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AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
INTODUCTION
INTODUCTION
Landau expansion of the thermodynamic potential F in terms of M is
Landau expansion of the thermodynamic potential F in terms of M is
We should see a picture like which you see on this slide
We should see a picture like which you see on this slide
Experimental H/M vs
Experimental H/M vs
A.V.Korolev et al
A.V.Korolev et al
MOTIVATION I can show you more and more the same kind of typical
MOTIVATION I can show you more and more the same kind of typical
MOTIVATION
MOTIVATION
In our AC experiment: f < 100 Hz, ha< 4 Oe 1. Only the 1-st harmonic
In our AC experiment: f < 100 Hz, ha< 4 Oe 1. Only the 1-st harmonic
EXPERIMENT
EXPERIMENT
We have experimental dependencies: 1.Tm = f(H) 2.
We have experimental dependencies: 1.Tm = f(H) 2.
RESULTS
RESULTS
EXPERIMENT and THEORY
EXPERIMENT and THEORY
EXPERIMENT and THEORY
EXPERIMENT and THEORY
A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys
A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys
A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys
A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys
Landau second-order phase transition theory of ferromagnetic materials
Landau second-order phase transition theory of ferromagnetic materials
Congratulations, Yuri
Congratulations, Yuri
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
MOTIVATION
MOTIVATION
MOTIVATION Nonlinear effects are decreasing with increasing
MOTIVATION Nonlinear effects are decreasing with increasing
“kink-point method”
“kink-point method”
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
AC-susceptibility method for Curie temperature determination
I.K. Kamilov, Kh
I.K. Kamilov, Kh
EXPERIMENT and THEORY m
EXPERIMENT and THEORY m
Magnetization curve from the ferro- or ferrimagnetic samples with very
Magnetization curve from the ferro- or ferrimagnetic samples with very
Field dependence of the AC magnetic susceptibility of gadolinium
Field dependence of the AC magnetic susceptibility of gadolinium
Polycrystalline Ni59Cu41 sample
Polycrystalline Ni59Cu41 sample

Презентация: «AC-susceptibility method for Curie temperature determination». Автор: Korolyov. Файл: «AC-susceptibility method for Curie temperature determination.ppt». Размер zip-архива: 1538 КБ.

AC-susceptibility method for Curie temperature determination

содержание презентации «AC-susceptibility method for Curie temperature determination.ppt»
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1 AC-susceptibility method for Curie temperature determination

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

2 INTODUCTION

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.

3 Landau expansion of the thermodynamic potential F in terms of M is

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

L. D. Landau and E. M. Lifshitz, Statistical Physics, 2nd ed. Nauka, Moscow, 1964; Pergamon, Oxford, 1980

INTODUCTION

4 We should see a picture like which you see on this slide

We should see a picture like which you see on this slide

5 Experimental H/M vs

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

6 A.V.Korolev et al

A.V.Korolev et al

, PHYS. SOLID STATE, 52, 561-567, 2010

INTODUCTION

7 MOTIVATION I can show you more and more the same kind of typical

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

234 K

226 K

M2 (emu/g)2

LINIAR

La0.85Sr0.15MnO3 single crystal

NONLINIAR

8 MOTIVATION

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.

9 In our AC experiment: f < 100 Hz, ha< 4 Oe 1. Only the 1-st harmonic

In our AC experiment: f < 100 Hz, ha< 4 Oe 1. Only the 1-st harmonic

(no higher-order harmonics) 2. ?’ >> ?’’ THEREFORE ?’ = ?M/?H

sample

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)

10 EXPERIMENT

EXPERIMENT

A.V.Korolev et al., PHYS. SOLID STATE, 52, 561-567, 2010

11 We have experimental dependencies: 1.Tm = f(H) 2.

We have experimental dependencies: 1.Tm = f(H) 2.

m = f(Tm) and we would like compare these data with theoretical functions.

EXPERIMENT

12 RESULTS

RESULTS

m = 2A/(Tm-TC) Tm = TC + bH2/3 b=3A-1(B/16)1/3

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

13 EXPERIMENT and THEORY

EXPERIMENT and THEORY

(Tm – H2/3) PLOT

14 EXPERIMENT and THEORY

EXPERIMENT and THEORY

Gd, polycrystalline ball: (1/?m – Tm) PLOT

m

15 A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys

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

16 A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys

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

EXPERIMENT and THEORY

17 Landau second-order phase transition theory of ferromagnetic materials

Landau second-order phase transition theory of ferromagnetic materials

describes magnetic experiments in the vicinity of the Curie temperature is not good enough. However, only at temperatures above the Curie temperature (a few degrees), the experiments are in very good agreement with the theory. Using the AC magnetic susceptibility method together with the theory we can find the value of the Curie temperature definitely.

CONCLUSION

18 Congratulations, Yuri

Congratulations, Yuri

19 AC-susceptibility method for Curie temperature determination
20 AC-susceptibility method for Curie temperature determination
21 MOTIVATION

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

22 MOTIVATION Nonlinear effects are decreasing with increasing

MOTIVATION Nonlinear effects are decreasing with increasing

temperature and Landau's theory is working better and better with increasing temperature. We guess that the theory should be effective at temperature more than Curie temperature.

23 “kink-point method”

“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)

24 AC-susceptibility method for Curie temperature determination
25 AC-susceptibility method for Curie temperature determination
26 AC-susceptibility method for Curie temperature determination
27 I.K. Kamilov, Kh

I.K. Kamilov, Kh

.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

28 EXPERIMENT and THEORY m

EXPERIMENT and THEORY m

Gd, polycrystalline ball

m

29 Magnetization curve from the ferro- or ferrimagnetic samples with very

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 [. ).

30 Field dependence of the AC magnetic susceptibility of gadolinium

Field dependence of the AC magnetic susceptibility of gadolinium

31 Polycrystalline Ni59Cu41 sample

Polycrystalline Ni59Cu41 sample

H/M

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