De l infrarouge, des faits et des mythes sur les electromagnons
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1 De l infrrouge, des fits et des mythes sur les electromgnons Ricrdo Lobo École Supérieure de Physique et Chimie Industrielles de l Ville de Pris lobo@espci.fr
2 Collbortors R. Schleck MPI, Stuttgrt C.S. Nelson G. L. Crr D. Colson CEA, Scly D. Lebeugle J.Y. Geslnd Brookhven Ntionl Lbortory Université du Mine, Le Mns H. Skt Tokyo University of Technology M.B. Lepetit J. Vrignon C. Mrtin R.L. Moreir CRISMAT, Cen, Frnce UFMG, Belo Horizonte, Brzil M. Czyous Université Pris 7 P. Rovillis
3 Rough definition of the Electromgnon Nt. Phys, Spin wve ctivted by electric field of light Is the electromgnon new fundmentl excittion? Wht is the reltionship between the electromgnon nd the mgneto-electric coupling? Is the electromgnon necessry excittion for ME coupling? Is the electromgnon restricted to multiferroics?
4 Light scttering Source Blck Box Photon in Photon out Opticl (infrred) conductivity Detector Hence the misnomer "center of zone" technique Better nme: "momentum verged" technique Elstic light scttering Brodbnd (whitelight) spectroscopy The interction with the electric field domintes
5 Wht is in the blck box? I(ω) R T R(ω) nd T(ω) ~ E 2 re rel functions. Reflected Power (Rel) Krmers-Kronig, simultion; fit; R & T inversion... Complex Opticl Function
6 The opticl functions Refrction index: light propgtion nd ttenution N = n + i k Dielectric function: microscopic polrizbility ε = ε + i ε = N 2 Opticl conductivity: high-frequency electricl trnsport σ = 2 v σ1 + i σ = i ε ω(1 ε) ε v = 8.85 x As/Vm
7 Phonons & the f-sum rule The f-sum rule (prticle conservtion): The f-sum rule for hrmonic excittions (e.g. phonons): The oscilltor strength:
8 Bck to the bsics: MnF 2 Antiferromgnet with T N = 67.5 K Spce group P4 2 /nmn (D 4h 14 ) Ferroelectricity not llowed c 5.0 Mgnetiztion (10-3 emu) Temperture (K) H // H // c
9 Fr-infrred excittions in MnF 2 Very fr-ir Fr-IR Tennnt & Richrds, J. Phys. C 10, L365 (1977) Extremely fr-ir Wever et l., J. Phys. Chem. Sol. 35, 1625 (1974) Allen et l., PRL 16, 463 (1966)
10 Infrred Mgnetic Excittions in MnF 2 Allen et l., PRL 16, 463 (1966) AFM resonnce Zone edge bi- mgnon
11 EPR using infrred c c
12 Is bi-mgnon n electromgnon? (Is the electromgnon restricted to multiferroics?) c c c The bi-mgnon in MnF 2 is ctivted by the electric field of light. Not its mgnetic field.
13 Is the bi-mgnon coupled to phonons? 5655 Frequency (cm -1 ) Spectrl Weight (Ω -1 cm -2 ) Bi-mgnon 0.1% Phonon T N Temperture (K) T N Temperture
14 Not just one e-mgnon in TbMnO 3 Pimenov et l., Nt. Phys, Vldés Aguilr et l., PRL, Most of the e-mgnon spectrl weight is t higher frequencies
15 TbMnO 3 : Sum-rule, Mgnons nd Phonons Tkhshi et l. PRL 101, (2008)
16 The electromgnon in TbMnO 3 reflectivity Reflectivity TbMnO 3 E // 6.5 K 60 K Wvenumber (cm -1 ) Trnsmission K 25K 5K simultion 5K Wvenumber (cm -1 )
17 Phonons Renormlize t T N in TbMnO 3 E // Frequency (cm -1 ) Temperture (K) W (T) = W(T)-W(50K) (Ω -1 cm -2 ) All phonons Mgnon Phonons 1 & T C Temperture (K) The electromgnon in TbMnO 3 gets its strength from phonons dominted by Tb nd Mn tomic movements T N
18 The electromgnon nd polriztion rottion (Is the e-mgnon relted to sttic coupling?) H // b Kimur et l., Nture 2003 Vldés Aguilr et l., PRL, The rottion of the polriztion does not hve lrge effect on the electromgnon
19 Sttic vs. Dynmic coupling Kimur et l., Nture 2003 Infrred contribution T C T N 35 Relxor behvior Dielectric constnt khz (Kimur) Infrred (Phonons + e-mgnon) 1 khz 10 khz 100 khz Goto et l. PRL Temperture (K) Sttic ME coupling is not dominted by phonons
20 The Electromgnon nd the lttice The Curious Cse of MnWO Ω TO / Ω TO (%) MnF 2 [ E // ] MnWO 4 [ E // (,c) ] MnWO 4 [ E // b ] Trnsmission K 100 K 200 K (T - T c ) / T c No phonon renormliztion Frequency [cm -1 ] no electromgnon!
21 So wht? Considering tht the electromgnon is spin wve ctivted by the electric field of light Is the electromgnon new fundmentl excittion? It needs phonon renormliztion nd phonon chrge, so Wht is the reltionship between the electromgnon nd the sttic mgneto-electric coupling? In TbMnO 3 ll the ction is in the MHz-GHz relxtion region! Is the electromgnon necessry excittion for ME coupling? MnWO4 does not seem to hve n electromgnon Is the electromgnon restricted to multiferroics? Not by the stndrd definition: MnF 2.
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