Dealing with these issues, we have prepared the amorphous alloy ribbons Fe 78−xCrxSi 4 Nb 5 B 12 Cu 1 with x = 1, 3, and 6, and then studied their magnetic and critical properties.. Thes
Trang 1Influence of Cr Doping on the Critical Behavior of
T L Phan1, P Q Thanh2, N Chau2, C X Huu3, D.-T Ngo4, T A Ho1, T D Thanh1,5, and S C Yu1
1Department of Physics, Chungbuk National University, Cheongju 361-763, Korea
2Faculty of Physics, Hanoi University of Science, Vietnam National University, Hanoi, Vietnam
3Department of Electronics and Communication Engineering, Danang University of Technology, Danang, Vietnam
4Department of Micro- and Nanotechnology, and Department of Energy and Storage,
Technical University of Denmark, Kgs Lyngby 2800, Denmark
5Institute of Materials Science, Vietnam Academy of Science and Technology, Hanoi, Vietnam
Though many previous works focused on studying Cr-doped Fe–Si–Nb–B–Cu amorphous alloys, magnetic-interaction mechanisms
in these materials have not been carefully investigated yet Dealing with these issues, we have prepared the amorphous alloy ribbons
Fe 78−xCrxSi 4 Nb 5 B 12 Cu 1 with x = 1, 3, and 6, and then studied their magnetic and critical properties Magnetization versus temperature and magnetic-field measurements, MHT, performed on a vibrating sample magnetometer reveal that the Cr-content increase in Fe 78−xCrxSi 4 Nb 5 B 12 Cu 1 reduces the TCfrom 430 K for x = 1 to about 322 K (for x = 6) This indicates the decline
of ferromagnetic (FM) exchange interactions between Fe atoms when there is the presence of Cr atoms We have also analyzed the
M(H) data at the temperatures in the vicinity of the TC using the modified Arrott plot method and the scaling hypothesis, and determined the values of the critical exponentsβ = 0.367–0.376 and γ = 1.315–1.338 These values are close to those expected for
the 3-D Heisenberg model with β = 0.365 and γ = 1.336, proving the existence of short-range FM order in the amorphous alloy
ribbons.
Index Terms— Critical behavior, Fe-based alloy ribbons, short-range ferromagnetism.
I INTRODUCTION
IT HAS been known that Fe-based amorphous alloys (either
in the bulk or ribbon form) exhibit many noticeable
prop-erties, which can give a large saturation magnetization and
the soft-magnetic behavior [1] Depending on the application
aspects, these properties can be easily modified by changing
elemental composition of alloys It has been realized that the
presence of Nb, Si, B, Cu, and Cr in Fe-based amorphous
alloys improves remarkably the corrosion resistance and the
soft-magnetic behavior [1]–[3] Particularly, the formation of
the amorphous phase becomes easy when many chemical
elements are simultaneously combined in Fe-based alloys
because of structural disorders related to the difference in
the atomic radii of the elements This also changes the
ferromagnetic–paramagnetic (FM–PM) phase-transition
tem-perature (the Curie temtem-perature, TC ) Based on these important
features, it has been fabricated and investigated the
amor-phous alloys for magnetic refrigeration applications using the
magnetocaloric effect [4]–[6] For conventional applications
in cooling systems, the TC of the amorphous alloys can
be controlled in the temperature range of 260–310 K For
example, the TCvalues (>400 K) of amorphous alloys ribbons
Fe78Nb5Si4B12Cu1and Fe73.5Nb3Si13.5B9Au1can be reduced
to lower temperatures by substituting partly Fe atoms by
Cr ones [4], [7], [8]
In reference to our work, there were many previous studies
on Cr-doped Fe–Nb–Si–B–Cu-based amorphous alloy ribbons
[2], [4], [7], [9] However, magnetic interactions in these
Manuscript received March 2, 2014; accepted May 17, 2014 Date of
current version November 18, 2014 Corresponding author: S C Yu (e-mail:
scyu@chungbuk.ac.kr).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2014.2325949
materials and their FM–PM phase-transition type have not been carefully studied yet It has been shown that the study
of the critical properties based on the Arrott plot method and the scaling hypothesis [10]–[12] are considered as an effect approach to elucidate the mentioned issues In this paper, we present a thorough study on the magnetic properties
of amorphous alloy ribbons Fe78−xCrxSi4Nb5B12Cu1 The experimental results reveal that the Cr-content increase reduces
remarkably the TC from 430 K (x = 1) to 322 K (x = 6), and
leads to the values of the critical exponents shifted toward those for the mean-field theory However, the alloy ribbons still have the nature of short-range FM order because their exponents are more close to those expected for the 3-D Heisenberg model
II EXPERIMENTALDETAILS Three amorphous ribbon samples of Fe78−xCrxSi4Nb5 B12Cu1(x = 1, 3, and 6) with the widths and thicknesses of 2–6 mm and 20μm, respectively, were prepared from
high-purity metallic elements (including Fe, Si, Nb, Cu, B, and Cr) using the melt-spinning technique The fabrication was carried out in a vacuum chamber at 10−4torr that pressure was main-tained using an Ar gas flow After preparation, X-ray diffrac-tion studies (based on a Bruker D5005 X-ray diffractometer) revealed that all the ribbon products were amorphous without any secondary phases [4] Magnetization versus temperature
and magnetic-field measurements, M (H , T ), were performed
on a vibrating sample magnetometer
III RESULTS ANDDISCUSSION Fig 1(a) shows temperature dependences of magnetiza-tion (M) normalized to the maximum value (Mmax) for the
amorphous alloy ribbons Fe78−xCrxSi4Nb5B12Cu1 under the
application of the magnetic field H = 100 Oe For each 0018-9464 © 2014 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Trang 2Fig 1. (a) M (T ) data normalized to the maximum value, M/Mmax and
(b) dM/dT versus T curves for the alloy ribbons in the field H= 100 Oe.
sample, a slight decrease of M with increasing temperature
is observed This decrease becomes rapid when the sample
is heated above the FM–PM phase transition temperature TC,
where magnetic moments become disordered under the impact
of the thermal activation energy By plotting the dM/dT versus
T curves, see Fig 1(b), the TC values determined from the
minima are about 430, 410, and 323 K for the alloy ribbons
with x = 1, 3, and 6, respectively A decrease of the TC
with increasing Cr-doping content in Fe78−xCrxSi4Nb5B12Cu1
demonstrates the weakening of exchange FM interactions
between Fe atoms Such the scenario leads to the reduction of
the M and magnetic-entropy change (Sm ) values [4], [7], [8].
To understand more thoughtfully the magnetic properties of
the alloy ribbons Fe78−xCrxSi4Nb5B12Cu1, we have measured
the magnetic-field dependence of magnetization at different
temperatures around the TC, M (H ) The recorded M(H )
data are shown in Fig 2 Similar to the M (T ) data shown
in Fig 1(a), the magnetization is gradually decreased with
increasing temperature The nonlinear M (H ) curves in the
FM region (as T < TC) become linear as T > TC, where
the alloy ribbons are paramagnetic At a given temperature,
the magnetization increases with the applied field H However,
no magnetization saturation is achieved This phenomenon was
also observed in many FM compounds [7], [13] due to
short-range FM order caused by magnetic inhomogeneity
In an attempt to further confirm the presence of short-range
FM order in the alloy ribbons, we have used the Arrott plot
methods [10], [11], which were developed from the
mean-field (MF) theory for a FM system exhibiting a second-order
magnetic phase transition and long-range magnetic
interac-tions [14] According to this theory, the free energy G L is
expanded in even powers of M as follows:
G L = aM2 + bM4+ · · · − HM (1)
where a and b are temperature-dependent parameters
Mini-mizing G L gives the following relation:
H /M = 2a + 4bM2. (2)
Fig 2. M (H ) curves at temperatures around the TC (with temperature
increments of 2 K) for the alloy ribbon with (a) x = 1, (b) x = 3, and (c) x= 6.
Within the framework of the MF theory, (2) can be generalized
to the scaling equation of state [11]
(H/M)1/γ = c1ε + c2M1/β (3)
where c1 and c2 are also temperature-dependent parameters, andε = (T − TC)/TCis the reduced temperature Meanwhile,
β and γ are the critical exponents associated with the
satura-tion magnetizasatura-tion, M s, and the inverse initial susceptibility,
χ0−1 respectively Equation (3) means that if magnetic interac-tions in a ferromagnet accurately obey the MF theory (i.e., it
has long-range FM order), the M1/β versus(H/M)1/γ curves
withβ = 0.5 and γ = 1.0 (the values of the exponents for the
MF theory [12]) around the TC are parallel straight lines, as
mentioned in the normal Arrott plots [10] However, the M1/β
versus(H/M)1/γ curves shown in Fig 3(a)–(c) for the alloy
ribbons do not exhibit these features In addition, if plotting
the M1/β versus (H/M)1/γ curves with β = 0.365 and
γ = 1.336 (the values of the exponents for the 3-D Heisenberg
model [12]), they are parallel straight lines around the TC, see
Fig 3(d)–(f) All of these features indicate the absence of long-range FM order and the existence of short-long-range order in the amorphous alloy ribbons Fe78−xCrxSi4Nb5B12Cu1
It should be noticed that the parallel straight lines of
M1/β versus (H/M)1/γ are just obtained for high enough
magnetic fields (H > 3 kOe), where magnetic moments are
almost aligned to the field direction Basically, the values of the exponentsβ and γ characterized for of short-range FM
interactions can be determined by using the modified Arrott
Trang 3Fig 3. M1/βversus(H/M)1/γ curves with (a)–(c)β = 0.5 and γ = 1.0,
and (d)–(f) with β = 0.365 and γ = 1.336 for the amorphous alloys with
x= 1, 3, and 6.
(MA) method, starting from the asymptotic relations [11], [13]
M s (T ) = M0(−ε) β , ε < 0 (4)
χ0−1(T ) = (h0/M0)ε γ , ε > 0 (5)
where M0 and h0 are the critical amplitudes As mentioned
above, because the exponent values of β = 0.365 and
γ = 1.336 are more suitable to the descriptions of the MF
the-ory in the plot of M1/β versus (H /M)1/γ, they are thus used as
the trial exponent values for the MA method [11], [13] With
these trial values and the MA plots shown in Fig 3(d)–(f),
the M s (T ), and χ0(T ) data obtained from the linear
extrap-olation in the high-field region (H > 3 kOe) to the M1/β
and(1/χ0)1/γ axes are then fitted to (4) and (5), respectively,
to achieve better β, γ , and TC values These new values of
β, γ , and TC are continuously used for the next MA-plot
processes until they converge to the stable values During
the best fitting process, the TC values determined from the
M (T ) curves would be used as a reference In Fig 4, it shows
the MA-plot processes for the M s (T ) and 1/χ0(T ) data, and
the determined values of β, γ , and TC for the alloy ribbons
Fe78−xCrxSi4Nb5B12Cu1; here, β = 0.367 ± 0.004, γ =
1.338 ± 0.018, and TC ≈ 430 K for x = 1, β = 0.370 ±
0.004, γ = 1.324 ± 0.013 and TC ≈ 411 K for x = 3, and
β = 0.376 ± 0.002, γ = 1.315 ± 0.006 and TC≈ 322 K for
x= 6
With the critical parameters determined, the MA plots
(i.e., M1/β versus (H/M)1/γ curves) for the M (H, T ) data
around the TC of the alloy ribbons show a set of parallel
straight lines at the fields H > 3 kOe In addition, the M1/β
versus (H/M)1/γ lines at the T
C pass through the origin, see Fig 5 These features are in good agreement with the
descriptions of the MA-plot method, and reveal the reliability
Fig 4. Ms (T ) and χ0−1(T ) data around the TC fitted to (4) and (5),
respectively, for the amorphous ribbons with (a) x = 1, (b) x = 3, and (c) x= 6.
Fig 5. Modified Arrott plots of M1/βversus(H/M)1γ with the obtained
critical exponents for Fe 78−xCrxSi 4 Nb 5 B 12 Cu 1 with (a) x = 1, (b) x = 3, and (c) x= 6.
of the values of the critical parameters Alternatively, checking the reliability of the determined values can be based on the
scaling hypothesis, which states that M is a function of ε and
H : M (H, ε) = |ε| β f±(H/|ε| β+γ ), where f+ and f− are the
analytic functions for T > TC and T < TC, respectively [12].
Trang 4Fig 6. Scaling plots of M /|ε| β versus H /|ε| β+γ for the M (H, T ) data
around the TC values of Fe78−xCrxSi4Nb5B12Cu1with (a) x = 1, (b) x = 3,
and (c) x= 6.
This equation implies that all M (H, T ) data fall onto two
universal branches f− and f+in the M /|ε| β versus H /|ε| β+γ
curves if the determined values of β, γ , and TC are correct
Interestingly, such the conditions completely satisfies with
our results if performing the scaling plots of M /|ε| β versus
H /|ε| β+γ, as shown in Fig 6 The critical values of β, γ ,
and TC determined in our work are thus reliable Notably,
though the Cr-content increase leads to the values of the
critical exponents shifted toward those for the MF theory, the
amorphous alloy ribbons still exhibit the nature of short-range
FM interactions because their exponentsβ = 0.367–0.376 and
γ = 1.315–1.338 are more close to those expected for the 3-D
Heisenberg model We believe that the doping of Cr atoms
changes the range of the exchange interaction J (r), the total
magnetic moment, and the spatial dimensionality of Fe-based
FM substances These factors directly influences magnetic
interactions in the alloy ribbons According to renormalization
group theory [15] applied for an exchange-interaction system,
the values of the critical exponents depend on the range of
the exchange interaction J (r) = 1/r d +σ , where d and σ
are the dimension and the interaction range, respectively The
MF exponents are valid for σ < 1/2, while the Heisenberg
ones are valid for σ > 2 The exponent values belong to
other universality classes if 1/2 < σ < 2 (such as the
3-D-Ising model, the tricritical MF theory, the mixture of
short-and long-range FM interactions withβ and γ values lying in
between the MF theory and the 3-D Heisenberg/Ising model)
It is necessary to emphasize that the random distribution of
Cr atoms in FM Fe-related amorphous substances would also
lead to the different values of the critical exponents when Cr-doping content is varied
IV CONCLUSION
We studied the magnetic and critical properties of the amor-phous ribbons Fe78−xCrxSi4Nb5B12Cu1 The results revealed that the Cr-doping weakened FM exchange interactions
between Fe atoms This reduced the magnetization M and the TC of the alloy ribbons Analyses of the M (H, T ) data
around the TCbased on the MA-plot method and the scaling hypothesis determined the exponents β = 0.367–0.376 and
γ = 1.315–1.338 These values are close to those expected
for the 3-D Heisenberg model, and characteristic of the short-range magnetic interaction type
ACKNOWLEDGMENT This work was supported by the Converging Research Center Program through the Ministry of Science, ICT and Future Planning, Korea, under Grant 2013K000405
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