Introduction to Heusler compounds: From the case of Fe

Introduction to Heusler compounds:

From the case of Fe ₂ VAl

Chin Shan Lue (呂欽山)

2017-03-28-NTU

Outline

1) Introduction to Heusler compounds Full-Heusler compounds

Half-Heusler compounds 2) Case study of Fe

VAl

3) Promising characteristics of Heusler compounds Thermoelectric properties

Spintronic applications

Topological materials

4) Summary

Full-Heusler compounds: X

YZ Half-Heusler compounds: XYZ

Heusler compounds

First full-Heusler Cu₂MnAl in 1903

More than 1000 real Heusler compounds

Fritz Heusler (Germany)

First half-Heusler NiMnSb in 1951

L

1 structure

Cu₂MnAl-type

16 atoms per unit cell

Fe₂VAl, Ru₂NbGa, Ni₂MnGa (HT), …

B2 structure

CsCl-type

2 atoms per unit cell

Co₂MnAl, Ru₂NbAl, Ru₂VAl, …

Common crystal structures of Heusler compounds

Anti-site disorder

First determination of crystal structure for Cu₂MnAl by Otto Heusler in 1934

DO

structure

BiF₃-type

16 atoms per unit cell Fe₃Al; Fe₃Ga; Fe₃Si, ...

C1

structure

MgAgAs-type

12 atoms per unit cell

NiMnSb, NiZrSn, CoTiSb, …

Half-Heusler XYZ

X = Y

X + void

Binary compounds X

Z

Various properties of Heusler compounds

Ferromagnetism: Co₂MnZ, Pd₂Mn(In,Sn), …

Superconductivity: Pd₂YSn (T_C = 4.9 K), Ni₂NbSn, Pd₂ErSn, …

Shape memory behavior: Ni₂MnGa (Martensitic transformation T_M = 220 K), … Semiconducting: Fe₂VAl, Ru₂TaAl, IrNbSb, NiHfSn, CoTiSb, …

Unusual physical behavior in Fe

VAl

Paramagnetic behavior in Fe

VAl by Webster & Ziebeck in 1983

(Fe_1-xV_x)₃Al

x=0.33 Fe₂VAl

Semiconductor-like in ρ T_c = 0 K Fe₃Al T_c = 790 K

semimetal

Possible 3d heavy fermion for Fe

VAl

Low-T C = C

+ C

= g T + b T

C/T = g + b T

Expected behavior for ordinary semimetals (low Fermi-level DOS)

g = 14 mJ/mol K

e F

B

th

 k N ( E )  m 3

2



g

Sommerfeld coefficient based on free electron model

100 50

*

e

  

e th

xp

m m g

g for Fe

VAl

g = 1.07 mJ/mol K²

Semimetallic Ru₂TaAl

e

 3

th xp

g g

from C. M. Wei et al.

Simple concept for heavy fermions

CeAl₃ g =1620 mJ/mol K² CeCu₆ g =1300 mJ/mol K² UBe₁₃ g =1100 mJ/mol K² U₂Zn₁₇ g = 500 mJ/mol K²

…….

hybridization

It is less likely to observe heavy fermion behavior in d-electron systems since the corresponding wave-functions of d-orbitals are more dispersive.

DOS

E E_F

E

k E_F

f-electrons f-electron heavy fermions

Spinel LiV₂O₄ g = 420 mJ/mol K²

d-electron heavy fermion???

Nat. Comm. 3, 981 (2012); PRL 113, 236402 (2014);

...….

s-electrons

Band structure calculations for Fe

VAl

郭光宇

Electronic structure, local moments, and transport in Fe₂VAl, D. J. Singh & I. I. Mazin, Phys. Rev. B 57, 14352 (1998)

Excitonic correlations in the intermetallic Fe₂VAl, R. Weht & W. E. Pickett, Phys. Rev. B 58, 6855 (1998)

Electronic structure and magnetism of Fe_3-xV_xX (X=Si, Ga, and Al) alloys by the KKR-CPA method, A. Bansil, et al., Phys. Rev. B 60, 13396 (1999)

Hybridization-induced band gaps in transition-metal aluminides, M. Weinert & R. E. Watson, Phys. Rev. B 58, 9732 (1998)

N(E

) = 0.08 states/eV atom

NMR evidence for semimetallic behavior in Fe

VAl

Low V-3d N(E

) = 0.11 states/eV atom Thermally excited carriers

across electronic bands near E

Korringa relation 1/T

T ~ C[N(E

)]

Activation energy E

~ 0.27 eV

Question of possible 3d heavy fermion for Fe

VAl

Small g = 1.5 mJ/mol K

Sample-dependent

Field-dependent

False heavy fermion behavior in Fe

VAl

For non-interacting magnetic clusters with spin J >1/2, the magnetic specific heat can be generated by the so-called multi- level Schottky function as

T k

H x g

B

B



unit formula

per population

% 36 . 0

7 . 3 ) 1 2 (

3











 f

J J g

J  



The low-T upturn in C is not intrinsic;

It is reasonably associated with magnetic clusters due to anti-site disorder in real samples.

Ru₂TaAl

Effects of magnetic clusters in Fe

VAl, Fe

VGa and Fe

TiSn

“Weak ferromagnetism induced by atomic disorder in Fe₂TiSn”, A. Ślebarski, M. B. Maple, et al., Phys. Rev. B 62, 3296 (2000)

“Kondo-type behavior in Fe_2-xM_xTiSn(M=Co,Ni)”,

A. Ślebarski, M. B. Maple, et al., Phys. Rev. B 63, 214416 (2001)

“Fe−3s core-level splitting and local magnetism in Fe₂VAl”, Phys. Rev. B 63, 054419 (2001)

“Superparamagnetism and magnetic defects in Fe₂VAl and Fe₂VGa”, J. Phys.: Condens. Matter 13, 1585 (2001)

“Structure and magnetic order in Fe_2+xV_1-xAl”, J. Phys.: Condens. Matter 13, 5487 (2001)

“NMR and Mössbauer study of spin dynamics and electronic structure of Fe_2+xV_1-xAl and Fe₂VGa”,

Phys. Rev. B 67, 224425 (2003)

“Transport and magnetic properties of the Heusler-type Fe_2-xV_1+xAl system (−0.01⩽x⩽0.08)”,

Phys. Rev. B 71, 094425 (2005)

“Evidence for cluster glass behavior in Fe₂VAl Heusler alloys”, Phys. Rev. B 78, 064401 (2008)

Band structure calculations for Fe

VAl

郭光宇

Electronic structure, local moments, and transport in Fe₂VAl, D. J. Singh & I. I. Mazin, Phys. Rev. B 57, 14352 (1998)

Excitonic correlations in the intermetallic Fe₂VAl, R. Weht & W. E. Pickett, Phys. Rev. B 58, 6855 (1998)

Electronic structure and magnetism of Fe_3-xV_xX (X=Si, Ga, and Al) alloys by the KKR-CPA method, A. Bansil, et al., Phys. Rev. B 60, 13396 (1999)

Hybridization-induced band gaps in transition-metal aluminides, M. Weinert & R. E. Watson, Phys. Rev. B 58, 9732 (1998)

More first-principles calculations on Fe

VAl

“Electronic structure and x-ray magnetic circular dichroism in Heusler-type Fe_2-xV_1+xAl: First-principles calculations”,

Phys. Rev. B 77, 134444 (2008)

“Density functional study of elastic and vibrational properties of the Heusler- type alloys Fe₂VAl and Fe₂VGa”,

Phys. Rev. B 80, 125108 (2009)

“Electronic and thermoelectric properties of Fe₂VAl: The role of defects and disorder”,

Phys. Rev. B 83, 205204 (2011)

“Effect of onsite Coulomb repulsion on thermoelectric properties of full- Heusler compounds with pseudogaps”,

Phys. Rev. B 84, 125104 (2011)

“Low-Dimensional transport and large thermoelectric power factors in bulk semiconductors by band engineering of highly directional electronic states”, Phys. Rev. Lett. 114, 136601 (2015)

“Quantum many-body intermetallics: Phase stability of Fe₃Al and small-gap formation in Fe₂VAl”,

Phys. Rev. B 95, 045114 (2017)

……

Thermoelectric materials

RSC Advances 5, 52 (2015)

Thermoelectric generator module

ZT: Figure of merit 熱電優質

ZT = 1 → 10.8%

ZT = 2 → 16.4%

T

/T

= 0.5 2 .

, with

, 1

1 ) 1

(

2 max

h c

h h c

c

h

T T

S T Z

T T T

Z T Z T

T

T   









 

 

Thermoelectric efficiency



Thermoelectric performance ZT = S

T/ 





Physical approach based on Mott equation,

DOS

E_F E

S: Seebeck coefficient

 : electrical resistivity



: electronic thermal conductivity



: lattice thermal conductivity

EF

E

e

E

E N E

N S e





 







  ( )

) ( 1 1

Chemical approach by partially substituting heavy elements and/or vacancies to enhance the phonons scattering and thus reduce the contribution of 

.

Naive expectation:

S = 200 V/K

 = 1000 W-cm

 = 2 W/m-K

ZT=1 at 500 K

Full-Heusler compounds with L

1-type structure

Total number of valence electrons per formula unit VEC = Z

= 24

A simple rule with number of valence electrons

In principles → Semiconductors In reality → Semimetals

Half-Heusler compounds with C

1-type structure

Total number of valence electrons per formula unit VEC = Z

= 18 In principles → Semiconductors

In reality → Semimetals

Fe₂VAl, Fe₂VGa, Fe₂TiSn, Ru₂NbGa, Ru₂TaAl, Ru₂TiSi, ….

NiTiSn, NiZrSn, NiHfSn, CoTiSb, FeVSb….

Thermoelectric studies of Fe

VAl and related compounds

Nishino et al., Phys. Rev. B 63, 233303 (2001)

C. S. Lue & Y. K. Kuo, Phys. Rev. B 66, 085121 (2002)

High  Large S

Nishino’s group

Phys. Rev. B 71, 094425 (2005) Phys. Rev. B 71, 245112 (2005) Phys. Rev. B 74, 115115 (2006)

………

C. S. Lue & Y. K. Kuo,

J. Appl. Phys. 96, 2681 (2004) Phys. Rev. B 71, 064202 (2005) Phys. Rev. B 72, 054116 (2005) Phys. Rev. B 75, 064202 (2007) Phys. Rev. B 78, 165117 (2008) Other groups

J. Alloys Compd. 349, 37 (2003) Phys. Rev. B 77, 224415 (2008) J. Appl. Phys. 111, 093710 (2012)

……..

Thermoelectric studies of Fe

VAl-based compounds

J. Appl. Phys. 115, 033704 (2014)

Optimized ZT ~ 0.2

Thermoelectric studies of half-Heusler compounds with Z

= 18

“Gap at the Fermi level in the intermetallic vacancy system RNiSn (R=Ti,Zr,Hf)”, Z. Phys. B 75, 116 (1989).

“Narrow band in the intermetallic compounds MNiSn (M=Ti,Zr,Hf)”, Z. Phys. B 80, 353 (1990).

“Band gap and stability in the ternary intermetallic compounds NiSnM (M=Ti,Zr,Hf):

A first principles study”,

Phys. Rev. B 51, 10443 (1995).

…..

“Effect of substitutions and defects in half-Heusler FeVSb studied by electron transport measurements and KKR-CPA electronic structure calculations”, Phys. Rev. B 70, 184207 (2004).

“Electronic structure and thermoelectric properties of half-Heusler Zr_0.5Hf_0.5NiSn by first-principles calculations”,

Appl. Phys. Lett. 113, 193705 (2013).

...

“Effect of Ti substitution on the thermoelectric properties of (Zr,Hf)NiSn half-Heusler compounds”, Appl. Phys. Lett. 86, 082105 (2005).

“Thermoelectric performance of half-Heusler compounds TiNiSn and TiCoSb”, Appl. Phys. Lett. 105, 013709 (2009).

“Thermoelectric property study of nano-structured p-type half-Heuslers (Hf,Zr,Ti)CoSb_0.8Sn_0.2”, Advanced Energy Materials 3, 1195 (2013).

...

Thermoelectric materials based on half-Heusler compounds

Translational Materials Research 2, 025001 (2015)

Half-metallic Heusler compounds

Half-metals Half-Heusler

100% polarization

A semi-empirical general rule: Slater-Pauling curve

Half-Heusler compounds

Hybridization between Ni and Mn in minority bands in NiMnSb

I. Galanakis, P. H. Dederiches, N. Papanikolaou, Phys. Rev. B 66 134428 (2002).

Slater-Pauling curve for full-Heusler compounds

Full-Heusler compounds

Hybridization between Co-Co and Mn in minority bands in Co₂MnSi(Ge)

I. Galanakis, P. H. Dederiches, and N. Papanikolaou, Phys. Rev. B 66 174429 (2002).

More first-principles calculations

Review article: J. Phys.:

Condens. Matter 19 315213 (2007).

“Computational investigation of half-Heusler compounds for spintronics applications”, Phys. Rev. B 95, 024411 (2017).

“First-principles calculation of the effects of partial alloy disorder on the static and dynamic magnetic properties of Co₂MnSi”, Phys. Rev. B 95, 094425 (2017).

Spin-resolved DOS for Co₂MnZ

Recent advances in the Heusler-based spin gapless semiconductors

HM SGS

Ti₂CoSi

L2₁ structure Cu₂MnAl-type XA structure

HgCu₂Ti-type

Ti Co Si

Inverse Heusler

Generalized Slater-Pauling rule for inverse Heusler compounds

S. Skaftouros, K. Ozdogan, E. Sasioglu, I. Galanakis, Phys. Rev. B 87 024420 (2013).

Possible SGSs: Theoretical studies

Appl. Phys. Lett. 102 022402 (2013)

Phys. Rev. B 77 014427 (2008)

Phys. Rev. B 91 094409 (2015)

Possible SGSs: Experimental studies

Phys. Rev, Lett. 110, 100401 (2013)

Polycrystalline Mn₂CoAl

Polycrystalline V₃Al

Thin film Ti₂MnAl Polycrystalline CrVTiAl

Phys. Status Solidi RRL 9 641 (2015) Phys. Rev. B 91 094409 (2015)

Appl. Phys. Lett. 121 053903 (2017)

Claudia Felser’s group

Topological materials in half-Heusler compounds

S. Chadov et al., Nature Materials 9, 541 (2010) Claudia Felser’s group

J. A. Logan et al., Nature Communications 9, 11993 (2016)

Band inversion

Topological materials in half-Heusler compounds

Hsin Lin et al., Nature Materials 9, 546 (2010)

Cava’s group

Evidence for topological behavior in half-Heusler compounds

“Observation of a topologically non-trivial surface state in half-Heusler PtLuSb (001) thin films”

J. A. Logan et al., Nature Communications 9, 11993 (2016)

“Large anomalous Hall effect in a half-Heusler antiferromagnet”

T. Suzuki et al., Nature Physics 12, 1119 (2016)

“Observation of unusual topological surface states in half-Heusler compounds LnPtBi (Ln=Lu, Y)”

Z. K. Liu et al., Nature Communications 7, 12924 (2016)

Topological materials in full-Heusler compounds

“Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in half metallic Heusler Co₂TiX (X=Si, Ge, or Sn)”

Guoqing Chang et al., Scientific Reports 6, 38839 (2016).

“Time-reversal-breaking Weyl fermions in magnetic Heusler alloys”

Zhijun Wang et al., Phys. Rev. Lett. 17, 236401 (2016).

Cava’s group

Single crystalline Co₂ZrSn

Our group

Summary

Theoretical people continue paying attention to Heusler

compounds, focusing on their thermoelectric, half-metallic, and topological properties.

Experimental people continue synthesizing novel Heusler

compounds and investigating their promising properties

for further applications.

Thanks for your attention!