Fe/Co…–B hard magnetic alloys - Nanyang Technological University


Fe/Co…–B hard magnetic alloys - Nanyang Technological University

Exchange interaction in rapidly solidified nanocrystalline

RE–„Fe/Co…–B hard magnetic alloys

Z. W. Liu, 1,2,a D. C. Zeng, 1 R. V. Ramanujan, 3 X. C. Zhong, 1 and H. A. Davies 2


School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640,



Department of Engineering Materials, University of Sheffield, Sheffield S1 3JD, United Kingdom


School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798,


Presented 11 November 2008; received 17 September 2008; accepted 21 November 2008;

published online 17 March 2009

The exchange interactions for rapidly solidified Nd/PrFe/CoB hard magnetic alloys with

remanence enhancement were studied by analyzing characteristic magnetic curves and Henkel plots.

The exchange coupling can be improved by increasing soft phase content within hard matrix. With

increasing temperature, the exchange interaction is enhanced due to the increased exchange length.

An increased recoil susceptibility was found for the alloys with improved exchange coupling.

Analysis of the microstructure parameters indicated that Co substituting Fe and introducing soft

-Fe,Co phase not only reduce the stray field effects but also enhance the exchange interaction.

© 2009 American Institute of Physics. DOI: 10.1063/1.3072717


The enhanced remanence and energy product for nanocrystalline

REFeB alloys result from the exchange coupling

between hard grains and, for nanocomposites, hard and soft

grains, which also influences the coercivity. The exchange

coupling occurs over the exchange length L ex=A/K, where

A is the exchange stiffness and K the magnetocrystalline anisotropy

constant. For nanocomposites, A and K can be described

as effective exchange stiffness and effective anisotropy

constant, respectively. 1

Since the mean grain size d g of hard magnetic phase for

nanocrystalline alloys lies between the domain wall width

and the critical single-domain size, a normal domain structure

with 180° domain walls cannot be formed, and the concepts

of nucleation or pinning-type magnets, successfully

used to analyze coercivity in sintered materials, will fail. 2 In

order to elucidate the coercivity mechanism study on the

interaction between the grains is important. In this work, the

exchange interaction for nanophase REFeCoB RENd,Pr

alloys is investigated by two well known methods, i.e.,

analysis of the characteristic magnetic curves and Wohlfarth’s

remanence analysis using so-called Henkel plots. The

modified Brown’s equation is also employed to analyze the

effects of microstructure and exchange coupling on the coercivity.


Nanocrystalline Nd1−yPryzFe1−xCox94−zB6 alloys with

various compositions were obtained by rapid solidification of

melt spinning, as described elsewhere. 3 The dg of all alloys

were determined as 35 nm by x-ray line broadening analysis.

The magnetic characterization of individual ribbon was

carried out using a 9T vibrating sample magnetometer



Author to whom correspondence should be addressed. Electronic mail:




The structure and properties for the experimental

Nd/Pr zFe/Co 94−zB 6 alloys have been published in our

previous papers. 4,5 The alloys with z=12, 12, or 12 consist

of single phase RE 2Fe/Co 14B or 2/14/1 phase,

RE-rich+2/14/1 phases, or -Fe/Co+2/14/1 phases

nanocomposite, respectively. The substitutions of Pr for Nd

and Co for Fe have no effect on the phase constitution.

A. Remanence enhancement

The temperature dependent remanence ratio Jr/J s for selected

alloys are shown in Fig. 1. Jr/J s0.5 at room temperature

RT, indicating remanence enhancement. Decreasing

RE content increases Jr/J s, as a result of the

disappearance of RE-rich phases and increasing volume fraction

of soft phase. The slight increase in Jr/J s between 200

and 500 K is an indication of enhanced exchange coupling.

FIG. 1. Color online Dependence of J r/J s on temperature for selected

nanocrystalline alloys and temperature dependence of exchange length for

Nd 0.25Pr 0.75 2Fe 1−xCo x 14B alloys inset.

0021-8979/2009/1057/07A736/3/$25.00 105, 07A736-1

© 2009 American Institute of Physics

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07A736-2 Liu et al. J. Appl. Phys. 105, 07A736 2009

FIG. 2. Color online Recoil loops on demagnetization curves for a

Nd 0.25Pr 0.75 zFe 0.95Co 0.05 94−zB 6 alloys with mean recoil susceptibility rec

T/kAm and b nanocomposite Nd 0.25Pr 0.75 8Fe 0.95Co 0.05 86B 6 at various


Since the values of A for NdFeB alloys can be obtained

2 6

approximately from the relation ATJsT and the anisotropy

field can be expressed as Ha=2K/Js, 7 LexJs/H a1/2 .

The calculated Lex for Nd0.25Pr0.752Fe1−xCox14B x

=0–0.3 alloys Fig. 1 inset based on experimental data 8–10

clearly indicates an increasing Lex with increasing temperature,

which leads to more effective exchange coupling.

B. Characteristic recoil loops

Figure 2a shows the recoil loops on the demagnetization

curves for Nd 0.25Pr 0.75 zFe 0.95Co 0.05 94−zB 6 alloys at

RT. Single phase alloy shows a completely reversible behavior

along the recoil line. The open loops for nanocomposites

are due to the rotation of magnetization of exchange-coupled

soft phase for fields not large enough to reverse the magnetization

of the hard magnetic phase.

The exchange coupling can be quantitatively described

by recoil susceptibility, defined as rec=dJ/dH, obtained

from recoil curves. The mean rec for each alloy is indicated

in Fig. 2a. Nanocomposites have high values of rec; the

larger the fraction of -Fe,Co phase the higher its value,

indicating stronger exchange coupling and more pronounced

exchange-spring behavior. 11

The recoil loops for

Nd0.25Pr0.758Fe0.95Co0.0586B6 alloy Fig. 2b show that

increasing temperature leads to steeper loops, i.e., increased

rec. The similar results can be also deduced from the recoil

loops for PrFeB alloys. 12 As the exchange coupling becomes

stronger with increasing temperature, the results demonstrate

that for the alloy with given composition and grain size,

enhanced exchange coupling leads to higher rec. FIG. 3. Color online Henkel plots of a various nanocrystalline

Nd 0.25Pr 0.75 zFe 0.95Co 0.05 94−zB 6 z=12,10,8,14 alloys and b at various

temperatures for nanocomposite Nd 0.75Pr 0.25 10Fe 0.95Co 0.05 84B 6.

C. Analyzing exchange coupling by Henkel plots

The most common method of quantitatively analyzing

the intergrain interactions is by constructing M plots Henkel

plots 13 based on the relationship MH=M dH

−1–2M rH, where M rH and M dH are defined as the

remanent magnetizations after applying a field H on a thermally

demagnetized sample and after applying a reverse field

on a previously saturated sample, respectively. For an assembly

of noninteracting single-domain particles, M =0. An increase

in the positive deviation suggests that the exchange

coupling was enhanced. A negative deviation of the plots

was interpreted as magnetostatic interactions dominating

when magnetization reversal occurs. 13

In Fig. 3a, for single phase alloy a large positive derivation

of M indicates that intergranular interactions are

dominated by exchange until reversal occurs, when M decreases

abruptly to small negative values as a result of the

cooperative switching of the exchange-coupled grains. For

nanocomposites M is also initially positive although much

weaker than for the single phase alloy, as the hard phase

prevents the demagnetization of the two-phase structure, but

become much more strongly negative after reversal. The

negative part is more pronounced in the nanocomposites

with higher -Fe,Co content, showing that the importance

of magnetostatic interactions increases with increasing soft

phase content. For RE-rich alloys, the magnetostatic interaction

becomes very small due to the existence of RE-rich

phases at the grain boundaries.

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07A736-3 Liu et al. J. Appl. Phys. 105, 07A736 2009

FIG. 4. Color online The plots of 0H CT/J ST vs 0H aT/J ST for

Nd 0.25Pr 0.75 8Fe 1−xCo x 86B 6 alloys.

For nanocomposite Nd 0.75Pr 0.25 10Fe 0.95Co 0.05 84B 6,

Fig. 3b indicates the temperature dependent exchange coupling

and magnetostatic interaction. When the temperature

increases from 200 to 400 K, the increasing intensity of positive

M implies the enhancing exchange coupling. The reason

related to increased L ex has been discussed early.

D. Analyzing the microstructural parameters

The temperature dependence of coercivity 0H c can be

analyzed using modified Brown’s equation: 14 0HcT min

=K ex0HN T−NeffJST. k, ex, and Neff are called mi-

crostructural parameters. k describes the influence of the

nonperfect grain surfaces on the crystal anisotropy. The effective

demagnetization factor Neff is due to enhanced stray

fields at the edges and corners of the grains. ex takes into

account the effect of exchange coupling. If the grains with

the smallest nucleation field are assumed to govern the whole

demagnetization process, the minimum nucleation field is


min = min 2K1/J s. 15 For randomly oriented grains the param-

eter min is equal to 1/2. 15 For single crystal RE2Fe 14B,

0H a=2K 1/M S. The above equation can be rewritten as

0H cT= K ex min 0H aT−N effJ ST. A plot of

0H CT/J ST versus 0H a T/J ST should yield a straight

line, having a slope 1/2 k ex and an ordinate intersection

−N eff. The value of k for decoupled NdFeB magnet was

found almost constant k=0.80.1. 16 Any variation in

k ex mainly results from exchange coupling, with smaller

values of k ex indicating stronger exchange coupling.

Figure 4 show the plots of 0H CT/J ST versus

0H aT/J ST and microstructural parameters for nanocomposites

with various Co contents. Co substitution decreases

both k ex and N eff, indicating that Co improves not only the

exchange coupling but also the microstructure. The improved

exchange coupling can be quantitatively explained by the

increased L ex due to decreased anisotropy constant by Co

substitution. The improved microstructure is demonstrated

by the enhanced J r and BH max at RT. 3 Co addition may lead

to more spherical grains and smoother grain boundary, therefore,

a reduction in local stray field.

The derived microstructural parameters versus RE content

for all alloys showed that decreasing RE content reduces

both parameters not shown here, indicating that introducing

and increasing the fraction of the -Fe,Co phase lead to

stronger exchange interaction and also reduce stray fields by

improving microstructure. N eff values for exchange-coupled

nanocomposites 0.1 are much smaller than for RE-rich

alloys due to the more polyhedral shapes of the partly decoupled

grains in RE-rich alloys.

The rather small values of k ex in remanence enhanced

alloys Fig. 4 illustrate the drastic influence of exchange

coupling on coercivity. For nanocomposites in current case,

soft magnetic grains are almost fully exchange coupled to

hard ones. The rotations within the soft grains are easier than

in the hard grains, which induce, via exchange coupling, an

enhanced rotation within the hard grain and this leads to a

decrease in H C and a drastic decrease in k ex. The decrease

in N eff is also related to the collective behavior of the

exchange-coupled grains. The smoothing effect of the exchange

interaction at the grain boundaries reduces the stray

field effect at the edges and corners of the grains.


The exchange interaction of nanocrystalline REFe/CoB

alloys has been investigated regarding to the composition

and temperature. The exchange coupling behavior and magnetization

process can be analyzed by characteristic magnetic

curves and Henkel plots. The analysis of microstructure parameters

indicated that Co substitution not only enhances the

exchange coupling but also improves the microstructure. Introducing

and increasing the fraction of the soft phase are

also beneficial to the exchange coupling, although at the expense

of the coercivity.


This work was supported by UK EPSRC, Guangdong

NSF No. 8151064101000084, SERC Singapore No.

062101003, Guangdong Provincial Science and Technology

Program No. 2008B010600005, and State Key Lab of Advanced

Metals and Materials No. 2008F-01.

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