INTRODUCTION

Traditional semiconductors are based on the control of charge carriers (n- or p-type). Magnetic-ion-doped semiconductors allow, in addition, the control of the quantum spin state (up or down), which have attracted great interest because of their potential applications in spintronics and blue-light emitting diode (LED) technologies [1, 2]. The main challenge for practical applications is the attainment of a Curie temperature TC above room temperature to be compatible with junction temperatures. So far, the highest Curie temperatures were obtained for MnxGa1 – xAs (x = 0.13) with TC = 190 K [3], as well as for (KxBa1 – x)(MnyZn1 – y)2As2 (x = 0.3, y = 0.15) with TC = 230 K [4]. The observation of ferromagnetism above room temperature reported by several authors has to be considered with caution, as these findings neither resulted in a device working at room temperature nor were confirmed by other groups.

Here we discuss how neutron scattering experiments can contribute to resolve the ongoing controversies about high-TC ferromagnetic semiconductors. The problems to be addressed are fourfold: (i) What is the solubility limit of the doped magnetic ions in the host compound? (ii) Where are the doped magnetic ions located in the host compound? (iii) What is the valence of the doped magnetic ions? (iv) What is the doping-induced enhancement of the ferromagnetic exchange interaction? The present paper provides answers to these questions by summarizing the few inelastic neutron scattering experiments performed for diluted magnetic semiconductors (DMS) in the past.

STRATEGY OF INELASTIC NEUTRON SCATTERING EXPERIMENTS ON DMS

The content of magnetic ions in DMS compounds is rather low, thus, the magnetic excitations can be associated with monomers and dimers resulting from the random distribution of the magnetic ions. The spin Hamiltonian of magnetic dimers is given by

$${{H}_{D}} = -2J{{{\mathbf{s}}}_{1}}\,\cdot\,{{{\mathbf{s}}}_{2}},$$
(1)

where J is the bilinear exchange parameter and si is the spin operator of the magnetic ions. It is convenient to base the diagonalization of (1) on the dimer states \(\left| {S,M} \right\rangle \), where S = s1 + s2 is the total spin and –S ≤ M ≤ S. For magnetic ions with si = 1/2, ferromagnetic (J > 0) and antiferromagnetic (J < 0) exchanges give rise to an S = 1 triplet and an S = 0 singlet ground-state, respectively. The energy separation ED between the singlet and triplet states is 2J, which can be directly measured by inelastic neutron scattering experiments. When the magnetic ions experience single-ion anisotropy, Eq. (1) should be extended by the Hamiltonian

$${{H}_{M}} = D{{({{s}_{z}})}^{2}}$$
(2)

for the case of axial anisotropy. Monomer excitations are governed by (2).

The doped magnetic ions inject charge carriers into the host compound which are expected to generate a sizable ferromagnetic component to the exchange interaction through Zener’s kinetic exchange mechanism [5]:

$${{H}_{{{\text{Zener}}}}} = {{J}_{H}}{{\Sigma }_{i}}{\mathbf{\sigma }} \cdot {{{\mathbf{s}}}_{i}},$$
(3)

where σ is the spin operator of the charge carriers and JH is the local exchange (Hund’s coupling) parameter. This mechanism favors a ferromagnetic alignment between the charge carriers and the magnetic ions. If the dimer ground state is a singlet, the application of (3) produces a spin flip of one of the magnetic ions, reducing the singlet-triplet splitting by [6]

$${{E}_{H}} = {{{{t}_{{{\text{eff}}}}}S} \mathord{\left/ {\vphantom {{{{t}_{{{\text{eff}}}}}S} {(2{{s}_{i}} + 1),}}} \right. \kern-0em} {(2{{s}_{i}} + 1),}}$$
(4)

where teff ⪡ JH is the hopping parameter. The successive decrease in the singlet-triplet splitting ED with increasing EH is schematically shown in Fig. 1. For sufficiently large values of EH, the magnetic response turns into a collective magnetic excitation, which can coexist with dimer excitations [7].

Fig. 1.
figure 1

Schematic picture illustrating the decrease in the singlet-triplet splitting and the turnover into collective magnetic excitations with increasing doping.

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MATERIALS INVOLVING CO-DOPING OF CHARGE AND SPIN

Doping with transition-metal ions produces both magnetic moments and charge carriers in the host compound. Up to the present, the inelastic neutron scattering investigations focused on pnictide and chalcogenide systems. The first inelastic neutron scattering experiments were performed for Co0.05Mg0.95O [8] with the aim to search for light permanent magnets. The observed energy spectra revealed the presence of both ferromagnetic and antiferromagnetic dimer couplings (Fig. 2). The data interpretation was later confirmed by a study of the magnetic excitations in CoO [9]. The compound MgO is a perfect insulator with a band gap of 7.8 eV, but very recently it was shown that doping by transition-metal ions decreased the band gap down to 2.8 eV [10], making CoxMg1 – xO a new and promising DMS candidate.

Fig. 2.
figure 2

Energy spectrum of neutrons observed for Co0.05Mg0.95O at T = 12 K and modulus of the scattering vector Q = 1.4 Å–1. The dashed line corresponds to the phonon scattering. The full and dashed arrows mark the observed dimer transitions involving antiferromagnetic and ferromagnetic exchange interactions Ji, respectively, with the assignments shown in the inset. Exchange interactions J1, J2, and J3 refer to nearest-neighbor, next-nearest-neighbor and third-nearest-neighbor pairs of Co2+ ions, respectively.

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The second inelastic neutron scattering experimental series were carried out for MnxZn1 – xTe [11]. Mn doping with x = 0.05 produced a downward shift of the dimer splittings, thereby proving the expectations illustrated in Fig. 1. However, the downward shift amounted only to a few percent, since the number of mobile charge carriers (holes) produced by Mn doping is rather small; thus, MnxZn1 – xTe cannot be considered as a useful DMS candidate.

The third inelastic neutron scattering experiments concerned MnxGa1 – xN, which aroused great interest driven by the prediction of Mn-induced ferromagnetism with Curie temperatures TC exceeding room temperature [12]. In spite of a large number of experimental studies, the conclusions remained highly controversial, as summarized by Nelson et al. [13]. A basic problem is the solubility of Mn ions in the host compound GaN, so that the investigated samples are often contaminated by Mn clusters or other phases which are ferromagnetic in nature, e.g., Mn3 – xGa (TC = 770 K) and Mn4N (TC = 738 K). For this reason, the observation of ferromagnetism above room temperature remains unsubstantiated. Recently, an experimental study was initiated for MnxGa1 – xN [14] in order to address the existing controversial issues. Polycrystalline samples were synthesized for x = 0.02 and 0.04 and analyzed by X-ray and neutron diffraction, showing little contamination by MnNy (y < 1). The doped Mn ions enter the host lattice close to the Ga sites with a displacement of about 0.3 Å along the z-direction. X-ray absorption near-edge structure (XANES) experiments confirmed the divalent nature of the Mn ions, so that the replacement of Ga3+ ions by Mn2+ ions creates holes in the system. The energy spectra observed in inelastic neutron scattering experiments for x = 0.04 revealed three partially resolved lines (Fig. 3a), which shows the intensity difference between T = 6 and 1.7 K, so that uncertainties about the background scattering are automatically eliminated. The three lines correspond to Mn2+ monomer (Mi) and dimer (Di) excitations, which could be distinguished from each other by considering the Q-dependence of the intensities [15] (Fig. 3b). The low-energy level schemes for Mn2+ monomers and dimers are shown in Fig. 3c, from which the parameters D = 0.029(3) meV and J = –0.140(7) meV can be extracted. The inelastic neutron scattering data obtained for x = 0.02 turned out to be very similar (but with smaller intensity) to those displayed in Fig. 3a. The independence of the antiferromagnetic exchange parameter J on the Mn content x means that the injected holes are localized to a large extent, so that they cannot generate a sizable ferromagnetic component. In fact, the concentration of mobile holes was measured to be <1018 cm–3 for crystalline MnxGa1 – xN (x < 0.1) [16]. In view of all these facts, it can be concluded that the ferromagnetism reported in the literature for MnxGa1 – xN is likely due to the presence of ferromagnetic impurity phases.

Fig. 3.
figure 3

(a) Energy spectrum of neutrons scattered from Mn0.04Ga0.96N for moduli of the scattering vector Q in the range 0.5 ≤ Q ≤ 1.5 Å–1. The data correspond to the intensity difference I (T = 6.0 K) – I (T = 1.7 K). The lines are the result of a Gaussian least-squares fit. The arrows denote the monomer (Mi) and dimer (Di) transitions. (b) Q-dependence of the neutron cross-section for Mn2+ monomers and dimers. The lines correspond to the calculated intensities, and the circles, squares, and triangles to the intensities observed for the transitions M1, D1 and D2, respectively. (c) Energy level splittings of Mn2+ monomers and dimers in Mn0.04Ga0.96N. The full arrows mark the observed transitions displayed in Fig. 3a. The dashed arrows refer to the remaining allowed transitions not observed in the inelastic neutron scattering experiments (the transition M1 could not be resolved from the elastic line, and the transition matrix element of D3 is an order of magnitude smaller than for D1 and D2).

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MATERIALS DECOUPLING CARRIER DOPING FROM SPIN INJECTION

During the last 5–10 years, novel DMS materials have been discovered, namely Li1–x(MnyZn1 – y)As [17] and (KxBa1 – x)(MnyZn1 – y)As2 [4], for which carrier doping is decoupled from the spin injection. Heterovalent carrier doping (x) and spin injection by isovalent substitution (y) occur in different crystallographic planes, which is highly beneficial to avoid the solubility problem addressed in the introduction. The first inelastic neutron scattering experiments on these novel DMS systems were recently reported for (KxBa1 – x)(MnyZn1 – y)As2 with x = 0.2 and y = 0.15 [6]. The undoped compound (x = 0) shows a well resolved peak at 14 meV corresponding to the singlet-triplet splitting of antiferromagnetically coupled Mn2+ dimers. For the doped compound (x = 0.2), the peak is shifted downwards to 13 meV and the linewidth is doubled. The authors of [6] argue that this observation is associated with the destruction of the Mn singlet ground-state, since the As bands become metallic and spin polarized upon doping and, thus, generate a Stoner continuum in the excitation spectrum.

CONCLUSIONS

The history of DMS materials involving co-doping of charge and spin started in 1996 with the compound MnxGa1–xAs (x = 0.035) exhibiting TC = 60 K [18]. The Curie temperature was subsequently increased and reached a maximum of TC = 190 K for x = 0.13 in 2013 [3]. Since then, no further increase in TC has been reported. Obviously, the most promising route is offered by DMS materials where charge and spin doping are decoupled: it took only 3 years to raise the Curie temperature up from TC = 50 K in 2011 [17] to 230 K in 2014 [4]. There is no reason to believe that this development has already leveled off. What is needed is a deepening of the understanding of the doping mechanism, for which an enhancement of inelastic neutron scattering studies on single crystals are highly desirable.