Gross R., Sidorenko A., Tagirov L. Nanoscale Devices

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Nanocrystalline Iron-Rare Earth Alloys: Exchange

Interactions and Magnetic properties

E. Burzo

, C. Djega–Mariadassou

Faculty of Physics, Babes-Bolyai University 400084 Cluj-Napoca,

Romania

LCMTR UPR 209 CNRS 2/8 Bat F Rue Henri Dunant 94320 Thiais,

France

Abstract: The exchange interactions in R

compounds are analyzed. The

contributions to R5d band polarizations are estimated. Then, the

physical properties of nanocrystalline Sm(Fe,Si)

alloys are studied in

correlation with possible technical applications. Finally, the magnetic

properties of the Nd

66.5-x

18.5

nanocomposite system with

M = V or Nb are analyzed.

Keywords: rare earth compounds, magnetic properties

Introduction

Nanocrystalline alloys have very interesting physical properties with a

large variety of useful technical applications [1]. The systems based on

rare-earth (R)-transition metals (M) are particularly interesting as materials

for permanent magnets. In this article we focus on R

and R

B-

based compounds. A characteristic feature of both systems is their low

Curie temperature T

. For R

compounds the highest T

value was

shown to be 477 K for R = Gd [2]. Somewhat higher Curie temperatures,

around 600 K, were found in R

B system [3]. The above values are

about half of the Curie temperature of pure iron, although the iron content

in the above compounds is about 90%. Furthermore, in both systems the

iron moments are close to that of pure iron. Due to the low T

values and

planar

anisotropies, the R

compounds have been considered as not

371

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 371–385.

372 E. Burzo, C. Djega–Mariadassou

useful for technical applications such as permanent magnets. At present, the

B is the basic component for high energy permanent magnets [3].

The low Curie points in both R

and R

B type compounds were

attributed to the strong distance dependence of the exchange interactions

[4]. The R

compounds crystallize either in hexagonal or orthorhombic

crystal structures. In both structures there are four different iron sites. In

contrast, the R

B compounds have a tetragonal structure. In this lattice

structure there are six crystallographically different iron sites, two R

positions and one boron site. The distances between iron atoms, d

FeFe

, in the

above systems cover a large range of values. The interactions between iron

atoms situated at distances d

FeFe

≤ 2.45 Å are negative, whereas the

exchange interactions between Fe atoms situated at larger distances than the

above value are positive. There are no negative exchange interactions, since

for the particular sites they are smaller than the positive ones. Nevertheless,

a considerable magnetic energy is stored in them. As a result, there is a

strong decrease of the Curie temperatures in both systems.

The exchange interactions in rare-earth-transition metal compounds are

rather complex. The exchange interactions of R-Fe type can be described by

Campbell’s model [5]. In this model the 4f electrons of the rare-earth

polarize their 5d bands and there are short-range 5d-3d exchange

interactions with neighbouring iron atoms. The local 4f-5d exchange

interactions are positive and the 4f and 5d moments will align parallel. An

additional contribution to 5d band polarization resulting from 5d-3d short

range interactions is also expected. The Fe(3d)-Fe(3d) exchange

interactions are short range.

In this paper we analyze the exchange interactions in R

and R

compounds. Then, we present the physical properties of Sm-Fe-Si-C

nanocrystalline alloys with the ratio R/(Fe,Si) close to 2/17 having possible

technical applications. In the last part, we report on the physical properties

of Nd-Fe-Cr-M-B nanocomposite magnets with M=V or Nb based on

B type and α-Fe.

Experimental and Numerical Methods

The Sm

17-x

and SmFe

9-y

nanocrystalline alloys were obtained by

high energy ball milling of Sm-Fe pre-alloyed powders and balanced

quantity

of silicon and samarium powders. The samples were heat treated

in vacuum at temperatures between 650

C and 1150

C. Carbonation of the

samples was achieved by reaction of the alloy powder with appropriate

amount of C

powder [6].

Nanocrystalline Iron-Rare Earth Alloys 373

The Nd

66.5-x

18.5

alloys with M=V or Nb were obtained by arc

melting the constituents under purified argon atmosphere. Then, flakes

were prepared by melt-spinning the alloys onto a cooper wheel in argon

atmosphere. The amorphous precursors of nanocrystalline alloys were heat

treated at 650

C from 0.5 to 10 min.

The X-ray analyses of Sm-Fe-Si alloys were performed with a Brucker-

type diffractometer. The crystal structures and lattice site coordinates were

obtained by Rietveld analysis by using the FULLPROF computer code in

the assumption of Thompson-Cox-Hastings line profile, which permitted

the refinement of the coexisting phases and also to take into account the

broadening of the diffraction lines induced by grain size and strain effects.

The mean grain sizes in Nd-Fe-Cr-M-B nanocomposites were determined

from the broadening of X-ray line by using the Scherrer formula [7, 8]. The

distribution functions of the grain sizes were also determined.

Magnetic measurements were performed in the temperature range 4.2-

800 K and fields up to 9 T.

Band structure calculations were performed by using the ab initio tight

binding linear muffin tin orbital method in the atomic sphere approximation

(TB-LMTO-ASA) [9]. In the framework of the local density approximation

(LDA), the total electronic potential is the sum of external, Coulomb and

exchange correlation energies [10]. The functional form of the exchange

correlation energy, used in the present work, was the free electron gas

parameterization of Von Barth and Hedin [11]. Relativistic effects were

included. The 4f states were treated as part of core. These electrons are not

part of the band structure, but the polarization of the 4f densities was

calculated self–consistently.

Exchange Interactions in R

and R

B Type

Compounds

As mentioned already above, the exchange interactions between R and Fe

atoms can be described as of 4f-5d-3d type, while those between transition

metals are of short-range 3d-3d type. According to the Néel-Slater curve,

for the rhombohedral

m type structure of the R

compounds, the

interactions between Fe atoms situated in dumbbell 6c sites are strongly

negative. The exchange interactions between Fe(9d)-Fe(18f) are weakly

negative [12]. The exchange interactions between iron atoms situated at

larger distances are positive and impose a parallel alignment of the iron

moments. Similar behaviour can be seen in the hexagonal P6

/mmm type

structure of R

compounds.

374 E. Burzo, C. Djega–Mariadassou

0 5 10 15

1.50

1.75

2.00

2.25

2.50

12k

12j

(µ

/atom)

-1)

J(J+1)

Fig. 1. The iron moments as function of De Gennes factor for hexagonal R

heavy rare-earths and yttrium compounds.

The dependences of the iron moments determined from band structure

calculations as function of De Gennes factor, G, are given in Fig. 1 for the

case of hexagonal R

compounds, where R is a heavy rare-earth or

yttrium. The iron moments follow linear dependences M

(0)+

where

= 4⋅10

-2

for all type of sites and G = (g

-1)

J(J+1) [13]. From

these data it can be seen that a fraction of (5-7) % of the iron moments is

induced by 4f-5d-3d exchange interactions when replacing Y by Gd. The

sequence of the decreasing the Fe moments is 4f > 12j > 12k > 6g. The iron

magnetic moments are sensitive to their local environments. We note that in

the above sequence the 4f and 12j are inverted, when only the spin

contributions are considered in the computing method.

The R5d band polarizations for R

(M = Fe, Co, Ni) as well as for

B (R= Gd,Y) compounds follow also linear dependences as a

function of the De Gennes factor, M

= M

(0)+

G (see Fig 2). The M5d

polarizations are translated to higher values as the magnetizations of the

transition metal sublattices are higher. The slopes β ≅ 1×10

-2

are nearly

the same for all R

systems. For the P6

/mmc type structure of R

compounds, where two R sites are present (2b and 2d), their M

values are

only slightly different and the mean value was only plotted in Fig. 2. A

higher difference between the M

band polarizations at R4f and R4g sites

can be seen in the R

B compounds. The observed differences can be

Nanocrystalline Iron-Rare Earth Alloys 375

correlated with their different local environments, with the R(4g) site

having a higher number of boron atoms in the first coordination shell.

0 5 10 15 20

0.00

0.25

0.50

0.75

RFe

0.5

(P6

/mmc)

(R3m)

(P6

/mmc)

(R3m)

(µ

/atom)

-1)

J(J+1)

Fig. 2. The computed 5d band polarizations for R

(M=Fe, Co, Ni) heavy-rare

earths compounds and GdFe

0.5

. The Y 4d band polarizations in Y

, Y

and YFe

0.5

are also plotted.

The R5d band polarizations for R

(M = Fe,Co,Ni) as well as for

B (R= Gd,Y) compounds follow also linear dependences as a

function of the De Gennes factor, M

= M

(0)+

G (see Fig 2). The M5d

polarizations are translated to higher values as the magnetizations of the

transition metal sublattices are higher. The slopes β ≅ 1×10

-2

are nearly

the same for all R

systems. For the P6

/mmc type structure of R

compounds, where two R sites are present (2b and 2d), their M

values are

only slightly different and in Fig. 2 only the mean value was plotted. A

higher difference between the M

band polarizations at the R4f and R4g

sites can be seen in the R

B compounds. The observed differences can

be correlated with their different local environments, with the R(4g) site

having a higher number of boron atoms in the first coordination shell.

The analysis of the data in Fig. 2 shows the presence of two contributions

to the R5d band polarization. The βG contribution is due to local 4f-5d

exchange and is the same for a given R atom. The M

(0) values obtained

by extrapolation of the M

vs G dependences to G = 0 are the same as those

induced on the 4d band by 4d-3d short range exchange interactions in the

compounds. Thus, this contribution can be only ascribed to the

presence of 5d-3d short range exchange interactions resulting from

hybridization effects.

376 E. Burzo, C. Djega–Mariadassou

The effect of short-range exchange interactions on the R5d band

polarization can be analyzed starting from Hamiltonian which takes into

account both 3d-5d and 5d-5d exchange interactions [14].

3553 5555

2 (0) (0) 2 (0)

dd d di dd d dj

JS S JS S

−−

∑∑

(1)

where J

3d-5d

and J

5d-5d

are the exchange parameters characterizing the 3d-5d

and 5d-5d interactions with i an j the nearest neighbors Fe and R atoms,

respectively, and S

(0) and S

(0) are the spin values characterizing the

systems with G = 0.

0 5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

(µ

/RM

8.5

or RFe

0.5

)

YFe

0.5

R3m

/mmc

(0)(

/atom)

Fig. 3. The M

(0) contributions to 5d band polarizations as a function of the

transition metal moments in the RM

8.5

(M=Fe, Co, Ni) rare earth compounds as

well as the mean value of M

in YM

0.5

The relation (1) can be analyzed in the molecular field approximation.

The effect of 5d-3d and 5d-5d exchange interactions is equivalent to an

internal field, H

exch

, acting on the R atom. This induces an additional

polarization to that resulting from 4f-5d local exchange, similar to that

evidenced on 3d band in rare-earth transition metal compounds [15]. The

internal field is H

exch

= N

5d-3d

+ N

5d-5d

where N

5d-3d

and N

5d-5d

are the

molecular field coefficients describing the R5d-Fe3d and R5d-R5d

exchange interactions. The R5d-R5d exchange interactions can be

neglected as compared to R5d-Fe3d, since the former are very small [14].

Thus, it the relevant result is that H

exch

is proportional to M

, where M

the total 3d magnetization per formula unit. Previously [15], we showed

that above a critical field, which determines the appearance of 3d magnetic

moments, M

is proportional to the exchange field, H

exch

. Supposing that

this relation is valuable for the 5d band, it follows that M

(0) = αM

. The

Nanocrystalline Iron-Rare Earth Alloys 377

(0) values determined in RM

8.5

(M = Fe, Co, Ni) and the mean value

obtained for YFe

0.5

compounds are plotted in Fig. 3 as a function of the

total transition metal magnetization corresponding to one R atom. There is

a linear dependence, in agreement with the above conclusions. The

determined slope is α = 0.028 ± 0.004. Assuming that the induced 5d band

polarization by short range 5d-3d exchange interactions is the same as that

induced in the Fe 3d band when changing the exchange interactions due to

substitution of a nonmagnetic rare earth by a magnetic one it is found that

(0) = (18×10

)

-1

exch

, where M

(0) is given in Bohr magnetons and

exch

in T . Supposing that N

5d-3d

≅ N

R-Fe

we can estimate also the induced

5d polarization, M

(0). For N

Fe-R

≅ 30, as found in R

compounds [16],

we obtained a value α = 0.011 somewhat smaller than that determined from

Fig. 3. This shows that the R5d band is more sensitive to exchange

interactions than the Fe3d band, and is comparable to that found for the 3d

band.

Nanocrystalline Sm-Fe-Si-C Alloys

As function of the thermal treatment process both stable and metastable

solid solutions can be formed in the Sm-Fe-Si system close to the

composition 2/17. Unlike in the cobalt rare-earth phase diagram, no

presence of a hexagonal CaCu

type structure was found in R-Fe system. In

the RCo

type compounds a deviation from 1/5 stoichiometry was shown.

The alloys were described by the formula R

1-s

5-2s

, where s rare-earth

atoms are substituted by s dumbbells pairs of cobalt [17, 18]. The presence

of metastable R

1-s

5+2s

phases was also reported [19]. For s = 0.22, a

TbCu

type structure can be invoked, while for s = 0.36 ÷0.38 a 1/9

stoichiometry was found with the alloys having P6/mmm type structure. If

s = 0.33, a single R atom out of three is substituted for by one dumbbell

pair and the stoichiometry is 2/17. If the dumbbell pairs are randomly

distributed, the structure remains hexagonal and is of P6/mmm type. This

structure is closely related to CaCu

one (see Table 1). In the theoretical

1-s

5+2s

system, the 3g sites occupation is not affected, while for

s = 0.22 the 2c site of the CaCu

-type structure would transform partially

into

Fe6l. The 2e sites are gradually occupied by iron. The Sm

1-s

5+2s

system exhibit experimentally only the metastable P6/mmm phase with

s = 0.36-0.38 consistent with SmFe

9-y

after annealing at 650-850

These alloys are nanocrystalline with grain sizes varying from 22 to 28 nm.

The 2/17 stoichiometry is approached when increasing the annealing

temperature

compared to the above mentioned. The P6/mmm type

structure changes to a rhombohedral

m type through an ordering

378 E. Burzo, C. Djega–Mariadassou

process of atoms. Thus, the 2e and 6l sites transform into 6c and 18h sites,

respectively. The 3g site splits from one third into 9d positions and two

third into the 18h sites in the rhombohedral 2/17 phase. The R1a site gives

rise to the R6c site in the

m type structure.

Table 1. Atom occupancies and positions in the R

1-s

5+2s

alloys having P6/mmm

space group [6].

Atom s = 0

1/5

s = 0.22

TbCu

type [20]

s = 0.33

2/17

s = 0.36

1/9

1Sm(1a) 1-s 1 0.78 0.66 0.64

2Fe(2c) 2(1-3s) 2 2 0 0

6Fe(6l) 6s 0 0 2 2

3Fe(3g) 3 3 3 3 3

2Fe(2e) 2s 0 0.44 0.66 0.72

In hexagonal R

based compounds the substitution of one Fe atom by

Si decreases the R(5d) band polarization by ≅ 0.04 µ

. This can be

correlated with the diminution of short range R(5d)-Fe(3d) exchange

interactions due to dilution effects.

0.0 0.4 0.8 1.2 1.6 2.0

8.50

8.55

8.60

8.65

8.70

12.40

12.45

12.50

17-x

a(Å) c(Å)

0.00 0.25 0.50 0.75 1.00

4.2

4.4

4.9

5.0

SmFe

9-y

a(Å) c(Å)

Fig. 4. Composition dependences of lattice parameters in Sm

17-x

z = 0 (•),

) and Sm

9-y

z = 0 (•), 1(

) alloys.

The composition dependences of the lattice parameters for

17-x

(z=0, 2) and SmFe

9-y

(z=0, 1) alloys are shown in

Fig. 4.

rhombohedral

type

structure

having

space group was

found for Sm

17-x

compounds with x ≤ 2.0. The metastable SmFe

9-y

solid solutions are formed up to y = 1.04 and crystallize in hexagonal

/mmm type structure. The a- and c-lattice parameters decrease when

replacing iron by silicon in Sm

17-x

system. The silicon atoms are

located in 18h sites. The same behaviour was shown for Sm

17-x

Nanocrystalline Iron-Rare Earth Alloys 379

carbonated samples, although a rather high increase of the cell parameters

was shown after carbonation. In the case of hexagonal P6

/mmm alloys, in

which the SmFe

9-y

and SmFe

9-y

C systems crystallize, the c lattice

parameters decrease while the a-parameters increase slightly. We note that

as in the 2/17 compounds the carbonation leads to a high increase of the cell

parameters. Domain sizes of 22 nm were found for the SmFe

9-y

C alloy

with y = 0.25. They decrease slightly to 18 nm for y = 1, according to the

role played by silicon on the nanostructure.

Fig. 5. Composition dependences of the Curie temperatures in Sm

17-x

(z=0, 2) and SmFe

9-y

(z= 0, 1) alloys.

450 500 550

2/17

1/9

(K)

Fig. 6. The dependence of the Γ values on the Curie temperatures.

380 E. Burzo, C. Djega–Mariadassou

The composition dependences of the Curie temperatures, T

, are given in

Fig. 5. The T

values of noncarbonated 1/9 and 2/17 samples increase

gradually showing the same trend, although the T

values are higher in the

1/9 phase. The increase of the Curie temperature on replacing iron by

silicon can be attributed to the reduction of the antiferromagnetic exchange

interactions relative to a slight increase of the Fe-Fe distances concomitant

with the filling of the d band by the p silicon electrons implying a shift to

strong ferromagnetic behavior. For example, in the

m type structure of

compounds, Si replaces Fe in the 18h sites, while the distances

Fe6c-6c and Fe9d-18f increase but remain just below 2.45 Å. The Curie

temperatures in carbonated samples are sensitively higher than those in

noncarbonated. Due to the increase of the lattice parameters by the presence

of interstitial carbon, the distances between iron atoms are larger. This leads

to a decrease or even cancellation of the contributions of the iron pair to the

negative exchange interactions. When substituting Fe by Si, in carbonated

samples, a decrease of the T

value is expected due to dilution effects as

well as hybridization effects of Fe3d, Si3p and C3p bands in agreement

with experimental observations.

The correlation between the Curie temperatures and the volume

variations can be analyzed by using the

kT dp d v

Γ= =

parameter

[21, 22]. Here, κ denotes the compressibility and v is the volume of the

cell. A linear dependence of the Γ values on the Curie temperatures was

reported starting from a model, which considers the 3d electrons as having

mainly a localized behavior [21, 23]. In this model the Γ value is given by:

ef f

3ln8

(1)

ef f b

kNg I

SS J I

Γ= + +

(2)

where N

is the Avogadro number, g is the Landé factor, I is the effective

intra-atomic exchange integral, which is reduced from its bare value I

, and

eff

is the effective exchange coupling parameter. Linear Γ vs T

dependences were found and described by the relation Γ = a - bT

with

a = 34.5 and b = 0.054 K

-1

for the 2/17 compounds and a = 47.5 and

b = 0.085 K

-1

for 1/9 alloys. These values are close to those determined in

C(N)

based compounds, where the values a = 38 and b = -0.06 K

-1

were reported [23]. The

eff

= values are 16.4 and 22.9 for the 2/17

Gross R., Sidorenko A., Tagirov L. Nanoscale Devices - Fundamentals and Applications

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