2017-04-18

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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.