Perpendicular magnetic anisotropy in insulating ferrimagnetic gadolinium iron garnet thin films
H. Maier-Flaig, S. Geprägs, Z. Qiu, E. Saitoh, R. Gross, M. Weiler, H. Huebl, S. T. B. Goennenwein
PPerpendicular magnetic anisotropy in insulating ferrimagnetic gadolinium iron garnetthin films
H. Maier-Flaig,
1, 2
S. Gepr¨ags, Z. Qiu,
3, 4
E. Saitoh,
3, 4, 5, 6, 7
R. Gross,
1, 2, 8
M. Weiler,
1, 2
H. Huebl,
1, 2, 8 and S. T. B. Goennenwein
1, 2, 8, 9, 10 Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching, Germany Physik-Department, Technische Universit¨at M¨unchen, Garching, Germany WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan Spin Quantum Rectification Project, ERATO, Japan Science and Technology Agency, Sendai, Japan Institute for Materials Research, Tohoku University, Sendai, Japan PRESTO, Japan Science and Technology Agency, Saitama, Japan Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Japan Nanosystems Initiative Munich, M¨unchen, Germany Institut f¨ur Festk¨oper- und Materialphysik, Technische Universit¨at Dresden, Dresden, Germany Center for Transport and Devices of Emergent Materials, Technische Universit¨at Dresden, 01062 Dresden (Dated: June 27, 2017)We present experimental control of the magnetic anisotropy in a gadolinium iron garnet (GdIG)thin film from in-plane to perpendicular anisotropy by simply changing the sample temperature.The magnetic hysteresis loops obtained by SQUID magnetometry measurements unambiguouslyreveal a change of the magnetically easy axis from out-of-plane to in-plane depending on the sam-ple temperature. Additionally, we confirm these findings by the use of temperature dependentbroadband ferromagnetic resonance spectroscopy (FMR). In order to determine the effective mag-netization, we utilize the intrinsic advantage of FMR spectroscopy which allows to determine themagnetic anisotropy independent of the paramagnetic substrate, while magnetometry determinesthe combined magnetic moment from film and substrate. This enables us to quantitatively evalu-ate the anisotropy and the smooth transition from in-plane to perpendicular magnetic anisotropy.Furthermore, we derive the temperature dependent g -factor and the Gilbert damping of the GdIGthin film. Controlling the magnetization direction of magneticsystems without the need to switch an external staticmagnetic field is a challenge that has seen tremendousprogress in the past years. It is of considerable interestfor applications as it is a key prerequisite to store infor-mation in magnetic media in a fast, reliable and energyefficient way. Two notable approaches to achieve this inthin magnetic films are switching the magnetization byshort laser pulses[1, 2] and switching the magnetizationvia spin orbit torques[3–5]. For both methods, materialswith an easy magnetic anisotropy axis oriented perpen-dicular to the film plane are of particular interest. Whileall-optical switching requires a magnetization componentperpendicular to the film plane in order to transfer angu-lar momentum[2], spin orbit torque switching with per-pendicularly polarized materials allows fast and reliableoperation at low current densities[3]. Therefore great ef-forts have been undertaken to achieve magnetic thin filmswith perpendicular magnetic anisotropy.[6] However, re-search has mainly been focused on conducting ferromag-nets that are subject to eddy current losses and thus of-ten feature large magnetization damping. Magnetic gar-nets are a class of highly tailorable magnetic insulatorsthat have been under investigation and in use in appli-cations for the past six decades.[7–9] The deposition ofgarnet thin films using sputtering, pulsed laser depositionor liquid phase epitaxy, and their properties are very wellunderstood. In particular, doping the parent compound(yttrium iron garnet, YIG) with rare earth elements is a powerful means to tune the static and dynamic magneticproperties of these materials.[7, 10, 11]Here, we study the magnetic properties of a gadolin-ium iron garnet thin film sample using broadband fer-romagnetic resonance (FMR) and SQUID magnetome-try. By changing the temperature, we achieve a transi-tion from the typical in-plane magnetic anisotropy (IPA),dominated by the magnetic shape anisotropy, to a per-pendicular magnetic anisotropy (PMA) at about 190 K.We furthermore report the magnetodynamic propertiesof GdIG confirming and extending previous results.[7]
I. MATERIAL AND SAMPLE DETAILS
We investigate a 2 . µ m thick gadolinium iron gar-net (Gd Fe O , GdIG) film grown by liquid phase epi-taxy (LPE) on a (111)-oriented gadolinium gallium gar-net substrate (GGG). The sample is identical to theone used in Ref. 12 and is described there in detail.GdIG is a compensating ferrimagnet composed of twoeffective magnetic sublattices: The magnetic sublatticeof the Gd ions and an effective sublattice of the twostrongly antiferromagnetically coupled Fe sublattices.The magnetization of the coupled Fe sublattices shows aweak temperature dependence below room temperatureand decreases from approximately 190 kA m − at 5 K to140 kA m − at 300 K.[8] The Gd sublattice magnetizationfollows a Brillouin-like function and decreases drastically a r X i v : . [ c ond - m a t . m t r l - s c i ] J un from approximately 800 kA m − at 5 K to 120 kA m − at300 K.[8] As the Gd and the net Fe sublattice magneti-zations are aligned anti-parallel, the remanent magneti-zations cancel each other at the so-called compensationtemperature T comp = 285 K of the material.[13] Hence,the remanent net magnetization M of GdIG vanishes at T comp .The typical magnetic anisotropies in thin garnet filmsare the shape anisotropy and the cubic magnetocrys-talline anisotropy, but also growth induced anisotropiesand magnetoelastic effects due to epitaxial strain havebeen reported in literature.[14, 15] We find that our ex-perimental data can be understood by taking into ac-count only shape anisotropy and an additional anisotropyfield perpendicular to the film plane. A full determina-tion of the anisotropy contributions is in principle pos-sible with FMR. Angle dependent FMR measurements(not shown) indicate an anisotropy of cubic symmetrywith the easy axis along the crystal [111] direction inagreement with literature.[16] The measurements sug-gest that the origin of the additional anisotropy fieldperpendicular to the film plane is the cubic magnetocrys-talline anisotropy. However, the low signal amplitude andthe large FMR linewidth towards T comp in combinationwith a small misalignment of the sample, render a com-plete, temperature dependent anisotropy analysis impos-sible. In the following, we therefore focus only on shapeanisotropy and the additional out-of-plane anisotropyfield. II. SQUID MAGNETOMETRY
SQUID magnetometry measures the projection of themagnetic moment of a sample on the applied magneticfield direction. For thin magnetic films, however, thebackground signal from the comparatively thick sub-strate can be on the order of or even exceed the magneticmoment m of the thin film and hereby impede the quan-titative determination of m . Our 2 . µ m thick GdIG filmis grown on a 500 µ m thick GGG substrate warranting acareful subtraction of the paramagnetic background sig-nal of the substrate. In our experiments, H is appliedperpendicular to the film plane and thus, the projectionof the net magnetization M = m /V to the out-of-planeaxis is recorded as M ⊥ . Fig. 1 shows M ⊥ of the GdIG filmas function of the externally applied magnetic field H .In the investigated small region of H , the magnetizationof the paramagnetic substrate can be approximated bya linear background that has been subtracted from thedata. The two magnetic hysteresis loops shown in Fig. 1are typical for low temperatures ( T (cid:46)
170 K) and fortemperatures close to T comp . The hysteresis loops unam-biguously evidence hard and easy axis behavior, respec-tively. Towards low temperatures ( T = 170 K, Fig. 1 (a))the net magnetization M = | M | increases and hence, theanisotropy energy associated with the demagnetizationfield H shape = − M ⊥ [17] dominates and forces the mag- − − −
50 0 50 100 150 µ H (mT) -40-2002040 M ⊥ ( k A / m ) a
170 K (1) (2) (3) MH z −100 mT 10 mT z − − −
50 0 50 100 150 µ H (mT) -4-2024 M ⊥ ( k A / m ) b
250 K (2) (3)10 mT z − H C + H C −100 mT H M z (1)
FIG. 1. Out-of-plane magnetization component M ⊥ mea-sured by SQUID magnetometry. For different temperatures,magnetically hard (170K, (a)) and easy (250K, (b)) axis loopsare observed. The arrows on the data indicate the sweep di-rection of H . The insets schematically show the magnetiza-tion direction M and H = H z with the film normal z atthe indicated values of H . netization to stay in-plane. At these low temperatures,the anisotropy field perpendicular to the film plane, H k ,caused by the additional anisotropy contribution has aconstant, comparatively small magnitude. We thereforeobserve a hard axis loop in the out-of-plane direction:Upon increasing H from −
150 mT to +150 mT, M con-tinuously rotates from the out-of-plane (oop) direction tothe in-plane (ip) direction and back to the oop directionagain. The same continuous rotation happens for the op-posite sweep direction of H with very little hysteresis.For temperatures close to T comp ( T = 250 K, Fig. 1 (b)), H shape becomes negligible due to the decreasing M while H k increases as shown below. Hence, the out-of-plane di-rection becomes the magnetically easy axis and, in turn,an easy-axis hysteresis loop is observed: After applyinga large negative H [(1) in Fig. 1 (a)] M and H arefirst parallel. Sweeping to a positive H , M first staysparallel to the film normal and thus M ⊥ remains con-stant [(2) in Fig. 1 (a)] until it suddenly flips to beingaligned anti-parallel to the film normal at H > + H c [(3) in Fig. 1 (a)]. These loops clearly demonstrate thatthe nature of the anisotropy changes from IPA to PMAon varying temperature. µ H (T) ω r e s / π ( G H z ) a µ H (T) − ∆ S ×
110 K0.3 0.4 0.5 µ H (T) − ∆ S ×
240 K T (K) − µ H i ( T ) b H ani = − M eff H shape = − M ⊥ H k = M ⊥ − M eff IPA PMA
Re ImRe Im
FIG. 2. Broadband FMR spectroscopy data reveiling a smooth transition from in-plane to perpendicular anisotropy. (a)
FMR resonance frequency plotted against H taken for three different temperatures (symbols) and fit to Eq. (3) (solid lines).For an IPA, a positive effective magnetization M eff (positive x -axis intercept) is extracted, whereas M eff is negative for a PMA. (inset) Exemplary resonance spectra (symbols) at 14 . ω res (solid lines). A complex offset S has been subtracted for visual clarity, plotted is ∆ S = S − S . (b) Anisotropy field H ani = − M eff as a function of temperature (open squares). Prediction for shape anisotropy H shape based onSQUID magnetometry data (solid line) from Ref. 18. The additional perpendicular anisotropy field H k = M ⊥ − M eff (red dots)increases to approximately 0 .
18 T at 250 K where its value is essentially identical to H ani due to the vanishing M ⊥ . III. BROADBAND FERROMAGNETICRESONANCE
In order to quantify the transition from in-plane to per-pendicular anisotropy found in the SQUID magnetome-try data, broadband FMR is performed as a function oftemperature with the external magnetic field H appliedalong the film normal.[19] For this, H is swept whilethe complex microwave transmission S of a coplanarwaveguide loaded with the sample is recorded at vari-ous fixed frequencies between 10 GHz and 25 GHz. Weperform fits of S to[20] S ( H ) | ω = − i Zχ ( H ) + A + B · H (1)with the complex parameters A and B accounting for alinear field-dependent background signal of S , the com-plex FMR amplitude Z , and the Polder susceptibility[21,22] χ ( H ) = M eff ( H − M eff )( H − M eff ) − H + i ∆ H ( H − M eff ) . (2)Here, γ is the gyromagnetic ratio, H eff = ω/ ( γµ ), and ω is the microwave frequency and the effective magneti-zation M eff = H res − ω res / ( γµ ). From the fit, the res-onance field H res and the full width at half-maximum(FWHM) linewidth ∆ H is extracted. Exemplary datafor S (data points) and the fits to Eq. (1) (solid lines)at two distinct temperatures are shown in the two in-sets of Fig. 2 (a). We obtain excellent agreement of thefits and the data. The insets furthermore show that thesignal amplitude is significantly smaller for T = 240 Kthan for 110 K. This is expected as the signal amplitudeis proportional to the net magnetization M of the sam-ple which decreases considerably with increasing temper-ature (cf. Fig. 2 (b)). At the same time, the linewidth drastically increases as discussed in the following section.These two aspects prevent a reliable analysis of the FMRsignal in the temperature region 250 K < T <
300 K (i.e.around the compensation temperature). Therefore we donot report data in this temperature region. Nevertheless,FMR is ideally suited to investigate the magnetic prop-erties of the GdIG film selectively, i.e. independent ofthe substrate, for temperatures below T comp .As all measurements are performed in the high fieldlimit of FMR, the dispersions shown in Fig. 2 (a) arelinear and we can use the Kittel equation ω res = γµ ( H res − M eff ) (3)to extract γ and M eff . It is customary to describe themagnetic anisotropy using M eff which can be related toan anisotropy field H ani along + z as M eff = − H ani = M ⊥ − H k for positive H . Here, H ani is given by thedemagnetization field H shape = − M ⊥ (along − z ) andthe anisotropy field H k of the additional perpendicularanisotropy (along + z ). Evidently, M eff can be deter-mined by linearly extrapolating the data to ω res = 0.The FMR dispersion and the fit to Eq. (3) (solid lines) areshown for three selected temperatures in Fig. 2 (a). At110 K (blue curve) M eff is positive. Therefore, M > H k indicating that shape anisotropy dominates, and the filmplane is a magnetically easy plane while the oop directionis a magnetically hard axis. At 240 K (red curve) M eff isnegative and hence, the oop direction is a magnetically easy axis. Figure 2 (b) shows the extracted M eff ( T ).At 190 K, M eff changes sign. Above this tempera-ture (marked in red), the oop axis is magnetically easy(PMA) and below this temperature (marked in blue),the oop axis is magnetically hard (IPA). The knowledgeof M ⊥ ( T ) obtained from SQUID measurements allowsto separate the additional anisotropy field H k from M eff g a10 − − − α b0 50 100 150 200 250 T (K) ∆ ω / π ( M H z ) c FIG. 3. Key parameters characterizing the magnetiza-tion dynamics of GdIG as a function of T : (a) g -factor g = γ (cid:126) /µ B , (b) Gilbert damping constant α and (c) inhomo-geneous linewidth ∆ ω / (2 π ) (red dots in Fig. 2 (b)). H k = M ⊥ − M eff increasesconsiderably for temperatures close to T comp while atthe same time the contribution of the shape anisotropy, H shape = − M ⊥ trends to zero. For T (cid:39)
180 K, H k ex-ceeds H shape which is indicated by the sign change of M eff . Above this temperature, we thus observe PMA. Weuse the magnetization M determined using SQUID mag-netometry from Ref. 18 normalized to the here recorded M eff at 10 K in order to quantify H k . The maximal value µ H k = 0 .
18 T is obtained at 250 K which is the highestmeasured temperature due to the decreasing signal-to-noise ratio towards T comp .We can furthermore extract the g -factor and damp-ing parameters from FMR. The evolution of the g -factor g = γ (cid:126) µ B with temperature is shown in Fig. 3 (a). We ob-serve a substantial decrease of g towards T comp . This isconsistent with reports in literature for bulk GIG and canbe explained considering that the g -factors of Gd and Feions are slightly different such that the angular momen-tum compensation temperature is larger than the mag-netization compensation temperature.[23] The linewidth∆ ω = γ ∆ H can be separated into a inhomogeneous con-tribution ∆ ω = ∆ ω ( H = 0) and a damping contribu-tion varying linear with frequency with the slope α :∆ ω = 2 α · ω res + ∆ ω . (4)Close to T comp = 285 K, the dominant contribution tothe linewidth is ∆ ω which increases by more than anorder of magnitude from 390 MHz at 10 K to 6350 MHzat 250 K [Fig. 3 (c)]. This temperature dependence of thelinewidth has been described theoretically by Clogstonet al.[24, 25] in terms of a dipole narrowing of the in- homogeneous broadening and was reported experimen-tally before[7, 16]. As opposed to these single frequencyexperiments, our broadband experiments allow to sepa-rate inhomogeneous and intrinsic damping contributionsto the linewidth. We find that in addition to the in-homogeneous broadening of the line, also the Gilbert-like (linearly frequency dependent) contribution to thelinewidth changes significantly: Upon approaching T comp [Fig. 3 (b)], the Gilbert damping parameter α increasesby an order of magnitude. Note, however, that due tothe large linewidth and the small magnetic moment ofthe film, the determination of α has a relatively largeuncertainty.[26] A more reliable determination of thetemperature evolution of α using a single crystal GdIGsample that gives access to the intrinsic bulk dampingparameters remains an important task. IV. CONCLUSIONS
We investigate the temperature evolution of the mag-netic anisotropy of a GdIG thin film using SQUID mag-netometry as well as broadband ferromagnetic resonancespectroscopy. At temperatures far away from the com-pensation temperature T comp , the SQUID magnetome-try reveals hard axis hysteresis loops in the out-of-planedirection due to shape anisotropy dominating the mag-netic configuration. In contrast, at temperatures close tothe compensation point, we observe easy axis hysteresisloops. Broadband ferromagnetic resonance spectroscopyreveals a sign change of the effective magnetization (themagnetic anisotropy field) which is in line with the mag-netometry measurements and allows a quantitative anal-ysis of the anisotropy fields. We explain the qualitativeanisotropy modifications as a function of temperature bythe fact that the magnetic shape anisotropy contribu-tion is reduced considerably close to T comp due to the re-duced net magnetization, while the additional perpendic-ular anisotropy field increases considerably. We concludethat by changing the temperature the nature of the mag-netic anisotropy can be changed from an in-plane mag-netic anisotropy to a perpendicular magnetic anisotropy.This perpendicular anisotropy close to T comp in combi-nation with the small magnetization of the material mayenable optical switching experiments in insulating fer-romagnetic garnet materials. Furthermore, we analyzethe temperature dependence of the FMR linewidth andthe g -factor of the GdIG thin film where we find valuescompatible with bulk GdIG[7, 25]. The linewidth canbe separated into a Gilbert-like and an inhomogeneouscontribution. We show that in addition to the previouslyreported increase of the inhomogeneous broadening, alsothe Gilbert-like damping increases significantly when ap-proaching T comp V. ACKNOWLEDGMENTS
We gratefully acknowledge funding via the priority pro-gram Spin Caloric Transport (spinCAT), (Projects GO944/4 and GR 1132/18), the priority program SPP 1601 (HU 1896/2-1) and the collaborative research center SFB631 of the Deutsche Forschungsgemeinschaft.
VI. BIBLIOGRAPHY [1] C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk,A. Tsukamoto, A. Itoh, and T. Rasing, Physical ReviewLetters , 1 (2007).[2] C.-H. Lambert, S. Mangin, B. S. D. C. S. Varaprasad,Y. K. Takahashi, M. Hehn, M. Cinchetti, G. Malinowski,K. Hono, Y. Fainman, M. Aeschlimann, and E. E. Fuller-ton, Science , 1337 (2014).[3] K. Garello, C. O. Avci, I. M. Miron, M. Baumgartner,A. Ghosh, S. Auffret, O. Boulle, G. Gaudin, and P. Gam-bardella, Applied Physics Letters , 212402 (2014).[4] I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten,M. V. Costache, S. Auffret, S. Bandiera, B. Rodmacq,A. Schuhl, and P. Gambardella, Nature , 189 (2011).[5] A. Brataas, A. D. Kent, and H. Ohno, Nature Materials , 372 (2012).[6] S. Ikeda, K. Miura, H. Yamamoto, K. Mizunuma, H. D.Gan, M. Endo, S. Kanai, J. Hayakawa, F. Matsukura,and H. Ohno, Nature Materials , 721 (2010).[7] B. Calhoun, J. Overmeyer, and W. Smith, Physical Re-view (1957).[8] G. F. Dionne, Journal of Applied Physics , 2142(1971).[9] J. D. Adam, L. E. Davis, G. F. Dionne, E. F. Schloemann,and S. N. Stitzer, IEEE Transactions on Microwave The-ory and Techniques , 721 (2002).[10] K. P. Belov, L. A. Malevskaya, and V. I. Sokoldv, SovietPhysics JETP , 1074 (1961).[11] P. R¨oschmann and W. Tolksdorf, Materials ResearchBulletin , 449 (1983).[12] H. Maier-Flaig, M. Harder, S. Klingler, Z. Qiu, E. Saitoh,M. Weiler, S. Gepr¨ags, R. Gross, S. T. B. Goennen-wein, and H. Huebl, Applied Physics Letters , 132401(2017).[13] G. F. Dionne, Magnetic Oxides (Springer US, Boston,MA, 2009).[14] S. A. Manuilov, S. I. Khartsev, and A. M. Grishin, Jour-nal of Applied Physics , 123917 (2009).[15] S. A. Manuilov and A. M. Grishin, Journal of AppliedPhysics , 013902 (2010).[16] G. P. Rodrigue, H. Meyer, and R. V. Jones, Journal ofApplied Physics , S376 (1960).[17] We use the demagnetization factors of a infinite thin film: N x , y , z = (0 , , , 10452 (2016).[19] The alignment of the sample is confirmed at low temper-atures by performing rotations of the magnetic field di-rection at fixed magnetic field magnitude while recordingthe frequency of resonance ω res . As the shape anisotropy dominates at low temperatures, ω res goes through aneasy-to-identify minimum when the sample is alignedoop.[20] H. Maier-Flaig, S. T. B. Goennenwein, R. Ohshima,M. Shiraishi, R. Gross, H. Huebl, and M. Weiler, arXivpreprint arXiv:1705.05694 .[21] J. M. Shaw, H. T. Nembach, and T. J. Silva, PhysicalReview B , 054416 (2013).[22] H. T. Nembach, T. J. Silva, J. M. Shaw, M. L. Schneider,M. J. Carey, S. Maat, and J. R. Childress, PhysicalReview B , 054424 (2011).[23] R. K. Wangsness, American Journal of Physics , 60(1956).[24] A. M. Clogston, Journal of Applied Physics , 334(1958).[25] S. Geschwind and A. M. Clogston, Physical Review ,49 (1957).[26] For the given signal-to-noise ratio and the largelinewidth, α and ∆ ω are correlated to a non-negligible degree with a correlation coefficient of C (intercept , slope) = − ..