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

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.

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.

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.

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!

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.

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

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.

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.

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

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

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…..

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

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.

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.

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.

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.

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.

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.

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

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

(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

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)

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)

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. 2004.

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

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

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

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………

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.

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).

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

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]

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)

First order AFM to FM transition Gd5Ge4 First order AFM to FM transition

Metamagnetic transition in Gd5Ge4 M K Chattopadhyay et al ( unpublished )

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

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

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

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)

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)

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’

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)

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)

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

Half Heusler NiMnIn alloys First order Austenite to Martensite phase transition

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

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)

(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

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

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)

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

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

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).

THANK YOU

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

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

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

L21 structure Ni Mn In

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.

Influence of disorder in vortex lattice melting:

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

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

Landau Theory Metastable state Stable state