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

Introduction Magnetic phase transitions FM PM Tc

TN TN

Magnetic field-induced transition

First-order phase transition Magnetization M Entropy Volume

Second-order phase transition TC

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

Thermodynamics Large ΔB Large Small CB,p

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

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

Magnetic refrigerant materials

Adiabatic temperature change

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?

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%

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

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

What makes Gd5Ge4-xSix have giant MCE? Single crystal Gd5Si1.7Ge2.3 Monoclinic (P1121/a) a = 7.585 Å b = 14.800 Å c = 7.777 Å β = 93.290 TC=240.4±1 K 0.05 T

B-T phase diagram

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

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

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

ΔTad = Tc•ΔSm/Cp > 15 K

Thermal expansion ΔL/L = (L(T)-L(T = 5 K))/L(T = 5 K) Transition at TC = 240.0 ±1.0 K T’C = 236.0 ±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

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

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

Magnetization 160-330 K Thermal hysteresis 3.4 K Field hysteresis 0.5 T

B – T phase diagram of MnFeP0.45As0.55 Ordering T: TC = 306 K T’C = 302.2 K Thermal hysteresis: 3.8 K ΔTC/ΔB = 4.2 K/T First order phase transition

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

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)

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

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.

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

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.

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)

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 = 0 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)

Heat capacity in field Adiabatic T change