1. Electronic properties of a ferromagnetic shape memory alloy: Ni-Mn-Ga
Talk at ‘Electronic Structure of Emerging Materials: Theory and Experiment’
at Lonavala-Khandala, 8th February, 2007
Electronic properties of a ferromagnetic shape memory alloy: Ni-Mn-Ga
Sudipta Roy Barman
UGC-DAE Consortium for Scientific Research, Indore
Part of university system fully funded by UGC. Besides in-house research, we provide advanced research facilities to University researchers.
Emphasis on Researchers in different academic institutions to work together.
Max Planck partner group project

2. What is a shape memory alloy?
SMA effect involves structural transition called martensitic (after F. Martens)
transformations which are diffusionless. It is a first order transformation and occurs
by nucleation and growth of a lower symmetry (tetragonal/orthorhombic) martensitic
phase from the parent higher symmetry (cubic austenitic) phase.

3. Ni-Mn-Ga is ferromagnetic, and exhibits magnetic SMA
SMA: Transformation from the martensite to austenite phase by temperature or stress.
FSMA: Entirely within the martensite phase, actuation by magnetic field, faster than conventional stress or temperature induced SMA.
10% Magnetic Field Induced Strain in Ni50Mn30Ga20 reported.
The magnetic moments without the external field
The rotation of the magnetic moments within the twins.
The redistribution of the twin variants.

4. Live simulation of the FSMA effect
Rotation of magnetic moments:
[Magnetocrystalline anisotropy<< Zeeman energy]
FSMA effect: change in shape [Magnetocrystalline anisotropy>> Zeeman energy]
10% Magnetic Field Induced Strain in Ni50Mn30Ga20 reported. Highest in any system till date.

5. Magnetic domains and twin bands
Topography image
MFM image
Magnetic force microscopy image of Ni2.23Mn0.8Ga in the martensitic phase at room temperature clearly shows the twin bands (width 10 micron) and magnetic domains (width 2-3 microns)
C. Biswas, S. Banik, A. K. Shukla, R. S. Dhaka, V. Ganesan, and S. R. Barman, , Surface Science, 600, 3749 (2006).

6. Smart actuator materials Potential fields of applications
                                 
    
                              
                           
                      
                         

7. A real actuator made from FSMA by Adaptamat
This demo is animated, but it shows the motion of the axis. The actuator can be driven faster/slower (average 70mm/s) and in bigger/smaller steps (accuracy <1μm).

8. The FSMA mechanism
Magnetic field induced strain =1- c/a

9. Overview of our collaborative work on
study of fundamental properties of Ni-Mn-Ga
Polycrystalline ingot preparation in Arc furnace, EDAX [In house]
Thermal, transport and magnetic studies: Differential Scanning calorimetry, Ac susceptibility; magnetization; resistivity; magnetoresistance; AFM, MFM
[Collaboration: SNBCBS,Kolkata; Suhkadia University, Udaipur; TIFR, Mumbai; RRCAT, Indore & In-house  Phys. Rev. B, 74, (2006) ; Appl. Phys. Lett. . 86, (2005); Surface Science, 600, 3749 (2006).]
Structural studies: X-ray diffraction [Collaboration: Banaras Hindu University, Banaras  Phys. Rev. B (2006, in press); Phys. Rev. B (2007, in press)]
Electronic structure: Photoemission spectroscopy (UPS and XPS); Inverse photoemission spectroscopy; theory (FPLAPW) [Collaboration: In-house and CAT, Indore  Phys. Rev. B, 72, (2005); Phys. Rev. B 72, (2005); Applied Surface Science, 252, (2006)]
Compton scattering [Collaboration: Rajasthan University, Jaipur; Sukhadia university, Udaipur, Spring-8, Japan  Phys. Rev. B (2007), accepted.]

10. Acknowledgments to the collaborators and funding agencies
Phd students: S. Banik, C. Biswas, and A. K. Shukla
RRCAT, Indore: A. Chakrabarti
UGC-DAE CSR, Indore: R. Rawat, A. M. Awasthi, N. P. Lalla, D. M. Phase, A. Banerjee, V. Sathe, V. Ganesan.
Banaras Hindu Univeristy, Banaras: D. Pandey, R. Ranjan
S.N. Bose Centre for Basic Sciences: U. Kumar, P. Mukhopadhyay
Sukhadia Univerisity, Udaipur: B. L. Ahuja
Rajasthan univeristy, Jaipur: B. K. Sharma
Department of Science and Technology, Govt. of India through SERC project ( ) and Ramanna Research Grant.
P. Chaddah and A. Gupta

11. Samples grown in house
Polycrystalline ingots of Ni-Mn-Ga alloys were prepared by melting in Arc furnace.
Appropriate quantities of Ni, Mn, and Ga of 99.99% purity melted under Argon atmosphere.
0.5 to 1% maximum loss of weight, possibility of difference in intended and actual composition.
The L21 phase is obtained after annealing at 1100K in sealed quartz ampules.
Annealing time for each sample is more than a week: to ensure homogenization.
The ingots were quenched in ice water.

12. Ni2MnGa is a Heusler alloy
L21 structure: Four interpenetrating f.c.c. sublattices with :
Ni at (1/4,1/4,1/4 ) and (3/4,3/4,3/4)
Mn at (1/2,1/2,1/2),
Ga at (0,0,0).
Ferromagnetism due to RKKY indirect exchange interaction.
Heusler alloys are famous for localized large magnetic moments on Mn.

13. Temperature dependent XRD: evidence of modulation
Austenite
Martensite structure more complicated than tetragonal!
7 layer (7M) modulation in 110 direction.
Ranjan, Banik, Kumar, Mukhopadhyay, Barman, Pandey, PRB (2006).

14. Phase coexistence in Ni2MnGa
(a) Hysteresis curve showing mole fraction of the cubic phase determined from Rietveld analysis of the XRD patterns.
(b) Ac-susceptibity; Decrease at TM due to large magnetocrystalline anisotropy in martensitic phase.
(c) Differential scanning calorimetry
Nice agreement between structural, magnetic and thermal techniques. Small width
of hysteresis K; highly thermoelastic (mobile interface, strain less).

15. Resistivity and magnetoresistance
T/Tc= 0.8
Metallic behaviour with a clear jump at TM.
Ref: M. Kataoka, PRB, 63, (2001)
Highest known magnetoresistance at room temperature for shape memory alloys. For x=0.35, MR is around 7.3% at 8T.
Experimental MR behavior agrees with the theoretical calculation.
Magnetic spin disorder scattering increases with increasing x.
C. Biswas, R. Rawat, S.R. Barman, Appl. Phys. Lett., 86, (2005)

16. Total energy calculations using Full potential linearized augmented plane wave (FPLAPW) method
Total energy includes the electron kinetic energy and electron-electron, electron-nuclear and nuclear-nuclear potentials.
Ab-initio i.e. no requirement of input parameters.
FPLAPW solves the equations of density functional theory by variational expansion approach by approximating solutions as a finite linear combination of basis functions. What distinguishes the LAPW method from others is the choice of basis.
Ref: www-phys.llnl.gov/Research/Metals_Alloys/Methods/AbInitio/LAPW/
WIEN code (P. Blaha, K. Schwartz, and J. Luitz, Tech. Universität, Wien, Austria, 1999)

17. Structure optimization for Ni2MnGa
Experimental c/a= 0.94.
Previous theory: c/a= 1.2, 1, etc.

18. Total energy contours for structural optimization of Ni2MnGa
For ferromagnetic martensitic phase, a= 5.88 Ǻ and c= 5.70 Ǻ, with c/a=0.97. Comapres well with expt. c/a=0.94.
Good agreement with experimental lattice constants: a= 5.88Ǻ, c= 5.56 Ǻ within 2.5%.
Tetragonal phase more stable than the cubic phase by 3.6 meV/atom.
Barman, Banik, Chakrabarti, Phys Rev B, 72, (2005)

19. Ni2MnGa  Ni-Mn-Ga
Increase Nickel
Ni2MnGa  Ni2+xMn1-xGa (Ni, Mn)  Ni3Ga (x=1)
Increase Manganese
Ni2MnGa  Ni2-yMn1+yGa (Mn, Ni)  NiMn2Ga or Mn2NiGa (y=1)

20. Structure optimization for Ni2.25Mn0.75Ga
Good agreement between the experimental and theoretical lattice constants:
Expt: a= Ǻ , c= Ǻ
Theory: a= 5.38 Ǻ, c= 6.70 Ǻ)
[within 1% for a and 2% for c].

21. Phase diagram of Ni2+xMn1−xGa
P= paramagnetic, F= ferromagnetic
C= cubic (austenite),
T= tetragonal (martensite) x
TC and TM determined by DSC and ac-chi measurements.
TC increases with Ni content i.e. x.
TC = TM for x= 0.2, large magnetoelastic coupling and gaint magnetocaloric effect.
TC < TM for x> 0.2, emergence of the new paramagnetic tetragonal phase, confirmed by high temperature XRD.
Banik, Chakrabarti, Kumar, Mukhopadhyay, Awasthi, Ranjan, Schneider, Ahuja, and Barman, PRB, 74, (2006)

22. Phase diagram vis-à-vis total energies
x= 0.25,
Ni2.25Mn0.75Ga
x= 0, Ni2MnGa
TM>TC
TM<TC PC PC
PC= paramagnetic cubic
FC= ferromagnetic cubic
FT= ferromagnetic tetragonal
PT= paramagnetic tetragonal
Total energies in meV/ atom 39 PT
322
253
kBTC ~ Etot(P) - Etot(F) 
Decrease in TC for x= 0.25
219 FC
3.6 FT FT
kBTM ~ Etot(C) - Etot(T) 
Increase in TM for x= 0.25

23. Experimental facilities for electronic structure studies
IPES spectrometer
XPS/UPS spectrometer
S. Banik, A. K. Shukla and S.R. Barman, RSI, 76, (2005).

24. UPS VB of Ni2MnGa compared to VB calculated from DOS
Calculated DOS
Non-modulated
Modulated
Good agreement between expt. and theory ; VB dominated by Ni 3d–Mn 3d hybridized states.
Ni 3d states with peak at –1.75 eV. Mn 3d states exhibit two peaks at –1.3 eV and –3.1 eV.
VB for non-modulated structure in better agreement with expt. So, influence of modulation diminishes at the surface.
Mn 3d dominated peak above EF.
Chakrabarti, Biswas, Banik, Dhaka, Shukla, Barman, PRB, 72, (2005)

25. Ni2+xMn1−xGa : effect of excess Nickel
Ni clustering, formation of Ni1 3d – Ni2 3d hybridized states at expense of Ni 3d– Mn 3d hybridized states.

26. Unoccupied states of Ni2+xMn1−xGa
Difference between expt. and theory:
Mn related peak is shifted by 0.4 eV. Indicates existence of self energy effects. Mn Ni
As x :
Ni peak intensity increases and Mn decreases.
Small shift of Mn peak to higher energies.
DFT is a ground-state calculation and the electron-electron interaction is considered in an average way. Deviation from DFT is quantified in terms of self-energy, where the real part gives the energy shift and the imaginary part gives the broadening. Mn related peak at 1.9 eV.

27. Magnetic moments of Ni2MnGa
Saturation magnetic moment of Ni2MnGa:
MCP: 4 mB
Magnetization: 3.8 mB
FPLAPW: 4.13 mB
Large magnetic moments on Mn, clear from spin polarized DOS.
Ni moment 10% of Mn, both aligned in same direction.
Decrease in saturation magnetization with increasing x.
B. L. Ahuja, B. K. Sharma, S. Mathur, N. L. Heda, M. Itou, A. Andrejczuk, Y. Sakurai, A. Chakrabarti, S. Banik, A. M. Awasthi and S. R. Barman, Phys. Rev. B (accepted).

28. Magnetic moments of Mn2NiGa
Increase Manganese : Ni2MnGa  Ni2-yMn1+yGa (Mn, Ni)  NiMn2Ga or Mn2NiGa (y=1)
Mn2NiGa:
Ni : (0.25,0.25,0.25)
Mn1: (0.75, 0.75, 0.75)
Mn2: (0.5, 0.5, 0.5)
Ga : (0,0,0)
TC=375K, TM=260K
It has been shown that direct interaction between adjascent incomplete $d$ shell atoms favors antiferromagnetic alignment.\cite{Zener51} More recently, the exchange pair interaction as a function of distance was calculated for Mn by greens-function technique in a Heisenberg-like model and an antiferromagnetic coupling at short interatomic distances was found that becomes ferromagnetic at larger distances.\cite{Hobbs??} According to Bebb {\it et al.} the critical distance for anti-ferromagnetic interaction is 2.87\AA.~Thus, Mn2$-$Mn2 or Mn1$-$Mn1 interactions (distance 4.14\AA),~ which are mediated by Ni, are ferromagnetic. %For the same reason, Mn atoms are in ferromagnetic configuration in Ni$_2$MnGa.
Charge density in 110 plane
Spin density in 110 plane
The Mn atom in Ni position (Mn1) is antiferrimagnetically aligned to the original Mn (Mn2) and the total moment decreases. Reason for opposite alignment is direct Mn-Mn interation. The nearest neighbours of Mn1 atoms are four Mn2 and four Ga atoms at a distance of 2.53Å.
Ni2MnGa: Four interpenetrating f.c.c. sublattice:
Ni at (0.25,0.25,0.25) and (0.75, 0.75, 0.75)
Mn at (0.5, 0.5, 0.5),
Ga at (0,0,0).

29. Why Mn1 and Mn2 magnetic moments are different?
Martensite
Austenite
Mn1
-2.21
-2.43
Mn2
2.91
3.2 Ni
0.27
0.32
Total
1.21
1.29
Strong hybridization between the down spin 3d states of Ni and Mn2 (n.n. 2.55Å)
compared to
Weaker hybridization between the up spin M=Ni and Mn1 3d states (2.73 Å)

30. Origin of the structural transition (the martensitic phase)
intensity
Lowering of the electron states related to the cubic to tetragonal structural transition: Jahn Teller effect (Fujii et al., JPSJ)
kinetic energy

31. Origin of the modulated phases in Ni2MnGa: Fermi surface nesting
If the Fermi surface (FS) has flat parallel portions i.e. if it is nested with nesting vector (vector joining the parallel portions of the FS), a pronounced phonon softening can occur at q resulting in a modulated pre-martensitic or martensitic phases.
Bungaro, Rabe, Dal Corso, PRB, 68, , (2003)
Cross section of the Fermi surface (a) with the (001) plane. The arrows are examples of nesting vectors q0=0.34(1,1,0).
(a) Minority spin Fermi surface of cubic Ni2MnGa.

32. Highly nested FS of Mn2NiGa
010
100
Minority spin hole type FS, Band 27, NV: 0.4{100},NA= 0.17 a.u.2 q1
Majority spin FS, band 29; NV: 0.44(100) & (010)
Minority spin FS, Band 29;
NV q1= 0.31{1,0,0};NA(q1)= 0.164a.u.2
NV q2= 0.46(1,1,0); NA= 0.034a.u.2

33. I hope I could give you a flavour of this important material .
Conclusions
I hope I could give you a flavour of this important material .
We will appreciate your suggestions and comments that might lead to new collaborations…..
Thank you for your attention.
Phase diagram determined from TM and TC variation as function of Ni excess (x). For x> 0.2, martensitic transition occurs in paramagnetic phase.
Phase co-existence shown, existence of a 7 layer modulated structure at low temperature for Ni2MnGa.
Ni2MnGa shows large negative magnetoresistance (7%) at room temperature due to s-d spin scattering.
Structure from total energy calculations, magnetic moments, occupied VB are in good agreement with experiment.
Self energy effects in unoccupied DOS.
Evidence of Ni cluster formation with Ni doping.
Origin of structural transition related to lowering of total energy; redistribution of states near EF.
Antiferrimagnetism in Mn2NiGa
Highly nested Fermi surface

34. Ni 2p of Ni2MnGa shows an interesting satellite feature
Satellite feature at 6.8 eV and 5.9 eV below Ni 2p3/2 and 2p1/2 peak respectively.
Satellite feature in Ni metal at 6 eV and 4.6 eV below Ni 2p3/2 and 2p1/2 peak respectively.
Band filling, Udc and 3d bandwidth are responsible for the binding energy shift of the main peak, satellite and decrease in satellite intensity.

35. Mn magnetic moment from XPS
Exchange splitting:
Occurs when the system has unpaired electrons in valance band.
3d5 (6S)
3s (2S) 5S
exchange 7S
Ground state hn
3s2
Exchange split peak is at
1167 eV (x=0, Austenite), Eex = 4.3 eV 
eV (x=0, Martensite), Eex = 5.1 eV
eV (x=0.1, Martensite), Eex = 4.8 eV
eV (x=0.2, Martensite). Eex = 4.4 eV
Mn moment decreasing with decrease in Mn content.
From theory: 3.4 mB (Fuji et al., JPSJ), 3.36 mB (Ayuela et al.JOP:CM)

36. Origin of satellite in Ni core level
The partially filled d states are treated as non-degenerate state interacting with s conduction states through s-d hybridization and with d states of other atoms through d-d transfer interaction giving rise to narrow d-band.
This initial mixing gives 3d94s ground state of Ni. EF 4s
3d9 2p
C-1 EF 4s
3d9 2p
C-1 EF
If screening is better: main peak, no satellite.
If screening is poor: satellite arises.
3d9
3d10 4s
Excited state
Ground state hn 2p c -1

37. Microscopic twin structure with field
Ref: Pan et. al. JAP. 87, 4702 (2000)
Magnetic domains and twin bands clearly observed. MR explained by twin variant rearrangement with field.
Magnetic force microscopy image of Ni2.23Mn0.8Ga in the martensitic phase at room temperature.

40. A basic actuator structure
A basic actuator consists of a coil and a MSM element.
                                                      
        
Actuator
An actuator produced by AdaptaMat which controls pressure in a pneumatic valve.
When magnetic field is applied, the MSM element elongates
in the direction perpendicular to the magnetic field.

41. Crystal structure at room temperature
Martensi te
Austeni te
Cubic
Tetragonal
Martensitic phase at room temperature.

42. Lattice constant variation with x in Ni2+xMn1-xGa
The spontaneous strain increases from 17.6% to 23% between x= 0.15 and Linear variation of lattice constants in alloys can be explained by Vegard’s law, This is expected because both Ni and Mn are 3d elements with similar electronic configuration and small size difference.

43. DSC and ac-susceptibility of Ni2+xMn1−xGa
Ms (TM) Mf As Af
205
189
216
234
0.24
434
408
423
447
0.35
537
523
553
582
DSC: [Rate 10 C/min]
Susceptibility:
[ 26 Oe field, Hz]
Albertini et al, JAP, , 2001
Small width of hysteresis K for x=0; highly thermoelastic (mobile interface, strain less).
Decrease of c at TM due to large magnetocrystalline anisotropy in martensitic phase. For x>0.2 TM>TC: change in c shape.
Banik, Chakrabarti, Kumar, Mukhopadhyay, Awasthi, Ranjan, Schneider, Ahuja, and Barman, PRB, 74, (2006)

44. Structure and magnetization of x= 0.35
Magnetization versus field M-H hysteresis loop at 293 K, the region close to H=0 is shown in the inset.

45. Photoemission (PES) and Inverse photoemission spectroscopy (IPES)

46. Characteristics of our PES workstation
PES station
Our aim..
Angle dependent XPS
Yes
Angle resolved PES No
Yes, using angle resolved analyzer
Base pressure
6 x mbar
LEED
Not available
Analyser energy resolution in UPS
100 meV
1 meV
Analyzer energy resolution in XPS
0.8 eV
0.4 eV (by monochromatic XPS)
Spatial resolution
100 mm
<10 mm
Temperature of expt.
150 K, RT
<15 K to RT (controlled)

47. The Inverse Photoemission Spectrometer work station
Photon detector and electron gun fabricated, interfaced with Labview
Two level Mu metal (Ni77Fe15CoMo) chamber.
Sample heating up to 950°C.
Indigenous design and assembly of the entire system involving purchase of more than 100 different items from 25 companies.
Gas filled photon detector
Mu metal: 77% Ni, 15% Fe, Co and Mo
Operating principle
Design
S. Banik, A. K. Shukla and S.R. Barman, RSI, 76, (2005).

48. Surface composition from XPS for sputtered surface
Ni 3p
Ga 3d
EDAX: Ni2.1Mn0.88Ga1.01
Sputtering:
0.5 keV: Ni2.6Mn0.4Ga0.99.
3.0 keV: Ni2.45Mn0.4Ga1.1.
Sputtering yield of Ni is less than Mn and Ga [For 0.5 keV Ar ions, Ni (1.3 atoms/ion) and Mn(1.9 atoms/ion)]
Mn 3p
Ion sputtering increases Ni content on the surface.

49. Surface Composition (20 A0)
Surface composition from XPS with annealing
T (0C)
Surface Composition (20 A0)
100
Ni2.47Mn0.44Ga1.09
200
Ni2.42Mn0.5Ga1.09
300
Ni2.25Mn0.71Ga1.03
350
Ni2.14Mn0.76Ga1.1
With increasing annealing temperature Mn segregates to surface.
At about 390oC the Ni:Mn ratio is same as that of the bulk (2.3).

50. Valence band spectrum of Ni2MnGa in martensitic phase

51. DOS calculation using the actual modulated structure
Non-modulated
7 layer modulated phase, Pnnm space group, 56 atoms/unit cell, a=4.215, b= and c=5.557 Å.
Modulated

52. Comparison: photoemission and theory
Cu2MnAl
D. Brown et al., PRB, 57, 1563 (1998)
Disagreement in Feature A.
Could overall agreement be better if modulation is considered?

53. Self energy effects in Ni2MnGa IPES
The states near EF are broader and the 1.9-eV peak is shifted toward higher energy by 0.4 eV w.r.t.calculated spectrum.
These differences could be related to existence of correlation effects.
DFT is a ground-state calculation and the electron-electron interaction is considered in an average way.
Deviation from DFT is quantified in terms of self-energy, where the real part gives the energy shift and the imaginary part gives the broadening. Self energy effects in the unoccupied states have also been observed in 3d transition metals like Cu.
Inverse photoemission spectrum of Ni2MnGa at room temperature in the FC phase, compared with the calculated conduction band of Ni2MnGa FC phase based on total, Mn, and Ni 3d PDOS. The IPES spectrum of Ni2.24Mn0.75Ga1.02 (x=0.24) in the FT phase is also shown.
Banik et al Phys. Rev. B, 74,

54. Compare with IPES spectra of Nickel and Manganese metal

55. Calculated Spin polarized energy bands of Ni2MnGa
Majority spin
Minority spin
* A parabolic majority spin band crosses EF near M and R points.
* Between -0.7 and -4 eV exhibit small dispersion and are related to Ni 3d-Mn 3d hybridized states.
* In the ΓX, ΓM or ΓR direction, no majority spin bands are observed between EF and -0.7 eV and no EF crossing is observed. Half metallic character along certain directions ( ΓX, ΓM and ΓR ) of the Brillouin zone with a gap of about 0.7 eV
* Future plan for experimental determination of band dispersion by ARPES.

57. Origin of the modulated phases in Ni2MnGa: Fermi surface nesting
Partial phonon dispersion of Ni2MnGa in the fcc Heusler structure, along the G-K-X line in the (110) direction. The experimental data taken at 250 K and 270 K.
Cross section of the minority-spin Fermi surface (a) with the (001) plane. The arrows are examples of nesting vectors q0=0.34(1,1,0).
(a) Fermi surface of cubic Ni2MnGa. (b) The fcc BZ is shown as a reference.
Bungaro, Rabe, Dal Corso, PRB, 68, , (2003)

58. Possibility of tuning the minority spin DOS near EF
x= 0.25
x= 0

59. Magnetoresistance and twin variant rearrangement
Ni2MnGa, in the martensitic phase exhibits a cusp like shape with two inflection points at 0.3 T and 1.3 T. This is due to the twinning and large magnetocrystalline anisotropy in the martensitic phase
At 150 K, x=0, x=0.1 and x=0.2 are at the martensitic phase. For x=0.1, the inflection points are observed at lower H. For x=0.2, MR is almost linear with a possible inflection point at 0.15 T.
C. Biswas, R. Rawat, S.R. Barman, Appl. Phys. Lett., 86, (2005)