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Title Spin-wave induced phonon resonance in multiferroic BiFeO$_3$
Permalink https://escholarship.org/uc/item/48b8h65t
Authors Xu, Zhijun Schneeloch, JA Wen, Jinsheng et al.
Publication Date 2018-03-02
Peer reviewed
eScholarship.org Powered by the California Digital Library University of California arXiv:1803.01041v1 [cond-mat.mtrl-sci] 2 Mar 2018 odcosadtepoo eoac 1,1]i conventiona in 16] [15, super resonance unconventional phonon the in and [11–14] conductors resonance spin the hidden resonance include a induced such revealing of thereby examples known system, Well un- same correlation. seemingly the a in in resonance mode cha a related the induces quantity where physical exist a an situations of or fre- Interesting mode specific another force. a with interactions at external by system driven physical is a that of quency mode amplit oscillatory the an of increase of sharp a ”resonance” to the refers as ef generally such resonance to waves, classical lead in could occur them that between fects interactions the concepts, cal d advanced fields, applications. in magnetic vice use for and potential electric tremendous offering as thereby such parameter e.g tha external more quasiparticles, to one hybrid sensitive be of could types which new [7–10], interact electromagnons to Such rise well. give as even materials multifer- can other to in limited occurs it not as is roics, be phenomenon can This dispersion [4–6]. magnon observed over and/or phonon an the strong of sufficiently modification is quasiparticles coupli these the When between solids. in excitations fundamental most the ar respectively, from fluctuations, spin arising and quasiparticles vibrations lattice are which excita different magnons, couple and Phonons also can par interactions order different te these coupling new eters, to of addition ult pursuit In the and, [1–3]. in nologies orders interactions these different tailor between to mately, interactions whi the with study platforms to fascinating provide multiferroics tem, hl usprilsaefnaetlyqatmmechani- quantum fundamentally are quasiparticles While sys- same the in coexisting orders ferroic multiple Having 2 ITCne o eto eerh ainlIsiueo Sta of Institute National Research, Neutron for Center NIST 3 eateto aeil cec n niern,Universi Engineering, and Science Materials of Department 10 nest sehne hnatfroantc(F)odrs order (AFM) antiferromagnetic BiFeO when multiferroic enhanced is the intensity in (111) around center zone ASnmes 63.20.kk,75.30.Ds,75.85.+t,75.25.-j,61. numbers: PACS D the via vibrations lattice ma fluctuations the external spin onto and an mapped lattice by are the excitations modified between be coupling novel can a it of and expected, is intensity hs“eoac”i ofie oavr arwrgo nenergy in region narrow very a to confined is “resonance” This 8 ainlIsiueo dacdIdsra cec n Tech and Science Industrial Advanced of Institute National .Yanagisawa, Y. unu odne atrDvso,OkRdeNtoa Labo National Ridge Oak Division, Matter Condensed Quantum erpr h ietosraino rsnne oei the in mode “resonance” a of observation direct the report We 5 aeil cec iiin arneBree ainlLa National Berkeley Lawrence Division, Science Materials 9 hjnXu, Zhijun colo hsc n srnm,Uiest fEibrh E Edinburgh, of University Astronomy, and Physics of School .L Winn, L. 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FIG. 1: Magnon and phonon neutron scattering cross sections in BFO. Data measured on HYSPEC at (a) 300 K and (b) 600 K are plotted in the energy-momentum plane near the nuclear Bragg peak (002) for Q along [111]. Relative intensities are shown on a linear ′′ color scale given by the vertical bar at right. Linear intensity profiles FIG. 2: χ (Q, ~ω) derived from energy scans performed at constant measured on HB1 at (c) 4 meV and (d) 20 meV are shown as a func- Q. (a)-(d) Longitudinal phonons measured near (111). (e) Zone- tion of Q scanned along [001] and centered on the magnetic Bragg center phonon measured at (220). (Red data points here correspond peak (0.5,0.5,1.5). All intensities have been divided by the Bose fac- to 650 K instead of 600 K.) (f) Transverse phonon (q=0.1) measured tor to obtain χ”. Error bars represent ±1 standard deviation. near (220). (g) and (h) Transverse phonons measured near (111). Lines are guides to the eye. All data were taken on HB-1 except for those in (d) which were measured on HYSPEC with a Q-integration width of 0.1 (r.l.u.) curs at an energy-momentumposition where one quasiparticle has strong spectral weight while the other does not; and (iii) the resonance intensity adds to the original quasiparticle in- dissolves. For temperatures well below TN the magnetic scat- tensity instead of appearing as a new mode. Our data thus re- tering intensity follows the Bose factor. The lattice contribu- veal a new and unique example of how phonons and magnons tion to χ′′(Q, ~ω) in panels (a) and (b) exhibits no significant can interact in multiferroic systems. Measurements made in changes between 300 K and 600 K, thus indicating that the an external magnetic field provide further confirmation of this phonon scattering also follows the Bose factor. This behav- unusual coupling, as the resonance intensity increases with ior is also expected and holds almost everywhere in recipro- field as does the ferroelectric polarization along [111]. This cal space that we probed. A more quantitative and extensive behavior suggests that the same type of DM interaction that survey is provided in Fig. 2 where the scattering from lon- couples the static spin and polar structures is also behind the gitudinal and transverse phonons in different Brillouin zones induction of this highly coherent resonance mode. and selected wave vectors are plotted. With one exception The low-energy magnon and phonon excitations in BFO (Fig. 2(a)), the phonon spectra exhibit a normal temperature can be measured simultaneously with neutron inelastic scat- dependence where energies slightly harden on cooling into tering [28] on single crystal samples [29, 30]. In Fig. 1 the ferroelectric phase and intensities follow the Bose factor. we plot the imaginary part of the generalized susceptibility However, when we examined the zone-center (q = 0) optic χ′′(Q, ~ω) obtained from measurements made near the (002) mode at (111), we discovered a significant and unexpected in- nuclear Bragg peak and for wave vectors along [111] at (a) tensity enhancement, or resonance, for T point cannot be ruled out, it is difficult to account for the large spectral enhancement of the original optic phonon mode near q = 0 when the crossing spin wave has almost zero spectral weight. Instead, we propose a scenario in which the coupling be- tween two static order parameters(ferroelectric and AFM) can be extended to couple excitations arising from fluctuations of these order parameters. The static spin structure in BFO (see Fig. 4a) consists of spins ordered antiferromagnetically along [111] with Q~ AF = (0.5, 0.5, 0.5) (q = π) and a cycloid or- der with long modulation along the perpendicular h011¯i di- rections [18]. When a spontaneous ferroelectric polarization is present, the free energy of the system can be lowered if the polarization P~0 is parallel to L~ × (S~i × S~i+1) because of the antisymmetric exchange (DM interaction) between neighbor- ing spins [33]. Here L~ is the vector connecting two adjacent spins S~i and S~i+1 along the direction of the cycloid. This ef- fectively couples the ferroelectric polar order at q = 0 to the AFM cycloid spin structure at q = π along [111]. The reason FIG. 3: Temperature dependence of χ”(T )/χ”(600K) for vari- behind this mapping of nuclear zone center (q = 0) to AFM ous phonons. (a) Zone-center (q = 0) optic phonons at (111) zone center (q = π), which is also the nuclear zone boundary, (black), (220) (red), and (200) (green). (For (220) the ratio is that the DM interaction is only sensitive to the chirality of χ”(T )/χ”(650K) is plotted because no 600 K data were measured.) the cycloid. The two anti-phase rows of spins shown in Fig. 4a The vertical dotted line denotes TN = 640 K. (b) LO phonon at have the same chirality; therefore the DM interaction couples Q=(1.1,1.1,1.1). (c) LA (red squares) and LO (red circles) phonons the AFM spin structure, with a periodicity of two sites along at Q=(1.9,1.9,0). (d) TA phonon at Q=(2,0.4,0). Error bars represent fitting errors. [111], to the spontaneous polarization, which has half the pe- riodicity, i. e. just one site along [111]. When a spin-wave excitation forms near q = π from fluctu- ations of the ground state spin configuration, one would nat- rection, the resonant response disappears. The ratio measured urally expect the lattice polarization to fluctuate in a related at other locations always remains close to one for both optic manner due to the DM coupling, leading to a lattice mode and acoustic modes. Surprisingly, the resonance is only ob- near q = 0. In the Supplemental Materials we give a simpli- served clearly at Q = (1, 1, 1). Itis muchreduced,if notcom- fied picture of how a “magneto-phonon”mode can be induced pletely suppressed, at the equivalent positions Q = (2, 2, 0) by such a dynamic DM interaction, having a linear dispersion and (0, 0, 2). Since our neutron scattering measurements are near q = 0 similar to that of the spin wave near q = π (see sensitive to phonons polarized along Q, this implies that the Fig. 4b). More detailed theoretical work is definitely required intensity enhancement is associated primarily with atomic dis- to develop a quantitative understanding of this novel dynamic placements (polarizations) along h111i. coupling. It is also important to understand that this is a map- There are several possible origins of the resonance. One ping of one magnon near q = π to a lattice mode around is the coupling that exists between the magnetic order and q =0, which differs from the creation of a two-magnon mode the phonon modes, i. e. magneto-elastic coupling that gives near q =0 by combining two magnons near q = π. rise to “magneto-vibrational” modes [31, 32]. In this case The strength of the induced “magneto-phonon” mode de- both phonon dispersions and intensities can be modified by pends on many factors including the magnitude of the spin the onset of magnetic order. However, this type of coupling fluctuation ∆S, the strength of the antisymmetric interac- generally affects the phonon energies and intensities over a tion, and the presence of a non-collinear spin structure (i. e. large range of momentum, not at a single value of Q and en- S~i × S~i+1 6= 0). It should vanish upon warming above TN ergy as is observed in our case. Another possibility is a direct when the N´eel order melts. It is a second order effect that coupling between a spin-wave excitation and an optic phonon is not expected to be strong, which explains why previous mode where they cross each other [5]. And in fact, the spin- neutron and x-ray scattering studies did not detect this mode wave dispersion in BFO [26] does approach the low-energy near q = 0. However, a resonance can occur if another mode optic phonon branch near q = 0 and ~ω ∼ 7 meV. However, crosses the induced mode so that at the crossing point the two the spectral weight of the spin-wave excitations in a G-type modes have the same energy and momentum. If we examine AFM system is governed by a structure factor that is typically Fig. 4b, we can see that this magneto-phonon mode crosses largest at the AFM wave vector q = π (the AFM zone center) the lowest-energy polar optic phonon branch in BFO around and zero at q =0 (the nuclear zone center). While in principle 7 meV for q ∼ 0.02 A˚ −1 to 0.05 A˚ −1 (depending on the di- such a direct coupling between the two modes at this crossing rection of ~q) based on the known spin-wave dispersion [26]. 4 FIG. 4: Schematic diagram showing how spin-wave excitations near q = π can be mapped onto lattice vibrational modes near q = 0. (a) Spins in the cycloid plane and the corresponding lattice polariza- FIG. 5: Magnetic Bragg peak and (111) phonon measured under ex- tion along [111]. The small arrows are fluctuating (precessing) spins ternal magnetic field at 300 K on BT7. (a) Magnetic Bragg peak (red) and fluctuating polarizations (green). (b) A spin wave mode at ~ ~ (0.5,0.5,0.5). (b) and (c) Longitudinal phonons measured near (111) (π +q, ω) is mapped to a lattice mode at (2q, 2 ω). Solid lines rep- for q=0 and q=0.1, respectively. resent the spin-wave (near q = π) and optic phonon (near q = 0) dis- persions, and the dashed line represents the magneto-phonon mode mapped from the spin-wave dispersion. netic field is applied along [11¯0], which is known to induce a magnetic phase transition [30, 37] (see the field-dependent This naturally explains why optic probes such as Raman spec- changes in the magnetic Bragg peak shown in Fig. S1a). troscopy [19, 20, 34, 35] or infrared spectroscopy [36], which While the exact spin structure of the high field phase of BFO is are sensitive only to modes at q = 0, are unable to detect unknown,which is unlikely a simple collinear AFM phase, the the resonance: the crossing occurs at a small but non-zero q ferroelectric polarization along [111] increases significantly as discussed above. The reason why the resonance appears with field [37], suggesting an enhancement of the asymmetric at q = 0 in our neutron inelastic scattering measurements is spin interaction. Consistent with the picture described above, that the instrumental wave vector resolution is comparatively we find that the zone center (q = 0) phonon is also enhanced coarse near (111) (∼ 0.1 A˚ −1 in the transverse direction). by the field whereas the q = 0.1 phonon remains the same in Thus a nominal scan at q = 0 will pick up the resonance in- all phases (see Fig. 5b and 5c). tensity because it is located at a wave vector that lies within We have discovered a magnetically induced enhancement the instrumental resolution. Another consequence is that the of the lowest-energy zone-center optic phonon at (111) in resonance is only pronounced near (111) since the spin excita- BFO. This enhancement is located far from any strong mag- tions are only coupled to h111i polarization fluctuations, and netic excitation or magnetic Bragg peak, which indicates that the resonance will likely only occur for optic phonons having this effect is due to an entirely new mechanism that cou- the same polarizations as the magneto-phonon mode. ples lattice and spin fluctuations. Our results suggest that, in Note that the exact form of the interaction is not essential addition to the commonly observed coupling between static here - the central requirement is that the same type of cou- spins and ferroelectric polarizations, the asymmetric spin in- pling (which is assumed to be an asymmetric DM interaction) teractions in this multiferroic system contribute to a highly between the static spin and polar structures is also present be- unusual resonance that occurs only at reciprocal space loca- tween the spin and lattice fluctuations; this results in a signifi- tions where a polar phonon mode coincides with a “magneto- cant enhancement, or resonance, of the polar phonon intensity phononmode” that is inducedby the spin excitations, and they at a specific wave vector and energy. Evidence supporting the do so without affecting the phonon or magnon dispersions. validity of this model is observed when a large external mag- ZJX, JAS, GDG, and GYX acknowledge support by Office 5 of Basic Energy Sciences, U.S. Department of Energy under [18] I. Sosnowska, T. P. Neumaier, and E. Steichele, Journal of contract No. DE-SC0012704. JW and RJB are also supported Physics C: Solid State Physics 15, 4835 (1982). by Work at Lawrence BerkeleyLaboratory and UC Berkeley [19] R. Haumont, J. Kreisel, P. Bouvier, and F. Hippert, Phys. Rev. was supported by the Office of Basic Energy Sciences (BES), B 73, 132101 (2006). [20] P. Rovillain, M. Cazayous, Y. Gallais, A. Sacuto, R. Lobo, Materials Sciences and Engineering Division of the U.S. De- D. Lebeugle, and D. Colson, Phys. Rev. B 79, 180411 (2009). partment of Energy (DOE) under Contract No. DE-AC02-05- [21] R. de Sousa and J. E. Moore, Phys. Rev. B 77, 012406 (2008). CH1231 within the Quantum Materials Program (KC2202) [22] A. 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