속전자계의 다체이론, p119
My first foolish & expensiveattempt to spin-lattice:Invar Problem
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Multiferroic Physics
FE FM/AFM
Ferroelastic
charge spin
lattice
mn mnmnm mmn nn HEHEFF , ,0 ME term
Major issues• Spin-lattice coupling • New types of J• Broken Inversion Symm.• Spin-orbit coupling• DM Interaction
FerroelectricityInversion symmetry broken
MagnetismTime-reversal symmetry broken
+ ++- --
+ ++- --
+ ++- --
Ferromagnet
Antiferromagnet
P
P
P=0
noncentrosymmetric Magnetic Systems
Dzyaloshinskii-Moriya Interaction arising from spin-orbit coupling: Skyrmion
Similar physics with Dresselhaus/Rashba interaction
Low energy dynamics: Electromagnon, spin-lattice coupling etc.
Non-collinear spin structureCoupling to charge dipole
Dzyaloshinskii-Moriya interaction
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Principle of Neutron Scattering
Incident neutrons
Scattered neutrons
전기적중성질량 스핀1/2
강한투과력전기적중성
물질내동력학적에너지범위와일치에너지~ meV
자기구조와동력학스핀1/2
원자수준부터나노수준파장Å~nm(열중성자& 냉중성자)
동위원소간구별산란밀도대비법
원자핵과의반응
전기적중성질량 스핀1/2전기적중성질량 스핀1/2
강한투과력전기적중성 강한투과력전기적중성
물질내동력학적에너지범위와일치에너지~ meV
자기구조와동력학스핀1/2 자기구조와동력학스핀1/2
원자수준부터나노수준파장Å~nm(열중성자& 냉중성자)
동위원소간구별산란밀도대비법
원자핵과의반응 동위원소간구별산란밀도대비법
원자핵과의반응
),()/exp(1),(Im STkB
Hexagonal RMnO3h-RMnO3 (R=Sc, Y, Ho, Er, Tm, Yb, and Lu)
Ferroelectricity from MnO5 tilting: Tc > 1000 K Mn spin forms noncollinear 120˚ structure: TN < 100 K Extensive studies on spin lattice coupling
Atomic shiftMagnon phonon
coupling
S. Lee et al., Nature 451, 805 (2008)S. Petit et sl., PRL 99, 26604 (2007)
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Hexagonal StructureA=Ho, Er, Tm, Yb, Lu, Y, Sc
2-dim. Hexagonal RMnO3
J. S. Kang, JGP et al., PRB 71, 092405 (2005)
1 representation 2 representation
3 representation 4 representation
E. F. Lewy-Bertaut in 1960sA. Munoz et al., PRB (2000)
ex
eu
Z=0 plane
Ф
Z=1/2 plane
1 2
Mn1
Noncollinear 120º Structures
JG Park’s GroupPRB (2003); PRL (2004); PRB (2005)PRB (2008); PRB (2009); PRB (2010)
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Part I: Magnon-magnon coupling
ToF inelastic neutron scattering
detectors
sample
ω 2
Momentum & energy changes of neutron Magnetic excitation at low Q & Phonon at high Q Time of Flight (ToF) technique: pulsed beam &
2D detector
Time
Distance
Moderator
FermiChopper
Sample
Detectors
Neutron path
tdet
Ei
Ef
texp
∆∆
10 % at ~ 5 Å-1
Magnon
Phonon
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Time-of-Flight Experiments• AMATERAS of J-PARC,
Japan• MERLIN of ISIS, UK
Direct Geometry Chopper Spectrometer
~180o in the horizontal plane; ± 30o in the vertical plane
020
40
60
80 meV0
10
20 meV
Detector Coverage
ω(m
eV)
Ei=70 meV Ei=25 meV
ω(m
eV)
Ei=250 meV
Total mass ~1.8 g
Spin Hamiltonian: YMnO3
T. J. Sato et al., PRB 68, 014432 (2003)
2 21 2,
zij i j i i i
i j i iH J S S D S D S n
Easy plane Easy axisExchange
J1 J2 J1c-J2c D1 D23 meV 2.3 meV 0.018 meV 0.3 meV -0.007 meV
J Park, JGP et al., PRB 68,104426 (2003)
T Chatterji et al., PRB 76, 144406 (2007)X. Fabreges et al., PRL 103, 067204 (2009)H. J Lewtas et al., PRB 82, 184420 (2010)
Parameters for YMnO3
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Full spin waves dispersion curvesJ1=-9 meV, J2=-1.4 meV, J3=0 meV, J1’=-0.018 meV, D1=-0.28 meV, and D2= 0.006 meV
Noncollinear magnets
Noncollinear order Transverse-longitudinal coupling Breaking O(3) symmetry
Not invariant under spin rotation or reflection
x x y y z zi j i j i jij
H J S S S S S S ( )i iS R S
i iS S
x x y y z zi j i j i jij
H J S S S S S S
Ferromagnet Conserves O(3) symmetry
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nonlinear effects in Spin waves
Roton-like minimum: W. Zheng et al., PRL (06)
Magnon decay & Flat mode : M. E. Zhitomirsky and A. L. Chernyshev, PRL (06); : O. A. Starykh, A. Chubukov, & A. G. Abanov, PRB (06)
See also a recent review: M. E. Zhitomirsky, & A. L. Chernyshev, Rev. Mod. Phys.85, 219–242 (2013)
Quantum montecarlo studyW. Zheng et al., PRL 96, 057201
(2006)
Nonlinear spinwave theoryA. L. Chernyshev et al., PRB 79, 144416 (2009)
Minimum, Flat mode, Magnon decay
Roton-like minimum
J. Oh et al., PRL 111, 257202 (2013)
Flat mode
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Spectrum broadening
Noncollinear magnets Transeverse-longitudinal coupling Magnon decays into two magnon states
M.E. Zhitomirsky et al., RMP 85, 219 (2013)A. L. Chernyshev et al., PRL 97, 207202 (2006), PRB 79, 144416 (2009)
12! Γ ; ⋯,
≃ 21 magnon 2 magnon
Triangular AFM
Magnon Decay Rate
Γ 2 ;
Spectrum broadening
Linewidth broadeningObservation of linewidth broadening in LuMnO3
Two magnons DOS
J. Oh, et al., PRL 111, 257202 (2013)
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Part II: Magnon-phonon coupling
Magnon: Y1-xLuxMnO3 Weak high energy peaks Minimum in AB direction Limitation of J1-J2 model ?
2 21 2
,
zij i j i i i
i j i iH J S S D S D S n
J1=4 meV, J2=1.8 meV, D1=0.28 meV, D2=-0.02 meV
J1=12.5 meV, J2=0.97 meV, D1=0.18 meV, D2=-0.018 meV
J1=9 meV, J2=1.4 meV, D1=0.28 meV, D2=-0.02 meV
J. Oh et al., Nat. Commun. 7, 13146 (2016)
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LuMnO3: J1-J2 Model ToF INS experiment at MAPS beamline of ISIS in UK Two peaks at K: J1≠J2 Three peaks at M & Λ: J1>J2 J1/J2=6.4 while DFT result is 1.15 [I. V. Solovyev et al., PRB 86, 054407 (2012)]
J. Oh et al., PRL 111, 257202 (2013)
J1=9 meV, J2=1.4 meV, J1c-J2c=0.018 meV,D1=0.28 meV, D2=-0.02 meV
Noncollinear magnets
'
' cos sin
spin phonon ji i j i jij
x x y y z z z y y zspin phonon ji i j i j i j i j i j i j i j i j
ij
H H H e u u S S
H H e u u S S S S S S S S S S
1 phonon 0,2 magnon 1 magnon
Linear magnon-phonon coupling
Exchange stiction Hamiltonian
≃ 2 ≃Transeverse Longitudinal
Modulation of J is dominant Noncollinear structure:
Transverse-longitudinal coupling Direct mixing of magnon and
phonon
Exchange DM Single-ionJ Dxy τxz
2.71 meV -0.013 meV -0.05 meVLuMnO3 [H. Das et al., Nat. Communs. 5, 2998 (2014)]
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Spin lattice HamiltonianExchange striction model Mn-O bond length change DFT phonon calculation & powder inelastic
neutron scattering at AMATERAS, J-PARC Estimate α from pressure experiments
Exchange striction model
Calculated & measured phonon DOS
α // 14
Estimated α For YMnO3
La2CuO4: 6~7CuCrO2: 30
T. Lancaster et al., PRL 98, 197203 (2007) D. P. Kozlenko et al., JETP 82, 193 (2005) M. C. Aronson et al., PRB 44, 4657 (1991) K. Park et al., PRB 94, 104421 (2016)
2 · · ·
Optical phonons Several optical phonons below 25 meV Possible coupling of inplane phonons with magnons ?
J. Varigon et al., arxiv 1203.1752v1 R. Basistyy et al., PRB 90, 024307 (2014)
(E1 symmetry)
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Magneto-elastic mode
' ij ijspin phonon O i i O j j i jij
H H H e u e u S S
Additional high energy peaks at zone boundaries: magneto-elastic (ME) mode
Downward shift at B point: level repulsion between magnon & phonon.
α =16 (Pressure exp.: 14) J1=J2 (DFT calc.: 0.8~1.15)
(meV) J1 J2 D1 D2 α (no dim.)
YMnO3 2.5 2.5 0.28 -0.02 16 Y0.5Lu0.5MnO3 2.7 2.7 0.28 -0.02 20LuMnO3 3 3 0.28 -0.02 16
YMnO3
LuMnO3
Y0.5Lu0.5MnO3
Dynamical structure factor
· · ·
Einstein phonon model Magneto-elastic mode energy ~ 20 meV Two magnon coupling due to noncollinear spin structure
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Results
' ij ijspin phonon O i i O j j i jij
H H H e u e u S S
in (meV) J1 J2 D1 D2 α (no dim.)
YMnO3 2.5 2.5 0.28 -0.02 16 Y0.5Lu0.5MnO3 2.7 2.7 0.28 -0.02 20LuMnO3 3 3 0.28 -0.02 16
Parameters
YMnO3
LuMnO3
Y0.5Lu0.5MnO3
Calculation
Experiment
Calculations reproduce high energy signals Magneto-phonon mode: phonon having magnon character Downward shift near B point
Linewidth broadening Calculated linewidth shows singular behavior near B & D point of LuMnO3 Consistent with the experimental result
J. Oh et al., Nat. Commun. 7, 13146 (2016) Decay rate: Γ , ∑, ;
, , ,
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IBS-CCES Emergent Phenomena Grouphttp://magnetism.snu.ac.kr
Joosung OhHasung Sim
Ho-Hyun Nahm
Acknowledgment: A. L. Chernyshev (UC), H. Woo, T.G. Perring (ISIS), W. J. L. Buyers, Z. Yamani (CINS), S.W. Cheong (Rutgers), A Baron (Spring8), K. Nakajima, S. Ohira-Kamamura (J-PARC), Y. Yoshida, H. Eisaki (AIST)
Summary RMnO3: We have identified magneto-
elastic mode together with magnon-magnon coupling and its linewidth broadening in noncollinear magnets (Y,Lu)MnO3.Nat. Comm. (2016), PRL (2013)
CuCrO2: We found two clear evidence of magnon-phonon coupling: Roton-like minima at zone boundary, magnetic character of phonon intensity, which is enhanced at zone boundary below TN.PRB (2016)
More general remark: In a noncollinear magnet, phonon mixes with magnon, resulting in a creation of magneto-elastic excitation.