Table Of Content

Magnetic Anisotropy, Spin Pinning and Exchange Constants of (Ga,Mn)As films Ying-Yuan Zhou, Yong-Jin Cho, Zhiguo Ge, Xinyu Liu, Malgorzata Dobrowolska, and Jacek K. Furdyna Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA We present a detailed investigation of exchange-dominated nonpropagating spin-wave modes in 7 a series of 100 nm Ga1−xMnxAs films with Mn concentrations x ranging from 0.02 to 0.08. The angular and Mn concentration dependences of spin wave resonance modes have been studied for 0 both as-grown and annealed samples. Our results indicate that the magnetic anisotropy terms of 0 2 Ga1−xMnxAs depend on the Mn concentration x, but are also strongly affected by sample growth conditions;moreover,themagneticanisotropyofGa1−xMnxAsfilmsisfoundtobeclearlylinkedto n theCurietemperature. Thespinwaveresonancespectraconsistofaseriesofwellresolvedstanding a spin-wavemodes. TheobservedmodepatternsareconsistentwiththePortisvolume-inhomogeneity J model,inwhichaspatiallynonuniformanisotropy fieldacts ontheMnspins. Theanalysisofthese 9 exchange-dominated spin wave modes, including their angular dependences, allows us to establish 2 theexchangestiffness constants for Ga1−xMnxAs films. ] PACSnumbers: i c Keywords: s - l r I. INTRODUCTION ples increased to a range from 55 K to 115 K. Note that t m T followsageneralruleforbothas-grownandannealed C . Incorporating Mn ions into III-V semiconductors samples: it increases with increasing concentration x. t a makes it possible to achieve ferromagnetic order in m semiconductor nanostructures1. It is known that the III. EXPERIMENTAL SETUP - spin waves in a magnetic system are determined by d (and can be used to obtain) the exchange and mag- n neticanisotropyparameters2,3,4,5,6,andarethusparticu- In this study we have measured the angular depen- o larlyusefulforaquantitativeunderstandingofferromag- denceofFMRforeachspecimen(both as-grownandan- c [ netisminGa1−xMnxAs2. Inthispaperweuseferromag- nealed) in three geometries7. FMR measurements were netic resonance (FMR), a powerful tool for investigating carriedoutat9.46GHzusingaBrukerelectronparamag- 1 magneticanisotropyandexchangeconstantsinferromag- netic resonance spectrometer. The applied dc magnetic v netic materials7, to investigate a series of Ga Mn As field H was in the horizontalplane, while the microwave 7 1−x x 1 films with different Mn concentrations x. In all sam- magnetic field was acting vertically on the sample. The 7 ples studied we observe a multi-mode spin wave reso- sample was placed in a suprasil tube inserted in a liq- 1 nance (SWR) spectrum. We will focus on the detailed uidheliumcontinuousflowcryostat,whichcouldachieve 0 description of such SWRs, and the relationship between temperatures down to 4.0 K. 7 these spin wave modes and the Mn concentration x in TheGa1−xMnxAslayerswerecleavedintothreesquare 0 Ga Mn As. pieces with edges along the [110] and [110] directions. / 1−x x t Each square piece was then placed in three different ori- a entations. Geometry1 is whenthe sampleplane andthe m II. SAMPLE FABRICATION [110]edgearevertical,whichallowsmeasurementwithdc d- magnetic field H oriented at any angle between Hk[001] n A series of Ga Mn As films were grown by molecu- (normal orientation) and Hk[110](in plane orientation). 1−x x o Geometry2iswhenthesampleplaneandthe[010]direc- lar beam epitaxy (MBE) on semi-insulating GaAs (001) c tion are vertical, which allows us to measure FMR with substrates. A 100 nm-thick GaAs buffer was first grown v: at the substrate temperature 600◦C to achieve an atom- field orientations between Hk[001] and the in-plane ori- i entation Hk[100]. Geometry 3 is when the sample plane X ically flat surface. The substrates were then cooled to 250◦Cforgrowthofa2nmlowtemperatureGaAsbuffer, is horizontal, allowing us to map out the FMR when H r is confined to the layer plane. a followedby100nmGa Mn AslayerswithvariousMn 1−x x concentrations (x = 0.02, 0.025, 0.04, 0.045, 0.055, 0.06, 0.07 and 0.08). The thickness of (Ga,Mn)As samples IV. RESULTS AND DISCUSSIONS is specifically selected to reliably determine the effect of annealing on SWRs. All as-grown specimens exhibited ferromagneticorder,withCurie temperatureT ranging A. Magnetic Anisotropy C from 50 K to 80 K. Pieces of samples cleaved from each specimen were then annealed in N gas for one hour at Multi-mode SWR spectrum was observed in all sam- 2 280◦Cinordertoexaminetheeffectofannealingonmag- ples. Our analysisofthe data wascarriedoutas follows. netic properties. As a result of annealing T of the sam- Wefirstobtainedthemagneticanisotropiesandg-factors C 2 6 As-grown GaMnAs at 4K x=0.02 5 4 M-H2 x=0.04 4 H4|| nit) u Oe) 3 arb. x=0.06 Magnetic anisotropy field (k 012456 A5n0ne a4Hle54M|d5| -GHa2M60nA s a65t 4K70 (a7)5 of microwave absorption ( (a) x=0.02 xx==00..0067 3 ve x=0.04 2 (b) erivati D 1 x=0.07 0 40 60 80 100 120 140 (b) Curie temper ature Tc (K) 3 4 5 6 7 8 9 10 dc magnetic field (kOe) FIG. 1: The effective anisotropy term 4πM −H2⊥ and the in-plane cubic anisotropy H4k versus the Curie temperature FIG.2: TheSWRspectra at 4K when theexternaldcmag- of (a) as-grown samples, and (b) annealed samples at T = 4 netic field is perpendicular to the film (Hk[001]) for (a) as- K. The solid and dashed lines are guides for theeye. grown samples and (b) annealed samples. by fitting the angular dependence of the strongest resonance line to a theoretical uniform FMR model using a gatethisfeatureindetail,wehavechosenfourspecimens nonlinearleastsquaresmethod8. Ourfittingresultsshow grown at similar conditions, with Mn concentration x = that the magnitude of perpendicular uniaxialanisotropy 0.02,0.04,0.06 and0.07. Figure 2 showsthe SWR spec- H2⊥hastendstoincreasewithMnconcentrationx,while tra at T = 4 K for both as-grown and annealed samples thein-planecubicanisotropyH4kdecreaseswithx. How- when the dc magnetic field H is normal to the sample ever,therelationbetweenthemagneticanisotropyterms plane (Hk[001], i.e., θ = 0◦). In both cases the SWR H and x is strongly influenced by the individual growth spectraconsistofseveralwell-resolvedstandingspinwave condition of each sample. Furthermore, we find that modesseparatedbyroughlyequalfieldincrements. Note the term 4πMeff = 4πM −H2⊥3 is linearly increasing that the SWR fields are increasing with the Mn concen- withtheCurietemperatureT inbothas-grownandan- trationx,exceptinthecaseofoneannealedsamplewith C nealed specimens, and H4k is monotonically decreasing Mn concentration x = 0.07. Importantly, the as-grown with T , with the exception of annealed specimens with sampleshavealargermodeseparationthantheannealed C the highest values of TC. The results are shown in Fig. samples,whichindicatesthat the exchangestiffness con- 1. Since an earlier report9 shows an empirical relation- stant D is larger in the as-grown samples, as discussed ship T ∼ p1/3, we immediately note that there exists a later. C tight relationship between magnetic anisotropy and the As H is rotated away from the perpendicular orienta- holeconcentrationp. However,thedataforas-grownand tion, the low-field spin wave modes gradually disappear, annealed samples follow different slopes as a function of and eventually only one narrow resonance line remains T , suggesting that there exists a fundamental differ- C at a critical angle θ . We will refer to it as the uniform c ences between as-grownand annealed samples regarding mode. For angle θ > θ the spectrum generally con- H c magnetic anisotropy. Nevertheless, the distinct charac- sists of two wide resonance lines. We identify the mode teristics which we observe may provide useful insights lying at the higher field as an exchange-dominated sur- into the origin of magnetic anisotropy in Ga1−xMnxAs face spin wave mode10,11. The angular dependence of films. the SWRs revealsthe nature ofsurface spin pinning and its dependence on the magnetization orientation. Using the Puszkarski surface inhomogeneity (SI) model10, it is B. SWR Spectra found that, as the magnetization rotates from the perpendicular to the in-plane orientation, the surface spins It is the spin pinning at sample surfaces that induces are evolving from a strong pinning condition to a weak spin-waveexcitationintheFMRexperiment. Toinvesti- pinning condition, with a turning point at the critical 3 angleθ 11. NotethatforHk[001]the pinning isnotonly surprising, because T – which usually go hand-in-hand c C strong,butalsononlocalized,i.e.,themagneticspinsap- withthestrengthoftheexchangeinteraction–arehigher peartobe affectedbyaspaciallynonuniform anisotropy in the annealedsamples thanin the as-grownfilms. One field12,suggestedbyalinearmodeseparationatthisori- possibleexplanationisthattheaveragedistancebetween entation. C. Exchange Constants 10 We will now focus on the SWR spectrum obtained for 2 m) 8 Hk[001]. ItisfoundthatthepositionsoftheSWRmodes T n as-grown comply witha linearmode separationmodelforHk[001] (B 6 when a symmetrical parabolic magnetic anisotropy is g assumed along the growth direction z (|z| ≤ L/2): D/ 4 annealed 4πM∗(z) = 4πM∗(0)(1−4εz2/L)13. Here ε is the dis- 2 tortion parameter of the film, L = 100 nm is the film thickness, and 4πM∗(0) = 4πM −H2⊥ −H4⊥. In this 0.00 0.02 0.04 0.06 0.08 situationthepositionofthen-thSWRmodeforHk[001] Mn (x) is given by the Portis relation12: FIG. 3: The exchange stiffness constant D as a function of Mnconcentrationxforas-grownandannealedGaMnAsfilms. 1 D Hn =H0−(n− )(4/L)(4πM∗(0)ε )1/2, (1) The lines are linear fits. 2 gµ B whereµ istheBohrmagneton,nisanoddinteger,and B substitutional Mn ions (which links T to D) is changed H = ω/γ +4πM∗(0) is the position of the theoretical C 0 by the annealing process sufficiently to cause such a re- uniform mode. Here ω is the angular frequency of the sult. Indeed, significant changes in the lattice param- microwavefieldandγ isthegyromagneticratio. Theex- eter of (Ga,Mn)As have been observed experimentally. changestiffnessconstantD,whichgivesameasureofthe However, the exact mechanism of such behavior is not strength of the exchange interaction, can be determined understood and requires further study. from the difference of the adjacent SWR modes by: D ∆Hn21,n2L2 V. SUMMARY AND CONCLUSIONS = . (2) gµ 16(n2−n1)2(4πM∗(0)ε) B In summary, we carried out a detailed experimental Note that the value of 4πM∗(0)ε, the depth of parabolic study of SWRs in thin Ga Mn As films with a wide 1−x x potential well, can be roughly evaluated from the field range of Mn concentrations x. The analysis of the data separation between the highest and the lowest SWR allowedus to establishthe followingimportantmagnetic modes observedfor Hk[001]11. In the special case where properties of these films: magnetic anisotropy, surface only two modes are observed (see Fig. 2, x = 0.07), it spin pinning, and the exchange stiffness constant. The is interesting that ∆H ≈4πM∗(0)ε, so that D can be 1,3 magnetic parameters obtained from this analysis were satisfactorilyestimatedsimplyfromtheseparationofthe studied as function of x and/or T of the specimens. C two modes. We observe a significant change of magnetic properties Using Eq. (2), we can obtain the value of D/gµ for B between as-grown and annealed samples. The results all samples. The data for four optimally-grown samples clearly show that the study of SWRs provides valuable are plotted as function of Mn concentration x in Fig. information about the strong correlation between struc- 3. The figure clearly shows that D is closely related to tural and magnetic properties of these materials. x. In particular, for as-grown samples D decreases very quickly as x increases. On the other hand, although the data for annealed samples suggest that D also decreases Acknowledgment as x increases, the change is much smaller in this case. The most important characteristic shown in Fig. 3 is that D decreases after annealing, especially for low Mn This work was supported by the NSF Grant DMR06- concentration samples. This experimental result is quite 03752. 1 H.Ohno,“Makingnonmagneticsemiconductorsferromag- 2 J. König, T. Jungwirth, and A. H. MacDonald, “Theory netic,” Science, vol. 281, pp.951-956, 1998. 4 of magnetic properties and spin-wave dispersion for ferro- 8 X. Liu, W. L. Lim, L. V. Titova, M. Dobrowolska, J. K. magnetic (Ga,Mn)As,” Phys. Rev. B, vol. 64, pp. 184423, Furdyna, M. Kutrowski, and T. Wojtowicz, “Perpendicu- 2001. larmagnetization reversal, magneticanisotropy,multistep 3 X.Liu,Y.Sasaki,andJ.K.Furdyna,“Ferromagneticres- spin switching, and domain nucleation and expansion in onance in Ga1−xMnxAs: Effects of magnetic anisotropy,” Ga1−xMnxAs films,” J. Appl. Phys., vol. 98, pp. 63904, Phys. Rev. B, vol. 67, pp. 205204, 2003. 2005. 4 T. G. Rappoport, P. Redliski, X. Liu, G. Zaránd, J. K. 9 A. H. MacDonald, P. Schiffer, and N. Samarth, “Ferro- Furdyna,andB.Jankó,“Anomalousbehaviorofspin-wave magnetic semiconductors: moving beyond (Ga,Mn)As,” resonancesinGa1−xMnxAsthinfilms,”Phys. Rev. B,vol. Nature Materials, vol. 4, pp.195-202, 2005. 69, pp.125213, 2004. 10 H. Puszkarski, “Theory of surface states in spin wave res- 5 S.T.B.Goennenwein,T.Graf,T.Wassner,M.S.Brandt, onance,” Prog. Surf. Sci.,vol. 9, pp.191-247, 1979. M. Stutzmann, J. B. Philipp, R. Gross, M. Krieger, K. 11 X. Liu, Y. Y. Zhou, and J. K. Furdyna,“Angular Depen- Zu¨rn, P. Ziemann, A. Koeder, S. Frank, W. Schoch, and denceof Spin WaveResonances and Surface Spin Pinning A.Waag,“Ferromagnetic ResonanceinGa1−xMnxAs,”J. in Ferromagnetic (Ga,Mn)As Films,” Phys. Rev. B, sub- Supercond., vol. 16, pp.75, 2003. mitted. 6 S.T.B.Goennenwein,T.Graf,T.Wassner,M.S.Brandt, 12 A.M.Portis,“Low-lyingspinwavemodesinferromagnetic M. Stutzmann, A. Koeder, S. Frank, W. Schoch and films,” Appl. Phys. Lett., vol. 2, pp.69-71, 1963. A. Waag, “Spin wave resonance in Ga1−xMnxAs,” Appl. 13 Y.Sasaki,X.Liu,T.Wojtowicz,andJ.K.Furdyna,“Spin Phys. Lett., vol. 82, pp.730, 2003. wave resonances in GaMnAs,” J. Supercond., vol. 16, pp. 7 X. Liu and J. K. Furdyna, “Ferromagnetic resonance in 143-145, 2003. Ga1−xMnxAs dilute magnetic semiconductors,” J. Phys.: Condens. Matter, vol. 18, pp.R245–R279, 2006.