FMR linewidth in BaIn1.5Fe10.5O19 single crystal

Journal of Magnetism and Magnetic Materials 86 (1990) 391-396 North-Holland

391

FIVIR L I N E W I D T H I N B a l n L s F e l o . s 0 1 9 S I N G L E C R Y S T A L

W i e s l a w A. K A C Z M A R E K

1

Institute of Physics, A. Mickiewicz Unioersity, 60-780 Poznah, Poland

Received 6 December 1988; in revised form 26 June 1989 Ferromagnetic resonance, FMR, has been observed in a Balnl.sFe]0.5019 ferrite single crystal. The FMR resonance field Hr~ , effective linewidth AHetf, and effective Landau-Lifshitz-Gilbert damping parameter ?terr were obtained at 22.67 GHz for temperatures from 80 to 425 K and for two sample orientations in the applied field, namely perpendicular and parallel to the easy magnetization axis. The FMR parameters reveal anomalous values near the characteristic temperature Tcr ffi 204 K in qualitative agreement with previous measurements of magnetization and magnetocrystal~ine anisotropy constants. The absorption line for all temperatures is Lorentzian and for Tcr extreme exchange narrowing is observed with the correlation time of the dipolar field % ~*1.5 x 10- ]3 s and the exchange constant J / k e z 5 K. The effective linewidth for T < Tcr fits the empirical formula AHetr ffi AHcr(T/Tct) -~,~. Since the present material at low temperatures cain be classified as a random spin system, AH(T) has also been analysed in terms of another empirical form suggestedi previously: A F = F ( T ) - F o F1 exp(- T/To). Agreement was obtained with this model for temperatures up to To = 91 K. The effective parameter ?%it for T~ < T < T¢ is temperature independent and for T < T~r, dependent. k

1. Introduction T h e m o t i v a t i o n o f this s t u d y is to u n d e r s t a n d the p h y s i c a l origin o f the a n o m a l o u s l o w - t e m p e r a ture l i n e w i d t h o f the f e r r o m a g n e t i c r e s o n a n c e o f Balnl.sFelo.5019 m o n o c r y s t a l s . I n d e e d a r e m a r k a b l y different b e h a v i o r is o b s e r v e d for single crystals of p u r e B a - f e r r i t e o n the o n e h a n d a n d for the ferrite s u b s t i t u t e d b y n o n m a g n e t i c m e t a l i o n s M e 3+ o n the other, the l i n e w i d t h d e c r e a s i n g l i n e a r l y with t e m p e r a t u r e [1]. F r o m m a n y investig a t i o n s of d i f f e r e n t M - t y p e h e x a g o n a l ferrites it is well k n o w n t h a t crystal structure is sensitive to the r a d i u s o f the s u b s t i t u t e d ions in Fe-sites, b u t is c r y s t a l l o g r a p h i c a l l y s t a b l e ( P 6 3 / m m c space group). R e l i a b l e p r e p a r a t i o n o f high q u a l i t y m o n o c r y s t a l s is r a t h e r easy. However, o n a c c o u n t o f the a c t u a l e x p e r i m e n t a l c o n d i t i o n s special h e a t t r e a t m e n t m u s t b e used to e l i m i n a t e defects c r e a t e d b o t h d u r i n g free n u c l e a t i o n o f crystals a n d while prei Present address: Research School of Chemistry, The Australian National University, G.P.O. Box 4, Canberra, A.C.T., 2601, Australia.

paring samples undergoing mechanical treatment. T h e general p i c t u r e t h a t e m e r g e s f r o m the e a r l y s t u d y is t h a t in the 0 < x < 0.6 r a n g e o f I n 3+ substitution, m a g n e t i c p r o p e r t i e s like M s - the s a t u r a t i o n m a g n e t i z a t i o n a n d K u - the m a g n e t o crystalline a n i s o t r o p y c o n s t a n t , a r e n o t t o o differe n t f r o m those for Ba~-ferrite w i t h x = 0; the m a t e r i a l is ferrimagnefic b e l o w a w e l l - d e f i n e d C u r i e t e m p e r a t u r e T~. FOr x > 3 the m a g n e t i c syst e m has c a n t e d o r d e r i n g w i t h a m o r e o r less helical configuration. I n a d d i t i o n , the m a g n e t i c p r o p e r t i e s a r e f i e l d - d e p e n d e n t [2]. I n the d i l u t e f e r r i m a g n e t i c regime (0.6 < x < 3) the s i t u a t i o n is n o t so simple. I n the low t e m p e r a t u r e r a n g e the m a g n e t i c o r d e r - d i s o r d e r t r a n s i t i o n t e m p e r a t u r e is o b s e r v e d to increase with I n s u b s t i t u t i o n [3]. T h e c o l l i n e a r N t e l m o d e l [4] c a n n o t b et a p p l i e d in the i n t e r p r e t a t i o n as was p r o p o s e d p r e v i o u s l y [2]. M o r e o v e r , it was suggested t h a t b o t h t r a n s i t i o n t e m p e r a t u r e and low-temperature anomalies of macroscopic m a g n e t i c p r o p e r t i e s m a y b e i n t e r p r e t e d as a result o f spin r e o r i e n t a t i o n a n d the p o s s i b i l i t y o f the a p p e a r a n c e o f these m a g n e t i c a n t i p h a s e helical structures b a s e d o n Mori~ya's rule [5,6]. A s t u d y o f

0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

392

W.A. Kaczmarek / FMR linewidth in Balnl.zFelojOj9

the temperature dependence of the relaxation processes may throw light on these suggestions.

magnetic field H eff consists of anisotropy, quantum-mechanical exchange and dissipation components H int

=

H ~ s + H ex + H I°ss.

(2)

2. Experimental Note that for the effective linewidth technique, relaxation should be described in terms of damping based on the L a n d a u - L i f s h i t z - G i l b e r t equation

2.1. Preparation and method The chemical composition of BalnxFe12_xO19 ferrite with x = 1.5 was chosen for our investigation because it has several advantages. It is in the center of the interesting range of In 3+ ion substitution (0.6 < x < 3), and for which much macroseopic data has already been published [7]. Single crystals of Balnl.5Fe10.5019 were grown by the free nucleation method [8]. The samples to be examined by F M R were subjected to mechanical treatment with the aim of obtaining polished spheres (diameter 0.3-0.4 ram). Thermal treatment was applied to prepare samples without crystal defects and mechanical strain. Finally we obtained magnetically uniform crystals, they were oriented by the Lane method in the (010) plane and [001] direction (perpendicular - (n) and parallel - (p) to easy magnetization axis, respectively). The composition and crystal structure were determined by X-ray diffraction, and the lattice constants measured at room temperature were a - (0.598 + 0.005) n m and c - (2.386 + 0.05) nm. Magnetic measurements were performed by means of a Faraday-type balance, in a magnetic field of 0.75 T, and F M R with a conventional reflection cavity K-band spectrometer 0 ' = 22.67 GHz). The temperature was varied between 77 and 450 K. 2.2. Effective F M R linewidth The basic equation of motion governing the magnetization in a saturated single domain ferrite at the resonance condition, is given in the usual way as a M / a t = ,/( M x H en ),

(1)

where ~, = - g l e I / 2 m e is the gyromagnetic ratio and H en -- H + Hint is an effective magnetic field. The material contribution H int to the effective

dM/dt

= y ( M × H elf )

-(X/rM))[M× (MxH°")],

(3)

where h is the damping parameter. We can define an effective peak-to-peak linewidth ( A H e n - AHpp), in terms of an effective damping parameter ~eff and the constant F M R frequency ~ for T - - T~, and obtain a useful relation ABel f = 2~keff¢d//'y24'ffMs.

(4)

3. Results and discussion Figs. 1 and 2 present the results of the F M R experiment for a wide temperature range, obtained for two orientations of the sample: external magnetic field parallel (p) and perpendicular (n)

10 !

~ = 22.67 GHz ( n ) ~ Hr ~ ~ ' ~

9

o8

/f-

© ~

7

(p)

~

6

Hr ~

5

-

0

100

j

,Tc~ 354K

200

300

400

500

T (K) Fig. 1. FMR resonance field at 22.67 GHz in BaInl.sFelo.5019 a single crystal polished sphere versus temperature at two sample orientations: applied dc field perpendicular - (n) and parallel - (p) to the easy magnetization axis. Horizontal line (Hr) indicates free spin resonance at this frequency.

W.A. Kaczmarek / FAIR linewidth in BalnLsFelo.jOl9

600 500 400 300

lOO o

0

100

200

300

400

T (K) Fig. 2. Temperature dependence of the FMR linewidth in the sample. The temperature Tot here is taken as the temperature at

which the uniaxial state becomeseither stable or unstable.

to the easy magnetization axis. Both figures demonstrate the effect of magnetocrystalline anisotropy, exchange and dissipation due to an effective magnetic field H at, on the resonance field Hr~ and peak-to-peak linewidth AHpp. These effects cause the values of the F M R parameters for BaInl.sFel0.5019 and BaFel2019 polished samples to have different absolute magnitudes and temperature dependences [1]. It is well known that with increasing In 3+ substitution there is a linear decrease in Curie temperature T~, magnetization M and the magnetocrystalline anisotropy fields H K. In this instance at every temperature the observed differences between field values H ~ ) and H ~ ) (fig. 1) are smaller than for Ba-ferrite. As yet the question of the temperature dependence of the F M R parameters in these similar materials is still unanswered. For a qualitative explanation and dividing the experimental data we can distinguish between the low and high temperature portions of figs. 1 and 2. In the high temperature range for T ~ T~ there are increasing thermal fluctuations in the spin system as H int-* 0. This leads to the anticipated behavior near the transition temperature T~ -- (354 + 5) K where the relations Hr~~ -* ~ / y and AHpp -'* oo are satisfied. Only one essential observation from this seems to be important for further discussion, namely the F M - P M transition range becomes extended because persistent

393

short range magnetic order is observed. Thus, for our sample only the average value of T¢ can be obtained. From fig. 1 the transition range is estimated to be from 330 to 450 K. Now we can assume that if the low temperature situation of the spin system is similar, long distance magnetic ordering forces are weak and a short range coupling dominates. On the~ one hand in BaInl.sFel0.5 O19 the main contributions to the "material field" Hint are from blocks i n which ferrimagnetic coupling still exists, as in Ba-ferrite, but on the other hand In 3+ ions present between blocks induce magnetic exchange breaking giving rise to "superparamagnetism". In the high temperature range the magnetic system can be completely polarized by an applied field and w i t h decreasing temperature more and more block moments find the thermal activation insufficient to liberate them from the local anisotropy, so ithat the fraction of block moments locked into their quasirandom orientations increases. In an earlier paper [9], we reported an anomaly in the low temperature magnetization and magnetocrystanine anisotropy as well as the critical spin-reorientation temperature Tcr = (204 + 5) K. In view of the: theory [10] this anomaly can now be referred to as the "canting transition". We will first discuss the case of BaInl.sFe~0.5O19 near the critical temperature Tcr which can help us to understand the more, complex situation occurring in the "canting region". On the basis that what is observed is an exchange narrowed dipolar broadened resonance we make an approximate determination of the r~levant parameters, using the results established for a simple cubic lattice of spinel blocks, and conSidering nearest neighbors only. For all temperattlres the F M R absorption line is Lorentzian with a width at half-height AHI/2 = v~AHpp. For dipolar coupling only, the line would be Gaussian and much broader. An approximate value of the dipolar linewidth A H d can be found by using the result established for a simple cubic lattice [11]: AH d = 2 5~/~]-.1Vfle~S(S + 1)~to3, (ro is the nearest-neighbor distance) in our case r0 = 0.35 nm, between Fe 3+ ions in octa- and tetra-hedral sites, S - 5 g - - 2 to give A H d = 5480 G. When there is an exchange energy -EJ~iSiSj, and the exchange is important such that VHr'r e < 1 for extreme narrow-

394

W.A. Kaczmarek / F M R linewidth in Baln l.sFelo.5019

ing, (¢c is the correlation time of the dipolar field in the presence of exchange) then the line is Lorentzian with a width AHI/2 = a3"t(AHd)2%. At lower frequencies i.e. I, < 35 G H z and for the extreme narrowing line limit the ~ effect applies [12]. Under these conditions and from experimental results we can conclude that in Balnl.sFel0.5019 for a critical temperature T~r ffi 204 K we have extreme exchange narrowing, with ~-~P)= 2.9 × 10-13s and "r~n) ffi 1.5 × 10-13s. In this way from the above two correlation times for both sample orientations we can find approximate values of J,.j for nearest neighbors using the expression % = 0 . 3 h / J ~ S ( S + 1) : J ( P ) / k n ~- 3 K and J ( ~ ) / k n = 5 K. Two different values for the exchange interaction within the spinel block are a key result in the explanation of the anisotropic linewidth observed in the sample. In the sample where exchange coupling is dominant the linewidth is angularly dependent in the whole temperature range in this limit. The larger value of the exchange integral j(n) for the plane perpendicular to the easy magnetization axis testifies to the high "'magnetic cohesion" that parallels the well known crystallographic cohesion f o r Ba-ferrites seen during mechanical treatment. The low-temperature behavior in In-substituted Ba-ferrites cannot be fully described by any of the existing theories [13-17]. The reason is t h a t the existing models refer to

6

0

0

~

,

T~)= 1.3143

300

T cr=204 K

polycrystalline or glassy materials and analyses of ESR linewidths in simple spinel monocrystals have been inconclusive [18-21]. In this situation we now return to the experimental linewidth values and present the data parametrization in phenomenologlcal form. Of all the predictions of phenomenological renormalization for magnetic systems with random tmiaxial anisotropy [22] only the low temperature critical behavior is consistent. From ESR experiments in spin-glass like systems with long-range order for T---, Tcr there is obviously a power-law behavior AH=At

(5)

-'or,

where t = T/Ter - 1 and 7~ - 1.3 [23]. The value of "y is the same as the asymptotic critical susceptibility exponent, which may or may not depend on disorder [24]. For BaInLsFe10.5019 we can achieve a very good fit (fig. 3) with a similar exponential law

AHppffi AH

(T/T

)

,

where the temperature T~ here it is taken as the temperature at which the uniaxial state becomes either stable or unstable. Both AH~ and ,/~ values are different for two sample orientations: AH¢<~) ffi 160 G, AH~n) ffi 80 G, 3,~ ) -- 1.2538 and 3'~r~) -- 1.3143. Our definition of T~ introduced a difference between the last two equations and thus, we have ( T / T ~ ) - L Note that the canted spin configuration starts from T~r with decreasing temperature. On the other hand, since the present material at low temperatures can be classified as a random spin system we have analysed this T dependence in terms of an empirical form suggested earlier [25]:

a r ( x ) = r ( x , T ) - ro(x)

200

= F , ( x ) exp[ - T / T o ( x ) ] .

0

(6)

100

200

301)

T (K) Fig. 3. A fit of experimental values of AHpp to the equation A H ffi A Her( T / Ter) -v~'. The dots are experimental points. The estimated accuracy of the FMR linewidth measurement was

(-b lO~)A/~pp.

(7)

It was tested for a very wide variety of randomized spin systems [21,26,27]. We can rewrite eq. (7) as:

arffi F ( T )

-

ro = r, exp( - T / T o ) ,

(8)

where F ( T ) ffi A Hpp, Fo ffi A He, and F 1 and TO are empirical parameters determined from the data:

W.A. Kaczmarek / FMR linewidth in Baln n.jFeto.zOi9 515 G, 980 G and 91 K, 86 K for the (n) and (p) respectively. We note that the parameter values are dependent on field orientation but the values of To as was shown earfier are roughly the same for both geometries [27]. On fig. 4 we plot the scaled width AF/F~ versus a function of the scaled temperature (T/TO), namely e x p ( - T/TO). As can be expected from the discussed new equation for the pure random spin system all the data ought to straddle the "45 o line". Only in the low temperature range, below To can this be observed for our samples. In this way we show that B a - I n - f e r r i t e can be included with materials, with random spin system in temperatures up to To. The advantages of this fitting procedure is not only in the estimation of temperature To (the value of which is similar to the temperature where a characteristic bend is observed on the saturation magnetization curve), but we can also obtain the quantitative difference in linewidth for the situation when a randomized spin system will be fully developed. On fig. 5 we show the temperature dependence of 8(AF) which is a measure of the disagreement between data from the present experiment and that expected for the " r a n d o m model", directly obtained from fig. 4. Clearly, within the limits of error of the experiment we can note that values of 8(AF) are twice as high for (13) orientation as for (n). A uniaxial magnetocrystalline anisotropy field

0.5 =

(p)

/

0.4'~ 0.30.2 0.1 o.o 0.0

0.1

0.2

0.3

0.4

0.5

exp(-T/To) Fig. 4. The "scaled" plot used to test the validity of eq. (8). Points representdata for both sample orientations,obtained by using F1 and To values: 515 G, 980 G and 91 K, 86 K for (n) and (p) respectively.

395

300"

0

~f"

0

=

(p)

•

(n)

/ /.'/

/

*

f

m

i

m

.

"

i

•

100

•

i

200

T (K) Fig. 5. Temperature dependence of 8(AF), a measure of the disagreement between the present experimental data and that expected for the "random" model - eq. (7), (shown on fig. 4 as "45 o line").

H K in the c direction can explain the occurrence of non-zero values of 8i(AF) and its higher value in the easy direction. The O(AF) temperature dependence follows a similar course as was found for magnetocrystalline anisotropy constants K I ( T ) or K2(T ) [28]. With inoreasing temperature up to 125 K the ~(AF) ( T ) is a simple linear function and for higher temperatures after crossing a maximum near T = 150 K iboth ~(AF) and K1 are observed to decrease. Both the above attempts to describe the F M R linewidth in B a - I n - f e i r i t e have negative attributes: a clear singularity for T - * 0 in the first procedure and the intrOduction of two additional fitting parameters /'1 and TO in the second, and both equations cannot be expected to apply over the entire regime of temperatures. On the basis of eq. (4) from the experimental data we can obtain the values of the damping parameter h. Results are presented in fig. 6. Values of ~, ( M s, A H, T ) dependence calculated ~or different temperatures ought to be shown in a 3-D figure but here we only make a general point and therefore in fig. 6 put the projection of A(T) on the 4~rMs-AH plane. In the high temperature range the value of ~, is temperature indepefMent and eq. (4) is fulfilled with ~,¢n)~. 120 MI-Iz and X
W.A. Kaczmarek / FMR linewidth in Baln L.sFelo.~Ol9

396 3000

/ 150

100 ~ m

has been partly supported by the fund of the Polish Academy of Sciences CPBP 01 04 II 1.13.

~

~

References !so . \

~

•

~

x(p)

300 35O 4OO

0

200

400

600

800

z3~-Ipp (G) Fig. 6. Projection of the FMR damping parameters X on the 4~rM,-AH plane obtained in the specimen for different temperatures. The solid lines are a solution of eq. (4), (see text)• For temperatures T - , T~, ?~becomes temperature independent.

agreement between A H (p) and A H (n). At low temperatures )~ is temperature dependent and increases like AH. For T = 77 K values of X(") ~- 850 MHz and X(P)~-1500 MHz respectively are obtained. From this we can see that the damping parameters (~,(P) in particular) are very sensitive to the stability of the magnetic system in In-substituted Ba-ferrites. The main causes for the T-dependent region of ~, are the progressive disappearance of the long range linear spin arrangement and the development of a random magnetic system with decreasing temperature. Finally we conclude that it is not surprising that the F M R results for BaInt.sFe10.5019 confirm the "canting transition" which was observed earlier for substituted Ba-ferrites. However, in the absence of a satisfactory theoretical description, the fits presented above may describe the results e q u a l l y well in the reported temperature range. Moreover one must still find a consistent interpretation of the low-temperature resonance data which integrates these spin-spin interaction terms with all other temperature-dependent mechanisms which give rise to linewidth in unstable ferrimagnetic phases. Acknowledgements Numerous useful discussions with Professor J. Pietrzak are greatfully acknowledged. This work

[1] L.M. Siiber, E. Tsantes and W.D. Wilber, J. Magn. Magn. Mat. 54 (1986) 1141. [2] T.M. Perekalina, M.A. Vinnik, R.J. Zavercva and A.P. Schurova, Zh. Eksp. Teor. Fiz. 59 (1970) 1490, in Russian. [3] Sh.Sh. Bashkirov, A.B. Liberman and V.I. Sinyavskii, Zh. Eksp. Teor. Fiz. 69 (1975) 1841, in Russian. [4] L. Nrel, Ann. Phys. (Paris) 3 (1948) 137. [5] L.I. Koroleva and L.P. Mitina, Phys. Slit. Sol. (a)5 (1971) K55. [6] T. Moriya, Phys. Rev. 120 (1960) 91. [7] H. Kojima, in: Ferromagnetic Materials, vol. 3, exl. E.P. Wohlfarth (North-Holland, Amsterdam, 1982). [8] R.O. Savage and A. Taubcr, J. Aaner. Ceram. Soc. 47 (1964) 13. [9] W.A. Kaczmarek and J. Pietrzak, Phys. Silt. Sol. (a)98 (1986) K43. [10] P.A. Beck, Phys. Rev. B32 (1985) 7255. [11] P.W. Anderson and P.R. Weiss, Rev. Mod. Phys. 25 (1953) 269. [12] P.M. Levy and R. Raghavan, J. Magn. Magn. Mat. 54 (1986) 181. [13] Y. Yafet and C. Kittel, Phys. Rev. 87 (1952) 290. [14] A. Kaplan, Phys. Rev. 116 (1959) 888; 119 (1960) 1460. [15] E.B. Boltich, A.T. Pedziwiatr and W.E. Wallace, J. Magn. Magn. Mat. 66 (1987) 317. [16] P.W. Anderson, in: Amorphous Magnetism II, exls. ILA. Levy and R. Hasegawa (Plenum Press, New York, 1977). [17] A.T. Ogielski, Phys. Rev. B32 (1985) 7384. [18] P. Monod, A. Landi, C. Blanchard, A. Devi.lle and H. Hurdequint, J. Magn. Magn. Mat. 59 (1986) 132. [19] C. Vittoria and C.M. Williams, J. Magn. Magn. Mat. 54 (1986) 1193. [20] C. Blanchard, A. Deville, A. Boukenter, B. Champagnon and E. Dural, J. de Phys. 47 (1986) 1931. [21] S.M. Bhagat, D.J. Webb and M.A. Manheimer, J. Magn. Magn. Mat. 53 (1985) 209. [22] M. F'gdmle, J. Magn. Magn. Mat. 65 (1987) 1. [23] P.M. Levy and C.G. Morgan-Pond, Phys. Rev. B30 (1984) 2358. [24] W.U. Kellner, T. Albrecht, M. F~lhnle and H. Kronmilller, J. Magn. Magn. Mat. 62 (1986) 169. [25] S.M. Bhagat, M.L. Spano and J.N. Lloyd, Solid State Commun. 38 (1981) 261. [26] S.M. Bhagat and H.A. Sayadian, J. Magn. Magn. Mat. 61 (1986) 151. [27] M.J. Park, S.M. Bhagat, M.A. Manheimer and K. Moorjani, J. Magn. Magn. Mat. 59 (1986) 287. [28] W.A. Kaczmarek and J. pletrzak, Acli Phys. Pol. A73 (1988) 379.