1. Raja Ramanna Centre for Advanced Technology, Indore
Kinetically arrested first order magneto-structural
phase transitions: glass-like phenomena
Sindhunil Barman Roy
Raja Ramanna Centre for Advanced Technology, Indore

2. Plan of the talk:
Some technologically important materials of current interest
-- giant magnetoresistive materials, giant magnetocaloric materials,
giant magnetostrictive materials or magnetic shape memory alloys.
2. These functional magnetic materials often show a temperature and
magnetic field induced first order phase transition (FOPT).
Key to the functionality is the magnetic field induced FOPT,
—metamagnetic transition.
3. Discuss metamagnetic transition in three classes of magnetic material:
(a) Gd5Ge4: para-antiferro-ferromagnetic transition
(b) Half Heusler alloys-NiMnIn: para-ferro-incipient antiferromagnetic transition
(c) Binary-CeFe2 alloys : para-ferro-antiferromagnetic transition
In these materials often the FOPT gets kinetically arrested → leads to glass-like non-equilibrium phenomenon.

3. A brief history of magnetocaloric effect Magnetocaloric Effect
A magnetic solid heats up when magnetized and cools down when
demagnetized .
Originally discovered in iron by E Warburg in 1881.
Thermodynamics of MCE was understood independently by
Debye (1926) and Giaque( 1927). Both of them suggested that
MCE could be used to reach low temperature in a process known
as adiabatic demagnetization.
An adiabatic demagnetization refrigerator was constructed and
utilized by Giauque and McDougal (1933) to reach 0.53, 0.34
and 0.25K starting at 3.4 , 2.0 and 1.5K , respectively using a
magnetic field of 0.8T and 61g of Gd2(So4)3.8H2O as the
magnetic refrigerant.

4. Suitable MCE materials for refrigeration:
Two quantitative characteristics of MCE :
Isothermal entropy change,
SM(T)H = HI  HF (M(T,H)/ T)H dH
Adiabatic temperature change,
Tad(T)H = HI  HF (T/C(T,H))H (M(T,H)/ T)H dH
The material should have large (M(T,H)/ T)H
and low C at the temperature of interest.

5. Large (M(T,H)/ T)H  Large MCE
(M(T,H)/ T)H is large for a ferromagnet near its Curie temperature ( TC ).
So, one needs a ferromagnetic material with TC around RT.
Gd with TC around 290K is a potential MCE material for RT refrigeration.
In 1998 Ames Lab. Iowa + Astronautics Technology Center in Madison, Wisconsin, USA demonstrated a magnetic refrigeration unit that operated at room temperature.
However, the device required a cryogenically cooled superconducting magnet, making it impractical for homes. Also Gd is costly!

6. Materials with giant MCE: Newer Promise
Gd5(GexSi1-x)4 alloys ; discovered in late 1990s.
TC around room temperature ;MCE 2-4 times larger than Gd.
Giant MCE in Gd5(Ge,Si)4 is correlated with a first order
magneto-structural transition.

7. Shape Memory Alloys and large magnetostriction
Materials with T and H induced Martensitic transition
Common knowledge amongst metallurgists that Martensitic transition is FOPT

8. Plan of the talk:
1. Some technologically important materials of current interest
-- giant magnetoresistive materials, giant magnetocaloric materials,
giant magnetostrictive materials or magnetic shape memory alloys.
2. These functional magnetic materials often show a temperature and
magnetic field induced first order phase transition (FOPT).
Key to the functionality is the magnetic field induced FOPT,
—metamagnetic transition.
3. Discuss metamagnetic transition in three classes of magnetic material:
(a) Gd5Ge4: para-antiferro-ferromagnetic transition
(b) Half Heusler alloys-NiMnIn: para-ferro-incipient antiferromagnetic transition
(c) Binary-CeFe2 alloys : para-ferro-antiferromagnetic transition
In these materials often the FOPT gets kinetically arrested → leads to glass-like non-equilibrium phenomenon.

9. Magnetic field induced transition – Metamagnetic transition
What is a Metamagnet ?
“Magnets which undergo first-order phase transition in an increasing magnetic field are called metamagnets.”
Principles of Condensed Matter Physics
P. M. Chaikin & T. C. Lubnesky, p175.
“ Metamagnet, a material with antiferromagnetic order in zero external field that undergoes a first-order phase transition to a phase with non-vanishing ferromagnetic moment in an increasing external field.”
Principles of Condensed Matter Physics-
P. M. Chaikin & T. C. Lubnesky, p 677.

10. Working definition :
A system which undergoes magnetic field induced first order
magneto-structural phase transition involving large increase
in magnetization

11. First order phase transition (FOPT):
Ehrenfest’s scheme

12. Phenomenology of a first order phase transition
(Principles of Condensed Matter Physics, Chaikin & Lubensky (1995))
f(T,H) = (r/2)S2 – wS3 +uS4 ; r = a(T-T*)
T* is the limit of supercooling
T*<T1<TC
T=T1
T = TC
T*<T2<T1<TC
T=T2
T=T*
Supercooling is a ubiquitous phenomenon, seen in nature in clouds, and plants
surviving below 00 C…..

13. Limit of superheating T**
T > TC
T = T**

14. Effect of disorder on a FOPT ?
Common idea  disorder broadens a first order transition and
ultimately turns it into a second order transition.
Formal approach  Disorder influenced landscape of transition
temperature or field -- transition temperature can be different
locally (Imry and Wortis, Phys. Rev. B 1979), gives the impression of a globally broadened first order transition (Soibel et al, Nature 2000).
Disorder also causes phase-coexistence between stable and metastable
phases.

15. What establishes a FOPT experimentally?
Latent heat in materials with broadened FOPT is not easy to measure.
It is easier to detect : V
S  Latent heat
(a) Hysteresis due to superheating/supercooling
(b) Phase-coexistence
Key features of a FOPT  metastability: supercooling and superheating.
Disorder introduces phase-coexistence.

16. Study of FOPT in functional magnetic materials : experimental approach
Easily measurable bulk properties like ac-susceptibility,
dc-magnetization, resistivity, heat capacity and magneto-striction can be powerful observable.
With T and H are the control parameters, one looks for hysteresis and
metastability in such bulk properties.
Certain signatures in these bulk properties are indicative
of phase-coexistence.
Visual evidence of phase-coexistence can be obtained in
mesoscopic scale using scanning micro-Hall probe,
microscopic scale using MFM.

17. Plan of the talk:
1. Some technologically important materials of current interest
-- giant magnetoresistive materials, giant magnetocaloric materials,
giant magnetostrictive materials or magnetic shape memory alloys.
2. These functional magnetic materials often show a temperature and
magnetic field induced first order phase transition (FOPT).
Key to the functionality is the magnetic field induced FOPT,
—metamagnetic transition.
3. Discuss metamagnetic transition in three classes of magnetic material:
(a) Gd5Ge4: para-antiferro-ferromagnetic transition
(b) Half Heusler alloys-NiMnIn: para-ferro-incipient antiferromagnetic transition
(c) Binary-CeFe2 alloys : para-ferro-antiferromagnetic transition
In these materials often the FOPT gets kinetically arrested → leads to glass-like non-equilibrium phenomenon.

18. Magnetic materials of current interest at RRCAT, Indore:
RE5(Ge,Si)4, RECu2 , RE(Cu,Co)2 ; MCE materials for gas liquefaction
Half Hesuler alloys: NiMnIn, NiMnSn, NiFeGa, CoNiGa, CoMnSi.
RhFe and NiMn alloys.
These are materials with multifunctional properties: MCE, GMR,Magnetostriction, shape memory effect.
Motivation: Examine the interplay between deeper scientific basis of the
physical properties of functional materials and their technological applications.
CeFe2 and its alloys– Test bed materials system for demonstrating the typical characteristic features of a disorder influenced FOPT and kinetic arrest of FOPT.

19. CeFe2 alloys Structure : FCC , C15-Laves Phase.
Ferromagnet; TCurie ≈ 230 K ;
eff ≈ 2.15 B / formula unit.
The FM state is on the verge of a
magnetic instability.
Turns into a Low-T AFM state on small (2-5%)
doping with Co, Al, Ru, Ir etc.

20. Ferromagnetic to antiferromagnetic transition in CeFe2 alloys
Resistivity
ac-Susceptibility
Dc-magnetization

21. First order nature of the FM-AFM transition in CeFe2 alloys
First order nature of the FM-AFM transition is well established:
Neutron diffraction study -- Kennedy and Coles 1992
Thermal expansion study -- Ali and Zhang, 1992

23. (SM(T,H)/H)T = (M(T,H)/ T)H.
SM(T)H = HI  HF dSM(T,H)T = HI  HF (M(T,H)/ T)H dH

24. First order FM-AFM transition in CeFe2 alloys: Thermal hysteresis
DC-magnetization study
Magnetization measured with three different experimental protocols:
(1) Zero field cooled (ZFC)
(2) Field cooled cooling (FCC)
(3) Field Cooled warming (FCW)
TNC > TNW ;
Effect of disorder induced
landscape of TN
K J S Sokhey et al Solid St. Commun (2004)
M K Chattopadhyay et al , Phys. Rev. B (2003)

25. Metamagnetic transition in Ru-doped CeFe2 alloys
Isothermal field variation study of dc-magnetization
H**
HMD H*
HMU
HMU < HMD
S B Roy et al, Phys. Rev. B (2005)

27. FM-AFM transition in CeFe2 alloy studied with Hall probe
AFM+FM state
AFM state
FM state
S B Roy et al Phys. Rev. Lett

28. Temporal evolution of the AFM-FM phase-coexistence:
evidence for metastability
Sample measured over 160 minutes in ZFC state at 60K and field 20 kOe 28

29. a metamagnetic material.
Phase-coexistence is a key parameter for the associated functionalities in
a metamagnetic material.
Phase-coexistence can be controlled with the external magnetic field.
Disorder profile of the materials concerned is important for tuning phase-coexistence.
Percolation path for good conductivity can be achieved early ; large magneto-resistance with lower applied H
Phase-coexistence i.e. large inhomogeneity
over a wide H-region; good for MCE
5%Ru-doped CeFe2
4%Ru-doped CeFe2

30. M vs T plot for 4%Ru-doped CeFe2 alloy

31. Kinetic arrest of first order transition process:
anomalous M-H and R-H loop.
….To conclude, we have observed unusual history effects in magnetization and magnetotransport measurements across the FM-AFM transition in Ce(Fe0.96Al0.04)2, and have discussed similarities with earlier single-crystal data on R0.5Sr0.5MnO3 across another first-order FM-AFM transition. We have argued that the kinetics of this FM-AFM transition is hindered at low T………

32. Magnetic-glass state in CeFe2 alloys
Liquids freeze into crystalline solids via a first order phase transition.
Some liquids called ‘glass formers’ experience a viscous retardation of nucleation and crystallization in their supercooled state.
In the experimental time scale the supercooled liquid ceases to be ergodic and it enters a glassy state.

33. Standard definition of ‘glass’ : ‘A noncrystalline solid material which yields broad nearly featureless diffraction pattern’.
Alternative definition: ‘A liquid where the atomic or molecular motions are arrested’.
Within this latter dynamical framework, ‘glass is time held still’
S Brawer . Relaxation in Viscous Liquids and Glasses (The American Ceramic Society Inc. Columbus, Ohio, 1985).

34. Arrest of FM-AFM transition in 4%Ru-doped CeFe2 :
cooling rate dependence
Frozen-in FM fraction is more with higher cooling rate.

35. Relaxation results at
various T on the FCC path
Time dependence of M can be fitted with Kohlrausch-Williams-Watt stretched exponential function :Φ(t) ~exp[-(t/τ)β]

36. Contrasting magnetic response between MG and Re-entrant Spin-glass
Au82Fe18  representative of re-entrant spin-glass family
4%Ru doped CeFe2  representative of magnetic-glass
CHUFF
Chaddah et al
Phys. Rev. B 2008
S B Roy & M K Chattopadhyay, Phys. Rev. B (2009)

38. First order AFM to FM transition
Gd5Ge4
First order AFM to FM transition

39. Metamagnetic transition in Gd5Ge4
M K Chattopadhyay et al
( unpublished )

40. Field (H)- temperature (T) Phase Diagram of Gd5Ge4
H Tang et al Phys. Rev. B 2004

41. First order AFM-FM transition in Gd5Ge4
T Dependence of Magnetization in Gd5Ge4

42. H dependence of M in Gd5Ge4
Chattopadhyay et al,
Phys. Rev B, 2004

43. Mesoscopic evidence of phase-coexistence across
AFM-FM transition in Gd5Ge4 :
Scanning of AFM-FM transition with a
micro-Hall probe.
Sample dimension 1mm x 1mm; resolution
10 micron
J D Moore et al Phys. Rev. B (2006)

44. Micro-Hall probe imaging of AFM- FM transition
J D Moore et al Phys. Rev. B (2006); G Perkins et al J Phys CM (2007)

45. Formation of a new non-equilibrium magnetic state arising out of a kinetically arrested first order phase transition in Gd5Ge4.
This ‘non-equilibrium magnetic state’ is distinctly different from a ‘spin-glass’

46. Metastability of the low-H and low-T ZFC state in Gd5Ge4:
Gd5Ge4 polycrystal
Gd5Ge4 single crystal
S B Roy et al Phys. Rev. B (2006)
S B Roy et al Phys. Rev. B(2007)

47. Gd5Ge4: Relaxation results at various T on the FCC path
Time dependence of M can be fitted with Kohlrausch-Williams-Watt stretched exponential function :
M(t)exp[-(t/)]
Indicates Glass-like behaviour
S B Roy et al Phys. Rev. B (2006)

48. H- T Phase diagram of Gd5Ge4 :
H Tang et al Phys. Rev. B 2004
S B Roy et al Phys. Rev. B (2006)

50. Half Heusler NiMnIn alloys
First order Austenite to Martensite phase transition

51. Sutou et al. Appl. Phys. Lett. 85, 4358 (2004)

52. First order Austenite-Martensite phase transition in Ni50Mn34In16
X-Ray Diffraction
ac-Susceptibility
DC magnetization
M vs H
M vs T
V K Sharma et al,J Phys CM (2007)

54. (SM(T,H)/H)T = (M(T,H)/ T)H.
SM(T)H = HI  HF dSM(T,H)T = HI  HF (M(T,H)/ T)H dH

55. Protocol 1: 300 K  ZFC 150K  242 K
Protocol 2: 300 K  ZFC 242K
Protocol 3: 300 K  ZFC 30K  242 K

56. Scanning Hall probe imaging of the metamaagnetic transition in Ni50Mn34In16: thermomagnetic history effects
Protocol 2: 300 K  ZFC 236 K
Protocol 3: 300 K  ZFC 30K  236 K
V Sharma et al (J. Phys. Condens. Matter 2010)

57. cooled cooling (FCC) and field cooled warming (FCW)
Magnetization measured under 3 different protocols: zero field cooled (ZFC), field
cooled cooling (FCC) and field cooled warming (FCW) 57

58. Broad Outlook
Disorder influenced First Order Phase Transition plays an important
role in the functional properties of
(a) Giant magnetocaloric materials
(b) Magnetic Shape Memory Alloys.
(c) Giant magnetoresistive materials.
(d) Mn-oxide materials showing Colossal Magnetoresistance
(e) Vortex-matter of type-II superconductors.
(f) Exchange spring magnets.
(g) Relaxor ferroelectrics
Functionality of the materials concerned can be tuned by tuning the characteristics of FOPT
Underlying First Order Phase Transition often gets kinetically arrested, giving rise to glass-like non-equilibrium behaviour.
Disorder magnetic materials can be relatively simple mediums to study
such kinetic arrest of FOPT and glass-like non-equilibrium phenomena

59. Acknowledgement:
M K Chattopadhyay, V. K. Sharma, M A Manekar and K J S Sokhey and ( RRCAT, Indore).
P. Chaddah ( UGC-DAE CSR, Indore).
K. Nigam ( TIFR, Mumbai).
J. Moore, L. Cohen and G. Perkins ( IC, London).
V. K. Pecharsky and K. Gschneidner (Ames Lab., USA).

60. THANK YOU

61. Large Magnetocaloric effect in Gd5(Ge,Si)4
Gschneidner & Pecharsky, Annual Rev. Matr. Science (2000)

62. Magnetocaloric Effect & Magnetic Refrigerator
Ordered
spins
Magnetic refrigeration is an economic and environmentally sound alternative to vapour-cycle refrigerators and air conditioners.
It offers considerable operating cost savings by eliminating the most inefficient part of the existing refrigerators – the compressor
It uses a solid refrigerant and a common heat transfer fluids (e.g. water, air or helium gas) with
no ozone-depleting and global-warming effects.
This solid refrigerant heats up when magnetized and cools down when demagnetized -- magnetocaloric effect (MCE).
Random
spins
The stronger the MCE the higher the efficiency of the device

64. Study of phase-coexistence across a FOPT:
minor hysteresis loop (MHL ) technique

65. L21 structure Ni Mn In

67. A sample with disorder can have a spatial distribution of the phase transition field/temperature in a general first-order transition, hence broadening the (HC,TC) line into a band. This disorder would also cause the (H*,T*) and (H**,T**) lines to be broadened into bands.

68. Influence of disorder in vortex lattice melting:

69. Measurement of MCE: contd.
Indirect measurements: From magnetization (M) and heat capacity:
If the magnetization and entropy are continuous functions of T
and H, then the infinitesimal isobaric-isothermal magnetic entropy
change can be related to M , H and absolute T using one of the
Maxwell relations,
(SM(T,H)/H)T = (M(T,H)/ T)H.
After integration this yields isothermal entropy change,
SM(T)H = HI  HF dSM(T,H)T = HI  HF (M(T,H)/ T)H dH

70. P V T Tcr PV Isotherms – Vander waal’s gas
P* - Limit of Supercooling of Gas
P** - Limit of Superheating of Liq P*
PC1
T2<T1
PC1
P** P*
PC2
PC2
P** V
Supercooling/Superheating & hysteresis

71. Landau Theory
Metastable state
Stable state