1. Magnetocaloric effects in intermetallic compounds
• Introduction
• Experimental results & discussion
• Conclusions
Magnetic phase transitions
Magnetocaloric effects & Magnetic refrigeration
- Magnetic-refrigerant materials
2nd order phase transition & MCE
1st order phase transition & MCE

2. Introduction Magnetic phase transitionsFM PM Tc

3. TN TN

4. Magnetic field-induced transition

5. First-order phase transition
Magnetization M
Entropy
Volume

6. Second-order phase transitionTC

7. Magneto-caloric effect & Magnetic refrigeration
Adiabatic
ΔTad
Isothermal ΔSm T
T+ΔT S N ΔQ ΔQ
Absorb heat T
T-ΔT S N
Cooling effect

8. Thermodynamics
Large ΔB
Large
Small CB,p

9. Superconducting magnet
Magnetic field
Metal Gd sphere 3 kg
Energy efficiency 20%-60%
Cooling power 200 W-600 W
C.O.P 2-9
ΔT = 4.5 K for 1.5 T ΔT = 11K for 5 T
Superconducting magnet Gd

10. Permanent magnetic field
Space: 114 x 128 x 12.7 mm3
Field strength:  2 T
Nd2Fe14B magnet
Lee et al. JAP (2002)

11. Magnetic refrigerant materials

12. Adiabatic temperature change

13. What are important for MR?
Ordering T: TC = 295 K
Field change: ΔB = 5 T
FWHM : δTFWHM = 65 K
MAX entropy change:
-ΔSm(max) = 8.5 J/kgK
Relative cooling power
RCP(S) = -ΔSm(max)*δTFWHM
=552 J/kg
Cooling power
What are important for MR?

14. Experimental results & discussion
Second order magnetic phase transition & MCE Gd
Sth(max) = RLn(2J+1)=17.3 J/molK; Sth(max) = 110 J/kgK <10%

15. TC = 298 K
ΔB = 2 T
ΔTad = 1.7 K
Hashimoto et al (1982)

16. First-order magnetic phase transition & MCE
Orthorhombic
Orthorhombic
Pecharsky et al (1997)

17. What makes Gd5Ge4-xSix have giant MCE?
Single crystal
Gd5Si1.7Ge2.3
Monoclinic (P1121/a)
a = Å
b = Å
c = Å
β =
TC=240.4±1 K
0.05 T

18. B-T phase diagram

19. Magnetization
Field-induced magnetic phase transition
PM FM
Field hysteresis
1 T

20. Magnetic entropy changes
TC = 240 K
ΔB = 5 T
ΔS(max) = 30.5J/kgK
δTFWHM = 18K
RCP(S) = 549 J/kgK
Effect of magnetic anisotropy is small

21. Specific heat capacity
Gd5Si1.7Ge2.3
at TC ΔS = 11.0 ± 0.5 J/molK
Latent heat L = 2.63 ± 0.12 kJ/mol

22. ΔTad
= Tc•ΔSm/Cp
> 15 K

23. Thermal expansion ΔL/L = (L(T)-L(T = 5 K))/L(T = 5 K)
Transition at
TC = ±1.0 K
T’C = ±1.0 K
Thermal hysteresis
ΔT = 4 K
ΔLa/La = 6.8x10-3 >0
ΔLb/Lb = -2.0x10-3 <0
ΔLc/Lc = -2.1x10-3 <0
Relative volume change
ΔV/V = 2.7x10-3
Clausius-Clapeyron relation
dTC/dp = 3.2 ± 0.2 K/kbar
M. Nazih et al. 2002

24. Transition-metal based compound: MnFeP1-xAsx
Crystal structure (0.15  x  0.65)
Fe2P-type; Hexagonal
Space group P-62m
At transition
Δc/c > 0
Δa/a < 0
ΔV/V < 0
There is no crystallographic
symmetry change.
Magnetic moment
4 µB/f.u.
Fe-layer
Mn-layer
Fe-layer 3g
1b/2c 3f

25. H O T X-T phase diagram Composition dependence of TC PM AF FM X
Bacmann et al. JMMM(1994)

26. Magnetization K
Thermal hysteresis 3.4 K
Field hysteresis 0.5 T

27. B – T phase diagram of MnFeP0.45As0.55
Ordering T:
TC = 306 K
T’C = K
Thermal hysteresis:
3.8 K
ΔTC/ΔB = 4.2 K/T
First order phase transition

28. Specific heat capacity
Tp= 296 K
Latent heat :
L = 526 J/mol
Cp = 550 J/kgK
(T > 300 K)

29. Magnetic entropy changes
TC = 306 K
ΔB = 5 T
-ΔS(max) = 18.3 J/kgK
δT = 21.3 K
RCP(S) = 390 J/kg
ΔTad =Tc•ΔSM/Cp
ΔTad = 10 K (ΔB=5 T)

30. MnFeP1-xAsx Magnetic entropy change in different compositions
Isothermal magnetic entropy changes:

31. Conclusions
MCE is closely related to the critical behavior of magnetic
phase transition.
Second order transition gives broad MCE peak. MCE is small.
First order transition gives sharp MCE peak. MCE can be large.
2. Gd5Si1.7Ge2.3 has a simultaneous structural and magnetic phase
transition at 239 K. This transition is a first order transition with
thermal hysteresis  7.4 K and with field hysteresis 1 T.
The MCE related with first order phase transition is quite large.
Effect of magnetic anisotropy on MCE in this material is negligible.
MnFeP1-xAsx (0.25<x<0.65) has a first order phase transition
with thermal hysteresis  3.4 K and field hysteresis  0.5 T.
The MCE related with this transition is also quite large.

32. 4. Advantages of MnFeP1-xAsx as a magnetic refrigerant
1. Large MCE
2. Tunable ordering temperature( between 168 and 332 K)
3. Small hysteresis
4. Lower cost : MnFe(P,As):
Mn,Fe,P,As(99%, 150$/kg)
Gd-Si-Ge Gd:
Gd(4N): 4000 $/kg.
Fe-Rh:
Rh: 12000$/kg

33. Acknowledgment
This work is supervised by E. Brück, J.H.K. Buschow, F.R. de Boer.
Collaborators: L. Zhang, W. Dagula, X.W. Li
Financially supported by the STW.

34. Bean-Rodbell model
Gibbs free energy
G = Gex + GH + Gdist + Gentr + Gpress
Volume change is due to the effect of magnetization.
Tc: Curie temperature
T0: Curie temperature (not compressible)
V : volume
V0 : volume(absent of exchange interaction)
N: number of atoms/V0
K: compressibility
σ: relative magnetization
(J =1/2)

35. η < 1 corresponds to 2nd order phase transition
Bean et al. PR(1962) 2 1
η = σ
J=1/2
Set P = 0
η = 0; σ = TC = T0
η < 1 corresponds to 2nd order phase transition
η > 1 corresponds to 1st order phase transition
For MnFeP0.5As0.5 η = 1.62, J = 2, T0 =250 K
R. Zach et al. JAP (1998)

36. Heat capacity in field
Adiabatic T change