DensityDensity--functional theoryfunctional theory investigationsinvestigations

of the of the electronic, magnetic and structural propertieselectronic, magnetic and structural properties

of doped of doped copper (I) nitride, Cucopper (I) nitride, Cu33NN

A.E. PhillipsA.E. Phillips2 November 20052 November 2005

BackgroundBackground

•• Modern computing usesModern computing uses–– ferromagnetic memory storageferromagnetic memory storage–– semiconductor logic gatessemiconductor logic gates

•• SpintronicsSpintronics allows us the possibility allows us the possibility of combining these functions on a of combining these functions on a single chip.single chip.

CuCu33NN•• antianti--ReOReO33 structurestructure•• large large cuboctahedralcuboctahedral site for site for

dopantdopant metal atomsmetal atoms•• energetically metastableenergetically metastable•• previous work:previous work:

–– experimental: Cu, Li, Pd experimental: Cu, Li, Pd dopantsdopants–– theoretical: DFT on theoretical: DFT on undopedundoped, ,

Cu, PdCu, Pd

•• Main focus: magnetic Main focus: magnetic properties of transition properties of transition metalmetal--doped Cudoped Cu33N.N.

F. Gulo et al., Angew. Chem. Int. Ed. 43, 2032 (2004)

U. Zachwieja & H. Jacobs, J. Less-Common Met. 170, 185 (1991)

M.G. Moreno-Armenta et al., Solid State Sciences 6, 9 (2004)

U. Hahn & W. Weber, Phys. Rev. B 53, 12864 (1996)

TheoryTheory

•• DensityDensity--functional theory (DFT)functional theory (DFT)•• Implementation: Implementation: DMolDMol33

•• Functional: Functional: PerdewPerdew--BurkeBurke--ErnzerhofErnzerhof ((pbepbe))–– a form of generalised gradient a form of generalised gradient

approximation (GGA)approximation (GGA)•• Basis set: Basis set: double numeric + double numeric +

polarisationpolarisation ((dnpdnp))–– localised AO basislocalised AO basis

B. Delley, J. Chem. Phys. 113, 7756 (2000)

J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)

Preliminary calculationsPreliminary calculations

•• Need to check:Need to check:–– calculations match reasonably with calculations match reasonably with

previous workprevious work–– results have converged with respect to results have converged with respect to

calculation parameterscalculation parameters•• atom_rcutatom_rcut = where basis functions are = where basis functions are

truncatedtruncated•• kpointskpoints = grid in reciprocal space used to = grid in reciprocal space used to

integrate over the FBZintegrate over the FBZ

Preliminary calculationsPreliminary calculations

•• selected parameters:selected parameters:–– atom_rcutatom_rcut = 9 = 9 bohrbohr–– kpointskpoints = 8 = 8 ×× 8 8 ×× 88

•• bulk Cu: bulk Cu: EEcohcoh = 3.45 eV = 3.45 eV (3.43 (3.43 eV)eV)

•• NN22: : EEbondbond = = ––5.19 eV 5.19 eV ((––4.90 eV)4.90 eV)–– ll = 1.106 = 1.106 ÅÅ (1.098 (1.098 ÅÅ))–– νν = 2349.7 cm= 2349.7 cm––11

(2358.6 cm(2358.6 cm––11))

Convergence tests: cohesive Cu energy wrt k-point grid

-0.1270

-0.1265

-0.1260

-0.1255

-0.1250

4x4x4 6x6x6 8x8x8 10x10x10 12x12x12

grid size

E coh

/Ha

CuCu33NN

•• EEff = 1.32 eV = 1.32 eV (0.868 eV)(0.868 eV)

•• cc = 3.849 = 3.849 ÅÅ((3.807 3.807 ÅÅ, , 3.82 3.82 ÅÅ))–– BirchBirch--MurnaghanMurnaghan

equation of stateequation of state–– expand bulk modulus to expand bulk modulus to

first orderfirst order

•• semiconductingsemiconducting–– indirect band gap = 0.27 indirect band gap = 0.27

eV eV (0.25 eV, 0.23 eV)(0.25 eV, 0.23 eV)

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

3.65 3.70 3.75 3.80 3.85 3.90 3.95

c /Å

E /e

V

Ef = E(Cu3N) – 3E(Cu) – 0.5E(N2)

Metal dopingMetal doping

•• Place atoms at centre of unit cellPlace atoms at centre of unit cell•• Fit as before to EOSFit as before to EOS

•• All All metallicmetallic (Pd semi(Pd semi--metallic)metallic)•• Ni, Cr, Fe metastableNi, Cr, Fe metastable w.r.tw.r.t. . undopedundoped

material; material; Li, Pd stableLi, Pd stable

Metal dopingMetal dopingEn

ergy

[eV]

wavevector DoS

-20

-10

0

10

X R M Γ R

undoped

Ener

gy [e

V]

wavevector DoS

-20

-10

0

10

X R M Γ R

Cr

Ener

gy [e

V]

wavevector DoS

-20

-10

0

10

X R M Γ R

Fe

Ener

gy [e

V]

wavevector DoS

-20

-10

0

10

X R M Γ R

Ni

•• The nickel derivative is The nickel derivative is not not magnetic!magnetic!

•• Can be explained by simple Can be explained by simple electronelectron--transfer model: 4transfer model: 4ss electrons electrons fall into 3fall into 3dd band, filling it (3band, filling it (3dd8844ss22 →→33dd101044ss00))

Ener

gy [e

V]

wavevector DoS

-20

-10

0

10

X R M Γ R

Ni

DoS

[1/e

V]

Energy [eV]

-10

-5

0

5

10

-10 -5 EF 5

Ni

Magnetism modelMagnetism model•• Use 2 Use 2 ×× 1 1 ×× 1 1 supercellsupercell•• Keep lattice constants at optimised singleKeep lattice constants at optimised single--

cell valuescell values

•• CuCu33N.N.FeFe seems to have the most potential seems to have the most potential for magnetic superconductor applications.for magnetic superconductor applications.

MM more stable configurationmore stable configuration ∆∆EE /eV/eV

FeFe ferromagneticferromagnetic 0.06520.0652

CrCr antiferromagneticantiferromagnetic 0.1890.189

Diffusion modelDiffusion model

•• Keep lattice parameters Keep lattice parameters constantconstant (!)(!)•• Keep using 2 Keep using 2 ×× 1 1 ×× 1 1 supercellsupercell•• Move Move dopantdopant atom gradually in [100] atom gradually in [100]

directiondirection

Diffusion of M in Cu3N.M

0

2

4

6

8

10

12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

M displacement / lattice parameter

Ener

gy /e

V

Cr Ni Li Pd Fe

ConclusionsConclusions

•• Good agreement with previous Good agreement with previous experiment and calculationexperiment and calculation

•• New doped systems:New doped systems:–– Fe is Fe is ferromagneticferromagnetic–– Cr is Cr is antiferromagneticantiferromagnetic–– Ni is Ni is not magneticnot magnetic

•• CuCu33N.N.FeFe potentially useful as a potentially useful as a magnetic semiconductormagnetic semiconductor

•• Fe, Cr, Ni derivatives should all be Fe, Cr, Ni derivatives should all be synthesisable by diffusionsynthesisable by diffusion

Further workFurther work

•• Allow lattice to Allow lattice to relaxrelax during during diffusiondiffusion–– should lower energy barriershould lower energy barrier

•• Allow Allow different positionsdifferent positions for for dopantdopantatomatom–– Li is known to displace CuLi is known to displace Cu

•• Investigate different doping Investigate different doping concentrationsconcentrations–– what interactions between what interactions between dopantsdopants are are

there?there?

AcknowledgementsAcknowledgements

•• Professor Cathy StampflProfessor Cathy Stampfl•• Dr Carl CuiDr Carl Cui•• Aloysius SoonAloysius Soon

•• Computing resources provided by Computing resources provided by the the Australian Centre for Advanced Australian Centre for Advanced Computing and CommunicationsComputing and Communications(AC3)(AC3)

DensityDensity--functional theoryfunctional theory investigationsinvestigations

of the of the electronic, magnetic and structural propertieselectronic, magnetic and structural properties

of doped of doped copper (I) nitride, Cucopper (I) nitride, Cu33NN

A.E. PhillipsA.E. Phillips2 November 20052 November 2005