AC-susceptibility method for Curie
temperature determination.
Experiment and theory
A.V. Korolev, M.I. Kurkin, Ye.V. Rosenfeld
Institute of Metal Physics, Ural Branch of Russian
Academy of Sciences
INTODUCTION
There are a lot of different methods for determination of
Curie temperature TC
I would like to recall you only one of them.
Belov-Goriaga (Belov-Arrott) method.
This method is very famous and very popular in literature.
The method is based on the second-order phase
transitions Landau theory for ferromagnetic materials.
INTODUCTION
L. D. Landau and E. M. Lifshitz, Statistical Physics, 2nd
ed. Nauka, Moscow, 1964; Pergamon, Oxford, 1980
Landau expansion of the thermodynamic potential F in
terms of M is usually used for processing the results of
magnetic measurements
F = F0 – MH + (1/2)A(T – TC)M2 + (1/4)BM4
TC ,A, B = const;
after minimization:
H/M = A(T – TC) + BM2 ; T=const:
H/M = a + BM2
We should see a picture like which you see on this slide
400
THEORY: H/M = a + BM
2
H/M
300
T > TC: P-state
200
a>0
T = TC
100
a=0
a<0
T < TC: F-state
0
0
2000
4000
M
2
6000
8000
INTODUCTION
Experimental H/M vs. M2 dependencies without demagnetization
correction for the Gd sample in the shape of flat parallelepiped in the
vicinity of the assumed TC of Gd.
V.I. Zverev et al., JMMM (2011), doi:10.1016/j.jmmm.2011.05.012
300 K
280 K
INTODUCTION
A.V.Korolev et al., PHYS. SOLID STATE, 52, 561-567, 2010
Gd, polycrystalline ball
360
300
298 K
3
H/M (cm /g)
240
180
T=286K
288
292
296
298
120
60
286 K
0
0
2000
4000
6000
2
M (emu/g)
8000
2
10000
MOTIVATION
I can show you more and more the same kind of typical graphs. And every time we find a
row non-linear curves near Tc at low temperature. But the step by step increasing
temperature changing occurs and non-linear curves become more and more linear. This is
most clearly illustrated in this slide. The temperature range is from 226 to 234 K. We see
that the experimental points at 234 and 233 K, practically lie on a straight line.
A.V.Korolev et al., Phys. Met. Metallogr. 98, S1, s86-s93, 2004
LINIAR
La0.85Sr0.15MnO3
single crystal
234 K
226 K
NONLINIAR
M2 (emu/g)2
MOTIVATION
The displayed data suggest that the Landau theory "does not
work" near T = Tc ± (0.01-0.02) Tc. Method of determining the
Tc from such data, in my opinion, is not justified. At the same
time, we can assume that this theory should well describe
experiment near Tc, but at T > Tc +(~0.02)Tc . The above data
have motivated us to study the temperature dependence of the
differential susceptibility. It has long been known (K.P. Belov,
Magnetic Transitions (Fizmatgiz, Moscow, 1959;
Consultants Bureau, New York, 1961) that temperature
dependence of differential susceptibility =M/H has the
maximum at T = Tm, which moves from Tc to high
temperature region with increasing field.
Modern magnetometers with DC and AC options:
MPMS, PPMS (Quantum Design, USA)
DC-option
H(t)=const ≤ 50 kOe
AC-option
h(t) = hasin(t)
sample
In our AC experiment:
f < 100 Hz, ha< 4 Oe
1. Only the 1-st harmonic (no
higher-order harmonics)
2. ’ >> ’’
THEREFORE
’ = M/H
EXPERIMENT
A.V.Korolev et al., PHYS. SOLID STATE, 52, 561-567, 2010
Gd, polycrystalline ball
0,020
m
H=10 kOe
15
20
30
40
50
 = M/ H
Tm
0,015
0,010
0,005
280
290
300
310
320
T (K)
330
340
EXPERIMENT
We have experimental dependencies:
1.Tm = f(H)
2. m = f(Tm)
and we would like compare these
data with theoretical functions.
THEORY
We have to solve the cubic equation
BM3 + A(T – TC)M - H = 0
for a value of the T = Tm, which corresponds to the m,
under the condition
 (Tm,H)/T = 2M(Tm,H)/TH = 0
RESULTS
1.m = 2A/(Tm-TC)
2.Tm = TC + bH2/3
b=3A-1(B/16)1/3
EXPERIMENT and THEORY
(Tm – H2/3) PLOT
Gd, polycrystalline ball
340
330
Tm (K)
320
310
TC = Tm(H=0)+ = 289 K
 = NMs0Gd/k = 2 K
300
Tm(H=0) = 287 K
290
0
200
400
600
2/3
H
800
1000 1200 1400
2/3
(Oe)
EXPERIMENT and THEORY
Gd, polycrystalline ball: (1/m – Tm) PLOT
EXPERIMENT and THEORY
A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d
Phys.Solid State, Vol. 45, No. 8, 2003, pp. 1484–1486.
La0.85Sr0.15MnO3 single crystal: (Tm – H2/3) PLOT
EXPERIMENT and THEORY
A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d
Phys. Solid State, Vol. 45, No. 8, 2003, pp. 1484–1486.
La0.85Sr0.15MnO3 single crystal: (1/m – Tm) PLOT
CONCLUSION
1. Landau second-order phase transition theory of
ferromagnetic materials describes magnetic
experiments in the vicinity of the Curie
temperature is not good enough.
2. However, only at temperatures above the Curie
temperature (a few degrees), the experiments
are in very good agreement with the theory.
3. Using the AC magnetic susceptibility method
together with the theory we can find the value
of the Curie temperature definitely.
Congratulations, Yuri
MOTIVATION
It has long been known (K. P. Belov, Magnetic Transitions (Fizmatgiz, Moscow,1959;
Consultants Bureau, New York, 1961) that temperature dependence of differential
susceptibility has the maximum at T = Tm, which move from Tc to high temperature
region with increasing field
MOTIVATION
1.Nonlinear effects are decreasing with increasing temperature and Landau's
theory is working better and better with increasing temperature.
2.We guess that the theory should be effective at temperature more than
Curie temperature.
Gd, polycrystalline ball
360
T=286K
294
298
300
T>TC
T<TC
3
H/M (cm /g)
240
180
120
2
~MS (T=286K)
60
TC
294K
3
43 = 7.9 cm /g
0
0
2000
4000
6000
2
M (emu/g)
8000
2
10000
“kink-point method”
I.K. Kamilov, Kh.K. Aliev
“Second-order phase transitions
in ferromagnetic materials in weak fields near
the Curie point” UFN, 26, 696–712 (1983).
(И.К. Камилов, Х.К. Алиев,
УФН, 140 N4, с. 639, 1983)
360
300
2
M (emu/g)
2
240
180
T=286K
288
290
292
294
296
298
120
60
0
0
2000
4000
6000
3
H/M (cm /g)
8000
10000
• I.K. Kamilov, Kh.K. Aliev “Second-order
phase transitions in ferromagnetic
materials in weak fields near the Curie
point” 26 696–712 (1983) И.К. Камилов,
Х.К. Алиев,
УФН, 140 N4, с. 639, 1983
EXPERIMENT and THEORY m
Gd, polycrystalline ball
Magnetization curve from the ferro- or ferrimagnetic samples with very
low coercive force HC << HS and anisotropy field HA << HS (points experiment; straight line – theory [. ).
Reference sample: ball (yttrium garnet ferrite)
100
M (Gs)
50
HS
M = H/N
N=4
0
-50
T=2K
-100
-800 -600 -400 -200
0
200
H (Oe)
400
600
800
Field dependence of the AC
magnetic
susceptibility of gadolinium
Reference sample: ball (yttrium garnet ferrite)
0.25
'=3/4
' = dM/dH
0.20
0.15
0.10
0.05
0.00
-1000
-750
-500
-250
0
H (Oe)
250
500
750
1000
Polycrystalline Ni59Cu41 sample
H/M