AC-susceptibility method for Curie temperature determination.

Experiment and theory

A.V. Korolev, M.I. Kurkin, Ye.V. RosenfeldInstitute 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.  

L. D. Landau and E. M. Lifshitz, Statistical Physics, 2nded. 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

INTODUCTION

0 2000 4000 6000 80000

100

200

300

400

a<0a=0 T < TC: F-state

T > TC: P-state

H/M

M2

T = TC

THEORY: H/M = a + BM2

a>0

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

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

INTODUCTION

300 K

280 K

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

INTODUCTION

0 2000 4000 6000 8000 100000

60

120

180

240

300

360

298 K

Gd, polycrystalline ball

H/M

(cm

3 /g)

M2 (emu/g)2

T=286K 288 292 296 298286 K

A.V.Korolev et al., Phys. Met. Metallogr. 98, S1, s86-s93, 2004

M2 (emu/g)2

MOTIVATIONI 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.

La0.85Sr0.15MnO3

single crystal

226 K

234 K

NONLINIAR

LINIAR

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.

MOTIVATION

DC-optionH(t)=const ≤ 50 kOe

AC-option h(t) = hasin(t)

sample

Modern magnetometers with DC and AC options:MPMS, PPMS (Quantum Design, USA)

In our AC experiment:f < 100 Hz, ha< 4 Oe 1. Only the 1-st harmonic (no higher-order harmonics)2. ’ >> ’’ THEREFORE’ = M/H

280 290 300 310 320 330 3400,005

0,010

0,015

0,020

Gd, polycrystalline ball

=

M/H

T (K)

H=10 kOe 15 20 30 40 50

Tm

m

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

EXPERIMENT

We have experimental dependencies:1.Tm = f(H) 2. m = f(Tm) and we would like compare these data with theoretical functions.

EXPERIMENT

RESULTS1.m = 2A/(Tm-TC)2.Tm = TC + bH2/3 b=3A-1(B/16)1/3

THEORY

We have to solve the cubic equationBM3 + A(T – TC)M - H = 0for a value of the T = Tm, which corresponds to the m, under the condition (Tm,H)/T = 2M(Tm,H)/TH = 0

0 200 400 600 800 1000 1200 1400

290

300

310

320

330

340Gd, polycrystalline ball

Tm(H=0) = 287 K

Tm (

K)

H2/3 (Oe)2/3

TC = T

m(H=0)+ = 289 K

= NMs0

Gd/k = 2 K

EXPERIMENT and THEORY

(Tm – H2/3) PLOT

EXPERIMENT and THEORY

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

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

EXPERIMENT and THEORY

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

0 2000 4000 6000 8000 100000

60

120

180

240

300

360

T>TC

Gd, polycrystalline ball

TC 294K

H/M

(cm

3 /g)

M2 (emu/g)2

T=286K 294 298

43 = 7.9 cm3/g

~MS

2(T=286K)

T<TC

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.

“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)

0 2000 4000 6000 8000 100000

60

120

180

240

300

360

M

2 (em

u/g)

2

H/M (cm3/g)

T=286K 288 290 292 294 296 298

• 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

Gd, polycrystalline ball

EXPERIMENT and THEORY m

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 [. ).

-800 -600 -400 -200 0 200 400 600 800

-100

-50

0

50

100

Reference sample: ball (yttrium garnet ferrite)

M

(G

s)

H (Oe)

T = 2 K

HSM = H/N

N=4

Field dependence of the AC magnetic

susceptibility of gadolinium

-1000 -750 -500 -250 0 250 500 750 10000.00

0.05

0.10

0.15

0.20

0.25Reference sample: ball (yttrium garnet ferrite)

'

= d

M/d

H

H (Oe)

'=3/4

Polycrystalline Ni59Cu41 sample

H/M