Low temperature magnetic excitations in amorphous light rare-earth—transition-metal thin films

Journal of Magnetism and Magneuc Materials 92 (1991) 353-358 North-Holland

353

Low temperature magnetic excitations in amorphous light rare-earth-transition-metal thin films * P e n g Chu-Bing, Dai D a o - S h e n g , F a n g Rei-Yi a n d Liu Z u n - X i a o Department of Physics, Peking UmverstO, Be~jmg, P.R. China Received 16 March 1990; in revised form 11 June 1990

The temperature dependence of magnettzatlon has been studt,~d on amorphous R - T (R = Ce, Pr, Nd. T = Fe. Co, NO thin films. It was found that both spin wave exc~tauons and b a n d exc~tauons exist for most R - F e samples m temperature range T0 - 2 0 0 K, and a marked devmuon from Bloch T 3/2 is noted at T < To in all R - T samples. Tt) is the temperature belov, which the T 3/2 law is unsmtable to describe the temperature dependence of the magneuzauon. To ranges from 10 to 100 K. The deviauon is accounted for the magnetic structure transit~c,a a n d can be explained by Kaneyoshrs theory

1. Introduction We found that the temperature dependence of magnetization for amorphous S m - T (T = Fe, Co. Ni) samples deviated from the Bloch T 3 '2 law at low temperature ( T < T~), and can be explained by both the Bloch T 3/2 and Stoner T 2 law in the temperature range T0-200 K [1,2]. Similarly, the deviation from the T ~,'2 law has also been noted in re-entry spin glass alloys at T < Tf (freezing temperature) [3]. Korenblit et al. [4] pointed out that spin wave excitations at long wavelengths are suppressed completely in the amorphous rare-earth alloys with asperomagnetic states, and spin wave excitations at all wavelengths do not exist in the amorphous rare-earth alloys with speromagnettc state. According to the local crystal field model suggested by Harris et al. [5] and the characteristics of nonlinear magnetic structure for amorphous rare earth alloys, Kaneyoshi [6] made a thorough discussion on the dispersion relationship of magnetic excitations, aod found that spin wave excitations do not exist it, alloys w~th strong random local amsotropy. In order to establish the effect of the magnetic structure phase transitton on mag-

* Supported by Nattonal Science Foundatton.

netic excitations, we investigated the temperature dependence of magnetization for amorphous R - T thin films (R = Ce. Pr. Nd: T = Fe. Co. Ni).

2. Preparation~ of samples and measurements The amorphous R - T thin films ~ere prepared by a vacuum evaporation method [2]. The composition of the samples is tabulated in table 1. Since the Curie temperature T~ of the samples rapidly decreases with the increase of rare earth composition, T~ is very low when x > 0.5: therefore, we only studied the magnetic excitations of samples with composition x < 0.5. By using an extracting magnetometer [2]. we measured both the temperature dependence of magnetization o(T, H ) in the temperature range 1.5-200 K at dtf~'erent external magnetic fields and the ~'-'~llc,uucp~,,acm.~~~-~ . . . . . . .v,~ .,l,~,,.,,.,,~,v,,:~': ....... . . . . .,,, '~',,,, m~gnel~c field range 0-7 T at different temperature~. By extrapolation from the high-field linear part of the magnetization curve to H = 0 Oe at aifferent temperatures we obtained the temperature dependence of spontaneous magnetization oo(T). We found that the characteristics of magnetic excita-

0364-8853/91/$03 50 'L 1991 - Elsevier Sctence Publisher,, B V. (North-Holland)

C -B. Peng et al. / Amorphous rare.earth-transmon-metal thin films

354

Table 1 The composmon of amorphous R,T l _ , thin films (the numbers gwen are the x values) R~ Fe 1_,

R~Col

-

R.,Nh

~

_,

Ce

Pr

Nd

Ce

Pr

Nd

Ce

Pr

Nd

0.12 0.28 0.53

0.08 0.34 0.42

0.04 0.14 0.24 0.35 0.44

0.09 0.26 0.34

0.06 0.13 0.32 0.41

0.07 0.17 0.24 0.32

0.07 0.14 0.20

0.11 0.17 0.19 0.26

0.10 0.16 0.19 0.21 0.30

tions are similar between oo(T) and o(T, H), and thus the o(T, H) can reflect the characteristics of magnetic excitations [2]. Therefore, we can study the characteristics of magnetic excitations by using o(7", H).

Ao-/~

°t

J.o

3. Results For most magnets, the temperature dependence of magnetization o ( T ) in low temperature can be described [6] by o(T)

T/

- aT 3/~-

=%(1

b T 5/2 . . . .

< 0.5.

),

(1)

In the external magnetic field, eq. (1) can be expressed as

o(T, H ) = o o [ 1 - a ( H ) T -b(H)T

s/2 . . . .

].

(2)

Ao/% = % - o(T, H ) = B1T3/2 oo (3)

( B i o c h ' s T 3/2 l a w ) ,

where the T 5/~" term is neglected, B~ is dependent on the exchange interaction constant and the structure of the samples. For some itinerant magnets, Stoner excitations may exist, o(7", H) ceq be written as o,,=

o(T, H) oo

TNt/~41 700

I,~oo

2.100

~ Soo

F~g. 1. Aa/ao as a functmn of T 3/" 0 © © Pra3aFeo66, ~ 1 ~ Ceo s,Feo ss experimental data. - fitted result H = 7 T The fitted curve A o / % = BIT ~/2, for Pro~4Feo6t,, no = 98.85 e m u / g , b 1 = 7 . 0 2 × 1 0 --5 K - ~ - ' , for CeouFeo~, K, oo=119.59 emu/g, B I = 7 3 7 × 1 0 -_s K-~/z.

3/2

Eq. (2) can be expressed as

~o/oo

0~

= B , T 2,

(4)

where Bz is related to Fermi energy. The experimental data were fitted by both eq.

Table 2 To and the temperature range m which etther Bloch T a/: or Stoner T 2 xs suitable to describe the characteristics of magnetic excitations in R - T (R = Ce, Pr, Nd; T = Fe, Co, Ni) samples a~ Sample

To(K)

T 3/2 statable (K}

T 2 statable (K)

Ceo 12Feu ss Ceo 2sF% 72 Ceo 5sFeo47 Pro 34Feo 66 Ndo o,~Feo,~6 Ndo 14Feu ~6 N d , :4Fe. v~ Nd o 35Fco65 Ndo a4Feo 5¢, Smo 17Feo s~ Smo 24F% 7t,

10 70 70 70 70 96 70 100 100 10 20

10-200 70-200 70-200 70-200 70-200 96-200 70-170 100-200 100-200 10-200 20-180

no 100-200 100-200 no no no 70-200 100-190 no 42-200 70-200

a) For Ceoo,~Cooy I, Ndo 17Coo s.a, Pro l~Nq)sl, Ndo loNio 9o, To ts not defined because the magnehzatlon o(T, H ) for these samples cannot be well fitted by rather eq. (3) or eq. (4).

C.-B. Peng et al / Amorphous rare-earth-transttton-metal thin .hires

~r/~

355

q8 k

I

I® % *

o05"

03 o

-~0.$ :

7;0

*'70

z~t}i

0

t~,o

zo#oo

.~.~

- [rl"(}J,~tf~ao " ~ ° -*(#)

Fig. 2. h o / o o as a function of T 312, T 2 for C%28Feo72, respectively. The full line represents the fitted result, the dots are experimental data ( o e e T 3/2, © 0 © T2). H = 7 T, % = 94.13 emu/g. The fitted curve A a / o o = B t T 3" 2 A o / o ° = B2T ~, respectively, where B I = 1.99 x 10- s K - 3/2 B2 = 1.26 x 10- 6 K -2.

(3) and eq. (4). Some of the results are summarized in figs. 1 to 7 and table 2. 3.1. A m o r p h o u s R - F e

( R = Ce, Pr, N d ) thin f d m s

'$ 0

- ~0

dependence

of mag-

n e t i z a t i o n o(T, H) can be well fitted by eq. (3) (figs. 1 to 3); moreover, in some R - F e samples, o(T, H) can also be fitted well by eq. (4) (see figs.

"0

:ZOO~IT¢~-)

F~g. 4. The temperature dependence of magnetization for Ceo 2sFeo 7 2 . 0 0 0 experimental data, - fitted results. The fitted curve o(T, H ) = 00(1 - B1T 3' 2 _ B:,T:L where % = 94.09 emu/g, B I = 1.85 x 10 -s K -3~ .., B,, = 9.48 x 10 -s K - :

2 and 3). This shows that spin wave excitations exist in R - F e samples, and that both spin wave excitations and Stoner excitations exist in some R - F e alloys (see fig. 4). On the contrary, at T < To, the experimental data cannot be explained by either eq. (3) or eq. (4), and the marked devmuon f r o m t h e B l o c h T 3/'- l a w o c c u r s . I n f a c t . a t T < To. the experimental

A t T > T o, t h e t e m p e r a t u r e

, O

data

also cannot

be descrtbed

by

e q . (2). I n fig. 4, t h e m a g n e t i z a t t o n rapidly

with

decreasing

0(7", H )

temperature

increases at

T<

T..

a tO

o, t2

• ee

o08

"t

O./2

.~oo8

o o~

- O.Oq-

o@

o

@0@ #l@ 0

OO

..J

ol

Cr, "TO0

i.e¢,O0

i

*

t oaoo

~oooo

~o0 m

aoooo

~o0

% (

I Ta (I~a) 4~0ooo

F*g. 3. A o / o o as a functton of T 3/2. T 2 for Nd0:.~F~v+. respecuvely. The dots represent ( N O T 3/2, + + + T : ) experimental data. ~ fitted result. H = 7 T % = 85.69 e m u / g . The fitted curve ,.~o/oo = B1T 3/" , where B t = 5.03 × 10 - s K - 3 / 2 : ,..Xo/% = B , J 2. where B: = 3.38)<10 6 K - : .

O0

0

~

IOOOO

aOooo

m

3o000

R

~o00

T a tic~)

Fig 5. A o / o o a,,, a functton of T ~ : T: for Ce, u~Cq~t. respecmel~ ~ fitted result. ~ 7"; " © © © 7--"experimental data. H = 7 T. oo = 105 85 e m u / g . The fitted cur~e ~ o / % = b l T3 2. where B t = 2 2 9 x 1 0 ~ K - ~ z. _Xo:oa= B, T Z , ~ h e r e B + = i 4 3 × l O K -z

C.-B. Peng et al. / Amorphous rare-earth-transmon-metal thin f i l m s

356

3.3. Amorphous R-Ni (R = Ce, Pr, Nd) thin fihns Similar to R - C o samples, the temperature dependence of magnetization o(T, H) for R - N i samples cannot be fitted well by either eq. (3) or eq. (4) (see fig. 7). Spin wave excitations may not exist in the temperature 1.5-200 K in R - N i samples (R = Ce, Pr, Nd).

~,~-

ee

0

2 _a*.~ ,*"

-o./0 0

700

t#oo

z/o0

a,.$oo

Fig. 6. 8a/o0 as a function o f T 3/2 for N d 0 ivCoos3. - fitted value, N O e x p e r i m e n t a l data. H = 7 T, oo = 88.20 e m u / g , b I = 3.25 × 10- 5 K - ,a/2

4. Discussions

4.1. Hamiitonian of the R-Fe system

and another magnetic phase may take place [7,8,10].

The Fe d-electron magnetic moment is well-defined and localized in Fe alloys. The Hamiltonian describing [5] the R - F e system can be written as

3.2. Amorphous R-Co (R = Ce, Pr, Nd) thin films

H = H t + H12 + H2,

None of o(T, H) for all R - C o alloys can be described with either the Bloch T 3/2 or the Stoner T 2 law in the temperature range 1.5-200 K (see figs. 5 and 6). Even though some of o(7", H) for C e - C o samples can be fairly, fitted with eq. (3), there is a large difference between the experimental data and the fitted values (see fig. 5).

o z~

- 010

EJIL JlJ2

H12 =

(5)

-- EJI24"4,, M t

H2

=

- Y'~J2i('~ 11'1"2

_

Y'l)

^"

I"

where J, J ' are site indices for Fe and R sites, respectively. Hi(H2) gives the Hamiltonian of the Fe(R) subnetwork, - DY:~,,~2, represents the local random anisotropy energy of the R subnetwork. H:2 represents the d - f exchange interaction, J~2 > 0. The magnetization o(T) at each temperature per R - F e unit can be given by

o,~;0

0

"1 = -

O o

o ( v ) = (1 - x ) < £ > + x<£'>,

0

(6)

-a20 ....

0

!

n

|

7"00

1~oo

~1oo

,~-3DO

II

700

t#o0

21o0

~-~oo

~

]

Fig 7 A a / o o as a function of T ~/2 for P r o l g N % s t, Nd.i,Nh~ fitted result, ~ Pro l q N h j s l , O O © N d , IoNiogo experimental d a t a H = 7 T. 3"he fitted curve A o / o . = B1T ~"'", for Pr ol~Nh~sl, o~3 =13.8 e m u / g , B 1 = 7 . 3 2 × t0 s K- L'2, for N d o m N t o , , ~ t. 0 o = 3 4 7 e m u / g , B I = I 6 4 x 10-s K-~/2

where x is alloy R , T I completely. coupling by

the composition of rare earth R for ,. It is complicated to solve eq. (5) For simplicity, we dissociate the d - f using MFA. H12 becomes

/

j

(7)

C.-B Peng et al. / Amorphous rare-earth-transmon.metal thin fibns

357

and eq. (5) becomes H = Hni + H22,

H,, = - , - x < g ' > J , , E L ,

(8)

J

O J

Hi1(/422 ) can be regarded as an Fe(R) subnetwork Hamiltonian in an "external field" exerted by the R(Fe) subnetwork. It is well known that the dispersion relationship of spin wave excitations described by H~ (see eq. (8)) can be expressed as ~o= Dlq z

T
(9)

where q is the wave vector, and D t is correlated with the Fe subnetwork structure, exchange constant J~ and the "'external field" exerted by the R subnetwork. On the R subnetwork, the spin wave excitations are suppressed by the scattering of local random anisotropy. As we suggested in ref. [2], the anisotropy rapidly decreases with increasing temperature, this behavior is characterized by T~. Below T0, the amsotropy is large, the magnetic structure is nonlinear [6] on the R subnetwork, and the spin wave is retarded; above T0, the anisotropy is small, the spin wave excitations may exist. On the other hand, To reflects the effects of magnetic structure transitions [7,8,10] on spin wave excitations. For instance, at T < 20 K, both asperomagnetic structure and speromagnetic structure [7,8] coexist on the amorphous N d - T (T = Fe, Co, Ni) thin films; at T = 20 K, the transition from speromagnetic to paramagnetic s~ructure occurs. Above To, the effect of the magnetic structure phase transition on magnetic excitations almost disappears, spin wave excitations exist; below To, the effect exists, and the deviation from Bloch T 3/: takes place. Since the anisotropy decreases more rapidly with increasing temperature in Ce, S m - F e samples than in Pr, N d - F e samples, TO is lower for Ce, S m - F e alloys than To for Pr, N d - F e alloys (see table 2).

0

t#.~O

TOO

ztoO

,zSO0

Fig. 8...%o/0o as a functmn of T 3 2 for C%2~Fel)72 experimentaldata, ~ fitted result usnngeq. (11 ).

Using Kaneyoshi's theory [9], the magnetic excitations described by H2_, (see eq. (8)) can be expressed as oa2 = ~ao + / 3 1 k 2 + irk 7~2

T<< To

~2 = D z k 4 + i v , k 9

T > To,

(10)

wher~ %, ill, D , , v and r ' are correlated with the anisotropy strength D , exchange constant J~2 and "'external field" exerted by the Fe subnetwork. Although the spin wave (see eq. (9)) can propagate on the Fe subnetwork, nt is scattered and dccayed by the local random amsotropy of the R subnetwork. Based on these constderauons, the magneuc excitations which follow from eq. (5) can be characterized by = ¢o= D ' k

+/3-'k-" "

T << To T>

(11)

To.

The experimental data can be well fitted b~ eq. (11) for the R - F e system. The result for Ceo2sFe0v2 is shown m f:g. 8.

( R = Ce. Pr. N d ) atto"s

The Ni d-electron is ~tinerant, its magnetic moment is small• thus, the magnetic moment of R - N i alloys is dominated b5 that of R: moreover, the exchange constant J l z is much smaller than the local random aniotropy D in the R - N i alloxs. Therefore. the Ni magnetic moment m R,N~I ,

358

C-B. Peng et al / Amorphous rare-earth-transmon-metal thin films

alloy because the reversion of ion spm dose not increase anisotropy energy. t"/

5. Conclusions

ta 05 a~ O

•

$0

a

too

R

t~O

T

(I~,)

Fig, 9 The temperature depcqdcnce of magn,-tlzatton for Sin. t ~Ni. H7 in temperature range 1 5-150 K. ee~l) exper,mental data, ~ fitted re,,ult. The fitted curve oCT, It) = n,(I - n i t I ~ ' - a ~ T t), where Oo~18.4 emu/g, a 1 = ! . 7 0 7 × 1 0 2 K ~ : , a : = 4 . 7 1 × 1 0 a K I, H = 4 T .

disappears at x -- 20-25% [11] and the Curie temperature T~ for R - N i alloys is low. Furthermore, the temperature dependence of magnetizatr, on ¢)( F, t l ) for R - N i (R = Ce, Pr, Nd) alloys cannot cxt)lained by the Bloch T a : law in the temperaturc range 1.5- 200 K. 4 3. M a g n c t t c e ~ c t t a t , m s m R - C o ( R = ('e, t't: Nd) allm'~

The characteristics of magnetic excitations below 1~) in R - C o alleys is similar to that in R - F e alloys, Ho~,cvcr, it is difficuh to account for the charactcristics of magnetic excitations at T > T() in R - C o alloys. This phenomenon deserves further research. It is interesting that the temperature dependence of magnetization 0(7", H ) for amorphous Sn'l() i~ Ni,,)s7 thin films in the ternperature range 1.5 150 K c,',m be well illustrated by (see fig. 9). o(l', t t ) : Thl,, m a V

o()(I-,:17 "l ' - a , T t ). be due

(12)

t o the e x i s t e n c e o f ' , t n g l c - l o n

excitations al vcr~,' l o w )empcrature in Sm(, !aNl()s7

(a) The characteristics of magnetic excitations in amorphous R - T (R = Ce, Pr, Nd; T = Fe, Co, Nil were discussed. Below T~., the deviation from the Bloch T 3/2 is noted for all R-T alloys; above T(), the spin wave excitations exist in R - F e samples, but do not exist in R-Co, Ni samples. This phenomenon is illustrated by the magnetic structure transition and Kaneyoshi's theory. (b) T() reflects the influence of the magneti,. structure transitions on spin wave excitations at low temperature.

Reicrences [11 I)m Dao-Shcng. Fang ReI-Yu Lm Zun-X,ao and Wan I[ong, Acta Phys. Sm~ca 35 11986) 1502; ann ~ee Chinese Phys. 7 (1987) 918 (m Engl.sh). 121 Feng (ht. B,ng, Dal Dao-Sheng, Fang ReI-YI and Llu Zun-Xlao, J Magn Magn Mat. 79 (1989) 11 13] S M Bhagat, M L Spano, It S. ('hen and K V Ran. Sohd ,";late ('ommun 33 (1981)) 303 141 I.Y Korenbht and E.F. Shender, J. Phys. F 9 (1979) 2245. 151 R.H. Harris, M. Phschke and M.J. Zuckermann, Phys. Rcv. Lett. 31 (1973) 160 161 T. Kaneyosh,, Plenary talk on. Intern. Symp. on Magnettsm at,d AmoJphous Materials, Bdlatonszeplak, l l~,ngary (October 1985) 171 Dal Dao-Sheng, Fang ReI-YI, Lut Zun-Xlao, Wan Hong, Lan Jmn and J, Yu-Pmg, Acta Phys. Smtca 35 (1986) 475. 181 Fang REI-Yt. Dal Dao-Sheng. Ltu Zun-Xmo, Wan Hong and JI Yu-Pmg, J Magn Magn. Mat 58 (1986) 273 I91 T. Kaneyoshl, ! Magn Magn Mat 18 (1980)1343, J. Plays I- 9 (1979) L37. 110] l)ao-sheng Dal, Rul-yl Fang. L.~-ta: Tong, Zun-x:ao Lu:, Zcng-jun Zhao and Zhao-hua Lm, J Appl Phys 57 (1985) 1589 Ill] R Arrc,,c-boggtano, J. Chappcrt, J M I) ('no), A. Ltcnard and J.P Reboudlat, ,I de Phy,, 37 (1976) C6-771.