1. 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 There are a lot of different methods for determination of Curie temperature T C 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. 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 = F 0 – MH + (1/2)A(T – T C )M 2 + (1/4)BM 4 T C,A, B = const; after minimization: H/M = A(T – T C ) + BM 2 ; T=const: H/M = a + BM 2 INTODUCTION

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

5. Experimental H/M vs. M 2 dependencies without demagnetization correction for the Gd sample in the shape of flat parallelepiped in the vicinity of the assumed T C of Gd. V.I. Zverev et al., JMMM (2011), doi:10.1016/j.jmmm.2011.05.012 INTODUCTION 300 K 280 K

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

7. A.V.Korolev et al., Phys. Met. Metallogr. 98, S1, s86-s93, 2004 M 2 (emu/g) 2 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 T c 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. La 0.85 Sr 0.15 MnO 3 single crystal 226 K 234 K NONLINIAR LINIAR

8. The displayed data suggest that the Landau theory "does not work" near T = T c ± (0.01-0.02) T c. Method of determining the T c from such data, in my opinion, is not justified. At the same time, we can assume that this theory should well describe experiment near T c, but at T > T c +(~0.02)T c. 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 = T m, which moves from T c to high temperature region with increasing field. MOTIVATION

9. DC-option H(t)=const ≤ 50 kOe AC-option h(t) = h a sin(  t) sample Modern magnetometers with DC and AC options: MPMS, PPMS (Quantum Design, USA) In our AC experiment: f < 100 Hz, h a < 4 Oe 1. Only the 1-st harmonic (no higher-order harmonics) 2.  ’ >>  ’’ THEREFORE  ’ =  M/  H

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

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

12. RESULTS 1.  m = 2A/(T m -T C ) 2.T m = T C + bH 2/3 b=3A -1 (B/16) 1/3 THEORY We have to solve the cubic equation BM 3 + A(T – T C )M - H = 0 for a value of the T = T m, which corresponds to the  m, under the condition   (T m,H)/  T =  2 M(T m,H)/  T  H = 0

13. EXPERIMENT and THEORY (T m – H 2/3 ) PLOT

14. EXPERIMENT and THEORY Gd, polycrystalline ball: (1/  m – T m ) PLOT

15. A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys.Solid State, Vol. 45, No. 8, 2003, pp. 1484–1486. La 0.85 Sr 0.15 MnO 3 single crystal: (T m – H 2/3 ) PLOT EXPERIMENT and THEORY

16. A.V. Korolev, M. I. Kurkin, and E. V. Rosenfel’d Phys. Solid State, Vol. 45, No. 8, 2003, pp. 1484–1486. La 0.85 Sr 0.15 MnO 3 single crystal: (1/  m – T m ) PLOT EXPERIMENT and THEORY

17. 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.

18. Congratulations, Yuri

21. 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 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.

23. “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).Second-order phase transitions in ferromagnetic materials in weak fields near the Curie point (И.К. Камилов, Х.К. Алиев, УФН, 140 N4, с. 639, 1983)

27. 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, 1983Second-order phase transitions in ferromagnetic materials in weak fields near the Curie point

28. Gd, polycrystalline ball EXPERIMENT and THEORY m

29. Magnetization curve from the ferro- or ferrimagnetic samples with very low coercive force H C << H S and anisotropy field H A << H S (points - experiment; straight line – theory [. ).

30. Field dependence of the AC magnetic susceptibility of gadolinium

31. Polycrystalline Ni59Cu41 sample H/M