Current Issues & Understandings for Magnetic Semiconductors Kwang Joo KimDepartment of Physics, Konkuk University, Seoul, Korea

* 1960s : recognition of spin-related phenomena due to existence of ferromagnetism () in semiconductors (at low temp.) (2) 1980s : research on magneto-resistance, magneto-optics etc. on ferromagnetic semiconductors (FM) with low Curie temperature (TC) (3) 2000s : discovery of FMs with high TC > 100 K (e.g., Ga1-xMnxAs) stimulated research on materials & devices that can manipulate both charge & spin spintronics

* Device requirement to overcome existing MOSFET technology- 4 Gbit DRAM (54 nm gate length & access time < 0.1 ns) using Si technology- Spintronics device may operate by supplying smaller amount of current (which should be spin-polarized) than existing ones- Possible to achieve higher speed, lower power consumption, higher integration density by using concept of spintronics (?)

History of Ferromagnetism in Semiconductors

* Possible candidates of electrodes (source & drain) for spintronics- Ferromagnetic metals (e.g., NiFe) good: abundant carriers weak: shottky-barrier formation, spin relaxation - Conventional semiconductors (e.g., Si, GaAs with ferromagnetism) good: developed technology weak: low Curie temperature (TC 200 K)- Oxide compounds (e.g., Fe3O4 (ferrimagnetic), ZnO ) good: chemical stability weak: underdeveloped technology

Field-Effect Transistor

* Magnetic semiconductors (ordered compounds) EuSe, EuO (NaCl); CdCr2S4, CdCr2Se4 (spinel) with TC 100 K (La,Sr)MnO3 (perovskite) with TC 350 K Fe3O4 with TC 800 K (called half-metal, but behave like semiconductor) : difficult to be compatible with conventional semiconductors (IV, III- V, II-VI) for electronic device applications

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* Diluted magnetic semiconductors IV, III-V, II-VI semiconductors doped by magnetic elements, e.g., 3d transition metal (TM) : Ga1-xMnxAs, Cd1-xMnxTe, Si1-xMnx with rather low TC 200 K for device applications (narrow band gap) Oxide semiconductors doped by magnetic elements, e.g., TM-doped ZnO, SnO2, TiO2, In2O3 with TC above room temperature (wide band gap) Ga1-xMnxN, Si1-xFexC, : TC above room temp. (wide band gap)

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* Magnetic Hysteresis

*SiC:Fe (3C, Eg = 2.4 eV)TC ~ 300KM-H (at 300K by VSM) M-T (by SQUID) Methods for checking ferromagnetism

In DMS, TM ions substitute cationic sites and so created charge carriers mediate ferromagnetic alignment of magnetic TM ions.

* Can the ferromagnetism be properly explained theoretically (based on electronic structure)? * Any distinct properties of carriers in ferromagnetic regime (e.g., mobile or localized (magnetic polaron))?* Can DMSs properly supply spin-polarized current in wide temperature range?

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Extrinsic origin Intrinsic origin Magneticcluster

Spin-polarizedConduction bandConceptual electronic structure

*Theoretical background for diluted ferromagnetism* RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction (a) indirect exchange coupling of local magnetic moments via carriers (conduction electron or hole) (b) hybridization (such as s-d & p-d) bet. carrier and local ion is important * Effective Hamiltonian

kF, J0: Fermi wavevector & overlap integral (related to electronic structure)

Theoretical predictions by Dietl et al., Science 287, 1019 (2000)*(1) Strong dependence of Curie temperature on magnetic impurity density & hole density (2) For same hole density, smaller spin-orbit splitting (of valence bands) leads to higher TC leads to preference of light elements (also with stronger p-d hybridization)(3) Formation of magnetic polaron helps maintain ferromagnetism

* Calculated for 5% Mn and hole density p = 3.5 X 1020 cm-3* Predicted TC > 300 K for GaAs with Mn density of 10% : never achieved (TC ~ 170 K)* Predictions for GaN & ZnO are good (but no p-type ZnO tested)* For Si, TC ~ 130 K predicted but for some exp. TC > 300 K defect control is important

Expected spin-polarized electronic structure of Zn1-xTMxO*

Ti3+(d1) Mn2+(d5)Co2+(d7)

* Formation of spin-split donor band* Under molecular-field approx. TC [S(S+1)x]1/2Jsd for x < 0.17 S: ionic spin Jsd: exchange int. bet. IB & 3d stronger for more hybridization Room-temp. measurements byVenkatesan et al, PRL 93, 177206 (2004)

* No clear explanation on relation between magnetism & conductivity (carrier transport)* DMS properties have been observed for some later reports on ZnMnO important to understand defect-related properties

*Magnetic polaron model [Coey et al., Nat. Mater. 4, 173 (2005)] * Polaron formation is known to be efficient in TiO2.

-Rutile: small polaron (larger ) s ~ 100, m* ~ 20me, aH = 0.26 nm

-Anatase: large polaron (smaller ) s ~ 31, m* ~ me, aH = 1.6 nm

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High IB density

Low IB density As x increases, superexchange coupling of magnetic ions via O2- ion leads to antiferromagnetic alignment Decrease of m at high TM doping

Saturation magnetization (m) decreases asO2 partial pressure during film depositionprocess increases. IB (or carrier) density decreases with increasing O2 partial pressure O vacancies significantly contribute to IB (or CB)

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(1) Three distinct crystalline phases rutile: tetragonal, a=4.593, c=2.959 anatase: tetragonal, a=3.785, c=9.514 brookite: orthorhombic, a=5.436, b=9.166, c=5.135

(2) Thermodynamic stability rutile stable anatase, brookite metastable (easily converted into rutile at high temp.)

(3) Band structure rutile direct band gap (~3.3 eV) anatase indirect band gap (~3.8 eV) * wide band gap

Ferromagnetism in wide-band-gap TiO2rutile type TiO2anatase type TiO2

*TiO2-:Ni For Ni-doped rutile TiO2- films, lattice constants increase linearly Unit-cell volume increase for x = 5 at.% from that of undoped TiO2- is about 0.6% Ionic radius () (octahedral site) Ti4+(3d0) : 0.745

Ni2+(3d8): 0.830 Ni3+(3d7, low): 0.700 Ni3+(3d7, high): 0.740 Ni4+(3d6): 0.620Above 6 at.%, Ni clusters areobserved as marked by *XRD

*X-rayPhotoelectronspectroscopy(TiO2-:Ni) Both 2p3/2 and 2p1/2 lines are split into two peaks

Binding energy difference between the two peaks of ~ 3.5 eV lead to an interpretation that they are due to Ni2+ and Ni3+ ions Mater. Chem.. Phys. 77, 384 (2002).

Finite density of Ni2+ ions in TiO2- :Ni is likely to induce an increase of lattice constants.

Through Doniach-Sunjic line-shape fitting Ni 4 at.% Ni 9 at.% (with Ni clusters) Ni2+:Ni 3+ = 3.5:6.5 Ni2+:Ni 3+ = 5.3:4.7

For Ni (9 at.%) Ni clusters was detected by XRD Inversion of XPS intensity ratio is attributable to Ni clusters (Ni0) The 2p binding energies of electrons in Ni0 are known to be close to those in Ni2+ within 1 eV Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Co., 1992. Ni clusters tend to exist at the surface region and are likely to interact with oxygen ions, thus, having effective ionic valences9 at.%Ni cluster4 at.%

*Hall Effect Measurements (TiO2-:Ni)

Up to 5 at.%: p-type conductivity (p ~ 1019 cm-3) attributable to Ni2+ & Ni3+ substitution of Ti4+ sites

At higher Ni doping: n-type conductivity attributable to creation of Ni clusters

*Vibrating Sample Magnetometry (TiO2-:Ni)

Ni (4 at.%) doped TiO2- XPS Ni2+:Ni 3+ = 3.5:6.5 spin moment Ni2+(t2g6eg2) Mspin = 2 B Ni3+(t2g5eg2) Mspin = 3 B Cal. MS 2.7 B/Ni Exp. MS 3 B/Ni

The observed magnetic moment is attributable to the alignment of Ni impurity spins.

Ferromagnetic strength is likely to be related to mobile carrier (hole) density Decrease in net magnetization with increase of Ni content : increase in antiferromagnetic superexchange coupling strength between neighboring Ni ions via a nearby O2- ion (as in NiO) is possible

*TiO2-:Co* Intrinsic ferromagnetism persists at high Co doping (for Ni, Fe, Mn, 6 at.%).

* Large saturation magnetization (Ms) as in Ni doping.

* Co ions have valences +2 & +3 (by XPS).

* Ferromagnetic strength decreases with increasing Co content (probably due to antiferromagnetic Co2+-O2--Co2+).

*TiO2-:Fe* No thickness dependence: rare possibility for surface segregation of Fe * Neither Fe cluster nor Fe3O4 was detected * Ferromagnetism is due to magnetic polaron rather than moble carrier x = 1.3 at.%: p-type 1018 cm-3 x = 2.4 at.%: p-type 1017 cm-3 x = 5.8 at.%: insulating

*TiO2-:Mn* p-type samples exhibited ferromagnetism.

* Ferromagnetic strength is not related to hole density.

* Mn3+(d4) & Mn4+(d3) ions are dominant.

*A. Kaminski et al., PRL 88, 247202 (2002).polaronicmodelTC > 400 K for all samples SQUID

** Saturation magnetization per dopant ion differs significantly (large for Co & small for Mn) in agreement with ZnO case (IB picture)

* Ferromagnetic strength persists at high Co doping (12 at.%) compared to others ( 6 at.%)

* Conduction type change from n to p by TM doping (no p-type in ZnO)

TiO2:TM (Ni, Co, Fe, Mn)

*Pure TiO2- & TiO2-:Sb* Ferromagnetism is observed for pure TiO2- films (stronger for rutile than anatase)

* Sb doping leads to an increase of saturation magnetization

Spin-polarized energy band structure FLAPW calculation for rutile TiO2- (with O vacancy)(Hong & Kim, J. Phys:C 21,195405 (2009)** DOS indicates net spin-polarization of Ti d-bands (due to lattice distortion) and resultant net magnetic moment of 0.22 B/Ti for rutile TiO2- (no such result obtained for anatase TiO2-).

Transport properties of spin-polarized carriers*(1) MagnetoresistanceMR = [(H) - (0)]/(0)

* Increase in resistivity at low temp. (positive MR) is attributable to s-d exchange coupling.* Decrease in resistivity at high temp. (negative MR) is attributable to magnetic polaron (formed near O vacancy), which is unstable at low temp.

ZnMnOZ. Yang et al., JAP 105, 053708 (2009)

*VxFe3-xO4Negative MR due to carrier hopping

*(2) Anomalous Hall effect

RHall = (HR0 + 4MRs)/d = ROHE + RAHE = VH/Ixd: sample thicknessR0: ordinary Hall coeff. (= -1/ne) due to classical Lorenz forceRs: anomalous Hall coeff. due to asymmetric scattering from spin-orbit interaction under magnetization indicating carrier-mediated ferromagnetism (s-d exchange)

Electrical Resistivity*Linear behavior can be understood in terms of polaronic hopping of spin-polarized carriers.

*Stand on a new world and look beyond it for another oneRoom-temperature ferromagnetism is observable for 3d TM-doped wide-band-gap III-V (e.g., GaN), II-VI (e.g., ZnO), VI-VI (e.g., SiC), & other oxide (e.g., TiO2) DMSs. * Some results are still controversial. Both carriers in valence or conduction bands (via p-d or s-d exchange coupling) and impurity bands (via magnetic polaron) contribute to ferromagnetism. * need to independently control density of carriers and density of TM ions to better understand ferromagnetism. * high carrier density, low TM density (low defects) exchange coupling (high carrier mobility, low M) often appears for non-oxide DMSs * low carrier density, high TM density (high defects) magnetic polaron (low carrier mobility, high M) frequently appears for oxide DMSs

*Optical properties p-d hybridization(bandgap expansion)p-d exchange(bandgap shrink)

* Spin-exchange interaction is likely for low Mn and Fe doping.

MnTe films (MBE grown)*NiAs (hexagonal)Semiconducting & p-type (p ~ 1019 cm-3)

*MnSb films (MBE grown)Metallic behavior & p-type (p ~ 1021 cm-3)

High Curie Temp. ~ 600 K

*TiO2-:Fe Ionic radius () (octahedral site) Ti4+(3d0) : 0.745

Fe2+(3d6, low): 0.750 Fe2+(3d6, high): 0.920 Fe3+(3d5, low): 0.690 Fe3+(3d5, high): 0.785 Fe4+(3d4): 0.725 * Anatase samples show larger variation of lattice constants than rutile ones.

*TiO2-:Fe Mossbauer SpectroscopyFor x = 5.8 at.%, only Fe3+ ions are detected,excluding possibility of Fe3O4contribution to ferromagnetism.

Spinel Fe3O4:(Fe3+)[Fe2+,Fe3+]O2-4

Isomer shift (mm/s) ferro paraX = 2.4 at.% 0.49 0.97 (Fe3+) (Fe2+) X = 5.8 at.% 0.28 0.27 (Fe3+) (Fe3+)

*Snells lawFresnels equationsSpectroscopic Ellipsometry (SE)Ellipsometry can measure dielectric function D = E optical conductivity = (-i/4)( - 1) J = E:Contains information on optical transition in solids knowledge of electronic structure

*Jones matrixIntensity of photonI = k0 + k1 cos2(A-As) + k2 sin2(A-As)ki = ki (Im) cos = cos (k0, k1, k2) tan = tan (k0, k1, k2) Fourier transformationGet & SE Measurement process(0 = tan )

*Interband transition (absorption)Electricdipole approximationTransition ratee.g., s p, p d

*InAsInP1234 eVGaAsInNAlAsGaPGaNZnTeZnOBand-gap Distribution of Semiconductors GeSiCuAlO2ZnSeCdTeSnO2TiO2ZnS