amorphous magnets and magnetic metallopolymers

AMORPHOUS MAGNETS AND MAGNETIC METALLOPOLYMERS

G. A. Petrakovskii, S. S. Aplesnin, and V. P. Piskorskii

UDC 538.1:539.213

Introduction ................................................ , .................. i. Stochastic Magnetic Systems with Competing Exchange Interactions ........... 2. Magnetic Properties of Metallopolymers ..................................... Conclusion ...................................................... . .............. Literature Cited ...............................................................

842 842 852 861 862

INTRODUCTION

Among the many important problems within the general topic of the magnetism of magnetically disordered systems, the problem of establishing the magnetic ground state is of enor- mous importance [i, 2]. In the present work, first of all, the results of investigating magnets inwhich magneticorder is established in conditions with the competitionof stochastically mixed ferromagnetic and antiferrimagnetic exchange interactions are presented. The thermodynamic characteristics of such systems will also be subjected to definite scrutiny. Second, the results of investigating the magnetic properties of new magnetic materials --metallopolymers -- are presented. Investigations of these materials are still only in the initial stages. However, it may be expected that they will be developed, in view of the technological convenience of obtaining these materials and the potential multiplicity of their properties.

i. STOCHASTIC MAGNETIC sYSTEMS WITH COMPETING EXCHANGE INTERACTIONS

The physical properties of a material in a thermodynamic equilibrium state under specified external conditions are determined by its chemical composition. However, the atomic system may be frozen into a nonequilibrium state, as in amorphous materials, and then the description of physical properties of the system requires not only knowledge of the chemical composition but also specification of the structure of the material. Only the magnetic properties of atomically disordered systems are of interest here~ and therefore the atomic structure and the external conditions will be assumed to be specified.

The question of the atomic structure of an amorphous material is undoubtedly of the greatest importance. However, it will be assumed here that the problem of describing and finding this structure falls outside the framework of the present discussion. In addition, lattice models of disordered materials will be primarily considered.

Thus, the first topic to which attention will be turned is the interesting and difficult problem of finding the basic state and determining the thermodynamic characteristics of lattice magnetic systems with competing exchange interactions [3]. Disorder of the spin orien- tation of such systems at crystal-lattice points is due to the presence of competing (in sign and magnitude) exchange interactions. The magnetic properties of such magnets are often described by the Heisenberg Hamiltonian

H = -- X I I~S fS~ , (1) ],m

where Ifm are exchange parameters; f, m are the crystal-lattice points; S~ is the spin operator at point f. As usual, consideration is limited to the case when Ifm ~e0 only for the nearest neighbors (NN), of which there are z.

L. V. Kirenskii Institute of Physics, Siberian Branch, Academy of Sciences of the USSR. Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. i0, pp. 46-68, October, 1984.

842 0038-5697/84/2710-0842508.50 �9 1985 Plenum Publishing Corporation

TABLE i. Comparative Characteristics of Crystalline (CR) and Amorphous (AM) Magnets

I Type of magnetic Temperature of Compo ~ order magnetic phase Source sition 1 trarmition

GR AN GR AN

FeF2 AFM FM 78 2'I Litterst [6] FeCI2 AFM FM 24 2t " [6] Bi~Fe409 AFM FM 2,65 620 [7] GdAt2 FM SG 170 16 ?dizoguchi, Kirkpairik [8] GdCu~ AFM FM 41 76 " [8] I(FeS: AFM SG 250 80 [9]

I n t h i s s i t u a t i o n , t h e f l u c t u a t i o n s o f I j m may be d e s c r i b e d e i t h e r i n t h e m o d e l o f r a n - dom l a t t i c e p o i n t s o r i n t h e mode l o f r andom b o n d s . I n t h e f i r s t , t h e b i n d a r y a l l o y AxB~-x i n w h i c h s p i n s SA and S B a r e r a n d o m l y s p r e a d o v e r l a t t i c e p o i n t s w i t h c o n c e n t r a t i o n s x and (1 -- x ) , r e s p e c t i v e l y , i s c o n s i d e r e d . The e x c h a n g e p a r a m e t e r I j m may e v i d e n t l y t a k e t h e three values IAA , IBB , IAB differing in magnitude and sign [4].

In the model of random bonds, the spin at each lattice point is fixed (i.e., identical atoms are considered), while the exchange interactions Ifm fluctuate in magnitude and sign. This situation may arise, for example, when there ms a superexchange interaction through various anions. In the simplest case, the exchange parameter Ifm may take two values J and K [5]. This simplest case of the random-bond model will be considered here.

Before proceeding to the analysis of the given model, some relevant experimental results are considered.

It has now been experimentally established that amorphization of magnetically ordered crystals may be associated with a shift in the type of magnetic order and to a sharp change, in particular, an increase in the temperature of magnetic phase transition~ Table 1 gives examples of such results. It is noteworthy that, in many cases, the sharp change in magnetic state occurs in the amorphization of small-scale magnetics, for which a strong dependence of the magnetic structure on the geometry of the exchange-bond distribution is characteristic. Theoretical description of such magnets requires the introduction of at least two different exchange parameters. The type of magnetic order and the temperature of the magnetic phase transition in quasi-small-scale magnets is determined by the weak exchange bind- ing the magnetic chains or layers. At the same time, such characteristics of amorphized material are determined preferentially by some averaged exchange.

Consider, for example, the behavior of some physical properties of the crystalline laminar antiferromagnet Bi2Fe~09 with amorphization [7, i0]. The Bi=Fe~09 crystal is characterized by an orthorhombic strucSure (spatialostructure group D~h) with elementary-cell parameters a = 7.950 2, b = 8.428 A, c = 6.005 A. In magnetic respects, the Bi2Fe~O9 crystal is a linear collinear antiferromagnet with a Ne~l temperature TN = 265~ The Fe 3+ ions in the BifFed09 crystal are distributed equally between tetrahedral and octahedral positions.

The crystal is reduced to the amorphous state by rapid quenching of the melt from 1300~ at a rate of ~i0 ~ deg/sec~ This is confirmed by the data of x-ray analysis and the pattern from differential thermal analysis (DTA). In Fig. i, thermograms of crystalline (I) and amorphous (2) Bi2Fe~09 are shown. The DTA data indicate that the state fixed by quenching is significantly nonequilibrium in thermodynamic terms, and is characterized by considerable heat liberation. The exothermal crystallization process of amorphous Bi2Fe409 occurs at 9200K. The data of optical measurements (IR spectra in the range 1600-400 cm -:, T = 3000K) [I0] show that, in amorphous BifFed09, there is significant rearrangement in the local surroundings of the iron atoms~ In Fig. 2, the dynamics of the variation in the IR spectra in the transition from the amorphous state to the crystal is shown: i) initial glass and heat treatment at 670, 770, 870~ 2) glass after heat treatment at 9200K; 3) heat treatment at 970~ 4) polycrystalline Bi2Fe409. The rearrangement, i~ particular, is expressed in the disappearance of tetrahedral coordinational cations Fe 3 �9 The set of data here presented permits the conclusion that the material obtained by rapid quenching of Bi2Fe~09 melt is amorphous.

843

.7

Fig. I

0

0

~00 d'O0 I~00' v. cm "~ Fig. 2

*- amorph. ~i,~,,0, x- after HT at ~0r

Fig. 3

Measurements show [7] that the initial antiferromagnetic Bi2Fe~09 crystal undergoes a sharp change in magnetic properties on amorphization. The most significant features of this change are: increase in the temperature of magnetic phase transition from 265 to 620~ and the appearance of spontaneous magnetization. In Fig. 3, the temperature dependence of the magnetization is shown for glass (0), a polycrystal (�9 and glass after annealing at 970 ~ (X). Measurements of the paramagnetic susceptibility (Fig. 4) show that the magnetic properties of amorphous Bi2Fe~09 are formed by the Fe ~+ ions. The magnetic structure of amorphous Bi2Fe40, when T < T N is characteristic of ferrimagnetics according to the results of measuring the temperature dependence of the magnetic susceptibility and the magnetization in strong magnetic fields at 4.2~ (Fig. 5). Thus, the example of Bi2Fe409 shows that the transition from a Heisenberg crystalline magnet to an amorphous state may fundamentally change its magnetic properties.

844

•o[ amorph, a;~Ic~ /

"---~ab H * 4 kOr :l

Fig. 4

~2

amorph. 6~mFe409

T: ~,~ K 6., =~4 G. cmSlg

i i I i i !

Fig. 5

Fig. 6

The given experimental data (Table i, Figs. 1-5) show, in particular, the importance of considering the magnetic state of a system with stochastically mixed ferro- and antiferromagnetic exchange interactions. A similar problem arises in studying crystalline solid solutions, for example, Co(Sz-xSex) a [ii, 12] and spin glasses. This problem is also of independent interest from the viewpoint of the general theoryof disordered systems [2].

The simplest formulation of this problem is as follows: to find the basic state, the spectrum of elementary excitations, and the basic magnetic characteristics of the magnetic system described by the Hamiltonian in Eq. (i) for spin S = 1/2 in the random-bond model with the distribution function of the exchange parameters Ifm in the form

(bm) = v8 (b~--K) + (l--v) 8 (b~--D, (2) where ~ is the concentration of negative (antiferromagnetic) K bonds; v = NK/Nbo; N K is the number of K bonds; Nbo = zN/2 is the total number of bonds; N is the number of lattice

points.

a) Ground State. The given problem does not have a rigorous analytical solution. Therefore, at the current stage of development of the theory, the only reliable method of solution is numerical analysis by the Monte Carlo method [2, 13, 14]. In this analysis, it is assumed that the most significant features of the ground state of the system described by the Hamiltonian in Eq. (i) with the distribution function in Eq. (2) and S = 1/2 is de-

scribed by the Ising component of Eq. (i)

845

.;2))) Fig. 7

0,5

FM

o%:L �9 "L:5

h,, 0,0~ 0,15:

q

-.... \

0 0 0~0/'/ 0,08

Fig. 8

H0 -- 1 ^ A 4 E ,mo, o., (3) f,m

^

where of = 2S~. mizing the energy.

1 1 I.t" 0 = ~ 11m~% T = - 7 E

of = • Th i s s p i n c o n f i g u r a t i o n c o r r e s p o n d s to t h e mean moment a t t h e p o i n t ( r e l a t i v e m a g n e t i z a t i o n o f t h e s y s t e m )

The spin configuration corresponding to the ground state is found by mini-

(4)

N

f In Eq. (4), the local field at the point f is introduced

(5)

~! = ~ I / ~ m . (6) IlZ

It is clear that the direction of the spin is uniquely associated with the sign of the local field af = sign(ef). Some results obtained by minimizing the energy in Eq. (4) by the Monte Carlo method in a simple cubic lattice (z = 6) i0 • i0 • i0 with periodic boundary conditions are given below. Details of the calculation procedure using the Monte Carlo method are given in [13-15].

In Fig. 6, the diagram of state in the plane (v, %) is shown, where % = K/J. Depending on the relation between the parameters v, k (at fixed z), the system may be in three states at T = 0: a disordered ferromagnet (FM), a spin glass (SG), and a disordered antiferromagnet (AF). These states are defined by the relations

846

l) FN: { < o ~ > } ,=/= 0, R = ; im{<o j , ~/+~>}-~- 0;

2) s~: { < o : > } = 0, R ---- 0, { < 0 : > 2} =/= 0; (7 )

3) AF: { < O f > } = O, R =7 ~= 0, {<Of~> ~} =/= 0.

Here < , . . > denotes the thermodynamic mean and { , . . } the configurational mean.

Two lines on this phase diagram have been given sufficient attention in the literature: = 0, in connection with the problem of diamagnetic dilution of magnets, % = --I, in connec-

tion with the problem of spin glass. The present results are in sufficiently good agreement with reliably established critical concentrations of existence of FM and AF states ~c FM and AF FM AF FM AF

Vc for these cases: Vc (X = 0) = 0.72; Vc (~ = 0) = 0.93; Vc (~ = --i) = 0.26; v c (~ = FM AF

--i) = 0.74; v c (~ = --20) = 0.072; v c (~ = --20) = 0.28. As an illustration, the sublattice magnetizations oi 2 and correlation functions for r = 1 and r = 4 are shown as a function of v in Fig. 7 fo~ various X~ together with the behavior of IR as a function of r for the AF region.

The interesting case of large negative x(I~ I > z) is considered in more detail. In Fig. 8, the correlation functions and mean magnetic moment Do in the region of FM existence are shown for X = --20. The critical point v~ M (X = -- 20) = 0.072 • 0.004. Monte Carlo calculations are performed in a "sample" of dimensions 12 x 12 x 12.

As shown below, in order to construct the theory of disordered spin systems it is important to know the distribution function P of the local molecular fields ef in Eq. (6). Such functions are shown in Fig. 9 for X = -- 20 with v = 0.052 (a), 0.072 (b), 0.15 (c), 0.25 (d), and 0.28 (e). In an ideal FM, P(e/J) takes the form of a delta function: P(E/J) = 6(r -- z); in an AF, P(e/K) = ~/zg(e/K-- z) + ~/2~(s + z). In the region of disordered FM, there is an asymmetric distribution of the local molecular fields. The asymmetry vanishes close to Vc ME = 0.072 and in SG phase the function P(e/K) is symmetric. Note that P(e/K) remains symmetric in the AF phase. However, if the function P(g/K) is divided into two parts, corresponding to the two sublattices of an ideal antiferromagnet re-

i [P~ (s) + P= (s)], then P~(s)=P~(--a), ~P:2(~)signsd~@O in the AF alized with ~ = 1 -- P(~) =~

state and P,(~)~2(~). ~PL2(~)sJgnsde= 0in the SF state. Thus, in the case of disordered FM, the distribution function P(E) resembles the distribution function of local molecular fields of a FM. Values of ~(0, ~) for different % < 0 are shown in Fig. i0.

At present, there scarcely exists an analytical theory capable of describing all the principal characteristics of the ground state of the given model. Various modifications of the molecular-field approximation represent the most advanced limited theories. Intensive investigations of this type were performed in [4, 16, 17]. In particular, the results obtained here for the critical concentration of FM--SG phase transition v[M for various % are

a

o ds

.-~0

b , c

0

o dO -~

Fig. 9

847

0,5

o;e,

Fig. i0

in good agreement with the results of [16, 17]. Without lingering over the details of such calculations of phase diagrams of states, attention is directed simply to [18], in which critical concentrations ~c FM, ~AF are found for large negative X on the basis of cluster analysis. The result

AF 2 l 1>z (8a) FM 2 d z -~l+dld-D, ~c - - - - z

depends on the coordination number z and the dimensionality of the lattice d. For d = 3, z = 6, it follows from Eq. (8a) that 9c FM = 0.068, 9c AF = 1/3, which is in fair agreement with

FM AF the values 9c = 0.072, 9c = 0.28 obtained by the Monte Carlo method [14]. For small X, the exchange J and K bonds change roles, so that

-FM 2 -AF v= ~ I - - - - , vc =I'~c,[kI<z -' (8b)

z

Th i s symmetry i s a l s o c o n f i r m e d by n u m e r i c a l c a l c u l a t i o n s .

b) Thermodynamic C h a r a c t e r i s t i c s , E l e m e n t a r y Magne t i c E x c i t a t i o n s . A s e r i e s o f t h e o - r e t i c a l me thods e x i s t s f o r d e t e r m i n i n g the. t he rmodynamic c h a r a c t e r i s t i c s o f s t o c h a s t i c mag- n e t s i f t h e g round s t a t e o f t h e m a t e r i a l a t T = 0~ i s known. The s i m p l e s t such a n a l y t i c a l method i s t h e m o l e c u l a r - f i e l d a p p r o x i m a t i o n . I n a number o f c a s e s , t h i s a p p r o x i m a t i o n g i v e s q u a l i t a t i v e l y c o r r e c t r e s u l t s . As an i l l u s t r a t i o n , c o n s i d e r t h e r e s u l t s o f c a l c u l a t i n g t h e temperatures of magnetic phase transition for three initial ground states::[16]

FM.: Tr = Z [ ( 1 - - ~ ) I " - b ~ K ] S ( S . + I ) / 3 k B ;

AF: T~ = - - z [ ( 1 - - v ) l - . I - v K ] S ( S - [ - 1 ) / 3 k B ; (9)

SG : T: - - {z[ ( l - - v ) / 2 q - vK~]}t~S (S- -[ -1) /3k B �9

The initial paramagnetic susceptibility of magnets with competing exchanges J and K, according to [16], obeys the Curie--Weiss law with a paramagnetic Curie temperature

O~ = z[ ( l - - v ) / + v K ] S ( S - l - - ) / 3 k B ,

which c h a n g e s s i g n when ~* = J / ( J -- K) .

With a more thorough analysis of the molecular-field method, as is well known, a series of serious deficiencies appear: for example, the low-temperature behavior of the thermodynamic characteristics, the insensitivity of the results of the theory to the geometry of the "magnetic" lattice, the incorrect (in the general case) prediction of the temperature behavior of the paramagnetic susceptibility of amorphous magnets. For example, a typical experimental result for the temperature dependence of the susceptibility X for an amorphous Fe4oNi~oP,~B~ shows significant deviation from the Curie--Weiss law [19]. This deviation may be explained within the framework of molecular-field theory, as shown in [20], on introducing a spatially correlated molecular field. The results of such calculations of x(T) [20] are shown in Fig. Ii for different values of the exchange dispersion A. The present Monte Carlo calculations show that the temperature dependence of the paramagnetic susceptibility may be complex in character. For example, in Fig. 12, the results of calculating the susceptibility for Co(S,_xSex) solid solutions are shown, together with experimental data (inset) [12]. In these cases, cluster models of the molecular field give more adequate results.

848

=l

4

0

i z~,O. /

/ . o,,4,

/ l / l e e /l~////~az

i

do

>, [o

0

Fig. ii

~ �9

s s 7Zr

Fig. 12

The fundamental basis for constructing the thermodynamics of disordered magnets is the excitation spectrum of the system against the background of the ground state. In the theory of the energy spectrum of disordered systems, the coherent-potential approximation is widely used [2]. Using this approximation, the problem of the magnetic excitation and temperature of magnetic phase transition in the lattice model of an amorphous magnet with competing exchange interactions is now considered [5]. The essence of the coherent-potential approximation (CPA) is that the disordered system is approximated by a translationally invariant crystal. If attention is confined to the ferromagnetic region of the phase diagram of the ground state on the plane of the parameters ~, X (Fig. 6), a ferromagnet with a mean moment at the lattice point o(O) < i may be chosen as the translationally invariant crystal, in a rough approximation. Since it is assumed that the ground state is defined, then o(0) is also known. Exchange in the system occurs with the coherent exchange parameter Ic(f -- m, E) depending on the excitation energy of the magnetic system E. The coherent parameter is found as follows. The equation for S~ (S = 1/2) is written in the approximation of [22] with the substitution ~ 2 S } ~ = ~ ( T ) ; the matrix of exchange parameters is divided into coherent and fluctuating components Ifm = Ic(f -- m) + ~fm" The equation for the Green's function G(E) = G:~(E) = ~ S ~ ! $ 7 ~i.: takes the form

A A A A A ( m - H~ -- U) G (e) = I , e = E/~ (10)

where Ic(f -- m) forms the translationally invariant matrix Hc, and ~fm forms the fluctua- tional matrix U. The zero approximation corresponds to the Green's function

^ ^ A 1 G O (~) = (12 -- klc) -I = -- ~eik(/-m) (2 -- z4~)-'; (11) N~

% - - 1 -- ?~, ~ = z--lXe~kh. h

The solution of Eq. (i0) may be expressed in terms of a T matrix and subjected to configurational averaging

A A A A A

{G} = Ge + Gc{T}Go (12)

8 4 9

TIT~

!

�9 - o , 5 o 0 , 5 . k

Fig. 13. Ratio of the magnetic-ordering temperature to the Curie temperature of an ideal isotropic FM T~ (I = I) as a function of I when ~ = 1/3: i) T~ (I)/ TcO (i), TcO (i) is the Curie temperature of an ideal FM, I ~ 0; 2) T~ (1)/T~ (i), T~ (I) is the Ne~l temperature of an ideal AFM; I ~ 0; 3)

O Tc AM (1)/T~ (i), T c (i) is the Curie temperature of an amorphous FM in CPA (the continuous curve corresponds to amorphization of an ideal FM and the dashed curve to amorphization of an ideal AF); 4) Tc(%)/T~ (i), Tc(1) is the Curie temperature of an amorphous FM in the approximation of a mean exchange parameter A = (2/3)J(i + I/2).

The properties of the magnetic system are described by c if {T} = O. Since T = U + c ~,

T is a function of Gc(~) and hence {T} = 0 is the equation for determining I c = Ie(~). In A A ^

the approximation of independent exchange bonds, T--~_Ip, where tp is the partial scatter- P ^

ing matrix for any pair of nearest neighbors, and the condtiion {T} = 0 reduces to {tp} = O. The matrix ~p is found accurately, and after configurational averaging with the distribution function in Eq. (2) an integral equation for Ic(fl) is obtained:

N -I ZeK/(u, -- X (a))-:g) =~}~ IX (co),),, "j;

(13)

: I z[l -- X--(l -- ),) ~] [(I-- X)(.i-- X)] -I, 2

where ~ = fl/zJ, X(m) = Ic(,.0/J is a dimensionless coherent parameter. The law of spin-wave dispersion in the effective translationally invariant medium is determined from the equation

o)--e~ReX(to) -~ O. (14)

For small ~, it is evidently found that e, AM Nk 2. The density of spin-wave states

g~ 6,), },, J=Sp{ I Jm<< S~IS7,, >>o,+~o} (15)

behaves in a complex manner as a function of ~ and 1. Using this density go("0, the Curie temperature Tc AM of an amorphous ferromagnet is estimated

Jz~: (0) ~ ~{' gcto(~ d~. (16 )

850

The results for z = 6, ~ = 1/3 are shown in Fig. 13. They correspond to the amorphization of a plane magnet. It is evident from Fig. 13 that, for IX[ << i, amorphization gives Tc AM > T[Rand it is possible for the antiferromagnetic crystal to be transformed to a disordered ferromagnet [23], as observed experimentally (Table i).

The above-used concept of a random magnet with competing exchange interactions of an "equivalent" translationally invariant ferromagnetic crystal is obviously very rough. In the theory of magnetically ordered crystals, it corresponds to replacement of the ferromagnet by an "equivalent" ferromagnet. A series of effects -- for example, the presence of optical branches in the spectrum of spin-wave excitations, the behavior in strong fields and the temperature dependence of the paramagnetic susceptibility -- is not even qualitatively described. It is important to stress that the ground state of the given spin system is a complex spin configuration consisting of two superposed subsystems of "up" and "down" spins. Therefore, it is necessary to develop a method of calculating the excitation spectrum of a Heisenberg magnet which would significantly reflect the presence of two spin subsystems [I0]. Below, the results of such a calculation are outlined in brief; they have been presented in detail by Kuz'min (see below).

The type and energy spectrum of the ground state may be described using the distribution function of the local fields P(s), which is a functional of p(Ifm) and is written in the form

P (s) = ~ ~"j8 (s - - sj), ~ P (s) de = 1, f P (s) sign ed~ = v, (17) ]

where r i s t h e m a g n i t u d e o f t he j - t h t ype o f l o c a l f i e l d ( c h a r a c t e r i z e d by a d e f i n i t e d i s - t r i b u t i o n of J and K bonds and spin states in a cluster with a central spin in the NN surroundings of z); Wj is the probability of its appearance; o is the relative magnetization of the system. As already noted, P(g) may be found by the Monte Carlo method.

--t /i o§ The equation for the Green's function OfT(E ) =of ~\alIS~>>E in the approximation of [22] is written in terms of the locator gf

GH': ~H'g/--g/ ~.~Vf~G~I,, g f : (E- -9 ) -1, Vim= 6m%,, (18a)

or in matrix form

A A AAA A A A O --- g - -gVG, g : ( rE - - e ) - ' , (18b)

^^^ A^

where ~ is a unit matrix and $ a diagonal matrix. Using the uncoupling {gVG} + {gV}{G}, configurational averaging of Eq. (18) is undertaken. The Green's function found in this

^

simplest case of averaging is denoted by Go

A A AA A G0 : d + {gV})'{g} (19)

and is called the zero approximation.

For the FM phase, averaging is performed directly using P(e), and in this case the Fourier transform of Go is

~ (el = g (e) [l + ~Mo (e)l-1; g (E) = J f - - . '

P(~) ~d~ (20) m 0 ( ~ ) = j E - ~ "

The spectrum of collective excitations of FM is determined from the equation 1-4- 7,:M0(E)=0 and has an acoustic branch Ea~(k) ~ k 2 at small k and optical branches characteristic of a ferrimagnet. On transition to the SG region, the spectrum becomes doubly degenerate and the acoustic branch takes on a linear dependence on k.

The most simple approach to describing AF is to consider an alternative lattice consisting of two sublattices 1 and 2 and to introduce the distribution function of local fields in the sublattices PI(e) and P2(r It is assumed that sublattice 1 is filled predominantly by "up" spins and is a disordered FM with a relative magnetization oi > 0 (when T < TN). Be- cause of the "mirror" properties of the sublattices, Pa(e) = PI("r o: = loa!, oI + o2 = 0.

851

a b . c d e

' I l i \ j

i / " Jl~'V, r l - - ' ~ j I / I \ '

., ~ [ fM}

Fig. 14

The matrix structure of Eq. (18b) is also retained in the AF phase; however, G is formed from the intra- and intersublattice Green's functions. After the above uncoupling and Fourier transformation with respect to the sublattices, the zero approximation is found (i, j are the indices of the sublattices)

G~ (q, E) = g# (E)IDo (q, E): G,/(q, E ) = - - M ~ ". Tq , (E) gj (E)/Do (q, E),

where

gi(~) : j P~('~)d;E__.~ , M~ (E)= S Pi(~)~d~E__~ ' D~ I --%'$M]M~

(21)

(22)

and the vectors q belong to a diminished Brillouin zone. The spectrum determined from the equation Do(q, E) = 0 is doubly degenerate because of the property M~(E) = M~(--E), and includes an acoustic branch Eac(q) ~ q at small q and a set of optical branches. Transition from the AF to the SG phases is reflected in a change in the distribution function: P~(e) = P2(e) = Pcc, while o~ = o2~0. However, as before, there is an acoustic branch of the spectrum with a linear (renormalized) dispersion law.

The spin-wave spectra of the system for a polycrystal in the direction [Iii] for I%1 >> z with increase in concentration are shown ~ Fig. 14 for an ideal FM with v = 0 (a), ~a disordered FM with v < ~e FM (b)) a SG with < ~ < ~F (c)) a disordered AF with ~ > AFc (d), and an ideal AF with v = 1 (e). The simplest distribution functions (the approximation of two mean local fields) are used here: P(e) = WA6(C -- EA) + WB~(e + [eBl), WA-- WB = in the FM state and P(~) = PI(g), WA-- WB = ~ in the AF state; 7(Q/2)=0, T(Q)=--I. The zero approximation is by no means trivial, because it reflects the type and energy structure of the ground state of the disordered magnet.

2. MAGNETIC PROPERTIES OF METALLOPOLYMERS

Metallopolymers are materials consisting of highly disperse particles of metals and a polymer matrix. This term was introduced in 1961 [24] to denote a new class of materials that are products of the interaction of polymer macromolecules with the surface of ultra- disperse metal particles. Physicochemical investigations show that metallopolymers form a very broad class of materials with diverse physical properties, in particular) combining the characteristics of metals and polymers [25]. For example, the study of electrical properties leads to the observation of metallopolymers with superconductivity and also confirms the important role of the chemical interaction at the metal--polymer phase boundary. In view of the paucity of investigations of the magnetic properties of metalloproperties) the problem of studying the physics of the formation of their static and dynamic magnetic characteristics takes on importance from fundamental and applied viewpoints. In fact, on the one hand, the use of very informative "magnetic" methods of physical investigation gives addi- tional possibilities for understanding the nature of the physicochemical properties of metallopolymers and, on the ~ther, the presence of transition metals in the polymer, together with the technological convenience of the process of producing metallopolymers, makes them interesting objects for producing technically important magnetic materials. Below, the results of investigating the magnetic and resonant properties of metallopolymers based on transition metals are given.

852

PE PTFE

Fig. 15

Fig. 16

a) Synthesis of Metallopolymers. Polymers are high-molecular compounds with a molecular mass of more than 5000. They are formed in the reaction of polymerization by successive addition of molecules of low-molecular materials (monomers) to the polymer chain. The polymer macromolecules formed, as a rule, have a chain structure; the number n of monomers in the macromolecule is called the degree of polymerization. In Fig. 15, monomeric chains of polyethylene (PE) and the copolymer of tetrafluoroethylene with ethylene, which, for brevity, is called polytetrafluoroethylene (PTFE). Many polymers, especially those with regular structure of the macromolecules, are capable of crystallization. Crystallization occurs here by the multiple addition of macromolecules in quasi-crystallite--lamellae (Fig. 16). Therefore, the polymer cannot be 100% crystalline. Polyethylene and polytetrafluoroethylene are typical polycrystalline polymers with 60-80% crystalline nature. Molecules in the polymer chain form a plane zigzag chain with an angle of i12 ~ The crystalline part of theoPoly- mer structure consists of a plate of dimensions 10-20 ~m and a thickness of around I00 A. The principal axes of the chains lie perpendicular to the plane of the plate. A typical PE macromolecule has a molecular mass of around 50,000 and a length of the order of 4500 A~ Even in the crystalline part of the polymer there is a large number of defects (cavities). Amorphous regions include an even larger number [26].

Many polymers are diamagnetic. However, there exist polymers -- for example, polymetal- phosphinates [27, 28] -- including transition-metal ions in the macromolecule. Such polymers include exchange-bonded chains of metal-atom spins. Recently, the possibility of also producing organic ferromagnets has been theoretically proven [29].

The magnetic properties of metallopolymers in which the method of monomolecular thermo- decay of solutions of metal compounds in the polymer melt is used to form metallic clusters in the natural cavities of the PE and PTFE matrices are investigated here [30]. According to modern concepts, polymer melts consist of separate spherolites, within which lamellas are retained, in somewhat distorted form, as unchanged sections of the structure of the initial polymer. As a result, the short-range order of the initial polymer is retained in the melt, but the cavities existing in the polymer become available for the introduction of metallic particles.

The essence of thermal methods of producing metallopolymers consists in decomposing thin suspensions of thermally unstable metal compounds in a polymer medium. Such compounds include, in particular, metal carbonyls with the formula Mx(CO)y, what M is a metal and x and y are integers. In view of the considerable weakening of the interatomic bonds, the carbonyls are very convenient sources for the production of highly disperse pure metals by thermal dissociation according to the scheme

853

T

M ~ ( c o ) ~ x M - i - y c o ~ .

In the process of thermal decay, volatile ligands and "hot" metals atoms are thus formed. In the medium of the polymer melt, clusters of metal atoms begin to grow and are stabilized in the polymer matrix. As a result of reaction between the gaseous CO liberated and the metal, by-products in the form of oxides and carbides may be formed. However, in typical conditions, the content of these products amounts to only a few wt. %. It is also found that increase in experimental temperature is associated with a corresponding increase in the degree of decomposition of the carbonyl by the basic reaction and the formation of by-products is sharply reduced.

The synthesis of the metallopolymers investigated here is based on high-pressure polyethylene and FT-40 polytetrafluoroethylene, as well as Fe, Co, Cr carbonyls. A mixture consisting of silicon oil and the initial polymer is intensively mixed at 200-250~ After homogenization of the polymer and the oil, the corresponding carbonyl dissolved in a low- boiling organic solvent is introduced, with mixing, into the solution. The resulting mixture is dried and washed with heptane oil. As a result, a powdery metallopolymer is obtained; its color depends on the metal content. The powder is carefully subjected to treatment by pressing at a pressure of 150 arm and a temperature of 125~ for PE and 280 C for PTFE.

b) Structure of Metallopolymers. A large number of Fe, Co, Cr, and Ni metallopolymers have been synthesized on the basis of PE and PTFE and investigated. Iron metallopolymers are considered in detail here, since their magnetic properties are the most interesting.

It is known [25] that a feature of metallopolymers obtained by the thermal-decay method is the significant mutual influence of the metal and the polymer. As a result of such influence, the molecular structure of the crystallizing polymers and electron structure of the surface metal atoms may be markedly altered, and free radicals may form. Therefore, the investigation of the metallopolymer structure in each specific case is a complex problem, solution of which requires a whole set of physicochemical investigations.

It is found by x-ray diffraction analysis that the introduction of iron into PE and PTFE does not lead to pronounced change in structure of the matrix up to concentrations of the order of 50%. Lines corresponding to massive iron are absent, except for a weak ~-Fe line in the sample consisting of PTFE + 50% Fe. To determine the dimensions of the clusters formed by the metal, the method of small-angle x-ray scattering is used [30]. A typical pattern is shown in Fig. 17. It is evident that, in the given materials~ there are clusters with a sufficiently narrow size distribution of the ~articles. The mean particle size is of the order of i00 ~; particles of the order of 20 A in size are also present. In the PE matrix, particles are positioned periodically, whereas for the PTFE-based metallopolymer no such periodicity is observed. It is interesting to note that the size of the metallopolymer particles may be regulated by the composition of the polymer matrix. Thus, the introduction of paraffin increases the cluster size [31].

For more detailed study of the structure of metallopolymers, the MDssbauer (nuclear gamma resonance) spectra of Fe-containing polymers are investigated. Characteristic results for samples of paraffin (P) + Fe, P + PE + Fe, and PE + Fe are shown in Fig. 18. The P + Fe spectrum has a hyperfine structure, since it is formed by comparatively large iron particles (~300 ~). The spectra of P + PE + Fe and PE + Fe are characteristic for an ensemble of superparamagnetic particles. A distinctive feature of all the spectra of Fe-containing metallopolymers based on PE and PTFE is the presence of quadrupole uncoupling. It may be assumed that quadrupole uncoupling arises as a result of surface bonds of the polymer macromolecules with a metallic cluster. This conclusion agrees both with the data of magnetic measurements and with measurements of the nuclear magnetic resonance (NMR) spectra at IH and I~F nuclei [30]. In fact, the NMR spectra of the initial polymer matrices include two lines: The wide line corresponds to the crystalline part of the polymer and the narrow line to the amorphous part of the polymer. The introduction of metal leads to the disappearance of a narrow spectral line, which may be explained by the interaction of metallic clusters with the amorphous part of the polymer with freezing of the mobility of the latter. The NMR data indicate that the introduction of metal particles begins with the amorphous regions. As a result, the material becomes more monolithin and "pseudocrystalline" and increases in thermo- stability by 50-80o. .

854

~4 PE, :O~/ce

i : : - - -- P T ' E * 3 0 ~ F e

: , , , 1

o 1#o ~,7

Fig. 17. Size distribution of particles in Fe-containing metallopolymers.

-.f~' -47 ,0 07 ,1.4. ~./V. mm/sec --3 ............... c~ .......... $Z>r-= ...... i

":-.~ PE ~3#~ :~o !

o , "'-... ,:..:,.,:., .."p ,2072 E ,2~,5i T:3~OK i

P+;~ I

Fig. 18

E 0

~a 0

L

/ i" �9 !

PE '~JO% Fe .

W

Fig. 19. Temperature behavior of the magnetization of Fe-containing metallopolymers: �9 ) samples cooled in zero magnetic field; �9 ) samples cooled in the measurement field H = 1.9 kOe.

c) Static Magnetic Properties of Metallopolymers. The magnetic properties of metallopolymers are measured using pendulum and "SKIMP" [32] magnetometers in the temperature range 1.6-300=K. Iron-containing polymers with 0.1-30% iron have been studied in most detail [31~ 33].

A characteristic feature of all the samples of Fe-containing polymers is the presence of a maximum temperature (Tm) on the curve of the magnetization ~ as a function of the

855

~H

E

Fig. 20

temperature T in the case when the sample is cooled from temperatures above T m to 4.2~ in the absence of a magnetic field. Cooling of the sample in the field leads to the disappearance of the maximum (Fig. 19). This effect is absorbed up to concentrations c = 0.1% Fe and in fields up to approximately 10e. In samples with concentrations c ~ 5% Fe, the susceptibility obeys the Curie-Weiss law at temperatures above Tm. In samples with a large concentration, the Curie-q4eiss law is not obeyed. A characteristic feature of the samples is the strong discrepancy of the magnetization in a field of i0 kOe (T = 4.2~ from the theoretical value associated with the Fe content.

A noncontradictory explanation of the magnetic properties of metallopolymers may be obtained on the basis of the assumption that the magnetic moments of the particles ~i are blocked in the field of magnetic anisotropy. In the simplest model, it may be assumed that the metallopolymer includes identical magnetic clusters characterized by the magnitude of the magnetic moment ~ and some effective uniaxial magnetic anisotropy K > 0. The axes of anisotropy of different clusters are randomly distributed in space. The magnetic energy of the cluster ~

Et = -- ~l H+KVsin~i , (23)

where H is the external magnetic field; V is the cluster volume; ~i is the angle between ~ and the axis of anisotropy of the particle gi It is readily evident that the ensemble of particles ~i at T = O~ and H = 0 has zero magnetization, while the magnetic susceptibility averaged over the ensemble is

X--= ~2/6KV. (24)

If such a system is cooled in a magnetic field to O~ in conditions of thermodynamic equilibrium, i.e., sufficiently slowly, the system will obviously be characterized by the spin moment (mean over the ensemble)

~=~.12. (25)

To investigate the temperature dependences of the magnetic properties, including those in the nonequilibrium state, consider for the sake of simplicity, a model in which the axis of easy magnetization of the particles is parallel to the external field. It is clear that, in the case of cooling of the sample in the field Hc = 0 to 0=K, the resulting magnetization of the sample will be zero. Since the number of moments oriented "to the left" and "to the right" along the axis of anisotropy is N/2, where N is the total number of particles in I g of the metallopolymer (MP). When the external field H is switched on, a nonequilibrium situation is produced (Fig. 20), and a "flux" of moments from region ~=~ to region ~=0 begins; this should lead to an increase in magnetization of the sample. This situation may be described by the kinetic equation

dN, = C~, (N -- NI) -- cI~NI. (26)

dt Here N, is the number of particles at the level ~--0, c2x and cz2 are the corresponding transition probabilities. For the case of a high barrier, that is

KV/#BT >> I, (27)

C2, and cza were calculated in [34]. Solution of Eq. (26) with the initial conditions N, = Na = N/2 gives the following expression for the mean moment in the cluster

856

f . . . .

' b

Fig. 21. Temperature behavior of the functions y (a) and ~ = th[(~H/KT) --(i/2)in(l + p/ (l--p)]

(b), shown schematically.

Z H

/

Fig. 22

< p > =t~ c z t - q ~ " [1 - - exp ( - - t,":)]. C2I -~- C12

Using the expressions for c2, and c~2 [34], it may be established that

where p = H/H A .

(28)

< ~ > ,~ th (tx H.'kl3T -- l ln l + ~.) [1-- exp (-- t/'.) ], (29) ' ' , 2 1 -

Here ~ i s t he t ime o f s u p e r p a r a m a g n e t i c r e l a x a t i o n , f o r which [35]

= x0exp (KV/kBT), (30)

To = I0-9-10 -I~ sec. It is obvious that t in Eq. (29) is in fact the measurement time tme~ For example, in the case of static magnetic measurements, tme ~ I sec. It is evident from Eq. (29) that, in the case where p + 0 and tme + ~, there is a conventional equilibrium situation, that is

< ~ > = tdh(pH/kBT ). (31)

It is clear that the temperature behavior of the magnetization is determined by the factor y = i -- exp(--tme/t); the dependence is very sharp (Fig. 21). Then T > Tm, Y ----- i; when T < Tm, y----- O. It is clear from Fig. 21 that the system described by Eq. (29) (H c = 0) is characterized by a maximum of magnetization at temperature Tm; Tm may be determined as the point of inflexion of the function y. It may readily be shown that, when Eq. (27) is satisfied, Tm may be determined from the relation

tmr ~oexp (KV/k B Tin). (32)

The experimental results are in good agreement with Eq. (32) [31]. Thus, in equilibrium conditions (T > Tm), the system behaves as a distinctive quasi-lsing paramagnet with moment

and in the case where p << i is described by Eq. (31). It should be emphasized again that Eqs. (29) and (31) are only valid when Eq. (27) holds. If Eq. (27) does not hold, the system can no longer be regarded as quasi-lsing. In this case, the expression for the mean magnetic moment (for the case when T > T m) may be obtained by averaging the magnetic moment with the Gibbs distribution function and energy in the form in Eq. (23). In a real situation, when

857

f

II

J

Fig. 23

the easy axes of the particles ~i are oriented randomly, averaging over the ensemble is re- quired to calculate the mean magnetic moment. In particular, Eq. (31) must be modified

(Fig. 22) :

< I~ > = ~ J th (~ H cos II (kBT) cos ~ sin ~d~ (33) 0

It is obvious that, as T § 0~ Eq. (33) gives the result in Eq. (25). Consider the temperature hysteresis. Suppose that the system is cooled to 0~ in Hc = 0. Since T = m for T = 0~ measurement gives the value of o determined by the susceptibility in Eq. (24). The ground state here is of spin-glass type

<~>~0, <~i>T-----0 (34)

Suppose that tme = T(Tm) when T = T m. Then for T > T m, measurements with the characteristic time tme give results described by a formula of the type in Eq. (33) (Fig. 23, curve i). When T < Tm, switching on the magnetic field leads to relaxation of the system from a state of the type in Eq. (34) to the thermodynamic-equilibrium state in Eq. (33) (when P << i). It is obvious that the measurable magnetic moment per cluster will be given by Eq. (29), averaged over the ensemble; this is shown schematically by curve 2 in Fig. 23. On cooling the MP in a field, the system at T ~ Tm is frozen, and the dependence o(T) follows curve 3 in Fig. 23, roughly speaking. Hysteresis phenomena should disappear in measurements in fields larger than the anisotropy field. Experiments confirm this conclusion. For the MPPE+30% Fe, it is found that H A ~i0 kOe. The magnetic properties of PTFE + Co are analo- gous to those of Fe-containing MP. The temperature behavior of the magnetization of PTFE + 10% Co is shown in Fig. 24. The magnetization of a sample cooled in a field of 10.2 kOe is 0.52 G.cm3/g; this is less than the characteristic value for massive cobalt by a factor of 54. The maximum of T m does not disappear in this field; this indicates a large anisotropy field. Metallopolymers based on Ni and Cr do not manifest a T m.

d) Resonant Properties of Metallopolymers. Most of the measurements of electron magnetic resonance (EMR) on metallopolymers have been performed using a PE-1307 ESR spectrom- eter at a frequency of 9.4 GHz in the temperature range 100-300~ Samples of PE + 10% Fe have been investigated in the temperature range 4.2-300~ at a frequency 9 = 29.3 GHz. The high electrical resistance of the polymer matrix and the small dimensions of the metallic clusters (~i00 ~) permit the use of the EMR method, disregarding the skin effect.

A characteristic feature of the EMR of all the metallopolymers investigated is the decrease in magnitude of the resonant magnetic field and the sharp increase in width of the resonance line on reduction in temperature (Figs. 25 and 29) [36]. It is natural to base the interpretation of the resonance properties on the above-established picture of the formation of static magnetic properties of metallopolymers. As established above, these magnetic properties are determined by an ensemble of superparamagnetic metal particles, the crystalline structure of which is distorted because of the influence of the polymer matrix. The distortion of the crystalline structure leads to sharp increase in the anisotropy field H A and decrease in magnetic moment of the particles in comparison with the corresponding massive metal (except for the case of Cr particles). Typical parameter values of the magnetic clusters for the metallopolymers on the basis of PTFE and iron and particle diameter

858

Fig. 24. Temperature behavior of the magnetization of a PTFE + 10% Co sample measured at 10.2 and 4.7 hOe: �9 ) sample cooled in zero magnetic field; Q) sample cooled in the measurement field.

I-I R, Oe

500~

~ooo S , "/ .i

too 200 ~K

~-I, kOe

oL_ 20

\~,

Fig. 25 Fig. 26

Fig. 25. Temperature behavior H R of samples of some metallopolymers, v=9.4 GHz. i) PE+ 10% Cr, 2) PE+40% NI, 3) PTFE+ 10% Co, 4) PTFE 20% Fe, 5) PE+ 30% Fe.

Fig. 26. Temperature behavior AH of samples of some metallopolymers, v= 9.4 GHz. i) PE+10% Cr, 2) PTFE+ 10% Co, 3) PE+ 40% Ni, 4) PE+ 30% Fe, 5) PTFE+20% Fe.

of the order of 50 ~, magnetic moment ~i03 PB, anisotropy field ~3"i0 ~ Oe. The significant influence on the magnetic behavior is exerted by the supermagnetic fluctuations of the magnetic moment with characteristic time T.

It may be expected from the general theory of magnetic resonance that the EMR parameters of an ensemble of noninteracting microparticles subject to superparamagnetic fluctuations should be described by the theory of resonance of spin systems with motion [37]. In the limit of long times m (T -~ > v), this theory gives a result coinciding with the approximation of independent grains [38]. There are no fundamental difficulties in giving this general theory specific form for the explanation of the resonance properties of metallopolymers. However, the construction of this theory requires a knowledge of the temperature dependences of the basic magnetic properties of metallic clusters H(T) and HA(T ) . Since these characteristics are unknown, consideration is restricted here to a rough qualitative theory.

Thus, consider a magnetic cluster ~ with axis of anisotropy ~t (Fig. 22). Its magnetic energy is given by Eq. (23). In the absence of superparamagnetic fluctuations, the

859

EMR frequency for this cluster is obviously determined by the conventional frequency of ferromagnetic resonance [38]

( ,od 'O ~- = [H cos (0~ - - ~j) + H.4 cos'-'~d [H cos (D~ - - ~ ) + HA cos 2~d . (35)

Resonant oscillations in each magnetic cluster (the clusters are assumed to be noninteracting) may develop against the background of a truly equilibrium or nonequilibrium (metastable) ground state, depending on the magnetic history of the sample. Note that the characteristic time of the experiment, determining the initial magnetic state of the resonating system, is the real time of conducting the experiment; this coincides with the characteristic time of static magnetic measurements tme. The characteristic time determining the efficiency of the averaging action of the superparamagnetic fluctuations on the EMR is the period of magnetic resonance oscillations ~v -~. It is clear that these times differ by approximately i0 z~

When thefrequencies are not very large (H < ]HA[) , the energy in Eq. (23) has two minima characterized by the equilibrium angles rpi and (pf ; these minima are separated by a potential barrier. For example, for the case of small fields (H<<Ha)~- 0, ~-----~ ; the corresponding EMR frequency is

I,I , , t~ toi I~ = t l a ! H c o s ~ i . ( 3 6 )

In conditions of thermodynamic equilibrium, the populations of states I and II conform to Boltzmann statistics. In the nonequilibrium state, they are determined by the magnetic history of the system.

It is clear from the foregoing that the resonance properties of metallopolymers may expediently be explained by considering the model of independent two-mode oscillators with eigenfrequencies w I and mll and the characteristic time of transition between these fre-

i i

quencies z (the time of the superparamagnetic fluctuations). The probabilities of popula- tion of states I and II (angles (p~ and ~) will be denoted by W I and wIl, respectively.

According to the general theory of magnetic resonance, in the presence of spin motion, the form function of the resonance line li(m) is [38]

l i ( ~ ) = Ro{IVi.A-- ' . I}, ( 3 7 )

where W i is a vector with components W I and wIl; I is a vector, all the components of which are i; %-i = J(~i -- mE) + ~i; gi is a diagonal matrix with elements (mi)eB = ~Bm~ (~, B take the values I and II); ~. is a unit matrix; ~i is the matrix of inverse lifetimes of the states I and II with elements (~i)~B = ~(~, mBi); m is the angular oscillation frequency; j = _vn-i- "

Using (37), it is simple to find that [o-o ] - - ] (~ / iO) i~ ' WlO)i ] (38)

A i . '

where

a, = O,,~' + ~ , - ~ ) " ' [(o1 '

+ B (oJ ~ 2~'c = ,o~ § o,J'; 2B, ' " - - ~ CO i - - O ) i .

The matrix ~i is chosen in the form

a;/ ~.t= el --el/'

f where fli = (T)-~ are inverse lifetimes of states I and II of the i-th cluster.

It follows from Eq. (38) that, for the case of fast superparamagnetic fluctuations

I, (,o) - - aT~ ~-, [ ( e l + e g ) (o, '-- ,~) + ~, ( e l - - U~)]-=,

and the resonance spectrum takes the.form of a single line shifted by the following amount with respect to the mean frequency mc l

t~ - - ~o~ = ?~i e~ - - ~'2~ ~ i t h ( ~ H c o s ~ t / k B T ) . ( 3 9 )

860

Note that 6 i in Eq. (39) is always larger than zero, by definition. The qualitative result for a metallopolymer is obtained by averaging Eq. (39) over all Oi. It is readily established that this averaged shift (for kBT >> ~H) is

<~--~>an =[.~H/k T, (a0)

where ~ ~ 0 is a quantity of the order of <8i> It is evident that the dynamic frequency shift is positive and inversely proportional to the temprature. Experiment eonfirt!~s this theoretical conclusion. The width of the metallopolymer EMR line in the given ease of fast fluctuations is of order

<~H >--.~.~/2 (41)

and hence should increase with reduction in temperature.

It follows from Eq. (38) that, in the approximation of slow superparamagnetic fluctuations, the resonance of each cluster includes two lines at frequencies mE and ~I. Thus,

in this case (i.e., at low temperatures), the usual result of the theory of "independent" grains may beused.

Note here that all the effects considered above are determined by the magnetic anisotropy and therefore, generally speaking, are of order H A . In constructing a more detailed theory, it must be taken into account that the parameters of the magnetic clusters ~ and K depend on the temperature, which may significantly change the results obtained above on the temperature dependence of the EMR spectrum of the metallopolymers.

CONCLUSION

Heisenberg magnets with competing exchange interactions are thus characterized by three types of magnetic order: a disordered ferromagnet, a disordered antiferormagnet, and a spin glass. The most important characteristic of these states is the distribution function of the local molecular fields. Its form depends significantly on the distribution function of the corresponding crystals. For example, for a disordered ferromagnet, it is asymmetric and extends significantly into the region of negative fields. The temperature dependence of the paramagnetic susceptibility of magnets with strongly fluctuating exchange may differ sharply from the Curie-Weiss law. Finally, the spectrum of elementary excitations is complex in the general case, including local state and optical and acoustic branches of the collective spin excitations.

The properties of the metallopolymers ~nvestigated here are determined by an ensemble of metallic particles of dimensions 50-100 A. The properties of these particles are strongly different from the properties of the corresponding massive metals as a result of the strong influence of the surface and the metal--polymer bonds. The static magnetic properties, in particular, the temperature magnetic hysteresis and the presence of a maximum temperature of the magnetic susceptibility Tm are explained by the existence of nonequilibrium (metastable) states with large relaxation times under definite conditions and finite observation time in the experiment. The resonant properties -- broadening of the EMR line and reduction in resonant field on reduction in temperature -- may be qualitatively explained on the basis of the theory of magnetic resonance in the presence of spin-system mobility. This behavior is associated with dynamic effects of compression and shift of the resonance on account of superparamagnetic fluctuations.

A few remarks may be made on the possible applications of metallopolymers. It seems that there are at least two such possibilities: to record information and as special coatings. For recording information, the temperature-hysteresis effect in polymers with sufficiently large Tm may be used, as well as the method of recording optical information pro- posed by Ya. A. Monosov [39]. The latter method was studied on P + Fe materials, with the conclusion that a threshold exposure of %10 -2 J/cm 2 exists.

The other possibility is associated with the production of coatings absorbing vhf elec- tromagnetic energy. The large magnetic anisotropy of metallopolymer microparticles and the possibility of using the influence of supermagnetic fluctuations on the resonance properties of metallopolymers for effective control of the resonant characteristics permits the hope that it may be possible to produce cheap, light, effective~ and broadband coatings of this type.

861

LITERATURE CITED

i. I. M. Lifshits, S. A. Gredeskul, and P. A. Pastur, Introduction to the Theory of Disordered Systems [in Russian], Nauka, Moscow (1982).

2. J. M. Ziman, Models of Disorder, Cambridge University Press (1979). 3. G. A. Petrakovskii, Usp. Fiz. Nauk, 134, 305 (1981). 4. M. V. Medvedev and A. V. Zaborov, Fiz. Met. Metalloved., 52, 472, 272 (1981). 5. E. V. Kuz'min and G. A. Petrakovskii, Zh. Eksp. Teor. Fiz., 73, 740 (1977); 75, 265

(1978). 6. F. G. L i t t e r s t , J. Physique, 36, L197 (1975). 7. K. A. Sablina, G. A. Petrakovskii, et al., Pis'ma Zh. Eksp. Teor. Fiz., 24, 357 (1976). 8. T. Mizoguchi, T. McGuire, R. Gambino, and K. S. Kirkpatrik, Phys. B, 86-88, 783 (1977). 9. G. A. Petrakovskii, K. A. Sablina, V. P. Tkonnikov, I. A. Volkov, and A. G. Klimenko,

Phys. Status Solidi (a), 70, 507 (1982). i0. G. A. Petrakovskii, K. A. Sablina, et al., Zh. Eksp. Teor. Fiz., 84, 592 (1983). ii. K. Adachi, K. Sato, and M. J. Takuda, Phys. Soc. Jpn., 26, 631 (1979). 12. G. A. Petrakovskii, A. G. Klimenko, et al., Fiz. Tverd. Tela, 2-4, 3676 (1982). 13. G. A. Petrakovskii and S. S. Aplesnin, Phys. Status Solidi (b), 117, 401 (1983). 14. G. A. Petrakovskii, E. V. Kuz'min, and S. S. Aplesnin, Fiz. Tverd. Tela, 2-3, 3147

(1981). 15. G. A. Petrakovskii, E. V. Kuz'min, and S. S. Aplesin, Fiz. Tverd. Tela, 2-4, 3298 (1982). 16. M. V. Medvedev, Phys. Status Solidi (b), 86, 109 (1977). 17. M. V. Medvedev and E. L. Rumyantsav, Phys. Status Solidi (b), 85, No. i (1977). 18. V. I. Ponomarev and E. V. Kuz'min, Fiz. Met. Metallov.,5, 65 (1983). 19. P. Gaunt, S. C. Ho, G. Williams, and R. W. Cochram, Phys. Rev. B, 23, 251 (1981). 20. M. F~hnle, G. Herzer, T. Egami, and H. KronmUller, J. MMM, 2-4, 175 (1981). 21. K. Adachi, M. Matsui, and M. Kawai, J. Phys. Soc. Jpn., ~, 1474 (1973). 22. S. V. Tyablikov, Methods of the Quantum Theory of Magnetism [in Russian], Nauka, Moscow

(1975). 23. E. V. Kuzmin, G. A. Petrakovskii, and S. Aplesnin, J. MMM, 15-18, 1347 (1980). 24. E. M. Natanson and M. T. Bryk, Usp. Khim., 41, 1465 (1972). 25. Yu. I. Kimchenko, Author's Abstract of Candidate's Dissertation, Moscow State University

(1977)o 26. Vo A. Kargin and G. L. Slonimskii, Brief Remarks on the Physical Chemistry of Polymers

[in Russian], Khimiya, Moscow (1967), pp. 44-60. 27. J. C. Scott, A. F. Garito, A. I. Heeger, P. Nannelli, and H. D. Gillman, Phys. Rev.,

BI2, 356 (1975). 28. R. E. Stahlbush, C. M. Bastusheck, A. K. Raychaandhuri, J. C. Scatt, D. Grubb, and H.

D. Gillman, Phys. Rev., B23, 3393 (1981). 29. I. A. Misurkin and A. A. Ovchinnikov, Usp. Khim., 46, 1835 (1977). 30. S. P. Gubin, I. D. Kosobudskii, et al., Dokl. Akad. Nauk SSSR, 260, 655 (1981); S. P.

Gubin and I. D. Kosobudskii, Usp. Khim., 52, 1350 (1983). 31. G. A. Petrakovskii, V. P. Piskorskii, et al., Fiz. Tverd. Tela, 25, 2644 (1983). 32. A. G. Klimenko, Magnetic, Electric and Resonant Properties of Magnetodielectrics [in

Russian], Kiev (1982), p. 178. 33. V. P. Piskorskii, G. A. Petrakovskii, et al., Fiz. Tverd. Tela, 22, 1507 (1980). 34. W. F. Brown, Phys. Rev., 30, 1677 (1963). 35. S. V. Vonsovskii, Magnetism {fin Russian], Nauka, Moscow (1971). 36. G. A. Petrakovskii, V. P. Piskorskii, et al., Fiz. Tverd. Tela, 25, 3256 (1983). 37. A. Abragam, Principles of Nuclear Magnetism, Oxford University Press (1961). 38. A. G. Gurevich, Magnetic Resonance in Ferrites and Antiferromagnets [in Russian],

Nauka, Moscow (1973). 39. Inventor's Certificate 717706, cl. 035/00 (USSR); Byull. Izobret., No. 7 (1980).

862

amorphous magnets and magnetic metallopolymers

Documents