Abstract
Spectroscopicmodesprovidethemostsensitiveprobeoftheveryweakinteractionsresponsibleforthepropertiesofthelong-wavelengthcycloidinthemultiferroicphaseofBiFeO3belowTN≈640K.ThreeofthefourmodesmeasuredbyTHzandRamanspectroscopieswererecentlyidentifiedusingasimplemicroscopicmodel.WhileaDzyaloshinskii-Moriya(DM)interactionDalong[−1,2,−1]inducesthecycloidwithwavevector(2ˇ/a)(0.5+,0.5,0.5−)(≈0.0045),easy-axisanisotropyKalongthe[1,1,1]directionoftheelectricpolarizationPinduceshigherharmonicsofthecycloid,whichsplitthe 1modesat2.49and2.67meVandactivatethe2modeat3.38meV.How-ever,thatmodelcouldnotexplaintheobservedlow-frequencymodeatabout2.17meV.WenowdemonstratethatanadditionalDMinteractionD′along[1,1,1]notonlyproducestheobservedweakferromagneticmomentofthehigh-fieldphaseabove18Tbutalsoactivatesthespectroscopicmatrixelementsofthenearly-degenerate,low-frequency 0and1modes,althoughtheirscatter-ingintensitiesremainextremelyweak.Evenintheabsenceofeasy-axisanisotropy,D′producesharmonicsofthecycloidthatsplit 1andactivate2.However,theobservedmodefrequenciesandselectionrulesrequirethatbothD′andKarenonzero.Thisworkalsoresolvesanearlierdisagreementbetweenspectroscopicandinelasticneutron-scatteringmeasurements.
