We calculate magnetization in magnetically doped semiconductors assuming a local exchange model of carrier-mediated ferromagnetic mechanism and using a number of complementary theoretical approaches. In general, we find that the results of our mean-field calculations, particularly the dynamical mean-field theory results, give excellent qualitative agreement with the experimentally observed magnetization in systems with itinerant charge carriers, such as ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ with $0.03lxl0.07,$ whereas our percolation-theory-based calculations agree well with the existing data in strongly insulating materials, such as ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}.$ We comment on the issue of non-mean-field like magnetization curves and on the observed incomplete saturation magnetization values in diluted magnetic semiconductors from our theoretical perspective. In agreement with experimental observations, we find the carrier density to be the crucial parameter determining the magnetization behavior. Our calculated dependence of magnetization on external magnetic field is also in excellent agreement with the existing experimental data.

Temperature-dependent magnetization in diluted magnetic semiconductors

The defining attribute of a diluted magnetic semiconductor (DMS) is the existence of dopant−carrier magnetic exchange interactions. In this letter, we report the first direct observation of such exchange interactions in colloidal doped CdSe nanocrystals. Doped CdSe quantum dots were synthesized by thermal decomposition of (Me4N)2[Cd4(SePh)10] in the presence of TMCl2 (TM2+ = Mn2+ or Co2+) in hexadecylamine and were characterized by several analytical and spectroscopic techniques. Using magnetic circular dichroism spectroscopy, successful doping and the existence of giant excitonic Zeeman splittings in both Mn2+- and Co2+-doped wurtzite CdSe quantum dots are demonstrated unambiguously.

Direct Observation of sp−d Exchange Interactions in Colloidal Mn2+- and Co2+-Doped CdSe Quantum Dots

Methods for introducing new magnetic, optical, electronic, photophysical, or photochemical properties to semiconductor nanocrystals are attracting intense applications-oriented interest. In this communication, we report the preparation and electronic absorption spectroscopy of colloidal ZnO DMS-QDs. Our synthetic procedure involves modification of literature methods known to yield highly crystalline and relatively monodisperse nanocrystals of pure ZnO to allow introduction of transition-metal dopants. We use ligand-field electronic absorption spectroscopy as a dopant-specific optical probe to monitor dopant incorporation during nanocrystal growth and to verify internal substitutional doping in Co2+:ZnO and Ni2+:ZnO DMS-QDs. To the best of our knowledge, these are the first free-standing oxide DMS-QDs reported. The synthesis of colloidal oxide DMS-QDs introduces a new category of magnetic semiconductor materials available for detailed physical study and application in nanotechnology.

Colloidal Transition-Metal-Doped ZnO Quantum Dots

Quaternary semiconductor Cu2MSnS4 (M = Co2+, Fe2+, Ni2+, Mn2+) nanocrystals have been successfully synthesized via a simple and mild solvothermal method. Cu2FeSnS4 and Cu2CoSnS4 show a spherical shape; Cu2NiSnS4 and Cu2MnSnS4 possess a nail-like structure and a rod-like structure. The four types of nanocrystals exhibit significantly different magnetic properties. Cu2FeSnS4 and Cu2CoSnS4 nanoparticles show ferromagnetic behavior; Cu2MnSnS4 and Cu2NiSnS4 nanorods exhibit superparamagnetic behavior at low temperature. The band gaps of Cu2MSnS4 (M = Co, Fe, Ni, Mn) nanocrystals are in the range of 1.2–1.5 eV, indicating a high potential application in low-cost thin film solar cells.

A general strategy for synthesis of quaternary semiconductor Cu2MSnS4 (M = Co2+, Fe2+, Ni2+, Mn2+) nanocrystals

Strong magneto-optical effect of Zn1−xCoxO near the optical band gap is reported. Magnetic circular dichroism (MCD) and Faraday rotation of Zn1−xCoxO (x=0.012 and 0.016) at 5 K are as high as 2°/cm Oe at 3.4 eV, which are about two orders larger than those of ZnO. Absence of strong Co2+ d–d* transition near the optical band gap makes Zn1−xCoxO an useful material for short-wavelength magneto-optical applications. Large magneto-optical effects and paramagnetic temperature dependence of MCD show a strong mixing of the sp bands of the host ZnO with Co2+ d orbitals. The polarity of the MCD peak is negative indicating the antiferromagnetic p–d exchange interaction.

Large magneto-optical effect in an oxide diluted magnetic semiconductor Zn1−xCoxO

Bound magnetic polarons (BMP's) in $p$-type ${\mathrm{Cu}}_{2}{\mathrm{Mn}}_{0.9}{\mathrm{Zn}}_{0.1}{\mathrm{SnS}}_{4}$ were investigated using magnetization measurements. The magnetization $M$ was studied from 2 to 60 K in magnetic fields up to 55 kOe. The data show the characteristic features of BMP's in the collective regime. In addition, the onset of antiferromagnetic order in the ``matrix'' surrounding the BMP's leads to anomalies in the BMP susceptibility at the N\'eel temperature of the matrix ${T}_{N}=8$ K. Below 15 K the low-field magnetization of the BMP's is quite anisotropic. A detailed analysis of the isothermal magnetization curves, based on Wolff's work but with some additional assumptions, separates the BMP contributions to $M$ from the contribution of the matrix. The analysis gives the spontaneous moment ${m}_{s}$ of a single BMP as a function of temperature $T$, and the concentration $N$ of BMP's. The value ${m}_{s}=143$ Bohr magnetons/BMP at the lowest temperatures is consistent with the expected radius of the hole orbit, of order 10 \AA{}. The observed $T$ dependence of ${m}_{s}$ is compared with theoretical calculations based on a model that assumes that the wave function in the absence of the $p$-$d$ interaction is hydrogenic. The calculated decrease of ${m}_{s}$ with increasing $T$ is somewhat slower than that deduced from the experimental data. The BMP concentration $N$, from an analysis of the magnetization data, is about $2\ifmmode\times\else\texttimes\fi{}{10}^{19}$ BMP/cm${}^{3}$ in all the samples. This $N$ is consistent with the observed hopping conductivity at low temperatures. High-field magnetization data, up to 300 kOe, show the canted-to-paramagnetic phase transition of the matrix. At 1.4 K the transition is near 225 kOe.

Bound magnetic polarons in p-type Cu 2 Mn 0.9 Zn 0.1 SnS 4

The work at Tufts University was partially supported by NSF Grant No. DMR-9219727. The research in Zaragoza was supported by CICYT Grant No. MAT94-0043. The
work at Brown University was supported by NSF Grant No. DMR-9221141. The Francis Bitter National Magnet Laboratory was supported by NSF.

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Magnetic ordering of the antiferromagnet cu2mnsns4 from magnetization and neutron-scattering measurements

The sp-d exchange energies, bound magnetic polarons, and magnetization have been studied in ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se and ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S. For x=0.02--0.05, magnetization measurements of the ${\mathrm{Co}}^{2+}$ ions at liquid-helium temperatures are adequately described by a modified Brillouin function for pure spin S=3/2 ions. In spin-flip Raman-scattering (SFRS) measurements from donor-bound electrons we observe a large Zeeman splitting of \ensuremath{\sim}4--10 meV at high magnetic fields, and bound magnetic polaron energies of 0.2--0.4 meV at B=0. The s-d exchange energy between conduction electrons and ${\mathrm{Co}}^{2+}$ ions, obtained by combining the SFRS and magnetization results, is found to be \ensuremath{\alpha}${\mathit{N}}_{0}$=274\ifmmode\pm\else\textpm\fi{}6 meV for CdSe, and \ensuremath{\alpha}${\mathit{N}}_{0}$=179\ifmmode\pm\else\textpm\fi{}4 meV for CdS. For ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se, from reflectivity measurements and the \ensuremath{\alpha}${\mathit{N}}_{0}$ value we obtain \ensuremath{\beta}${\mathit{N}}_{0}$=-2120\ifmmode\pm\else\textpm\fi{}50 meV.

Exchange energies, bound magnetic polarons, and magnetization in CdSe:Co and CdS:Co

Magnetization steps of nearest-neighbor exchange interactions in CdS(Co) and CdSe(Co) in fields to 60 tesla

The magnetization of cubic ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se, with x=0.003 and 0.007, was measured at temperatures 2\ensuremath{\le}T\ensuremath{\lesssim}50 K in magnetic fields H along the [100] and [111] directions. Data for H\ensuremath{\le}55 kOe were taken with a superconducting quantum interference device magnetometer. Other data in fields up to 200 kOe were taken with a vibrating sample magnetometer operating in a Bitter magnet. At the lowest temperatures the magnetization M at high magnetic fields is anisotropic: at a given T and for the same magnitude H of the magnetic field, M for H\ensuremath{\parallel}[100] is larger than for H\ensuremath{\parallel}[111]. The difference between the values of M for these directions reaches a maximum value of 19% at the lowest temperatures and when H\ensuremath{\simeq}150 kOe. As the temperature rises, the anisotropy of the high-field magnetization decreases gradually, becoming very small above 40 K. In low fields (H\ensuremath{\lesssim}10 kOe) the anisotropy is very small at all temperatures. These experimental results are generally in good agreement with theoretical calculations based on crystal field theory and on the assumption that only isolated ${\mathrm{Fe}}^{++}$ ions (singles) contribute to the magnetization. Minor discrepancies between experiment and theory remain, however.

T. Fries

Papers

Bound magnetic polarons in p-type Cu 2 Mn 0.9 Zn 0.1 SnS 4

Magnetic ordering of the antiferromagnet cu2mnsns4 from magnetization and neutron-scattering measurements

Exchange energies, bound magnetic polarons, and magnetization in CdSe:Co and CdS:Co

Magnetization steps of nearest-neighbor exchange interactions in CdS(Co) and CdSe(Co) in fields to 60 tesla

Anisotropy of the high-field magnetization of cubic Zn 1 − x Fe x Se