Ferromagnetism in manganese compound semiconductors not only opens prospects for tailoring magnetic and spin-related phenomena in semiconductors with a precision specific to III-V compounds but also addresses a question about the origin of the magnetic interactions that lead to a Curie temperature (T(C)) as high as 110 K for a manganese concentration of just 5%. Zener's model of ferromagnetism, originally proposed for transition metals in 1950, can explain T(C) of Ga(1-)(x)Mn(x)As and that of its II-VI counterpart Zn(1-)(x)Mn(x)Te and is used to predict materials with T(C) exceeding room temperature, an important step toward semiconductor electronics that use both charge and spin.

http://info.ifpan.edu.pl/SL-2/sl23sub/science_dietl.pdf

Zener Model Description of Ferromagnetism in Zinc-Blende Magnetic Semiconductors

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

We review the physical properties of diluted magnetic semiconductors (DMS) of the type AII1−xMnxBVI (e.g., Cd1−xMnxSe, Hg1−xMnxTe). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the AII1−xMnxBVI alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic AIIBVI ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half‐filled Mn 3d5 shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the AII1−xMnxBVI alloys. In particular, we discuss the mechanism of the Mn++‐Mn++ exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susc...

Diluted magnetic semiconductors

“…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Experiments on simple magnetic model systems

A giant magnetocaloric effect was found in MnAs, which undergoes a first-order ferromagnetic to paramagnetic transition at 318 K. The magnetic entropy change caused by a magnetic field of 5 T is as large as 30 J/K kg at the maximum value, which exceeds that of conventional magnetic refrigerant materials by a factor of 2–4. The adiabatic temperature change reaches 13 K in a field change of 5 T. The substitution of 10% Sb for As reduces the thermal hysteresis and lowers the Curie temperature to 280 K, while the giant magnetocaloric properties are retained.

Giant magnetocaloric effect of MnAs1−xSbx

The magnetic phase diagram of Mn${\mathrm{F}}_{2}$, in the $H\ensuremath{-}T$ plane, is determined in magnetic fields up to 200 kG directed along the [001] and [100] directions. The magnetic phase transitions appear as anomalies in the ultrasonic attenuation and/or the differential magnetization. Near the various second-order phase transitions, the attenuation of longitudinal sound waves exhibits $\ensuremath{\lambda}$ anomalies, whereas near the spin-flop transition (which is a first-order transition) the ultrasonic attenuation exhibits a sharp spike and/or an abrupt increase, depending on the mode of propagation. The spin-flop transition is accompanied by a spike in the differential magnetic moment. The N\'eel temperature is ${T}_{N}=(67.33\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode^\circ\else\textdegree\fi{}$K, and the triple point for H\ensuremath{\parallel}[001] is at ${T}_{3}=(64.9\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode^\circ\else\textdegree\fi{}$K and ${H}_{3}=119\ifmmode\pm\else\textpm\fi{}2$ kG. The field at the spin-flop transition (for H\ensuremath{\parallel}[001]) increases monotonically with temperature from 92\ifmmode\pm\else\textpm\fi{}1.5 kG at 4.2\ifmmode^\circ\else\textdegree\fi{}K to 119\ifmmode\pm\else\textpm\fi{}2 kG at the triple point. The curvature, at ${T}_{N}$, of the antiferromagnetic-paramagnetic boundary with H\ensuremath{\parallel}[001] is $\frac{{d}^{2}T}{d{H}^{2}}=\ensuremath{-}(3.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ifmmode^\circ\else\textdegree\fi{}$K/${\mathrm{G}}^{2}$. The curvature, at ${T}_{N}$, for the antiferromagnetic-paramagnetic boundary with H\ensuremath{\parallel}[100] is smaller by about an order of magnitude. The various phase boundaries are compared with the predictions of the molecular-field theory and other theoretical models.

Magnetic Phase Diagram of Mn F 2 from Ultrasonic and Differential Magnetization Measurements

The resistivity $\ensuremath{\rho}$ and the Hall effect are studied in seven $n$-type EuO single-crystal samples at temperatures $4.2\ensuremath{\le}T\ensuremath{\le}300$ K and external magnetic fields $0\ensuremath{\le}{H}_{\mathrm{ext}}\ensuremath{\le}150$ kOe. Attention is focused on three phenomena: (i) the anomalous Hall effect (or lack thereof), (ii) the resistivity peak near the Curie temperature ${T}_{C}\ensuremath{\simeq}69$ K, and (iii) the insulator-metal transition (IMT). The Hall data at $T\ensuremath{\ll}{T}_{C}$ indicate that the anomalous Hall term in EuO is small compared to the normal term and that the effective magnetic field which governs the Hall effect is equal to the magnetic induction $B={H}_{\mathrm{int}}+4\ensuremath{\pi}M$. On this basis it is assumed that the anomalous Hall effect is negligible at all temperatures. Measurements of $\ensuremath{\rho}({H}_{\mathrm{ext}}, T)$ vs $T$, show that as ${H}_{\mathrm{ext}}$ increases the resistivity peak decreases, becomes broader, and shifts to higher temperatures. The Hall data indicate that the resistivity peak is due to the combined effect of dips in the Hall mobility $\ensuremath{\mu}$ and in the carrier concentration $n$. Measurements of ${T}_{C}$ by several methods show that ${T}_{C}$ is several degrees lower than the temperature ${T}_{max}$ at which the zero-field resistivity is maximum. A new method for obtaining ${T}_{C}$ from magnetoresistance measurements is discussed. Near room temperature the resistivity of some samples decreases exponentially with increasing $T$, with an activation energy of \ensuremath{\sim} 0.3 eV at zero magnetic field. For these "activated" samples $\ensuremath{\rho}$ changes by many orders of magnitude near the IMT. In other samples (called "nonactivated") $\ensuremath{\rho}$ varies slowly with $T$ near room temperature and the resistivity change near the IMT is smaller. In both types of samples ${H}_{\mathrm{ext}}$ shifts the IMT to higher temperatures and makes the transition more gradual. Hall measurements show that in samples with a large IMT, the IMT is almost entirely due to a change in $n$, whereas in samples with a small IMT, the IMT is due to comparable changes in both $n$ and $\ensuremath{\mu}$. Near room temperature the Hall coefficient is $H$ independent in the nonactivated sample, but decreases substantially with $H$ in the activated samples. In both types of samples the Hall mobility at 298 K increases by \ensuremath{\sim} 25% when a magnetic field of 140 kOe is applied. This indicates that spin-disorder scattering is one of the main causes for the zero-field resistivity at room temperature. The various data are compared with earlier measurements by the groups at Lincoln Laboratory and at IBM, and are also discussed in terms of current theoretical models.

EuO. I. Resistivity and Hall Effect in Fields up to 150 kOe

A model for the high-field magnetization of II-VI semimagnetic compound semiconductors at low temperatures is presented. It applies for low Mn concentrations. The model explains quantitatively and without adjustable parameters the magnetization of ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$, ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$, ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$, ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$, and ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$ near 100 kOe for $Tl2$ K. At higher magnetic fields, magnetization steps are predicted. The first step is observed in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$ and ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$, and is used to determine the nearest-neighbor exchange constant. The results support a random distribution of Mn ions.

Technical saturation and magnetization steps in diluted magnetic semiconductors: Predictions and observations

The magnetic properties of both insulating and conducting single crystals of EuTe were measured at temperatures $0.4\ensuremath{\le}T\ensuremath{\le}273$ K in magnetic fields $0\ensuremath{\le}Hl150$ kOe. The insulating EuTe showed the behavior expected for an Heisenberg antiferromagnet and is believed to be representative of pure EuTe. For this insulating material we obtained a N\'eel temperature ${T}_{N}=(9.6\ifmmode\pm\else\textpm\fi{}0.1)$ K and a saturation magnetic moment ${\ensuremath{\sigma}}_{s}=(132\ifmmode\pm\else\textpm\fi{}3)\frac{\mathrm{emu}}{\mathrm{g}}(\frac{6.6{\ensuremath{\mu}}_{B}}{\mathrm{Eu}}\mathrm{ion})$. In the interval $10{T}_{N}lTl28{T}_{N}$, the insulating material obeyed the Curie-Weiss law with a Curie-Weiss constant $C=(27.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ (emu K/g Oe), and a paramagnetic Curie temperature $\ensuremath{\theta}=(\ensuremath{-}1\ifmmode\pm\else\textpm\fi{}2)$ K. Below ${T}_{N}$, the differential susceptibility $\frac{d\ensuremath{\sigma}}{\mathrm{dH}}$ in the insulating sample showed the following features: (i) At low fields, $\frac{d\ensuremath{\sigma}}{\mathrm{dH}}$ first increased with $H$, then passed through a broad maximum near 1 kOe, and finally assumed the constant value ${\ensuremath{\chi}}_{\ensuremath{\perp}}=1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ emu/g Oe. This low-field behavior corresponds to the rotation of spins in the {111} planes (analogous to spin flopping). (ii) At higher fields, in the canted phase, $\frac{d\ensuremath{\sigma}}{\mathrm{dH}}$ increased with $H$. (iii) The canted-to-paramagnetic transition was marked by a $\ensuremath{\lambda}$ peak in $\frac{d\ensuremath{\sigma}}{\mathrm{dH}}$. (iv) The transition field ${H}_{c}(T)$ was linear with ${T}^{\frac{3}{2}}$ in the interval $2\ensuremath{\le}T\ensuremath{\le}4.2$ K, but a small deviation from the theoretical ${T}^{\frac{3}{2}}$ law was observed below 2 K. At $T=0$, ${H}_{c}(0)=(72.2\ifmmode\pm\else\textpm\fi{}1)$ kOe, which leads to an intersublattice exchange field ${H}_{E}(0)\ensuremath{\cong}36$ kOe. The values of ${H}_{c}(0)$ and $\ensuremath{\theta}$ for the insulating material yield the nearest-neighbor and next-nearest-neighbor exchange constants $\frac{{J}_{1}}{k}=+(0.10\ifmmode\pm\else\textpm\fi{}0.03)$ K and $\frac{{J}_{2}}{k}=\ensuremath{-}({0.21}_{5}\ifmmode\pm\else\textpm\fi{}0.03)$ K, respectively. The results in the conducting single crystals (which were $n$ type) showed that the following magnetic properties were influenced by the presence of the charge carriers: (a) At $T\ensuremath{\lesssim}2{T}_{N}$, the zero-field differential susceptibility in the conducting samples was an order of magnitude larger than in the insulating sample. (b) The low-field behavior of $\ensuremath{\sigma}$ at temperatures well below ${T}_{N}$ suggested the existence of a spontaneous magnetic moment at $H=0$. (c) The $\ensuremath{\lambda}$ anomaly in $\frac{d\ensuremath{\sigma}}{\mathrm{dH}}$, at ${H}_{c}$, was reduced, or disappeared entirely. (d) The saturation moment ${\ensuremath{\sigma}}_{s}$ was slightly higher than for the insulating sample. (e) The paramagnetic Curie temperature $\ensuremath{\theta}$ was several degrees higher than for the insulating material. The presence of charge carriers had little or no effect on ${T}_{N}$, and only a small influence on the phase boundary ${H}_{c}(T)$. Some of the effects of the charge carriers can be explained qualitatively by de Gennes's model for the double-exchange interaction in antiferromagnets.

EuTe. I. Magnetic Behavior of Insulating and Conducting Single Crystals

The resistivity $\ensuremath{\rho}({H}_{\mathrm{ext}},T)$ and Hall effect were studied in ten $n$-type EuSe single-crystal samples with room-temperature carrier concentrations from 4.2 \ifmmode\times\else\texttimes\fi{} ${10}^{18}$ to 3.5 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ electrons/${\mathrm{cm}}^{3}$. The electrical measurements were performed at temperatures $1.6\ensuremath{\le}T\ensuremath{\le}300$ K and external magnetic fields $0\ensuremath{\le}{H}_{\mathrm{ext}}\ensuremath{\le}150$ kOe, and were supplemented by magnetization and differential susceptibility measurements to aid in the interpretation. The following phenomena were observed: (a) A very large peak in the zero-field resistivity occurred at a temperature ${T}_{max}$ which varied from \ensuremath{\sim} 7 to \ensuremath{\sim} 13 K, depending on the sample. (b) A negative magnetoresistance was observed for most temperatures and was very large near ${T}_{max}$. (c) However, in a limited temperature interval well above ${T}_{max}$, a positive magnetoresistance was observed at low fields (followed by a negative magnetoresistance at higher fields). (d) Below \ensuremath{\sim} 3 K, the zero-field resistivity increased rapidly with decreasing $T$, except for the sample with the highest carrier concentration. (e) The anomalous Hall effect was negligible at temperatures $T\ensuremath{\le}4.2$ K. Much of the data are interpreted in terms of band conduction. The mobility is then limited by spin-disorder scattering and it increases with increasing ${H}_{\mathrm{ext}}$, resulting in a negative magnetoresistance. This description fails when both $T\ensuremath{\lesssim}{T}_{max}$ and ${H}_{\mathrm{ext}}l1 \mathrm{to} 10$ kOe. Under these conditions, the very high resistivity is attributed to the localization (trapping) of electrons by the $s\ensuremath{-}f$ (or $d\ensuremath{-}f$) interaction. At temperatures for which the electrons are localized at ${H}_{\mathrm{ext}}=0$, a field of 1 to 10 kOe delocalizes the electrons and, therefore, leads to band conduction and a much lower resistivity. At higher fields there is a negative magnetoresistance (smaller than at low fields) due to the reduction in spin-disorder scattering of the band electrons. A model for the positive magnetoresistance, which focuses on the spin splitting of the conduction band by a magnetic field, is presented in the following paper.

S. Foner

Papers

Magnetic Phase Diagram of Mn F 2 from Ultrasonic and Differential Magnetization Measurements

EuO. I. Resistivity and Hall Effect in Fields up to 150 kOe

Technical saturation and magnetization steps in diluted magnetic semiconductors: Predictions and observations

EuTe. I. Magnetic Behavior of Insulating and Conducting Single Crystals

Resistivity and Hall effect of EuSe in fields up to 150 kOe