Anomalous magnetic viscosity in a -FeðCoÞ=ðNd,PrÞ 2 Fe 14 Bexchange-spring magnet Nguyen Hoang Haia, , Nguyen Chaua, Duc-The Ngob, Duong Thi Hong Gamc a Center for Materials Science, Han
Trang 1Anomalous magnetic viscosity in a -FeðCoÞ=ðNd,PrÞ 2 Fe 14 B
exchange-spring magnet
Nguyen Hoang Haia, , Nguyen Chaua, Duc-The Ngob, Duong Thi Hong Gamc
a
Center for Materials Science, Hanoi University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam
b Information Storage Materials Laboratory, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511, Japan
c
The Academy of Cryptography Techniques, 141 Chien Thang, Thanh Tri, Hanoi, Viet Nam
a r t i c l e i n f o
Article history:
Received 14 May 2011
Received in revised form
30 June 2011
Available online 8 July 2011
Keywords:
Magnetic relaxation
Exchange spring magnet
Hard magnetic material
Magnetic viscosity
Magnetic reversal
a b s t r a c t
This article presents an anomalous magnetic viscosity in a-FeðCoÞ=ðNd,PrÞ2Fe14B exchange-spring magnet A similar effect has been observed in non-interacting or weakly interacting systems but not
in a strong interacting magnetic systems We reported a new procedure to measure magnetic relaxation under various magnetic fields Changing the applied magnetic field by different field protocols during the reversal process, we found that a memory effect of the magnetization appeared if the field change is large enough The mechanism of the phenomenon can be explained in the model of conventional magnetic reversal in strong ferromagnetic systems with an energy barrier distribution The study of such magnetic relaxations can provide some information related to the energy barrier distribution function
&2011 Elsevier B.V All rights reserved
1 Introduction
Time dependence in strong magnetic systems provides many
interesting information and attracts considerable interest [1]
from the experimental and theoretical point of view Recently,
study of the dynamics of magnetic nanoscaled systems has been a
subject of many articles The magnetic nanoscaled systems are
assembly of magnetic nanoparticles Each particle has a
single-domain structure with the orientation of the magnetic moment is
dependent on magnetic anisotropy, effective applied magnetic
field, and temperature Isolated non-interacting magnetic
nano-particles behave as giant spins which theoretically described by
superparamagnetism Behaviors of interacting magnetic
nanopar-ticles are complicated due to the competing of different energy
types Since a pioneer article on the memory effects of dc
magnetization and magnetic relaxation in a weakly interacting
magnetic nanoparticle system [2], almost a hundred of related
articles have been published to investigate the nature of the
effects [2– ] According to Refs [2,9], though the full
under-standing of the nature of spin glass was unclear but the memory
effect of the magnetic relaxation under different applied magnetic
field and temperature protocols could be explained by the
hierarchical model of spin-glass-like phase of isolated
poly-dis-persed nanoparticles Other authors claimed that the magnetic
memory effects could simply be understood by the superpara-magnetism with a modification of the distribution of energy barriers[10,11] Magnetic memory effects have been commonly
in non-interacting or weakly interacting nanoparticle systems such as ferritin and Fe3N [11], Fe3O4 [12], g-Fe2O3 [5,13],
La0.6Pb0.4MnO3[14] Until now, there is no report on such type
of magnetic relaxation in strongly interacting systems, especially
in hard magnetic materials
The time dependence of the magnetization during the reversal process of a ferromagnetic system is interpreted by a thermally activated process related to the perfectly random crossing of energy barriers E of two-level metastable systems[15–17] The possibility PðtÞ that magnetization reversal occurs between time
0 and t, at temperature T can be written as PðtÞ ¼ 1expft=tðEÞg, whereastðEÞ is the relaxation time—the average crossing time for barrier energy E The Boltzmann–Arrhenius law relatingtðEÞ with the intrinsic relaxation timet0which corresponds to the crossing time of a barrier of zero height is tðEÞ ¼t0expfE=kBTg The variation of magnetization with time is given by[1,18]:
MðtÞ Mð0Þ¼
Z 1 0
2exp t
tðEÞ
1
DðEÞ dE where DðEÞ is the distribution function of the energy barrier which is normalized by R1
0 DðEÞ dE ¼ 1 The expression of the magnetic relaxation coefficient, S, is
S ¼ @M
@ln t¼2Mð0Þ
Z 1 0
t
tðEÞexp
t
tðEÞ
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Journal of Magnetism and Magnetic Materials
0304-8853/$ - see front matter & 2011 Elsevier B.V All rights reserved.
Corresponding author Tel.: þ 84 4 3558 2216; fax: þ84 4 3858 9496.
E-mail address: nhhai@vnu.edu.vn (N.H Hai).
Trang 2In this expression, the distribution function DðEÞ is weighted
by the function ðt=tðEÞÞexpft=tðEÞg which defines the so-called
energy window The weighting function is equal to zero
every-where except aroundtðEÞ ¼ t Due to this window, only a small
section of DðEÞ around t contributes to S The position of the
window, Ec, at a given time t and a fixed temperature T is
Ec¼kBT ln ðt=t0Þ The width of the window is approximately
equal to kBT[19] The effects of time and temperature are shifting
the energy window towards higher energy values, logarithmically
with time and linearly with temperature The effect of the applied
magnetic field is mostly changing the distribution function
We obtain the expression for the variation of magnetization
with time is
MðtÞ
Mð0Þ¼12
ZE c
0
As magnetization M(t) is a function of E, a scaling law in
T lnðt=t0Þmay be inferred The value oft0deduced from fitting to
experimental data varied from 1012to 5 107s[19]
If DðEÞ is nearly constant in the interval of energy barriers
which the magnetic moments can overcome during the
observa-tion time, the magnetizaobserva-tion is
MðtÞ
Mð0ÞC12kBTDðEcÞln t
t0
ð3Þ which is the so-called logarithmic approximation[20]
Exchange-spring magnets belong to a type of nanostructured
materials of which excellent hard magnetic properties are induced
by the combination of two mutually exchange-coupled phases:
the hard magnetic phase (e.g Nd2Fe14B, SmFeN) providing large
magnetic anisotropy, the soft magnetic phase (e.g bcc-Fe, bcc-FeCo)
providing a high saturation magnetization This combination may
arise a huge maximum energy product and exchange-spring
magnets have been considered as one of the best candidate for
high-performance permanent magnets[21,22]
We present the study of magnetic viscosity in a-FeðCoÞ=
ðNd,PrÞ2Fe14B exchange-spring magnet in this article We observed
an anomalous behavior in magnetic viscosity which can be
explained by the well-known magnetization reversal process[1]
2 Experimental
Exchange-spring magnet a-FeðCoÞ=ðNd,PrÞ2Fe14B was
fabri-cated by the conventional melt-spinning technique (Edmund
Bueller melt-spinner) in an Ar atmosphere and thermally
nano-crystallized in a similar way presented elsewhere [23] The
starting materials was adjusted to have the composition of
Nd2.25Pr2.25Fe73.8B16.5Co3Ti1Nb1Cu0.2 The tangential speed of the
cooper wheel was 30 m s1 to form amorphous ribbons The
nanocomposite magnet was obtained by annealing amorphous
ribbons in Ar at 590 1C in Ar gas followed by quenching in cooled
water The magnetic measurements were performed on a DMS
880 vibrating sample magnetometer (VSM) with a maximum
magnetic field of 13.5 kOe at room temperature Hysteresis loop
was obtained without demagnetizing field correction The
struc-ture examination was carried out by using a D5005 Bruker X-ray
diffractometer with Cu Karadiation
3 Results and discussion
Fig 1presents the XRD data of the sample annealed at 590 1C
for 5 and 30 min under Ar atmosphere The results show a
multi-phase structure of the soft magnetic multi-phasea-FeðCoÞ and the hard
magnetic phases NdFe B and PrFe B If the annealing time
was shorter than 20 min, a metastable phase of (Nd,Pr)2Fe23B3
still existed in the sample If the annealing time was longer, this phase was transformed to the (Nd,Pr)2Fe14B anda-Fe The pre-sence of Fe and Co to form FeCo alloy improves the saturation magnetization of this phase The optimal annealing conditions were 590 1C, 30 min
Hysteresis loop and recoil curves of thea-FeðCoÞ=ðNd,PrÞ2Fe14B
is given in Fig 2 The sample possesses good hard magnetic properties with the saturation magnetization, Msof 140 emu/g, the coercive field, Hcof 2.8 kOe, the magnetic squareness, Mr/Ms
of 0.8 (Mris the remanent magnetization), the energy product of
12 MGOe The exchange-spring behavior was presented by study-ing the isothermal remanent magnetization (mIRM) and the dc demagnetization (mDCD)[24] Interaction in the material is given
by the relation:
DM ¼ mDCDð12mIRMÞ here m¼M/Msis the reduced magnetization IfDM is negative, the particle interaction in the system is essentially governed by the dipole interaction, which is easier to be demagnetized than to be magnetized If theDM is zero, no particle interaction occurs in the system If the DM is positive, the system is dominated by the exchange interaction The field dependence ofDM in Fig 3
indicates the presence of the exchange coupling interaction between particles
Fig 1 X-ray diffraction patterns of sample annealed at 590 1C for 5 and 30 min.
-150 -100 -50 0 50 100 150
-10000 -5000 0 5000 10000 -150
-100 -50 0 50 100 150
H (Oe)
H (Oe)
Fig 2 Recoil demagnetization curves and hysteresis loop (inset) of the exchange-spring magnet.
Trang 3The relaxation of magnetization under a negative applied
magnetic field, H, of 3000 Oe as a function of time in the
exchange-spring magnet is illustrated inFig 4 The time
depen-dence of magnetization does not simply follow the logarithmic
law as described by Eq (3) in the whole range of measuring time
When the measuring time is small, a deviation from a linear
function was observed But with the measuring time larger than
about 90 s, the logarithmic dependence is obeyed The
logarith-mic dependence was deduced from Eq (2) by supposing that the
value of the distribution function DðEÞ is constant in the interval
of energy barriers The violation of logarithmic law have been
commonly observed in magnetic systems in which a large
distribution of the energy barrier are presented Such systems
normally follow the T lnðt=t0Þscaling law[19] The large
distribu-tion can be resulted from a large distribudistribu-tion of particle size
(EpKV, where K is the anisotropy field, V is the volume of the
particle) or a multi-phase character of the magnetic system In
our sample, there are at least two main phases of the soft
magnetic material a-FeðCoÞ and hard magnetic material
(Nd,Pr)2Fe14B In addition, the presence of Ti and Nb supporting
the formation of the amorphous state, the presence of Cu helping
the phase separation after heat treatments, created a multi-phase
nature of the sample However, the two main phases significantly contributed to the distribution function which may result to a variation in the value of this function, that caused the non-logarithmic dependence of magnetization The relaxation of the soft magnetic material is much faster than that of the hard magnetic one therefore after a short period of time the magnetic relaxation followed the logarithmic law We will conduct other experimental studies in that logarithmic regime
Now during the magnetic relaxation process under H1¼
3000 Oe, we switched the field to a new value, H2¼ 2500 Oe and left the system relax for 350 s before returning to the initial magnetic field as shown inFig 5 InFig 5, curve (a) presents a continuous decay of the magnetization under H1 in the similar way as displayed inFig 4 At t¼255 s, H2was applied which led
to a sudden change in the magnetization from 66.66 to
64.24 emu/g When H2 was applied, the magnetization was hardly changed (less than 0.1%) (curve (b)) indicating that the relaxation was halted At t¼ 600 s, the applied magnetic field was switched back to H1which caused another sudden change in the magnetization from 64.31 to 66.94 emu/g, then the relaxation continued as it was before applying H2 (curve (c)) Curve ðc0Þ obtained by shifting curve (c) to the left by a time period (which equals to the relaxation time under H2) in order to have a continuation of curve (a) (the inset of Fig 5) This behavior is similar to the memory effect in interacting Ni81Fe19 magnetic nanoparticles in which instead of the magnetic field, the tem-perature was switched[2] The process was repeated three times and the same behavior was observed (Fig 6) in which, three curves under H1combined as a continuous relaxation We can say that a memory effect is observed in the exchange-spring magnet For further studies, we argue that the change in magnetic field, in this case,DH ¼ H2H1¼500 Oe is large Let examine an extreme case whereDH is very small, smaller than the precision of the magnetic device (the VSM), that is no field changing It is clear that the magnetic relaxation will be a continuous process with no such magnetic memory effect therefore there will be a value of
DH smaller 500 Oe at which the memory effect starts to occur, as presented inFig 5
Fig 7 presents the relaxation of the magnetization with
DH ¼ 30 Oe, i.e., H2¼2970 Oe Obviously the memory effect is
0 3000 6000 9000 12000 -0.2
-0.1 0.0 0.1 0.2 0.3 0.4
-100
-50
0
50
100
150
H (Oe)
H (Oe)
IRM (emu/g)
DCD (emu/g)
Fig 3 The isothermal remanent magnetization (IRM), the dc demagnetization
(DCD) andDM plot (inset) of thea-FeðCoÞ=ðNd,PrÞ 2 Fe 14 B magnet.
-65
-60
-55
-50
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 -65
-60 -55 -50
t (s)
H = -3000 Oe
lnt (s)
Fig 4 Relaxation of magnetization under a negative applied magnetic field of
3000 Oe as a function of time in the exchange-spring magnet.
-70 -65 -60 -55
3.5 4.0 4.5 5.0 5.5 6.0 6.5 -70
-65 -60
-55
Δt = 22 (s)
ΔM = 0.22 (emu/g) (a)
(c’)
(c’)
t (s)
H1 = -3000 Oe
H2 = -2500 Oe
(c)
H1 = -3000 Oe
lnt (s)
Fig 5 Relaxation of the magnetization under negative applied magnetic fields
H 1 ¼ 3000 Oe and H 2 ¼ 2500 Oe When H changed from H 1 to H 2 then returned back to the initial value, the magnetization seems to continuously decay as it was before changing the field The inset presents the logarithmic dependence as time
Trang 4not present There is still an abrupt change from the curve (a) to
the curve (b) but less spectacularly Under the field H2¼2970 Oe,
the magnetization reduces almost linearly with time from
59.32 to 60.24 emu/g When the magnetic field returns to
H1, the highest value of the magnetization of curve (c) is much
lower than the magnetization in curve (a) We construct curve ðc0Þ
by shifting curve (c) to the left in order to have a continuation in
magnetic relaxation It is not likeFig 5 where curve ðc0Þ is an
immediate continuation of curve (a), InFig 7(the inset), there is a
gap between the two curves, which is characterized by
DM ¼ 1:15 emu=g andDt ¼ 100 s Precisely, there is a small gap
in Fig 5 with DM ¼ 0:22 emu=g and Dt ¼ 22 s, which is much
smaller than the gap appeared in Fig 7 The behavior was
observed when three such field protocols were repeated (Fig 8)
The decay rate of curves reduced from (b), (d), and (f) We
conducted the same measurement procedures with H2¼2950,
2980, 2990 Oe and observed very similar results (data not
shown)
When the magnetic system relaxed, instead of increasing the
applied magnetic field, we reduced it to H2¼ 3500 Oe and
the results are presented inFig 9 There is a huge reduction of
magnetization from 62.08 to 101.32 emu/g after the field change Then the system under H2magnetically relax in a similar way of curve (a) Curve (c) was obtained after a sudden but less spectacular jump from 104.10 to 100.45 emu/g and the magnetization almost did not change with time
To explain the results, we come back to Eq (1) The value of the magnetic viscosity is determined by the energy window and the distribution function The strong magnetic anisotropy in the sample came from the uniaxial anisotropy of the hard magnetic phase (Nd,Pr)2Fe14B which in turn is due to the strong spin–orbit coupling of the rare-earth elements [25] When the applied magnetic field is parallel to the easy axis, the energy barrier is determined by E ¼ KVð1H=HaÞ2[25,8], where K is the magneto-crystalline anisotropy constant, V is the volume of the particle,
Ha is the anisotropy magnetic field The anisotropy field of (Nd,Pr)2Fe14B can reach 70 kOe[25], so that the magnetic field applied on the sample is much lower than Ha As the result, ignoring the second order factor, we obtain EpH The reduce of the magnetization with measuring time inFig 4can be explained
by shifting to energy window towards higher energy values logarithmically with time
-60
-55
-50
-45
H1 = -3000 Oe
H
1 = -3000 Oe
H
2 = -2500 Oe
H
2 = -2500 Oe
H (Oe)
H
1 = -3000 Oe
H
2 = -2500 Oe
Fig 6 Relaxation of the magnetization under negative applied magnetic fields
H 1 ¼ 3000 Oe and H 2 ¼ 2500 Oe as a function of time The field protocol was
repeated three times.
-65
-60
-55
-50
-45
3.5 4.0 4.5 5.0 5.5 6.0 6.5 -65
-60 -55 -50 -45
H
1 = -3000 Oe
t (s)
H
1 = -3000 Oe
H
2 = -2970 Oe
lnt (s)
(c’) (a)
Δt = 100 (s)
ΔM = 1.15 (emu/g)
(a)
(b)
(c) (c’)
Fig 7 Relaxation of the magnetization under negative applied magnetic fields
H 1 ¼ 3000 Oe and H 2 ¼ 2970 Oe as a function of time The magnetization under
H 2 reduces almost linearly with time.
-60 -55 -50 -45
H
t (s)
Fig 8 Relaxation of the magnetization under negative applied magnetic fields
H 1 ¼ 3000 Oe and H 2 ¼ 2970 Oe as a function of time The field protocol was repeated three times.
-100 -80 -60
(c’) (b)
H
t (s)
H
(a)
Fig 9 Relaxation of the magnetization under negative applied magnetic fields
H 1 ¼ 3000 Oe and H 2 ¼ 3500 Oe as a function of time.
Trang 5If the field H changes, the energy barrier E changes accordingly
by an amount proportional to the change of the magnetic field,
DEpDH which means that the energy barrier distribution function
DðEÞ in Eq (2) is shifted to higher energy values If DðEÞ is shifted to
much relative to the weighted function ðt=tðEÞÞexpft=tðEÞg, the
overlap between these two functions is small, as the result, the
integration in Eq (1) is zero which is corresponding to the case of no
magnetic relaxation Applying to the results presented inFig 5, as
the applied field changed from 3000 to 2500 Oe, corresponding
to DH ¼ 500 Oe, the energy barrier increased significantly which
caused a halt in magnetic relaxation The magnetic moments in the
sample could not overcome the high energy barrier so that no
magnetic moment reversed When the field came back to the initial
value, the relaxation process continued as if there was no change in
the field, which is denoted by curve (a) and ðc0ÞinFig 5 The small
discontinuation characterized by DM ¼ 0:22 emu=g, Dt ¼ 22 s can
be ascribed to a lag time when the VSM changed the applied field
If the field change is small as indicated inFig 7(DH ¼ 30 Oe),
the energy barrier was lifted by a small value In the sample, the
distribution function is broad due to the presence of many magnetic
phases and also the distribution in size of particles Therefore, there
is still some moments with higher energy than others can overcome
the energy barrier so that the magnetic reversal occurred even the
possibility for that is much lower Mathematically, the shifting of
the distribution function relative to the weighted function in Eq (1)
reduces the overlap of these functions, which causes a smaller value
of the magnetic viscosity This can explain the fact that the linear
decay of the magnetization (Fig 5, curve (b)) is slower than the
logarithmic decay of curves (a) and (c) The magnetic relaxation in
this region may be comparable to the logarithmic relaxation after a
very long time The width of the distribution function can
deter-mine the range ofDH at which the memory effect starts to occur
The gap between curves (a) and ðc0Þ in Fig 7 characterized by
DM ¼ 1:15 emu=g,Dt ¼ 100 s cannot only be ascribed to relaxation
during the time for changing applied field of the VSM It is also due
to the relaxation of the magnetization as time under H2 In this case,
the magnetization change under H2of 0.92 emu/g is smaller than
DM ¼ 1:15 emu=g by an amount of 0.23 emu/g which is
compar-able to the magnetization gap of 0.22 emu/g appeared in Fig 5
We can proclaim that the change in magnetization between curves
(a) and (c) inFig 7originates from the magnetic relaxation under
H2 and the time lag of the machine Imagine that if we have a
system containing perfectly homogeneous particles with exactly
the same energy barrier, any increase in the applied magnetic field
above 3000 Oe will halt the relaxation Therefore, the relaxation
presented under H2is due to the large distribution in energy barrier
of the sample If the distribution function is broad,DH should be
high and vice versa in order to observe the magnetic memory effect
Put it in another way, measuring the field change at which the
magnetic memory effect starts to occur we can have an idea
about the value of the width of the energy barrier The above
arguments can be applied to explain the memory effect presented
in literature[2– ]
To check the validity of the theory of magnetic reversal, we
performed another field protocol in which H2¼ þ3000 Oe (Fig 10)
No memory effect is observed Each curve presents as a normal
relaxation in both negative and positive applied magnetic fields
The relaxation process depends strongly on the magnetic history of
the system In all curves (a) of the previous experiments and curve
(a) ofFig 10, the relaxation occurred after being saturated at a high
magnetic field of 13.5 kOe If the magnetic field is high enough to
obtain the major hysteresis loop that field can wipe out the
previous magnetic states From the hysteresis loop in the inset of
Fig 2, the magnetic field at which previous magnetic states can be
erased of 8.5 kOe was determined from the reversible part at high
magnetic fields Curves (c), (e), and (g) of Fig 10 are relaxation
processes after applying the magnetic field of 3 kOe which is smaller than the value of 8.5 kOe Therefore those relaxations are different after each time of changing the applied magnetic fields The values of magnetization at which the magnetic decay started reduced from curves (a) to (g) This, in fact, is the magnetization determined from the minor hysteresis loops, in which the previous magnetic states were partly wiped out Curves (b), (d), and (f) can
be explained in a similar way
4 Conclusion Anomalous magnetic viscosity have been observed in
a-FeðCoÞ=ðNd,PrÞ2Fe14B exchange-spring magnet under different field protocols, which can be explained in the model of conven-tional magnetic reversal in strong ferromagnetic systems Our study supports the theory of energy distribution which presented
to explain the relaxation in non-interacting and weakly interact-ing nanoparticles It also can provide some information related to the energy barrier distribution function
Acknowledgement This work is financially supported by the National Foundation
of Science and Technology Development (NAFOSTED Grant No 103.02.68.09) Authors would like to thank D Givord for fruitful suggestions
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