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Home , Birefringence

DielectricDielectric andand magneticmagnetic birefringencebirefringence inin ZnZn1-x1-xMnMnxxSeSe

M. F. Saenger1,2,*, D. J. Sellmyer2, R. D. Kirby2, T. Hofmann1,2, and M. Schubert1,2 1 Department of Electrical Engineering, University of Nebraska-Lincoln, 68588, U.S.A. ellipsometry.unl.edu 2 Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588, USA *[email protected]

Introduction Results Experiment

Interaction between long wavelength electromagnetic σ σ incident reflected radiation and bound and unbound electrical charge x = 0.00 x = 0.14 + − coil coil Formation of wurtzite planes normal Γ |+1/2> light carriers subjected to an external magnetic field causes The underlying mechanism of the giant Faraday 6 |-1/2> to the [111] direction causes optical birefringence precisely measurable using effect is the interaction between the spin of the [111] birefringence in dependance localized 3d5-electrons of the Mn ions and the m Ф generalized ellipsometry. ZnSe is an important II-VI of J mirror band electrons. When µ0H ≠ 0, the conduction semiconductor with a variety of applications in |-1/2> µ H the Mn concentration x. At x = 0.3 a and valence bands split, which is known as 0 θ optoelectronic devices. phase transformation from the |-1/2> sp-d exchange. Γ8 to the wurtzite structure |+1/2> sample Litvinov |+1/2> x [110] occurs. 2007 ZnSe oxide 10 nm Zn Mn Se ... 1-x x Zn1-xMnxSe

Zn, Mn Se Optical detection and quantification of GaAs (001) bulk MO birefringence possesses a temperature dependent magnetic 0.04 M /M x = 0.28 23 11 x moment as well as remarkable magnetooptic (MO) Mn M13 spectra for •Change due to the sp-d properties, which in conjunction with the two different 0.28 0.03 interaction. z [001] μ0H electronic properties suggest future applications θ sample for MO and spintronic devices. orientations. •The dielectric anisotropy is = 135°, 180° 0.02 0.13 taken into account when x = 0.13 modeling the MO effect. 0.01 0.02 Maximum Mueller matrix ε ρ birefringence Dielectric model 0.00 0.00 E ρ detected for x = 0.13 1.52.02.53.0 Generalized Ellipsometry measures the general optical i ρ i ρ The oscillations ρ ρ energy (eV) depend on the layer response of samples in terms of Mueller matrix elements, and allows thickness. for reconstruction of the , permeability, and magneto- ρ x = 0.02 electric response . ⊥ ⊥ θ = 135° ρ M /M θ = 0° ⎛( + ) ( +- ) 0 ⎞ 0.01 23 11 + − + − θ = 45 ° The dielectric anisotropy influences S ⎜ ⎟ No birefringence The Mueller matrix elements Mij Sensitive to chiral 1 ⊥ ⊥ the MO birefringence ( ) = ⎜ ( +- ) ( + ) 0 ⎟ detected for x = connect incident andS emergentM anisotropy + − + − 0.02 or lower. real-valued Stokes vector M (magnetic

2 ρ The MO birefringence depends also S M M ⎜ // // ⎟ 0.00 components: birefringence) 0 0 ( + ρ ) on the orientation of the sample. S M M ⎝ + − ⎠ I S M M S Therefore it is necessary to have a = p + I output μ H = S0 s ⎡ 0 ⎤ ⎛ 11 M 12 13M 14 ⎞⎡ 0 ⎤ 8.5 1.5 0 model which takes this effect properly I ⎜ ⎟ 1.8 T x = 0.28 = p − I ⎢ ⎥ M M S⎢ ⎥ into account. S1 s 1 ⎜ 21 22 23 24 ⎟ 1 I ⎢ ⎥ M M ⎢ ⎥ Continuum- -0.01 = ⎜ ⎟ E and E +Δ Discrete Higher energy S2 = 45 − I−45 ⎢ ⎥ M S⎢ ⎥ 0 0 0 exciton ⊥ 2.4 2.6 2.8 3.0 2 31 32 33 34 2 E Iσ ⎜ M ⎟ transitions excitons at CP transitions 8.0 0 ⎢ ⎥ ⎜ ⎟⎢ ⎥ transitions The formation of Photon energy (eV) 3 = + − Iσ − S E0 and E0+Δ0 ⊥ ⎣ 3 ⎦ ⎝ 41 42 43 44 ⎠⎣ 3 ⎦input

2 E wurtzite planes in 0 1.0 0 the [111] direction 7.5 // E0 -2 Highly sensitive to dielectric } }

causes an energy j j The diagonal elements of ε // ε -4

{ { birefringence. band gap shift E0 the dielectric tensor can -6 between the Re Im Re(ε ) × 1000 7.0 be obtined. The sample xy optical axis 2.6 2.7 with highest magnetic 0.5 v parallel (||) and 6 x = 0.02 ε × Loss-less Im( xy) 1000 i 3-Dim birefringence is also the Our message Lorentzian line dispersion Lorentz perpendicular ( ) x = 0.13 M typeJ CP c oscillator 4 0 pole to the [111] 6.5 sample with highest Mn x = 0.28 2 E J direction. x = 0.13 concentration. m i 0 m c 6.0 0.0 1.8 2.1 2.4 2.7 We studied the dielectric and magnetic-field induced v 1.5 2.0 2.5 3.0 anisotropic of Zn Mn Se thin films with h Photon Energy (eV) Photon energy (eV) 1-x x ( →m ) = E + ( 0 + 0 ) + generalized spectroscopic ellipsometry in the VIS-UV c g m 2 ω Landau spectral range for Mn concentrations of x = 0.00, 0.02,0.13 J v g ω and 0.28. The dielectric and the magnetic field induced in Zn1-xMnxSe were treated separately into the +c ( − )μ H + The dielectric anisotropy can be The ellipsometric model allows us to diagonal and off-diagonal components of the dielectric E c J 0 Zeeman J m measured in terms of the energy band measure the spd-exchange energy and tensor. J gap shift Landau shift. v Ec E We are able to quantify the shift of the band gap energy + [ ( ) − (m )] // ⊥ ⊥ // (±3/ 2) − E (±1/ 2) J sp-d exchange xMn E0 E0 E0 - E0 xMn v EL −4 −4 between the DF parallel and perpendicular to the optical axis eV eV meV 1×10 eV 1×10 eV caused by the formation of wurtzite domains with increasing μ0H x. . E 0.13 2.6491 (7) 2.6549 (5) 5.8 (9) 0.02 2 (1) 1.1 (3) - 0.28 2.6743 (5) 2.6784 (6) 4.1 (8) 0.13 8 (3) 1.2 (5) q , me The optical anisotropy occurs in the direction [111], which is 0.28 12 (3) 1.0 (4) in good concordance with previous TEM investigations. The dielectric anisotropy results in a red shift of the energy band The anisotropy is not proportional to the Loop measurements in dependance of gap parallel to the optical axis with a maximum for x = 0.13. Mn concentration x. For x closer to 0.13 the magnetic field can also be modeled. the anisotropy reaches at least one Measurements of the sp-d exchange energy at room MRSEC Q-SPINS Meeting, Lincoln, NE, October 5, 2007 maximum. temperature are presented and found a maximum value for 54th Midwest Semiconductor Conference, Lincoln, NE, October 6-7, 2007 the sample with maximum Mn concentration x = 0.28.