Cr2O3中反铁磁自旋波的低频拉曼光谱研究.pdf

第 43 卷第 5 期2023 年 10 月物理学进展PROGRESS IN PHYSICSVol.43 No.5Oct.2023Low-Frequency Raman Detection of Antiferromagnetic Spin Waves inCr2O3Dong Biao,CUI Jun,TIAN Yuan-zhe,WU Di,ZHANG QiNational Laboratory of Solid State Microstructures and Department of Physics,Nanjing University,Nanjing 210093,ChinaAbstract:The antiferromagnetic(AFM)spin waves are promising for being utilized in high-speed and energy-efficient information processing.However,the excitation and detection ofterahertz spin waves in AFM systems is challenging.Here,we demonstrate low-frequencyRaman spectroscopy as a powerful tool for spin-wave detection in AFM systems.We presenta systematic study of AFM magnons in Cr2O3,a prototypical uniaxial antiferromagnet,viaRaman measurements down to 2.3 cm1(69 GHz).We resolved the magnon Zeeman splittingand the spin-flop transition.We further determined the sign of angular momentum of themagnon branches via polarization-resolved Raman processes.We also obtained the anisotropyenergy,the g-factor,and the spin-flop field of Cr2O3as a function of temperatures and magneticfields.A spin-wave renormalization theory accounts for all experimental observations.Key words:antiferromagnetism;spin wave;low-frequency Raman spectroscopy;spin-flopCLC number:O469Document code:ADOI:10.13725/ki.pip.2023.05.002CONTENTSI.Introduction142II.Results and discussion143A.LFRS set-up and the magnetic structure ofCr2O3143B.Temperature dependence of the AFM magnon ofCr2O3144C.Temperature dependence of the magnon g-factorand the spin-flop field145D.Polarization-resolved magneto-Raman spectra ofmagnons146III.Conclusions148Acknowledgments148References148I.INTRODUCTIONAntiferromagnets with fast spin dynamics andsuperior robustness in external fields are promisingReceived date:2023-7-29 E-mail:for facilitating high-speed spin-based information pro-cesses and long-term data storage1-4.Antiferromag-netic(AFM)spin waves,which predominately locatein the terahertz regime,have the potential for beingused as information carriers and play a central rolein AFM-based spintronics and magnonics.However,unlike their ferromagnetic counterparts,it is challeng-ing to effectively excite and detect AFM magnons dueto their terahertz frequency5-7,especially in thin filmsand microstructures.Ferromagnetic spin waves are commonly launchedand probed with microwave resonance through mag-netic dipole transitions8-11,or with Brillouin lightscattering spectroscopy via inelastic scattering pro-cesses between photons and magnons12-16.Themajority of AFM spin waves are beyond the frequencyrange of those conventional approaches for ferromag-nets.On one hand,advances in terahertz opticsoffer new possibilities to address AFM magnons4,17-18,where the magnetic components of terahertz waves cou-ple with AFM spin waves,similar to the microwaveresonance.On the other hand,regarding the inelasticArticle ID:1000-0542(2023)05-0142-9142Dong Biao et al.:Low-Frequency Raman Detection of Antiferromagnetic Spin Waves in Cr2O3143light scattering approach of magnon detection,conven-tional Raman spectroscopy is hard to resolve magnonsbelow 100 cm1(3 THz).Hence,there exists adetection gap from 100 GHz to 3 THz between Bril-louin light scattering and regular Raman spectroscopy,which unfortunately coincides with the essential fre-quency range for most practical AFM magnonic sys-tems.Although a triple-stage spectrometer can resolveRaman shift down to 1 cm1level,it suffers fromcomplicated equipment settings and low efficiency dueto the photon loss from passing multiple gratings.The recent development of low-frequency Raman spec-troscopy(LFRS)based on Bragg notch filters and aregular single-stage spectrometer fills the gap betweenBrillouin light scattering and conventional Ramanmethods.In this work,we show that LFRS can be a power-ful tool for AFM spin wave detection down to 2.3 cm1(69 GHz).We choose the classic AFM insulator Cr2O3as a model system and perform a comprehensive inves-tigation of the sub-terahertz magnons in this system.II.RESULTS AND DISCUSSIONA.LFRS set-up and the magnetic structure ofCr2O3Chromium oxide(Cr2O3)is one of the classic AFMinsulators that has been extensively investigated overthe past decades19-22,and is the first material wheremagneto-electric coupling was discovered.Cr2O3isan easy-axis AFM with a corundum(hexagonal)crys-tal structure and a magnetic point group of3m.ItsNel temperature(TN)is 307 K.The magnetic struc-ture of Cr2O3is shown in Fig.1(b),and spins fromthe two sublattices are along with the trigonal c-axis(0001)23-24.The AFM spin wave of Cr2O3locates at0.165 THz at 0 K20,25,measured by high-frequencymicrowave resonance.Recently,terahertz spin pump-ing of AFM magnon was achieved in Cr2O326,andsignatures of magnon-phonon coupling was also re-ported27.The-cut single crystal Cr2O3fromPrMat.Inc.is used in this study.The experimental set-up of LFRS is schematicallyshown in Fig.1(a）.Magneto-Raman measurementsare conducted in the back-scattering geometry.Themagnetic field is applied perpendicular to the samplesurface(along the c-axis)and parallel to the directionof light propagation.A HeNe laser of 632.8 nm is usedas the excitation light source.The laser beam goesthrough a Bragg bandpass filter and gets focused ontothe Cr2O3single crystal by an objective,with a spotsize of 1 micron.Inelastically scattered photons arecollected and further filtered by multiple Bragg notchfilters,and finally sent to a single-stage spectrometerwith a liquid-nitrogen-cooled CCD array.The schematic Stokes and anti-Stokes processes forcreating and annihilating a magnon in Cr2O3,respec-tively,are illustrated in Fig.1(c).Cr2O3possessesa three-fold rotational symmetry along the c-axis.Itenables a quasi-angular momentum transfer of 3 hfrom the crystal lattice,which assists in the conser-vation of total angular momentum during the Ramanprocess.It can be viewed as the rotational analog ofthe umklapp process28.The total angular momentum(Jtot)consists of three parts,the magnons(Jmag),pho-ton(Jph),and crystal(Jcry),and needs to be conserved,which givesJtot=Jmag+Jph+Jcry=0.(1)As shown in the left panel of Fig.1(c),for a Stokesprocess under left-handed circular excitation and right-handed detection(+)configuration,Jphequals2 h,and the creation of a magnon with h angu-lar momentum gives Jmag=h,then the crystalcan offer 3 h quasi-angular momentum,Jcry=3 h,which conserves the total angular momentum.For acorresponding anti-Stokes process with the same+polarization configuration(the right panel of Fig.1(c),Jphequals 2 h,and the annihilation of a h magnongives Jmag=h,and Jcry=3 h,then Jtotis con-served.It indicates the polarization selection rules areopposite for magnons with opposite angular momentain Stokes and anti-Stokes processes.The selection rulesare also opposite between the two cross-circular config-urations(+and+),which allow the experimen-tal identification of the sign of magnon angular momen-tum via circular polarization-resolved Raman measure-ments.144Dong Biao et al.:Low-Frequency Raman Detection of Antiferromagnetic Spin Waves in Cr2O3Fig.1.(a)Schematic diagram of the low-frequency magneto-Raman spectroscopy set-up.A laser beam passes through thebandpass filter(BPF),then gets focused onto the sample by an objective,scattered by magnons.The scattered photonsare filtered by multiple Bragg notch filters(BNF)then collected by a spectrometer.(b)The magnetic structure of Cr2O3,only Cr atoms are shown.(c)Illustration of Raman processes and selection rules in systems with three-fold rotationalsymmetry,+and stands for right-handed and left-handed circular polarized light.B.Temperature dependence of the AFMmagnon of Cr2O3The magnon Raman spectra of Cr2O3at 10 Kwas shown in Fig.2(a).A pronounced Raman peakat 6.2 cm1(186 GHz)is the AFM magnon.A posi-tive(negative)Raman shift indicates the Stokes(anti-Stokes)processes.The temperature dependence of themagnon from 10 K to 320 K was shown in Fig.2(b),the black dashed line indicates the Nel temperature(307 K).The AFM magnon exhibits a general trendof softening as the temperature approaching TN.TheLorentz fitting of magnon peak positions and linewidthare shown in Fig.2(c).In addition to the overall red-shift,the magnon exhibits a slight blueshift in the tem-perature range of 100 K to 180 K,while the magnonlinewidth remains nearly constant below 200 K,thenincrease drastically when approaching TNdue to thethermal spin fluctuations near the transition tempera-ture.The magnon frequency of an easy-axis AFM isdescribed by following equation29-30,=2HEHA+(H/2)2 H(1 /2),(2)Dong Biao et al.:Low-Frequency Raman Detection of Antiferromagnetic Spin Waves in Cr2O3145Fig.2.(a)The magnon Raman spectra of Cr2O3at 10 K.The black circle is the experimental data.Red solid lines isthe Lorentz fitting.(b)Temperature-dependent Raman spectra of Cr2O3from 10 K to 320 K,the black dash line indicatesthe Nel temperature.(c)Peak positions(red circle)and the linewidth(blue circle)of magnons from 10 K to 320 K.(d)Anisotropy field(HA)extracted from the magnon frequency.where is the gyromagnetic ratio,=isthe ratio between the parallel and the perpendic-ular magnetic susceptibility with respect to the c-axis,and H is the external magnetic field appliedalong the easy-axis,HAand HEare the effectivefields associated with the uniaxial anisotropy and theexchange interaction,respectively.For zero exter-nal magnetic field,Eq.2 can be simplified as =2HEHA.The exchange field HEof Cr2O3doesnot change drastically with temperature and remainsnearly constant31,while,the HAof Cr2O3containstwo terms32:single-ion anisotropy(HSI)and mag-netic dipolar anisotropy(HMD).HMDdecreases mono-tonically with increasing temperature32,therefore,the slight blue shift of magnon frequency mainly comesfrom HSI,which is consistent with previous theories andexperiments20,32.Extracted anisotropic field from themagnon frequency is shown in Fig.2(d).C.Temperature dependence of the magnong-factor and the spin-flop fieldFig.3(a)displays the magneto-Raman spectra ofmagnons from 0 T to 9 T at 200 K.An external mag-netic field H lifts the degeneracy of the two AFMmagnons and leads to a magnon Zeeman splitting witha g-factor of 1.56,which is less than the typical magnong-factor of 2.As the field further increases to 9 T,aspin-flop transition happens.We performed magneto-Raman spectroscopy of Cr2O3at different tempera-tures.The extracted magnon frequencies are shownin Fig.3(b)for four temperature points(10 K,120K,200 K,and 250 K).Notably,our LFRS can detectmagnon modes as low as 2.3 cm1(69 GHz),as markedin figure.The temperature dependence of parallel(blueline)and perpendicular(red line)magnetic suscepti-bility obtained via vibrating sample magnetometry is146Dong Biao et al.:Low-Frequency Raman Detection of Antiferromagnetic Spin Waves in Cr2O3Fig.3.(a)Magneto-Raman spectra with unpolarized excitation and detection at 200 K.(b)Magnon peak positions at10 K(red),120 K(blue),200 K(purple),and 250 K(black),fitted with Eq.3(solid lines).(c)Measured temperaturedependence of parallel(blue line)and perpendicular(red line)magnetic susceptibility of Cr2O3,respect to the c-axis ofsample,from 10 K to 350 K.Black line indicates their ratio.(d)Temperature dependence of the magnon g-factor(left-axis)and the spin-flop field(right-axis)obtained from experiments(dots)and theory(lines).shown in Fig.3(c),and their ratio is indicated by theblack line.With Eq.2 and the measured susceptibil-ity,we calculated the magnon frequencies as shown inFig.3(b)with solid lines.They are in good agreementwith Raman results.The extracted g-factors and spin-flop fields are shown in Fig.3(d),the g-factors decreasesas raising the temperature.To further understand the temperature depen-dence of the magnon g-factor,we obtain the effectiveg-factor,geff,from the derivative of with respect toH,H,and ignore higher order termsgeff g0(1 2).(3)The temperature dependence of g-factor is solely fromthe anisotropy of magnetic susceptibility,.It orig-inates from the temperature-dependent occupancy ofthe Zeeman-split magnon levels,which modifies themolecular field.According to L.R.Maxwell et al.33,g0is 1.97.The calculated g-factor matches well with thedata,as shown in Fig.3(d).The temperature trend ofthe spin-flop field is shown in Fig.3(d),where Hspinflopincreases as the temperature decreases.We derived thespin-flop field from Eq.2Hspinflop=2HAHE1 .(4)As illustrated in Fig.3(d),the calculation agrees wellwith experiment.D.Polarization-resolved magneto-Ramanspectra of magnonsWefurtherperformedpolarization-resolvedmagneto-Raman spectra of magnons at 120 K withcross-circular configuration,as shown in Fig.4(a).The corresponding peak positions are presented inDong Biao et al.:Low-Frequency Raman Detection of Antiferromagnetic Spin Waves in Cr2O3147Fig.4.(a)Magneto-Raman spectra of Cr2O3with right-circular light excitation and left-circular detection(+)from 0 T to 9 T.(b)Magnon peak positions(black dots)for and mode(fitted with Eq.2),the spin-flop(SF)mode,the quasi-ferromagnetic(QFM)mode,and the flat mode.(c)and(d)Normalized degree of circular polarization(DCP)spectra of Cr2O3at 120 K(c)and 10 K(d),black dash lines denote the cutoff frequency.DCP is defined as(+)/(+).(e)Schematic spin motions of all observed magnon modes.(f)Linewidth of magnons asa function of magnetic fields at 120 K.Fig.4(b).The and mode denote the low andhigh frequency Zeeman-split magnon branches,whilethe solid lines are theoretical values based on Eq.2.According to the Raman selection rules as we discussearlier,the two cross-circular Raman schemes excitemagnons with opposite angular momenta,namely,the148Dong Biao et al.:Low-Frequency Raman Detection of Antiferromagnetic Spin Waves in Cr2O3creation of a magnon with+h(h)angular momentumin the Stokes process is more likely to be observedin+(+)channel.Therefore,the differencebetween the+and+Raman spectra providesinformation of the magnon helicity.Here,we definethe degree of circular polarization(DCP)of Ramanspectra,as(+)/(+),whichreflects the helicity of each magnon branch.As shownin Fig.4(c),the Zeeman-split and modes exhibitopposite magnon helicity as expected.When the magnetic field surpasses the 6 T at 120K,the spin-flop transition happens.Due to a slightmisalignment between the sample c-axis and the field,the spin-flop transition is not a perfect abrupt change,instead,it happens in a narrow magnetic field win-dow34.In this regime,the mode rapidly decreaseswith the magnetic field,which we referred as the spin-flop(SF)mode34.After the spin-flop transition,aso-called flat mode35appears at a finite frequencyof 2.6 cm1(78 GHz),instead of zero frequency inthe ideal case34,also due to the same misalignment.In the same field range,the SF magnon transformsinto the quasi-ferromagnetic(QFM)mode,which corre-sponds to the precession of the net magnetization,andit blue shifts with the field.The helicity of the QFMmode should eventually be the same as the mode,which it is clearly shown by the 10 K