Application of density functionaltheory to real materials problemsNicola SpaldinMaterials Department, UCSBFrom Harry Suhl’s lecture notes:In theoretical physics, one obective is to explainwhat has been seen in past experiments; the other isto predict what will be seen in future experiments.1) Explain experimentally observed behavior in (Ga,Mn)As2) Design new magnetic ferroelectricsHere we’ll use DFT to:MnGaAsMnGaAsRandom Alloy“DFH”Improved diluted magneticsemiconductorsUnusual magnetic behavior in DFHs:R.K. Kawakami et al., Appl. Phys. Lett. 77, 2379 (2000).• Can we grow thicker layers of MnAs, and would the propertiesbe desirable if we could?• What causes ferromagnetism in (Ga,Mn)As, and how can westrengthen it?• What is the effect of defects on the magnetic properties?• How does the arrangement of Mn ions affect magnetism andtransport?Design of new (and better!) spintronic materialsNiAs-type structureof bulk MnAs:Zincblende structureof (Ga,Mn)As:NiAs-typeGaAsMnLDOS HexagonalLDOS ZincblendehIn the minority band of ZB MnAs the Fermi Energy cutsthrough a dispersionless d-band. For large lattice spacing it isHalf MetallichNiAs-type is more stablewith smaller unit cellvolumehCrossover volume for largestresshBUT NiAs-type MnAs canaccommodate large distortionstherefore ZB MnAs is hardto stabilizeS. Sanvito and N.A. Hill, Ground state of half-metallic zincblende MnAs, PRB 62, 15553 (2000).¸Can we grow thicker layers of MnAs, and would the propertiesbe desirable if we could?• What causes ferromagnetism in (Ga,Mn)As, and how can westrengthen it?• What is the effect of defects on the magnetic properties?• How does the arrangement of Mn ions affect magnetism andtransport?Large spin-splitting of Mn-dorbitals The Fermi energy cuts throughthe Mn-d impurity band in themajority spin band Almost no-occupation of theMn-d orbitals in the minorityband – half-metallic! Mn impurity band stronglyhybridized with the As-p orbitalsof the nearest neighbors32 atom unit cell with 1 MnimpurityS. Sanvito, P. Ordejon and N.A. Hill, First principles study of the origin andnature of ferromagnetism in (Ga,Mn)As, PRB 63, 165206 (2000).Mülliken Population analysis shows:904.3)dMn()dMn( =Ø--↑- nn432.0)pAs()pAs( -=Ø--↑- nn Polarization per unit cellp-d antiferromagnetic exchange and the presenceof holes drive the ferromagnetic couplingMn dMn dAs pDo As antisites weaken the ferromagnetism in (Ga,Mn)As?Look at energy difference between the ferromagnetic andantiferromagnetic alignment of Mn ions in a large GaAs cellAFFMFAEE -=D No As antisites = strong FMorder Presence of As antisitesweakens FM alignment Picture of hole-mediatedexchange not strictly valid sinceferromagnetic order persists atcompensationFMAFMS. Sanvito and N.A. Hill, Influence of the local As antisite distributionon ferromagnetism in (Ga,Mn)As, Appl. Phys. Lett. 78, 1 (2001).¸Can we grow thicker layers of MnAs, and would the propertiesbe desirable if we could?¸What causes ferromagnetism in (Ga,Mn)As, and how can westrengthen it?¸What is the effect of defects on the magnetic properties?• How does the arrangement of Mn ions affect magnetism andtransport?majority spin minority spinCurrentin-planeCurrent outof plane•Calculate transport usingLandauer-Buttiker fomalsim•Strongly anisotropic•Not strictly 2-dimensional•Confinement to planesexplains high TcsS. Sanvito and N.A. Hill, Ab-initiotransport theory for digitalferromagnetic heterostructures,Phys. Rev. Lett. 87, 267202 (2001).h The Mn-d band is antiferromagnetically coupled with theAs-p band; holes in the As p band mediate ferromagnetismhAs antisites weaken the ferromagnetism and a transition toan antiferromagnetic alignment is possiblehDFHs are two-dimensional half-metals, with carriersconfined to the MnAs planehThicker layers of MnAs would have desirable properties butwill be hard to growComputational design ofnew multiferroics•Understand origin of each function separately (DFT)•Design a trial compound with required properties(intuition/experience)•Check that the trial compound indeed behaves as required(DFT)•Persuade an experimentalist to make and characterize it!Computational design of multifunctional materials,N.A. Spaldin and W.E. Pickett, JSSC, in pressPlan for designing for multifunctionality:Ferromagnetism and FerroelectricityHHMEEPPMMultiferroic magnetoelectricsHEsM PeReview: N.A. Hill,Ann. Rev. Mat. Res.32, 1-37 (2002).Why Do We Care?Device applications:w Multiple state memory elementsw Write to E / read from Mw Extra degree of freedomFundamental physics:w Nature of coupling between order parametersP M1/0 1/0Known ferromagneticferroelectrics:1) Nickel Iodine Boracite, Ni3B7O13IwFerroelectric, weak ferromagnetw24 atoms per formula unit and 8 fla units per unit cell!2) Mixed Perovskiteswe.g. B-site ordered Pb2(CoW)O6wFerroelectric from diamagnetic W6+wFerromagnetic from d6 Co2+wDilution low Curie temp.3) Simple PerovskiteswBiFeO3wYMnO3Why Are There So Few MagneticFerroelectrics?N.A. Hill, Why are there so few magnetic ferroelectrics?,J. Phys. Chem. B 104, 6694-6709 (2000).Requirements formagnetoelectric multiferroicityw Symmetryw Electrical Propertiesw Chemistry – “d0-ness”SIZE(pm)ION72.081.078.586.078.074.5V 4+d1Ti 3+d1Mn3+d4Zr 4+d0Nb 5+d0Ti 4+d0Outline – remainder….• What causes ferroelectricity?• (What causes ferromagnetism?)• How can we incorporate both?• A success story – BiMnO3Conventional mechanism forferroelectricity:Ligand field stabilization of emptycation d orbitals by oxygen p electrons:paraelectricferroelectricBUT magnetism requireslocalized electrons!In perovskite structure oxides the source ofmagnetic, localized electrons is usually thetransition metal d electronse.g. LaMnO3, SrRuO3, etc.Bad news!Ferromagnetism requires d electronsFerroelectricity requires “d 0-ness”INCOMPATIBLE!Why Are There ANY magneticferroelectrics?N.A. Hill and A. Filippetti, Why are there any magneticferroelectrics?, J. Mag. Mag. Mat. 242, 976 (2002).But….….Alternative mechanism for ferroelectricity:e.g. IV-VI compoundsPbTiO3, etc.Cation lone pair localizationneeds an ns2 pair of electronsU.V. Waghmare, N.A. Spaldin, H.C.Kandpal and R. Seshadri, Firstprinciples indicators of metallicity andcation off-centricity in the IV-VI rock-salt chalcogenides of divalent Ge, Sn andPb, PRB 67, 125111