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Reentrant magnetism - a low field study
Journal of Magnetism and Magnetic North-Holland Publishing Company
REENTRANT
Materials
MAGNETISM
147
38 (1983) 147- 158
- A LOW FIELD STUDY
M.A. MANHEIMER for Physical Sciences, College Park, MD 20740, USA
Laboratory
SM. BHAGAT Dept. of Physics and Astronomy,
University of Maryland,
College Park, MD 20742, USA
H.S. CHEN Bell Laboratories, Received
Murray Hill, NJ 07974, USA
10 March
1983; in revised form 9 May 1983
We report low field dc magnetization measurements on (Fe,Mn,_,),sP,,~Al, alloys at 4
1. Introduction Alloy systems with competing ferromagnetic and antiferromagnetic interactions on the one hand, and those with wide distributions of exchange energy on the other, have attracted a great deal of attention in recent years. One of the most fascinating aspects of these investigations has been the discovery of reentrant magnetism. It has been found that although some of these alloys show a typical Curie transition from paramagnetic (PM) to ferromagnetic (FM) behavior, the ferromagnetic state is unstable against further lowering of temperature. This low temperature “transition” manifests itself in a number of ways: (i) drop of the demagnetization-limited ac susceptibility [ 11, (ii) field dependent peak in ac susceptibility measured in presence of a dc field [2], (iii) rapid, exponential rise in the width of the ac hysteresis loop [2], (iv) vanishing of spontaneous magnetization [3], (v) reduction of spin wave energies measured by inelastic neutron scattering [4,5], (vi) 0304-8853/83/0000-0000/$03.00
0 1983 North-Holland
rapid increase in linewidth for ferromagnetic resonance [6], (vii) low temperature anomalies in the temperature dependence of magnetization [7], (viii) onset of “anisotropy fields” [8], (ix) onset of magnetic viscosity and (x) history dependent effects [9]. The low-temperature phase thereby has several properties usually associated with spin glass (SG) behavior in dilute alloys. In this sense, one talks of a ferromagnet to spin glass transition. Reentrant magnetism in a system therefore implies PM --, FM --j SG phase with reduction of temperature. Low magnetic field studies are fruitful because they are likely to provide insight into magnetic phenomena, which are most characteristic of intrinsic behavior. Here, we describe in some detail our low (I 50 Oe) field dc magnetization studies on an amorphous alloy series, (Fe,Mn, _,) 75 P,,$A13. We confirm earlier reports of reentrant behavior [2,10,1 l] and present a complete analysis of magnetization data not only in the FM phase but also in the SG phase. We describe the first measurements, to our knowledge, of the temper-
148
M.A. Manheimer
ature marking the onset of irreversibility at the FM -+ SG transition measured in the presence of a magnetic field. In addition, at low temperatures we identify two contributions to the magnetization. One of these follows the direction of the applied field (and is therefore reversible), while the other behaves like a frozen or permanent moment. We show that the temperature and field dependences of the reversible magnetization data can be collapsed in the form suggested by the scaling “laws” for magnetic phase transitions. However, in view of the irreversibility, one must be careful in trying to conclude that one has identified the FM -+ SG transformation as a continuous second-order phase transition. Finally, we associate the frozen moment with a spin-glass order parameter. Method Ribbons of (Fe,Mn,_,),,P,,$Al, with nominal values of x = 0.65, 0.70 and 0.80 were grown by the melt spinning technique. They were typically 1 mm wide and about 30 pm thick. For the present experiments several (8- 10) pieces, each 15 mm long, were tied securely to a copper holder and suspended, inside a stainless steel vacuum chamber C, from one arm of a Cahn 2000 microbalance (sensitivity = 0.1 pg) as shown in fig. 1.
To
Balance
Liquid Helium Tube
,
et al. / Reentrant magnetism
The lower 10 cm of C were made of Cu. A Cu-constantan thermocouple was attached to the outside of this copper can at the height of the sample center. A second vacuum jacked surrounded C and could be pumped to thermally isolate the sample space from cryogenic liquids. The sample temperature could be further controlled using a Karma wire heater wound (noninductively) around the can. During a measurement, an exchange gas pressure of = 200 pm He was maintained in C. Two sets of Helmholtz coils were fixed outside the cryostat, coaxial with the hangdown wire. One pair of coils was used to cancel the vertical component of the earth’s field, and had the sample at its center. The other pair produced both the measuring field and field gradient, and was positioned such that the field gradient was about 3% of the field at the sample. The applied fields were varied between 0.5 and 50 Oe. The temperature was varied between 4 and 300 K. Since the sample and thermocouple are separated in space we performed a calibration experiment, in which the sample was replaced by a single crystal of paramagnetic CuSO, . 5H,O. The later is known to have a susceptibility varying as (T + 0.6)) ‘. It was found that the apparent sample temperature required systematic corrections of, at most, 4 K. Repeated measurements lead us to suggest that the temperatures listed below are good to about 1 K. To measure the magnetization at a given temperature, we recorded the effective “magnetic” weight of the sample by taking the difference between the output of the balance in zero field and in an applied field B,. Two observations were taken at every T, first with the applied field B, and
Heater
B,=O B,= IO Oe
/Copper Tube
,w(n/“)
m
B,=B,=
IO Oe
+
Thermocouple, t%
6%
Imin He Exchange Gas
-
Fig. 1. Low-temperature
-Sample
probe used to measure
magnetization.
Fig. 2. Output of the electrobalance as a function of time for zero-field cooled (left) and 10 Oe cooled states (right). For each case, the measuring sequence for applied field (in oersted) is: B, = 0 + 10 * 0 + 10 + 0. Note the difference in gain settings.
M.A. Manheimer
et al. / Reentrant
its gradient in one direction, and next with the two reversed. This yields the quantities labelled W, ( B,, B,) and W, (B,, B,) in fig. 2 where we have plotted the output of the balance as a function of time. Here, B, is the field in which the sample was cooled. It was turned off before applying B,. It turns out that W, (0, B,)= W, (0, B,) at all temperatures if the sample has been cooled in zero (5 3 mOe) field to 4 K and then warmed up to the desired T. However, if the sample is cooled in a finite field W,(B,, B,) * W, (B,, B,) at low T. This indicates that, in the field-cooled state, the sample acquires a “frozen” or permanent magnetic moment at low T. It was found that W, + W, is independent of B,. Thus we associate W, + W, with a reversible component in the magnetization (M) and designate W, - W, as a measure .of the frozen or irreversible magnetization, labelled Mi. In order to obtain absolute values for M, the system was calibrated using a single length of Fe,,Ni,,P,,$Si, (Metglas 2826B) ribbon. Several independent measurements [12] have shown that, at 300 K, this material has 47rM = 4.8 kOe. Because of uncertainties in sample volume and shape effects we estimate that the absolute values of 4aM are accurate to about 10%. The relative values are probably good to about 1% except at the lowest applied fields.
a
magnetism
149
I.4x 4oe 0 10oe v 300e I c P
o.a0.6 0.4 0.2 -
OL 0v
IO
20
30
40
50
60
70
a0
90
loo 110 120
70
a0
90
100 110 Ix) 130 140
T(K)
b
1020
30
40
50
60
T(K)
2. Results 3.66
2.1. Reversible
magnetization
Fig. 3a, b and c shows the reversible magnetization of the alloys, as a function of temperature, for various values of the applied field, B,. As discussed above this component of magnetization is independent of the cooling field. In every case, the systems show reentrant magnetism in the sense that, as T is lowered, the magnetization first shows a large increase (defining T,) but on further cooling M drops again, essentially vanishing at low T. As shown earlier [ 10,l l] one can define an effective freezing temperature TF by using the linear drop in M at low T (see also, curve for W, + W, in fig. 5 below). Increasing B, favors the FM state. That is, the rise
f 0
IB1.2 -
c
(F60.6M"o.z)75 '16B6A'3
%\ ‘9 b
B,=20e
/ n
I
I
\ 1
40
I
80
/
I
120
I
I
160
I
I
200
I
I
240
I
.j
28k
T (K)
Fig. 3. Reversible magnetization as a function of temperature, for various values of applied field; (a) x = 0.65, (b) x = 0.70, (c) x = 0.80.
in M near T, shifts to higher T while the drop in M near T;” moves to lower T. Extrapolation to B, = 0 will yield the true transition temperature Tf discussed in section 3.1. For the x = 0.80 alloy, for
150
M.A. Manheimer
a
IO
20
30
b 80
2.0
54 52 50 40 46
42 40
et al. / Reentrant
magnelism
instance, an applied field of 10 Oe suppresses to below 4 K any evidence of the low T downturn. The sensitivity to applied field is remarkable. At first sight, one would expect only fields of the order of (kT,/p,) or (kTf/pB) to give significant effects. The present fields are several orders of magnitude smaller. In the intermediate temperature regime the large magnitudes of M, in fairly low applied fields, are highly suggestive of soft ferromagnetism. It is also useful to compare the present 4nM values with those obtained from other techniques. For instance, ferromagnetic resonance [ 131 data (in the x = 0.65 alloy) taken at 3-10 kOe applied fields give 4nM values only about 50 percent higher than our values at 30 Oe. In a magnetic sample, with an effective demagnetizing factor N, at low fields the magnetization will be given by A4 = B,/( l/x + N), so that when the FM state sets in and the low-field susceptibility x becomes very large M + B./N, independent of T. This was checked at several temperatures and in turn allowed us to determine N for our samples. Typically N < lo-*. Fig. 4a and b summarizes the magnetic isotherms of the x = 0.7 alloy in the neighborhood of T, and T,, respectively. As expected, the curves in fig. 4a indeed resemble those obtained in the neighborhood of a PM + FM transition. At high T, A4 is almost linear with B,. The non-linearity becomes sharper as T is reduced, producing the possibility of a non-zero intercept at the demagnetization limit, i.e., spontaneous magnetization M,. In fig. 4b one observes the same behavior except that now the role of temperature is reversed; the low T data show less curvature. The s-shaped isotherms at the lowest temperatures are probably symptomatic of magnetic hysteresis at very small B,. 2.2. Irreversible
Fig 4. Magnetic isotherms in the vicinity of T, (a) and T, (b). The left most (highest slope) line marks the demagnetization limit. The number labelling each curve is the temperature in kelvin.
or frozen magnetization
As described above, cooling in a magnetic field to 4 K causes the sample to acquire a frozen or irreversible magnetization, Mi. Fig. 5 shows IV, (10, 10) and W, (10, 10) as functions of temperature. M, is proportional to (W, - W,) and is also plotted in fig. 5. This kind of plot was used to
M.A. Manheimer
x x
0.
~~‘~
XX
I
-20 -
0
-
B,tt B, 0 Y,+t B,
A
0
•IDIFF
0 op" -60 0 IO
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to
T;
-40
+Ti
xSUM 20
30 T(K)
40
50
60
Fig. 5. W, (10, lo), A, and W, (10, 10). 0 as a function of temperature for x = 0.7. Also plotted is ( W, - W,), 0, which is proportional to the frozen magnetization M,, and ( W, + W,), X, which is proportional to the reversible magnetization, M. Note that the value for TF obtained by extrapolating to M = 0 is lower than T,*, so that the irreversibility sets in at finite M. As discussed in the text, TF and 7. approach each other as B, -+ 0.
et al. / Reentrant
151
magnetism
define the temperatures T* (B,), which mark the onset of irreversibility. We also determined TT by measuring W, and W, while cooling in a magnetic field. Fig. 6 shows such data and one notices that (W, - W,) becomes non-zero at essentially the same temperature as that marked in fig. 5 by the disappearance of Mi. We have measured Mi, as a function of T, for several combinations of B, and B,. We find that (i) Mi (30, B,) at 4 K is roughly one third of M at 77 K with B, = 30 Oe. However, even with B, = 1 Oe, one freezes in about 3% of the FM magnetization, (ii) TT reduces with increasing B, but is independent of B, for B, varied from 1 Oe to 30 Oe, (iii) Mi is independent of time over several hours, (iv) for small B, (s 4 Oe) the T-dependence of W, (B,, B, ), W,( B,, B,) and hence Mi is more complex (fig. 7). This effect is most marked for the x = 0.7 alloy. A vestige of this phenomenon can also be seen in the temperature variation of the reversible M, fig. 3b, B, = 1 Oe, where one notices a slight “bump” around 50 K. In fig. 7 the peak in Mi moves to higher T as B, is reduced. For the present, it is mainly an irritant since it interferes with any attempt to fix TT at low B, values.
6
300
pH-
I
Y
/d
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Bc=Ba=lOOe A 8, tt B,
‘3, +t B,
p/”o dt p/t
3 > r
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dd’
‘I
C
(FeO.7Mn0.3)75 P16B6A'
(Fe0.7Mn0.3),5F;6B6A'3
I 0
-3 0 I
I
60
40
80
T(K) Fig. 6. W, (IO, IO), A, and W, (10, IO), 0 measured for x = 0.7 sample while being cooled, and plotted as a function of temperature. Note the rapid increase in (IV,, - W,) for T c T:.
IO
20
30 40 T(K)
50
60
70
Fig. 7. W,, (30, 1) and W, (30, l), v and 0, respectively, for x = 0.7. Also shown are ( W, - W,), 0, proportional to M, and (W, + W,) 0 proportional to M. The unexplained peak at about 50 K in (IV, - IV’) makes it difficult to designate ri* at low fields.
152
M.A. Manheimer
et al. / Reentrant
magnetism
60
2.3. Viscous effects
I
I\1
In a spin glass one should expect to find viscous or time-dependent effects in the magnetization. As noted above, although the advent of Mi marks the onset of irreversibility, M, itself is not observed to vary with time. It is conceivable that Mi varies with time for T very close to TT but we are not able to measure this effect. On the other hand, we find that over some temperature regimes (depending on B,) the data show time dependence, which can be understood only if the reversible magnetization has viscous behavior with response times of minutes, the characteristic time of the present experiment. First (although not clear from fig. S), note that for B, parallel to B,, W,, shows a rapid rise to a value consistent with that of Mi (B,, T) followed by a slow increase towards a total magnetization larger than Mi. Next, consider the type of data shown in fig. 8, where we have plotted the time development of W, (1, 20) and W,( 1, 20). It is clear that application of B, antiparallel to B, causes the magnetization to grow along B,. However, every time B, is turned off and reapplied the system is initially found to have its magnetization pointing along the original direction of freezing. All these results are accounted for if M, (B,, T) is some fixed quantity while application of B, causes M to grow along B, in a viscous manner. The temperature intervals of viscous behavior are
I
I
20 -
I
01
0
I
I
IO
20
30
6, (Oe) Fig. 9. Temperature intervals, where viscous behavior has been observed, plotted as a function of measuring field, for the x = 0.7 sample.
shown in fig. 9, as a function of B,, and indeed viscosity effects set in at lower T with increasing
4. 3. Analysis and discussion 3. I. Characteristic
temperatures
Apart from the Curie temperature there are two characteristic temperatures of interest in each of
‘0 ‘0
Fig. 8. W, (1, 20) and W, (1, 20) at 20 K for x = behavior is evident for the W, data. The field B, is points labelled + and turned off at points labelled B, 1 f B, and + implies B, t 1 B,. A zero-signal been drawn as a guide to the eye.
0.7. Viscous turned on at 0; - means baseline has
I I
2I
\I 3
4I
5I
6I
7I
Fig. 10. Effective spin-freezing temperature 7;* (B,), determined from the low temperature magnetization drop, plotted as a function of B’/*. B, was the applied measuring field. A linear a extrapolation to B, = 0 gives the zero field freezing temperature for each of the samples.
M.A. Manheimer
et al. / Reentrant
153
magnetism
Ii 50 01
-.-0-O-
01
’
0.4
I
I
I
I
0.5
0.6
0.7
0.0
X
Fig. 11. Magnetic phase diagram at B, = 0 for (Fe,Mn,_,),, P,,$Al,, l ref. [16]; n ref. [2]; A this work. The lines have been drawn as a guide to the eye. Note, especially, that there are no data available in the immediate neighborhood of the multicritical point.
these alloys. At T: (B,) the reversible magnetization appears to vanish while at y (B,) the frozen moment goes to zero. T; (B,) was determined [ 11,121 by extrapolating the linear part of the drop in M at low T [see fig. 3a, b, c]. It is clear from fig. 10 that Tr* (B,) we can dereduces as Bil/= and by extrapolation termine the values of Tf = TF (0), which will give the FM-SG transition line in the T-x phase diagram (fig, 11) at B, = 0. We have already discussed the phase diagram in ref. [ 121. Here we just note that the present values of T, compare favorably with earlier data [2,14,15], except when T, was obtained by scaling analyses of high-field magnetization measurements [16]. It is important to note that none of the recent mean field theories [ 17,181 line at vanishing predicts an FM + SG transition M. Although such a line appeared in the original Sherrington-Kirkpatrick [ 191 phase diagram there is ample reason to distrust their solution in this temperature regime. Several theories [ 18,201 predict a field driven transition from FM + SG marked by the onset of irreversibility. It seems reasonable to identify TT (B,) as the characteristic temperature for this transition. Fig. 12 shows Ty as a function of B, for the present alloys. It should be noted that for the 0.7 alloy, on account of the complications discussed in
0
/
I
IO
20
I 30 8,
I
40
50
(be)
Fig. 12. Irreversibility temperatures T: (see text) plotted as a function of applied field Ea. As discussed in the text, in connection with fig. 7, it was not possible to determine Ti* for the 0.7 alloy at B, Q 5 Oe, hence the dots.
connection with fig. 7, it is not possible to obtain Ty directly at B, 5 5 Oe, hence the dotted curve. If, disregarding the peaks shown in fig. 7, we insist on getting TT from the zero of Mi even at low B, values, we get TT values which are unphysically large, i.e., the apparent value of q* for the 0.7 alloy becomes larger than that for the 0.65 alloy. Two points should be noted. First, the drop in TF with increasing B, is much faster than predicted by any theory with a credible choice of parameters. Second, even the functional form does not resemble the theoretical curve. Of course, we agree with theory that increasing B, suppresses TT. It is interesting to note that rough extrapolation of the TT to zero field yields values which are fairly close to the corresponding Tr’s (fig. 10). 3.2. PM-FM
transition
In the neighborhood of a Curie transition expects to find the following relations. Spontaneous
magnetization
M, - (c
one
- T)‘,
T,< T,, Initial
Critical
susceptibility
isotherm
x - (T-
T,)-‘2
T>, T,, M _ B’/s T=T,.
’ (1)
154
M.A. Manheimer
Fig. 13. AKB plot (see text) in the vicinity labelled by the temperature.
x
magneturn
of T, for the x = 0.65 alloy. The values are plotted
One of the consequences of these relationships is that the isotherms close to T,can be “straightened out” to yield the so-called Arrott-KouvelBelov (AKB) plots. In their simplest form, AKB plots consist of graphing M2 as a function of B/M. The intercepts along the M2 axis yield M, and those along the B/M axis give x. Concomitantly, T, corresponds to the isotherm through the origin. After correcting B, for demagnetization (hence B) we have prepared AKB plots for all of our alloys at roughly 2 K intervals spanning (T, 10) to (T, + 10) K. A typical set is shown in fig. 13. For T < T, only data above technical saturation were included. This implies that we can only use M values corresponding to B, > 15 Oe. Presentation of the data in this manner must not be construed to imply mean-field behavior. It is merely a convenient method for obtaining the intercepts which determine the spontaneous magnetization and the low-field susceptibility. The values of T, and the critical exponents j3 and y obtained from plotting the intercepts as functions
Table Critical
et al. / Reentrant
in arbitrary
units.
Each isotherm
of (T, - T) are given in table 1. It must be pointed out that the values of p and y are rather sensitive to the choice of T,. Since T, is determined to only = 1 K it seems reasonable to claim that /3 and y are essentially independent of x, with y = 1.5 and p = 0.4. These values of j3 and y are rather similar to those found for other amorphous alloys [21].
500
Tc=112 8=0.47. (F%.~
K 0
~=I.42 Mno.a ),5P,c%A’a d
200
-
100
100
,
$A
O0A
,
,
,
. * . x
/
+ 0 . 0
, , , 1000
Fig 14. Scaled X= 0.7 alloy.
magnetic
data
for (Fe,Mn,
_,),5P,,B~AI,
P
in the vicinity
alloys Y
*f
6)
8*
101 K
_! 105 106 109 II0 114 116 II8
K K K K K K K
3000
B/FP+Y
1 parameters
is
Y*
of
r,
for the
M.A.
Manheimer
et al. /
Having determined T,, p and y, it is gratifying to note that the data collapse into two curves, one for T > c and the other for T < T,, when A4 and B are appropriately scaled in accord with the relation
with 6 = (y/p + 1) and c = I(T“scaled” plot is shown in fig. 14. 3.3. FM-SG
T,.)/T,l.
B+O
A
transition
M, - (T-
=
T>
T$?*,
x - (T, - T)-y*, M
Once again,
-
T,,
T,< T,, T=
B’/6*,
we first use AKB-type
155
magnetism
they not only help to give /?* and y* but also fix Tf. However, in this case we find that the M* vs. B/M plots are not linear except in very [22] narrow ranges of B. From (l*) one can see that the intercepts Ms’ip* and (B/M)y:z should both be linear in IT - Tfl. Thus, in order to “straighten out” the isotherms [23], one can plot M”p* vs. and expect to find a series of parallel ( B/M)“Y* lines equally spaced in JT - Tf I. The results for the x = 0.7 alloy are shown in fig. 15 and the values of T,, /3*, y* also listed in table 1. It should be noted that for the x = 0.8 alloy T, has been obtained from fig. 10. No isotherms were obtained near T, since for B, z 10 Oe, the transition shifts to below 4 K and there is little, or no, dependence of M on T in the region of interest. Although, at first sight, it appears that y* increases significantly as x is reduced, one must keep in mind that the value of y* is quite sensitive to the choice of T,. A slight (l-2 K) reduction in Tf will cause y* to reduce by a sizeable (0.2-0.5) amount. Thus the variation exhibited in table 1 should not be treated too seriously and it seems fair to say that p* = 0.4, y* = 1.5. Fig. 16 shows the appropriate “scaled” plot and we note that the data do collapse for c 5 0.1.
A simple comparison of the isotherms of fig. 4b with those of fig. 4a would suggest that one should try to cast the data near Tf in the same form as discussed for the data near T,, except that the role of temperature should be reversed, that is, we should expect: (W
Reentranr
cl*)
T,.
plots because
12 -
0
2
4
6
8
IO
12
14
16
18
20
22
24
26
28
(B/M)“‘*
Fig. 15. Modified AKB plot (see text) in the vicinity T, = 49 K. The numbers refer to temperatures.
of T, for the x = 0.7 alloy. We have used B* = 0.37 and y* = 1.36 and obtain
156
M.A.
1000
-
Manheimer
et al. / Reentrant
Tf =49 K ,+
p*= 0.37
Fig. 16. Scaled magnetic
data in the vicinity
++++ +_+ +,+xXxX ,xX
of Tf for the x = 0.7 alloy.
From the foregoing discussion one may be tempted to conclude that the FM + SG transformation should be regarded as a continuous second-order phase transition. Looked at from the point of view of the collapse of ferromagnetism as T + T: this appears to be justified. However, one must not forget that if the system is “prepared” in a slightly different manner, that is, by cooling in a finite field, the ensuing magnetic state at T < T, is not the same but has a frozen moment component in it. 3.4. The frozen moment The temperature dependence of the frozen moment Mi turns out to be extremely interesting in its own right. If we plot Mi as a function of r = (TT( B,) - T)/y( B,), we obtain the results shown in fig. 17a and b; and note that for r 5 0.2 all the data fall on a single straight line, that is, for 0 < r < 0.2, 471Mi = p( r - q), independent of B, and B,. Here p = 1 and q = 0.015. We believe that the non-zero value of q reflects a slight systematic overestimate of TT (B,) and the equation should really read M, = r/471.
-/x
magnetism
(2)
The, more or less, universal behavior of iVfi suggests that Mi is a measure of some fundamental property of the SG state. One possibility is that when the SG state is prepared in an applied field one freezes in an “anisotropy” energy gap A,, which vanishes on subsequent increase of temperature. In such a picture Mi CC(N, - N, ) CC(1 exp( -A,/T)) = A,/T = (TF - T)/TT for T close to TT, in agreement with eq. (2). Here, N, and N, refer to the number of “up” and “down” spins. On the other hand, Mi could be related to the order parameter A recently introduced by Sompolinsky [20] to explicitly represent the onset of irreversibility at the transition to the SG phase. Indeed, Yeshurun and Sompolinsky [9] have recently related A to the difference between equilibrium and non-equilibrium values of the susceptibility. It is easy to show that in terms of a magnetization measurement done by our method, A will play the role of M,. In this sense, we can claim that in fig. 17a, b we have directly measured in the spin-glass order parameter in a reentrant alloy for the first time. Whereas in ref. [9] they found that A had both linear and quadratic dependences on 7, in our case A clearly has only a linear dependence; independent of applied field in the low field regime.
M.A.
Manheimer
a 0.5
0.4 I
c
2 0.3 ._ I
2 -I
0.2
ol; 0
0.1
0.2
0.3
0.4
E =
0.5
0.6
0.7
0.8
0.9
(I -T/Ti*)
b
r
I
I
I
I
I
I
I
I
et al. / Reentrant
magnetism
157
lowering T but disappears on further cooling b) for temperatures near and below the lower transition, the magnetization consists of two parts. First, there is the reversible component which drops on reducing T, follows the applied field, is independent of cooling field and exhibits viscous behavior over some ranges of T. Second, there is an irreversible, or frozen, component in the magnetization, which is independent of time but depends upon cooling field, reduces with increasing T and vanishes at a temperature TT determined by the applied field. The reversible part of M yields AKB plots and scaling behavior such as expected for a second order magnetic phase transition. For T close to y, the irreversible moment varies linearly with reduced temperature and provides a measure for the spin glass order parameter.
11
0.7 -
Acknowledgements
0.6 -
We are thankful to D.J. Webb for fruitful discussions. Our thanks are also due to L.M. Kistler for help with some of the data and M. Stanley for constructing some of the equipment.
References
oj&?y , , “i’“~%‘:’ 0
0.1
0.2
0.3
0.4
0.5
,
0.6
0.7
0.8
,I 0.9
[I] B.J. Verbeek, [2] [3] [4]
E = (I-T/T~*)
Fig. 17. Frozen magnetization Mi plotted versus reduced temperature in the vicinity of TF. Each data set was obtained after cooling the sample in 30 Oe. Measuring fields are as indicated. (a) Data for x = 0.65, (b) data for x = 0.7.
[5]
[6] [l]
4.Summary A careful study of the low field dc magnetization of amorphous (Fe,YMn, _X)75P,6B6A13 with x = 0.65, 0.70 and 0.80 has yielded the following results: a) all these alloys show reentrant magnetism, in that a spontaneous moment appears on
[8] [9] [lo] [ll]
G.J. Nieuwenhuys, G. Stocker and J.A. Mydosh, Phys. Rev. Lett. 40 (1978) 586. J.A. Geohegan and SM. Bhagat, J. Magn. Magn. Mat. 25 (1981) 17. S. Crane and H. Claus, Phys. Rev. Lett. 46 (1981) 1693. J.W. Lynn, R. Erwin, J.J. Rhyne and H.S. Chen, J. Appl. Phys. 52 (1981) 1738. S.M. Shapiro, CR. Fincher, Jr., A.C. Palumbo and R.D. Parks, J. Appl. Phys. 52 (1981) 1729. G. Aeppli, S.M. Shapiro, R.J. Birgeneau and H.S. Chen, Phys. Rev. B25 (1982) 4882. S.M. Bhagat, M.L. Spano and J.N. Lloyd, Solid State Commun. 38 (1981) 261. M.L. Spano and S.M. Bhagat, J. Magn. Magn. Mat. 24 (1981) 143. M. Manheimer, S.M. Bhagat, L.M. Kistler and K.V. Rao, J. Appl. Phys. 53 (1982) 2220. Y. Yeshurun and H. Sompolinsky, Phys. Rev. B26 (1982) 1487. M.A. Manheimer, S.M. Bhagat and H.S. Chen, Phys. Rev. B26 (1982) 456. M.A. Manheimer, S.M. Bhagat and H.S. Chen, J. Appl. Phys. 53 (1982) 7737.
158
M.A. Manheimer et al. / Reentrant magnetism
[12] See for instance: SM. Bhagat, S. Haraldson and 0. Beckman, J. Phys. Chem. Solids 38 (1977) 593. [ 131 D.J. Webb, (unpublished). [14] 0. Beckmann, K. Gramm, L. Lundgren, P. Svedhndh, K.V. Rao and H.S. Chen, Phys. Scripta 25 (1982) 676. [15] C.W. Chu, M.K. Wu, B.J. Jin, W.Y. Lai and H.S. Chen, Phys. Rev. Lett. 46 (1981) 1643. [16] Y. Yeshurun, M.B. Salamon, K.V. Rao and H.S. Chen, Phys. Rev. 24B (1981) 1536. [17] M. Gabay and G. Toulouse, Phys. Rev. Lett. 47 (1981) 201.
[ 181 J.R.L. de Almeida and D.J. Thouless, J. Phys. Al 1 (1978) 983. [19] D. Sherrington and S. Kirkpatrick. Phys. Rev. Lett. 35 (1975) 1792. [20] H. Sompolinsky, Phys. Rev. Lett. 47 (1981) 935. [21] P. Gaunt, SC. Ho, G. Williams and R.W. Cochrane, Phys. Rev. B23 (1981) 251. [22] Cf. fig. 3, ref. [lo]. (231 A. Arrott and J.E. Noakes, Phys. Rev. Lett. 19 (1967) 786.
REENTRANT
Materials
MAGNETISM
147
38 (1983) 147- 158
- A LOW FIELD STUDY
M.A. MANHEIMER for Physical Sciences, College Park, MD 20740, USA
Laboratory
SM. BHAGAT Dept. of Physics and Astronomy,
University of Maryland,
College Park, MD 20742, USA
H.S. CHEN Bell Laboratories, Received
Murray Hill, NJ 07974, USA
10 March
1983; in revised form 9 May 1983
We report low field dc magnetization measurements on (Fe,Mn,_,),sP,,~Al, alloys at 4
1. Introduction Alloy systems with competing ferromagnetic and antiferromagnetic interactions on the one hand, and those with wide distributions of exchange energy on the other, have attracted a great deal of attention in recent years. One of the most fascinating aspects of these investigations has been the discovery of reentrant magnetism. It has been found that although some of these alloys show a typical Curie transition from paramagnetic (PM) to ferromagnetic (FM) behavior, the ferromagnetic state is unstable against further lowering of temperature. This low temperature “transition” manifests itself in a number of ways: (i) drop of the demagnetization-limited ac susceptibility [ 11, (ii) field dependent peak in ac susceptibility measured in presence of a dc field [2], (iii) rapid, exponential rise in the width of the ac hysteresis loop [2], (iv) vanishing of spontaneous magnetization [3], (v) reduction of spin wave energies measured by inelastic neutron scattering [4,5], (vi) 0304-8853/83/0000-0000/$03.00
0 1983 North-Holland
rapid increase in linewidth for ferromagnetic resonance [6], (vii) low temperature anomalies in the temperature dependence of magnetization [7], (viii) onset of “anisotropy fields” [8], (ix) onset of magnetic viscosity and (x) history dependent effects [9]. The low-temperature phase thereby has several properties usually associated with spin glass (SG) behavior in dilute alloys. In this sense, one talks of a ferromagnet to spin glass transition. Reentrant magnetism in a system therefore implies PM --, FM --j SG phase with reduction of temperature. Low magnetic field studies are fruitful because they are likely to provide insight into magnetic phenomena, which are most characteristic of intrinsic behavior. Here, we describe in some detail our low (I 50 Oe) field dc magnetization studies on an amorphous alloy series, (Fe,Mn, _,) 75 P,,$A13. We confirm earlier reports of reentrant behavior [2,10,1 l] and present a complete analysis of magnetization data not only in the FM phase but also in the SG phase. We describe the first measurements, to our knowledge, of the temper-
148
M.A. Manheimer
ature marking the onset of irreversibility at the FM -+ SG transition measured in the presence of a magnetic field. In addition, at low temperatures we identify two contributions to the magnetization. One of these follows the direction of the applied field (and is therefore reversible), while the other behaves like a frozen or permanent moment. We show that the temperature and field dependences of the reversible magnetization data can be collapsed in the form suggested by the scaling “laws” for magnetic phase transitions. However, in view of the irreversibility, one must be careful in trying to conclude that one has identified the FM -+ SG transformation as a continuous second-order phase transition. Finally, we associate the frozen moment with a spin-glass order parameter. Method Ribbons of (Fe,Mn,_,),,P,,$Al, with nominal values of x = 0.65, 0.70 and 0.80 were grown by the melt spinning technique. They were typically 1 mm wide and about 30 pm thick. For the present experiments several (8- 10) pieces, each 15 mm long, were tied securely to a copper holder and suspended, inside a stainless steel vacuum chamber C, from one arm of a Cahn 2000 microbalance (sensitivity = 0.1 pg) as shown in fig. 1.
To
Balance
Liquid Helium Tube
,
et al. / Reentrant magnetism
The lower 10 cm of C were made of Cu. A Cu-constantan thermocouple was attached to the outside of this copper can at the height of the sample center. A second vacuum jacked surrounded C and could be pumped to thermally isolate the sample space from cryogenic liquids. The sample temperature could be further controlled using a Karma wire heater wound (noninductively) around the can. During a measurement, an exchange gas pressure of = 200 pm He was maintained in C. Two sets of Helmholtz coils were fixed outside the cryostat, coaxial with the hangdown wire. One pair of coils was used to cancel the vertical component of the earth’s field, and had the sample at its center. The other pair produced both the measuring field and field gradient, and was positioned such that the field gradient was about 3% of the field at the sample. The applied fields were varied between 0.5 and 50 Oe. The temperature was varied between 4 and 300 K. Since the sample and thermocouple are separated in space we performed a calibration experiment, in which the sample was replaced by a single crystal of paramagnetic CuSO, . 5H,O. The later is known to have a susceptibility varying as (T + 0.6)) ‘. It was found that the apparent sample temperature required systematic corrections of, at most, 4 K. Repeated measurements lead us to suggest that the temperatures listed below are good to about 1 K. To measure the magnetization at a given temperature, we recorded the effective “magnetic” weight of the sample by taking the difference between the output of the balance in zero field and in an applied field B,. Two observations were taken at every T, first with the applied field B, and
Heater
B,=O B,= IO Oe
/Copper Tube
,w(n/“)
m
B,=B,=
IO Oe
+
Thermocouple, t%
6%
Imin He Exchange Gas
-
Fig. 1. Low-temperature
-Sample
probe used to measure
magnetization.
Fig. 2. Output of the electrobalance as a function of time for zero-field cooled (left) and 10 Oe cooled states (right). For each case, the measuring sequence for applied field (in oersted) is: B, = 0 + 10 * 0 + 10 + 0. Note the difference in gain settings.
M.A. Manheimer
et al. / Reentrant
its gradient in one direction, and next with the two reversed. This yields the quantities labelled W, ( B,, B,) and W, (B,, B,) in fig. 2 where we have plotted the output of the balance as a function of time. Here, B, is the field in which the sample was cooled. It was turned off before applying B,. It turns out that W, (0, B,)= W, (0, B,) at all temperatures if the sample has been cooled in zero (5 3 mOe) field to 4 K and then warmed up to the desired T. However, if the sample is cooled in a finite field W,(B,, B,) * W, (B,, B,) at low T. This indicates that, in the field-cooled state, the sample acquires a “frozen” or permanent magnetic moment at low T. It was found that W, + W, is independent of B,. Thus we associate W, + W, with a reversible component in the magnetization (M) and designate W, - W, as a measure .of the frozen or irreversible magnetization, labelled Mi. In order to obtain absolute values for M, the system was calibrated using a single length of Fe,,Ni,,P,,$Si, (Metglas 2826B) ribbon. Several independent measurements [12] have shown that, at 300 K, this material has 47rM = 4.8 kOe. Because of uncertainties in sample volume and shape effects we estimate that the absolute values of 4aM are accurate to about 10%. The relative values are probably good to about 1% except at the lowest applied fields.
a
magnetism
149
I.4x 4oe 0 10oe v 300e I c P
o.a0.6 0.4 0.2 -
OL 0v
IO
20
30
40
50
60
70
a0
90
loo 110 120
70
a0
90
100 110 Ix) 130 140
T(K)
b
1020
30
40
50
60
T(K)
2. Results 3.66
2.1. Reversible
magnetization
Fig. 3a, b and c shows the reversible magnetization of the alloys, as a function of temperature, for various values of the applied field, B,. As discussed above this component of magnetization is independent of the cooling field. In every case, the systems show reentrant magnetism in the sense that, as T is lowered, the magnetization first shows a large increase (defining T,) but on further cooling M drops again, essentially vanishing at low T. As shown earlier [ 10,l l] one can define an effective freezing temperature TF by using the linear drop in M at low T (see also, curve for W, + W, in fig. 5 below). Increasing B, favors the FM state. That is, the rise
f 0
IB1.2 -
c
(F60.6M"o.z)75 '16B6A'3
%\ ‘9 b
B,=20e
/ n
I
I
\ 1
40
I
80
/
I
120
I
I
160
I
I
200
I
I
240
I
.j
28k
T (K)
Fig. 3. Reversible magnetization as a function of temperature, for various values of applied field; (a) x = 0.65, (b) x = 0.70, (c) x = 0.80.
in M near T, shifts to higher T while the drop in M near T;” moves to lower T. Extrapolation to B, = 0 will yield the true transition temperature Tf discussed in section 3.1. For the x = 0.80 alloy, for
150
M.A. Manheimer
a
IO
20
30
b 80
2.0
54 52 50 40 46
42 40
et al. / Reentrant
magnelism
instance, an applied field of 10 Oe suppresses to below 4 K any evidence of the low T downturn. The sensitivity to applied field is remarkable. At first sight, one would expect only fields of the order of (kT,/p,) or (kTf/pB) to give significant effects. The present fields are several orders of magnitude smaller. In the intermediate temperature regime the large magnitudes of M, in fairly low applied fields, are highly suggestive of soft ferromagnetism. It is also useful to compare the present 4nM values with those obtained from other techniques. For instance, ferromagnetic resonance [ 131 data (in the x = 0.65 alloy) taken at 3-10 kOe applied fields give 4nM values only about 50 percent higher than our values at 30 Oe. In a magnetic sample, with an effective demagnetizing factor N, at low fields the magnetization will be given by A4 = B,/( l/x + N), so that when the FM state sets in and the low-field susceptibility x becomes very large M + B./N, independent of T. This was checked at several temperatures and in turn allowed us to determine N for our samples. Typically N < lo-*. Fig. 4a and b summarizes the magnetic isotherms of the x = 0.7 alloy in the neighborhood of T, and T,, respectively. As expected, the curves in fig. 4a indeed resemble those obtained in the neighborhood of a PM + FM transition. At high T, A4 is almost linear with B,. The non-linearity becomes sharper as T is reduced, producing the possibility of a non-zero intercept at the demagnetization limit, i.e., spontaneous magnetization M,. In fig. 4b one observes the same behavior except that now the role of temperature is reversed; the low T data show less curvature. The s-shaped isotherms at the lowest temperatures are probably symptomatic of magnetic hysteresis at very small B,. 2.2. Irreversible
Fig 4. Magnetic isotherms in the vicinity of T, (a) and T, (b). The left most (highest slope) line marks the demagnetization limit. The number labelling each curve is the temperature in kelvin.
or frozen magnetization
As described above, cooling in a magnetic field to 4 K causes the sample to acquire a frozen or irreversible magnetization, Mi. Fig. 5 shows IV, (10, 10) and W, (10, 10) as functions of temperature. M, is proportional to (W, - W,) and is also plotted in fig. 5. This kind of plot was used to
M.A. Manheimer
x x
0.
~~‘~
XX
I
-20 -
0
-
B,tt B, 0 Y,+t B,
A
0
•IDIFF
0 op" -60 0 IO
%
to
T;
-40
+Ti
xSUM 20
30 T(K)
40
50
60
Fig. 5. W, (10, lo), A, and W, (10, 10). 0 as a function of temperature for x = 0.7. Also plotted is ( W, - W,), 0, which is proportional to the frozen magnetization M,, and ( W, + W,), X, which is proportional to the reversible magnetization, M. Note that the value for TF obtained by extrapolating to M = 0 is lower than T,*, so that the irreversibility sets in at finite M. As discussed in the text, TF and 7. approach each other as B, -+ 0.
et al. / Reentrant
151
magnetism
define the temperatures T* (B,), which mark the onset of irreversibility. We also determined TT by measuring W, and W, while cooling in a magnetic field. Fig. 6 shows such data and one notices that (W, - W,) becomes non-zero at essentially the same temperature as that marked in fig. 5 by the disappearance of Mi. We have measured Mi, as a function of T, for several combinations of B, and B,. We find that (i) Mi (30, B,) at 4 K is roughly one third of M at 77 K with B, = 30 Oe. However, even with B, = 1 Oe, one freezes in about 3% of the FM magnetization, (ii) TT reduces with increasing B, but is independent of B, for B, varied from 1 Oe to 30 Oe, (iii) Mi is independent of time over several hours, (iv) for small B, (s 4 Oe) the T-dependence of W, (B,, B, ), W,( B,, B,) and hence Mi is more complex (fig. 7). This effect is most marked for the x = 0.7 alloy. A vestige of this phenomenon can also be seen in the temperature variation of the reversible M, fig. 3b, B, = 1 Oe, where one notices a slight “bump” around 50 K. In fig. 7 the peak in Mi moves to higher T as B, is reduced. For the present, it is mainly an irritant since it interferes with any attempt to fix TT at low B, values.
6
300
pH-
I
Y
/d
,e
2oc
Bc=Ba=lOOe A 8, tt B,
‘3, +t B,
p/”o dt p/t
3 > r
Ti
IOC
dd’
‘I
C
(FeO.7Mn0.3)75 P16B6A'
(Fe0.7Mn0.3),5F;6B6A'3
I 0
-3 0 I
I
60
40
80
T(K) Fig. 6. W, (IO, IO), A, and W, (10, IO), 0 measured for x = 0.7 sample while being cooled, and plotted as a function of temperature. Note the rapid increase in (IV,, - W,) for T c T:.
IO
20
30 40 T(K)
50
60
70
Fig. 7. W,, (30, 1) and W, (30, l), v and 0, respectively, for x = 0.7. Also shown are ( W, - W,), 0, proportional to M, and (W, + W,) 0 proportional to M. The unexplained peak at about 50 K in (IV, - IV’) makes it difficult to designate ri* at low fields.
152
M.A. Manheimer
et al. / Reentrant
magnetism
60
2.3. Viscous effects
I
I\1
In a spin glass one should expect to find viscous or time-dependent effects in the magnetization. As noted above, although the advent of Mi marks the onset of irreversibility, M, itself is not observed to vary with time. It is conceivable that Mi varies with time for T very close to TT but we are not able to measure this effect. On the other hand, we find that over some temperature regimes (depending on B,) the data show time dependence, which can be understood only if the reversible magnetization has viscous behavior with response times of minutes, the characteristic time of the present experiment. First (although not clear from fig. S), note that for B, parallel to B,, W,, shows a rapid rise to a value consistent with that of Mi (B,, T) followed by a slow increase towards a total magnetization larger than Mi. Next, consider the type of data shown in fig. 8, where we have plotted the time development of W, (1, 20) and W,( 1, 20). It is clear that application of B, antiparallel to B, causes the magnetization to grow along B,. However, every time B, is turned off and reapplied the system is initially found to have its magnetization pointing along the original direction of freezing. All these results are accounted for if M, (B,, T) is some fixed quantity while application of B, causes M to grow along B, in a viscous manner. The temperature intervals of viscous behavior are
I
I
20 -
I
01
0
I
I
IO
20
30
6, (Oe) Fig. 9. Temperature intervals, where viscous behavior has been observed, plotted as a function of measuring field, for the x = 0.7 sample.
shown in fig. 9, as a function of B,, and indeed viscosity effects set in at lower T with increasing
4. 3. Analysis and discussion 3. I. Characteristic
temperatures
Apart from the Curie temperature there are two characteristic temperatures of interest in each of
‘0 ‘0
Fig. 8. W, (1, 20) and W, (1, 20) at 20 K for x = behavior is evident for the W, data. The field B, is points labelled + and turned off at points labelled B, 1 f B, and + implies B, t 1 B,. A zero-signal been drawn as a guide to the eye.
0.7. Viscous turned on at 0; - means baseline has
I I
2I
\I 3
4I
5I
6I
7I
Fig. 10. Effective spin-freezing temperature 7;* (B,), determined from the low temperature magnetization drop, plotted as a function of B’/*. B, was the applied measuring field. A linear a extrapolation to B, = 0 gives the zero field freezing temperature for each of the samples.
M.A. Manheimer
et al. / Reentrant
153
magnetism
Ii 50 01
-.-0-O-
01
’
0.4
I
I
I
I
0.5
0.6
0.7
0.0
X
Fig. 11. Magnetic phase diagram at B, = 0 for (Fe,Mn,_,),, P,,$Al,, l ref. [16]; n ref. [2]; A this work. The lines have been drawn as a guide to the eye. Note, especially, that there are no data available in the immediate neighborhood of the multicritical point.
these alloys. At T: (B,) the reversible magnetization appears to vanish while at y (B,) the frozen moment goes to zero. T; (B,) was determined [ 11,121 by extrapolating the linear part of the drop in M at low T [see fig. 3a, b, c]. It is clear from fig. 10 that Tr* (B,) we can dereduces as Bil/= and by extrapolation termine the values of Tf = TF (0), which will give the FM-SG transition line in the T-x phase diagram (fig, 11) at B, = 0. We have already discussed the phase diagram in ref. [ 121. Here we just note that the present values of T, compare favorably with earlier data [2,14,15], except when T, was obtained by scaling analyses of high-field magnetization measurements [16]. It is important to note that none of the recent mean field theories [ 17,181 line at vanishing predicts an FM + SG transition M. Although such a line appeared in the original Sherrington-Kirkpatrick [ 191 phase diagram there is ample reason to distrust their solution in this temperature regime. Several theories [ 18,201 predict a field driven transition from FM + SG marked by the onset of irreversibility. It seems reasonable to identify TT (B,) as the characteristic temperature for this transition. Fig. 12 shows Ty as a function of B, for the present alloys. It should be noted that for the 0.7 alloy, on account of the complications discussed in
0
/
I
IO
20
I 30 8,
I
40
50
(be)
Fig. 12. Irreversibility temperatures T: (see text) plotted as a function of applied field Ea. As discussed in the text, in connection with fig. 7, it was not possible to determine Ti* for the 0.7 alloy at B, Q 5 Oe, hence the dots.
connection with fig. 7, it is not possible to obtain Ty directly at B, 5 5 Oe, hence the dotted curve. If, disregarding the peaks shown in fig. 7, we insist on getting TT from the zero of Mi even at low B, values, we get TT values which are unphysically large, i.e., the apparent value of q* for the 0.7 alloy becomes larger than that for the 0.65 alloy. Two points should be noted. First, the drop in TF with increasing B, is much faster than predicted by any theory with a credible choice of parameters. Second, even the functional form does not resemble the theoretical curve. Of course, we agree with theory that increasing B, suppresses TT. It is interesting to note that rough extrapolation of the TT to zero field yields values which are fairly close to the corresponding Tr’s (fig. 10). 3.2. PM-FM
transition
In the neighborhood of a Curie transition expects to find the following relations. Spontaneous
magnetization
M, - (c
one
- T)‘,
T,< T,, Initial
Critical
susceptibility
isotherm
x - (T-
T,)-‘2
T>, T,, M _ B’/s T=T,.
’ (1)
154
M.A. Manheimer
Fig. 13. AKB plot (see text) in the vicinity labelled by the temperature.
x
magneturn
of T, for the x = 0.65 alloy. The values are plotted
One of the consequences of these relationships is that the isotherms close to T,can be “straightened out” to yield the so-called Arrott-KouvelBelov (AKB) plots. In their simplest form, AKB plots consist of graphing M2 as a function of B/M. The intercepts along the M2 axis yield M, and those along the B/M axis give x. Concomitantly, T, corresponds to the isotherm through the origin. After correcting B, for demagnetization (hence B) we have prepared AKB plots for all of our alloys at roughly 2 K intervals spanning (T, 10) to (T, + 10) K. A typical set is shown in fig. 13. For T < T, only data above technical saturation were included. This implies that we can only use M values corresponding to B, > 15 Oe. Presentation of the data in this manner must not be construed to imply mean-field behavior. It is merely a convenient method for obtaining the intercepts which determine the spontaneous magnetization and the low-field susceptibility. The values of T, and the critical exponents j3 and y obtained from plotting the intercepts as functions
Table Critical
et al. / Reentrant
in arbitrary
units.
Each isotherm
of (T, - T) are given in table 1. It must be pointed out that the values of p and y are rather sensitive to the choice of T,. Since T, is determined to only = 1 K it seems reasonable to claim that /3 and y are essentially independent of x, with y = 1.5 and p = 0.4. These values of j3 and y are rather similar to those found for other amorphous alloys [21].
500
Tc=112 8=0.47. (F%.~
K 0
~=I.42 Mno.a ),5P,c%A’a d
200
-
100
100
,
$A
O0A
,
,
,
. * . x
/
+ 0 . 0
, , , 1000
Fig 14. Scaled X= 0.7 alloy.
magnetic
data
for (Fe,Mn,
_,),5P,,B~AI,
P
in the vicinity
alloys Y
*f
6)
8*
101 K
_! 105 106 109 II0 114 116 II8
K K K K K K K
3000
B/FP+Y
1 parameters
is
Y*
of
r,
for the
M.A.
Manheimer
et al. /
Having determined T,, p and y, it is gratifying to note that the data collapse into two curves, one for T > c and the other for T < T,, when A4 and B are appropriately scaled in accord with the relation
with 6 = (y/p + 1) and c = I(T“scaled” plot is shown in fig. 14. 3.3. FM-SG
T,.)/T,l.
B+O
A
transition
M, - (T-
=
T>
T$?*,
x - (T, - T)-y*, M
Once again,
-
T,,
T,< T,, T=
B’/6*,
we first use AKB-type
155
magnetism
they not only help to give /?* and y* but also fix Tf. However, in this case we find that the M* vs. B/M plots are not linear except in very [22] narrow ranges of B. From (l*) one can see that the intercepts Ms’ip* and (B/M)y:z should both be linear in IT - Tfl. Thus, in order to “straighten out” the isotherms [23], one can plot M”p* vs. and expect to find a series of parallel ( B/M)“Y* lines equally spaced in JT - Tf I. The results for the x = 0.7 alloy are shown in fig. 15 and the values of T,, /3*, y* also listed in table 1. It should be noted that for the x = 0.8 alloy T, has been obtained from fig. 10. No isotherms were obtained near T, since for B, z 10 Oe, the transition shifts to below 4 K and there is little, or no, dependence of M on T in the region of interest. Although, at first sight, it appears that y* increases significantly as x is reduced, one must keep in mind that the value of y* is quite sensitive to the choice of T,. A slight (l-2 K) reduction in Tf will cause y* to reduce by a sizeable (0.2-0.5) amount. Thus the variation exhibited in table 1 should not be treated too seriously and it seems fair to say that p* = 0.4, y* = 1.5. Fig. 16 shows the appropriate “scaled” plot and we note that the data do collapse for c 5 0.1.
A simple comparison of the isotherms of fig. 4b with those of fig. 4a would suggest that one should try to cast the data near Tf in the same form as discussed for the data near T,, except that the role of temperature should be reversed, that is, we should expect: (W
Reentranr
cl*)
T,.
plots because
12 -
0
2
4
6
8
IO
12
14
16
18
20
22
24
26
28
(B/M)“‘*
Fig. 15. Modified AKB plot (see text) in the vicinity T, = 49 K. The numbers refer to temperatures.
of T, for the x = 0.7 alloy. We have used B* = 0.37 and y* = 1.36 and obtain
156
M.A.
1000
-
Manheimer
et al. / Reentrant
Tf =49 K ,+
p*= 0.37
Fig. 16. Scaled magnetic
data in the vicinity
++++ +_+ +,+xXxX ,xX
of Tf for the x = 0.7 alloy.
From the foregoing discussion one may be tempted to conclude that the FM + SG transformation should be regarded as a continuous second-order phase transition. Looked at from the point of view of the collapse of ferromagnetism as T + T: this appears to be justified. However, one must not forget that if the system is “prepared” in a slightly different manner, that is, by cooling in a finite field, the ensuing magnetic state at T < T, is not the same but has a frozen moment component in it. 3.4. The frozen moment The temperature dependence of the frozen moment Mi turns out to be extremely interesting in its own right. If we plot Mi as a function of r = (TT( B,) - T)/y( B,), we obtain the results shown in fig. 17a and b; and note that for r 5 0.2 all the data fall on a single straight line, that is, for 0 < r < 0.2, 471Mi = p( r - q), independent of B, and B,. Here p = 1 and q = 0.015. We believe that the non-zero value of q reflects a slight systematic overestimate of TT (B,) and the equation should really read M, = r/471.
-/x
magnetism
(2)
The, more or less, universal behavior of iVfi suggests that Mi is a measure of some fundamental property of the SG state. One possibility is that when the SG state is prepared in an applied field one freezes in an “anisotropy” energy gap A,, which vanishes on subsequent increase of temperature. In such a picture Mi CC(N, - N, ) CC(1 exp( -A,/T)) = A,/T = (TF - T)/TT for T close to TT, in agreement with eq. (2). Here, N, and N, refer to the number of “up” and “down” spins. On the other hand, Mi could be related to the order parameter A recently introduced by Sompolinsky [20] to explicitly represent the onset of irreversibility at the transition to the SG phase. Indeed, Yeshurun and Sompolinsky [9] have recently related A to the difference between equilibrium and non-equilibrium values of the susceptibility. It is easy to show that in terms of a magnetization measurement done by our method, A will play the role of M,. In this sense, we can claim that in fig. 17a, b we have directly measured in the spin-glass order parameter in a reentrant alloy for the first time. Whereas in ref. [9] they found that A had both linear and quadratic dependences on 7, in our case A clearly has only a linear dependence; independent of applied field in the low field regime.
M.A.
Manheimer
a 0.5
0.4 I
c
2 0.3 ._ I
2 -I
0.2
ol; 0
0.1
0.2
0.3
0.4
E =
0.5
0.6
0.7
0.8
0.9
(I -T/Ti*)
b
r
I
I
I
I
I
I
I
I
et al. / Reentrant
magnetism
157
lowering T but disappears on further cooling b) for temperatures near and below the lower transition, the magnetization consists of two parts. First, there is the reversible component which drops on reducing T, follows the applied field, is independent of cooling field and exhibits viscous behavior over some ranges of T. Second, there is an irreversible, or frozen, component in the magnetization, which is independent of time but depends upon cooling field, reduces with increasing T and vanishes at a temperature TT determined by the applied field. The reversible part of M yields AKB plots and scaling behavior such as expected for a second order magnetic phase transition. For T close to y, the irreversible moment varies linearly with reduced temperature and provides a measure for the spin glass order parameter.
11
0.7 -
Acknowledgements
0.6 -
We are thankful to D.J. Webb for fruitful discussions. Our thanks are also due to L.M. Kistler for help with some of the data and M. Stanley for constructing some of the equipment.
References
oj&?y , , “i’“~%‘:’ 0
0.1
0.2
0.3
0.4
0.5
,
0.6
0.7
0.8
,I 0.9
[I] B.J. Verbeek, [2] [3] [4]
E = (I-T/T~*)
Fig. 17. Frozen magnetization Mi plotted versus reduced temperature in the vicinity of TF. Each data set was obtained after cooling the sample in 30 Oe. Measuring fields are as indicated. (a) Data for x = 0.65, (b) data for x = 0.7.
[5]
[6] [l]
4.Summary A careful study of the low field dc magnetization of amorphous (Fe,YMn, _X)75P,6B6A13 with x = 0.65, 0.70 and 0.80 has yielded the following results: a) all these alloys show reentrant magnetism, in that a spontaneous moment appears on
[8] [9] [lo] [ll]
G.J. Nieuwenhuys, G. Stocker and J.A. Mydosh, Phys. Rev. Lett. 40 (1978) 586. J.A. Geohegan and SM. Bhagat, J. Magn. Magn. Mat. 25 (1981) 17. S. Crane and H. Claus, Phys. Rev. Lett. 46 (1981) 1693. J.W. Lynn, R. Erwin, J.J. Rhyne and H.S. Chen, J. Appl. Phys. 52 (1981) 1738. S.M. Shapiro, CR. Fincher, Jr., A.C. Palumbo and R.D. Parks, J. Appl. Phys. 52 (1981) 1729. G. Aeppli, S.M. Shapiro, R.J. Birgeneau and H.S. Chen, Phys. Rev. B25 (1982) 4882. S.M. Bhagat, M.L. Spano and J.N. Lloyd, Solid State Commun. 38 (1981) 261. M.L. Spano and S.M. Bhagat, J. Magn. Magn. Mat. 24 (1981) 143. M. Manheimer, S.M. Bhagat, L.M. Kistler and K.V. Rao, J. Appl. Phys. 53 (1982) 2220. Y. Yeshurun and H. Sompolinsky, Phys. Rev. B26 (1982) 1487. M.A. Manheimer, S.M. Bhagat and H.S. Chen, Phys. Rev. B26 (1982) 456. M.A. Manheimer, S.M. Bhagat and H.S. Chen, J. Appl. Phys. 53 (1982) 7737.
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M.A. Manheimer et al. / Reentrant magnetism
[12] See for instance: SM. Bhagat, S. Haraldson and 0. Beckman, J. Phys. Chem. Solids 38 (1977) 593. [ 131 D.J. Webb, (unpublished). [14] 0. Beckmann, K. Gramm, L. Lundgren, P. Svedhndh, K.V. Rao and H.S. Chen, Phys. Scripta 25 (1982) 676. [15] C.W. Chu, M.K. Wu, B.J. Jin, W.Y. Lai and H.S. Chen, Phys. Rev. Lett. 46 (1981) 1643. [16] Y. Yeshurun, M.B. Salamon, K.V. Rao and H.S. Chen, Phys. Rev. 24B (1981) 1536. [17] M. Gabay and G. Toulouse, Phys. Rev. Lett. 47 (1981) 201.
[ 181 J.R.L. de Almeida and D.J. Thouless, J. Phys. Al 1 (1978) 983. [19] D. Sherrington and S. Kirkpatrick. Phys. Rev. Lett. 35 (1975) 1792. [20] H. Sompolinsky, Phys. Rev. Lett. 47 (1981) 935. [21] P. Gaunt, SC. Ho, G. Williams and R.W. Cochrane, Phys. Rev. B23 (1981) 251. [22] Cf. fig. 3, ref. [lo]. (231 A. Arrott and J.E. Noakes, Phys. Rev. Lett. 19 (1967) 786.