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Onset of ferromagnetism at the multicritical point of amorphous alloys
Journal
of Magnetism
and Magnetic
Materials
S4-57
(1986) 271-272
ONSET OF FERROMAGNETISM ALLOYS
AT THE
271
MULTICRITICAL
P. MAZUMDAR, S.M. BHAGAT and M.A. MANHEIMER llepr. of Ph.vs., Unit. of Mqvlond. College Pork, MD 20742. USA
POINT
OF AMORPHOUS
*
point Study of low-field magnetic response of a-(FeNi),jGz, has heen extended to a-Fe,Ni,,, ~, P ,4 Bh near its multicritical diverges as (r,). In both cases. the magnetization disappears as [(x/.x,)-l]” for x + .Y: and the peak susceptibility ’ ’ for I + XI . therehy lending credence to the hypothesis that .Y, is a percolation threshold. [l ~(.~/.X,)
Magnetic phase diagrams of many alloy systems exhibit a multicritical point (x,): PM e SG line for x i x, and PM w FM/FM c-) SG lines for x > x,. Theorists have focussed on distribution of exchange to understand these phenomena. However, attention has recently been drawn [l] to the importance of dilution and connectivity in the magnetic “network”. Using Fe,Ni,,_,P,,$Al,(I). for which x, = 12.4, and dc magnetization (M) data, it was shown that the peak susceptibility x( Tsc;. x) diverges as (u, - _x))~ for x + s; while M drops below the demagnetization-limited value (M,) for x + XT and vanishes as (s - x,)“. These sharp changes in magnetic response strongly pointed towards percolation as the underlying cause. Further confirmation has been sought by performing the same experiments on the alloy series Fe,Ni,,_, P,,$ (II). The results are reported here. Fig. 1 shows the phase diagram of series II alloys. Note that in both I and II, (aTr/ax)>, 0 for .Y+.x:. Thus Tr is not monotonic as a function of _Yand must depend on at least two competing effects. Models based on the distribution of exchange alone will not be adequate. It is crucial to explicitly include the connectivity and the consequent frustration in the magnetic network
PI.
Consider the re-entrants, x > x,. The T dependence of M is as shown in fig. 2 for B, = 1 Oe. Note the temperature independent values M,(x). All the samples were roughly the same size and shape. If M, = M,, it should be independent of x. This is true for x 2 13. We have also checked that for x > 13, M, scales with sample shape as expected while for s Q Il. M, is virtually independent of shape. As before [l], these are understandable if X, marks the onset of a percolating FM cluster. Such a cluster would not grow to encompass every magnetic site until x is well above s,. Thus M, = M, when x -s, is relatively large. Close to s,, M, appears to be “limited” by some internal parameter. presumably the number of spins in the FM cluster. It is gratifying to note that despite a significant difference in s,. M, vanishes as [(x/xc) - lip with /3 = 0.3 + 0.1 for both series I and II (fig. 3, full points). When x C-Y,. the quantity of interest is xp = x( 7&. x). x is defined as M/B, with B, + 0 and its T-dependence is shown in fig. 4. Clearly. xp increases rapidly as z --) s, For both 1 and II. xp diverges as [l - (.Y/.Y,)]~~ with y = 1.5 f 0.2 (fig. 3. open points). As discussed in ref. [l]. the divergence of xi, could be described by a scaling hypothesis. However, it seems more reasonable to use a single picture to account for
Park. MD 20740, USA
* Lab. for Phys. %I.. College
I
I
I
1
FexN~eo-xP14B6 200
0/-
q-TSG PM
O-T, A-Tf
100
0
/
/
t
FM
P +A-----~~
T(K)
”
3
\A
SG
p#o-o-m,
5
7 xc
9
I
1
f
II
13
15
0
xFig, 1. The magnetic phase diagram that ar,/a.x > 0 near -xi.
0304-8853/86/$03.50
of Fe,Ni,,_,
C Elsevier
P,,B,.
Note
Science Publishers
Fig. 2. Temperature G 15 in an applied .Y 2 I?.
B.V.
50
100
T(K)
150
1
200
dependence of the magnetization for 9 G .x field 8, = 1 Oe. Note that M, = M, for
712
lO(
2 -gIC \
O,A-xp
.,A-Mp
%
h
25 Fig. 4. Behavior of the wsceptlhilit~ as function of temperature for the spin glashes x = 4. 5 and 7 showing the peaks x,, at the respective hpln glass temperaturea 7,,..
F’ig. 3. Log~log plot of peak susceptibility (0. 3 ) and magnet!13tion (0, A) a. 1(x - _xc)/.y, j (0. 0) refer to series I ;md (a. A) to II. scaled appropriately.
ing pdx~hilit); drnces
both
.W,, and x,,.
network
combined
ergies
(to account
ising.
For
geometrical fraction
.x-<.x~,
Onset with for xP
correlation
of sites
of percolation
on the magnetic
a distribution
the SG is
phase)
of exchange seems
presumably
length
in the “infinite”
(5).
while.
cluster
most
limited
< CI [ 1 -
I’)
controls
plausible
h-l,,. ‘The since
( Y/-Y, )] “aind
/ .\
percolation Pa
[(_\
_tc/
depcn-
theory
[3]
I]““.
en-
promby
yield5
become
the
for A > .vL the (or the percolat-
[I]
P. Mazumdar. S.M. Bhagat and M.A. Manheimer. _I Appl Ph>r. s7 (19X5) 347’). 121 Del. Wehh et al., .l. Ma&n. Mngn. Mat. 44 (19X4) 15X. [3] K. Zallrn. The Physics of Amorphou\ Solid\ (Wile\. New Yorh. 19X?)
of Magnetism
and Magnetic
Materials
S4-57
(1986) 271-272
ONSET OF FERROMAGNETISM ALLOYS
AT THE
271
MULTICRITICAL
P. MAZUMDAR, S.M. BHAGAT and M.A. MANHEIMER llepr. of Ph.vs., Unit. of Mqvlond. College Pork, MD 20742. USA
POINT
OF AMORPHOUS
*
point Study of low-field magnetic response of a-(FeNi),jGz, has heen extended to a-Fe,Ni,,, ~, P ,4 Bh near its multicritical diverges as (r,). In both cases. the magnetization disappears as [(x/.x,)-l]” for x + .Y: and the peak susceptibility ’ ’ for I + XI . therehy lending credence to the hypothesis that .Y, is a percolation threshold. [l ~(.~/.X,)
Magnetic phase diagrams of many alloy systems exhibit a multicritical point (x,): PM e SG line for x i x, and PM w FM/FM c-) SG lines for x > x,. Theorists have focussed on distribution of exchange to understand these phenomena. However, attention has recently been drawn [l] to the importance of dilution and connectivity in the magnetic “network”. Using Fe,Ni,,_,P,,$Al,(I). for which x, = 12.4, and dc magnetization (M) data, it was shown that the peak susceptibility x( Tsc;. x) diverges as (u, - _x))~ for x + s; while M drops below the demagnetization-limited value (M,) for x + XT and vanishes as (s - x,)“. These sharp changes in magnetic response strongly pointed towards percolation as the underlying cause. Further confirmation has been sought by performing the same experiments on the alloy series Fe,Ni,,_, P,,$ (II). The results are reported here. Fig. 1 shows the phase diagram of series II alloys. Note that in both I and II, (aTr/ax)>, 0 for .Y+.x:. Thus Tr is not monotonic as a function of _Yand must depend on at least two competing effects. Models based on the distribution of exchange alone will not be adequate. It is crucial to explicitly include the connectivity and the consequent frustration in the magnetic network
PI.
Consider the re-entrants, x > x,. The T dependence of M is as shown in fig. 2 for B, = 1 Oe. Note the temperature independent values M,(x). All the samples were roughly the same size and shape. If M, = M,, it should be independent of x. This is true for x 2 13. We have also checked that for x > 13, M, scales with sample shape as expected while for s Q Il. M, is virtually independent of shape. As before [l], these are understandable if X, marks the onset of a percolating FM cluster. Such a cluster would not grow to encompass every magnetic site until x is well above s,. Thus M, = M, when x -s, is relatively large. Close to s,, M, appears to be “limited” by some internal parameter. presumably the number of spins in the FM cluster. It is gratifying to note that despite a significant difference in s,. M, vanishes as [(x/xc) - lip with /3 = 0.3 + 0.1 for both series I and II (fig. 3, full points). When x C-Y,. the quantity of interest is xp = x( 7&. x). x is defined as M/B, with B, + 0 and its T-dependence is shown in fig. 4. Clearly. xp increases rapidly as z --) s, For both 1 and II. xp diverges as [l - (.Y/.Y,)]~~ with y = 1.5 f 0.2 (fig. 3. open points). As discussed in ref. [l]. the divergence of xi, could be described by a scaling hypothesis. However, it seems more reasonable to use a single picture to account for
Park. MD 20740, USA
* Lab. for Phys. %I.. College
I
I
I
1
FexN~eo-xP14B6 200
0/-
q-TSG PM
O-T, A-Tf
100
0
/
/
t
FM
P +A-----~~
T(K)
”
3
\A
SG
p#o-o-m,
5
7 xc
9
I
1
f
II
13
15
0
xFig, 1. The magnetic phase diagram that ar,/a.x > 0 near -xi.
0304-8853/86/$03.50
of Fe,Ni,,_,
C Elsevier
P,,B,.
Note
Science Publishers
Fig. 2. Temperature G 15 in an applied .Y 2 I?.
B.V.
50
100
T(K)
150
1
200
dependence of the magnetization for 9 G .x field 8, = 1 Oe. Note that M, = M, for
712
lO(
2 -gIC \
O,A-xp
.,A-Mp
%
h
25 Fig. 4. Behavior of the wsceptlhilit~ as function of temperature for the spin glashes x = 4. 5 and 7 showing the peaks x,, at the respective hpln glass temperaturea 7,,..
F’ig. 3. Log~log plot of peak susceptibility (0. 3 ) and magnet!13tion (0, A) a. 1(x - _xc)/.y, j (0. 0) refer to series I ;md (a. A) to II. scaled appropriately.
ing pdx~hilit); drnces
both
.W,, and x,,.
network
combined
ergies
(to account
ising.
For
geometrical fraction
.x-<.x~,
Onset with for xP
correlation
of sites
of percolation
on the magnetic
a distribution
the SG is
phase)
of exchange seems
presumably
length
in the “infinite”
(5).
while.
cluster
most
limited
< CI [ 1 -
I’)
controls
plausible
h-l,,. ‘The since
( Y/-Y, )] “aind
/ .\
percolation Pa
[(_\
_tc/
depcn-
theory
[3]
I]““.
en-
promby
yield5
become
the
for A > .vL the (or the percolat-
[I]
P. Mazumdar. S.M. Bhagat and M.A. Manheimer. _I Appl Ph>r. s7 (19X5) 347’). 121 Del. Wehh et al., .l. Ma&n. Mngn. Mat. 44 (19X4) 15X. [3] K. Zallrn. The Physics of Amorphou\ Solid\ (Wile\. New Yorh. 19X?)