Magnetic glassy state in combination with ferromagnetism in Fe0.05(SnTe)0.97Sb0.03 bulk alloy

In this study on Fe0.05(SnTe)0.97Sb0.03 bulk alloy, we found signatures of presence of both magnetic glassy state and ferromagnetism. The bulk alloy is prepared by modified solid state technique and the sample is characterized for its structural, electrical and magnetic properties. Electrical resistivity plot shows semiconducting nature of the sample, however below 25 K, a sudden increase in the electrical resistivity value is observed. The transport mechanism is explained on the basis of small polaron hopping (SPH) model and variable range hopping (VRH) model. A large bifurcation observed between zero-field cooled and field-cooled magnetization at low temperature hints towards existence of a magnetic glassy state. M-H curve exhibits hysteresis behaviour for the measurements carried out at 10, 100 and 300 K. However, absence of saturation of the curves at 10 and 100 K suggests co-existence of ferromagnetic and glassy state. Presence of magnetic glassy state can also be confirmed from the Arrott plot and AC Susceptibility measurement. The susceptibility curves are found to undergo relatively small shift of peaks with frequency and theoretical fitting of the data supports presence of a cluster-glass state.


Introduction
Dilute magnetic semiconductors (DMS), due to the charge and spin properties of electrons incorporated into a single material, are found to have potential applications in non-volatile memory storage, spintronic devices and magneto-optic devices [1][2][3][4]. DMS materials have been investigated a lot during the past decades for the purpose that they change the functioning of traditional semiconductor devices with the substitution of magnetic ions. Transition metal doped III-V and II-VI semiconductors were among the first to be explored as DMS materials. We have also worked on developing elemental semiconductor Tellurium as a DMS material. In that, we found a transition from paramagnetism to ferromagnetism on doping with magnetic ions whereas a small hysteresis curve was also observed on additional hole doping into the system [5]. In recent times, transition metal doped tin chalcogenides belonging to IV-VI group have been extensively studied due to their narrow band gap which is found to be useful in thermoelectric, photovoltaic and optical applications [6][7][8]. Tin Telluride (SnTe), having a narrow band gap of about 0.18 eV in the bulk form is one such material that is being explored for its magnetic properties [9].
SnTe has been studied both experimentally and theoretically to understand its magnetic properties. Possible presence of ferromagnetic or antiferromagnetic order or even spin glass state has been observed in Mn-doped SnTe thin films [10][11][12][13]. Theoretical studies on SnTe doped with V and Cr have found modifications of the band structure followed by spin polarization. The resultant magnetic effects brought about includes presence of both ferromagnetic and antiferromagnetic, half metallic phases in them [14]. For concentration of x > 0.2 at% in Sn 1−x Cr x Te, it exhibits ferromagnetism and there is a strong diamagnetic behavior observed below this concentration due to diamagnetic background of SnTe crystal [15]. Another study on Sn 1−x Cr x Te DMS system for low concentration of Cr from x = 0.004 to 0.012 shows spin-glass-like state due to short range direct magnetic interactions present in Cr-rich clusters [16]. On the contrary, Ge 1−x Cr x Te films shows Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. ferromagnetism which is the result of short-range order such as superexchange mechanism [17]. Ferromagnetism is also observed in Sn 1−x Fe x Te crystal for x = 0.01 up to 500°C [18]. Magnetic measurement of Ni doped PbTe showed paramagnetic phase at high temperature and a transition to ferromagnetism at low temperature [19].
Our past work on Fe doped SnTe system looked into the effect of hole doping on the magnetic properties of SnTe [20]. The hole-mediated exchange interactions were responsible for the ferromagnetic ordering in the sample. However, following a thorough examination of the literature, it was realized that no work pertaining to substitutional effect of donor impurities into hole doped semiconductor SnTe has been found in the literature. Further, can such a substitution result in an enhancement of magnetic ordering in the sample has not been studied. Hence our present study focuses on the effect of substitution of donor impurity (Antimony) into the hole doped SnTe having the general form Fe 0.05 (SnTe) 1−x Sb x with x = 0.03.

Methodology
Powders of Tin Telluride, Antimony and Iron having high purity (99.999%, Alfa Aesar) are measured for appropriate quantities and taken in a quartz tube ampoules to make Fe 0.05 (SnTe) 0.97 Sb 0.03 bulk alloy. The ampoule is sealed under conditions of high vacuum of >10 −5 Torr. Oxy-butane flame is used to repeatedly heat the sealed ampoules with periodic quenching in air. It is heated until a homogeneity is achieved. The heated ampoule is finally quenched in cold water. The ingots that are formed are crushed into fine powder and further used for characterization.
Temperature dependence electrical resistivity and magneto resistivity measurements are carried out using Quantum design make Physical Property Measurement System (PPMS) in the temperature range of 2 K-300 K. A study of electrical resistivity is also carried out in the presence of external magnetic fields of 0 T, 5 T and 8 T. AC and DC magnetization measurements are investigated using Superconducting Quantum Interface Device (SQUID) Magnetometer system equipped with a Pulse Tube Cooler. The Magnetization v/s Temperature (M-T) measurement is carried out in the temperature range of 10 K-300 K and the Hysteresis (M-H) measurement is performed in the magnetic field range up to 7 T. AC Susceptibility measurement is carried out at different frequencies in the temperature range of 10 K-300 K.

Structural studies
Rietveld refinement of XRD data is carried out for Fe 0.05 (SnTe) 0.97 Sb 0.03 bulk alloy using FullProf software. Figure 1 shows the XRD plot and Rietveld refinement plot. From the plot, it can be confirmed that the sample has only a single phase as no additional peaks are to be seen. The sample has a Rocksalt crystal structure belonging to Fm3m space group. The value of lattice parameters after refinement is found to be a = b = c = 6.313 47 Å and α = β = γ = 90°. There is a slight decrease in the value of lattice parameters with respect to that calculated from the XRD spectrum of Fe 0.05 (SnTe) 0.97 Sb 0.03 bulk alloy [21]. A slight shift in peak positions from that of Fe 0.05 (SnTe) bulk alloy is observed due to doping of Antimony into the Fe doped SnTe matrix.

Electrical resistivity
Using a PPMS system with external fields of 0 T, 5 T, and 8 T, the resistivity variation with temperature of Fe 0.05 (SnTe) 0.97 Sb 0.03 bulk alloy is investigated. The plots are shown in figure 2. The resistivity shows a decreasing nature with increase in temperature. With increase in magnetic field from 0 T to 8 T, the value of resistivity is seen to slightly increase. This happens due to Lorentz force which increases the probability of lattice scattering of electric charge, thereby increasing the resistivity with increase in magnetic field values [22].
SnTe can be characterized as a topological crystalline insulator in nature owing to its extremely low value of band gap [23]. We had seen in our study on Fe 0.05 (SnTe), a transition from metallic state to an insulating state under the influence of external magnetic field. In the present case, on introducing donor impurity Sb into SnTe, the value of resistivity is seen to gradually decrease with temperature. However, the curve does not show a typical semiconducting behavior whilst having a semiconductor property. For temperatures below 25 K, an upsurge in the resistivity value is observed. This behavior showcases transition from semiconducting state to an insulating state indicating presence of an insulating property at low temperatures. The insulating behaviour could be the result of localization effects of charge carriers as no pronounced change in resistivity can be observed in the presence of magnetic field.
The conduction mechanism of the semiconducting samples can be explained on the basis of various models like Thermally Activated Conduction, Small Polaron Hopping (SPH), Nearest Neighbour Hopping (NNH) and  Variable Range Hopping (VRH) model. These models are found to be dominant for a specific range of temperatures. The validity of each model can be confirmed by plotting graphs that correspond to the respective models i.e. ln(ρ/T) v/s T −1 for SPH, ln(ρ) v/s T −1 for NNH and ln(ρ) v/s T −1/4 for VRH and making a linear fit in the linear region of the graph. In the conventional resistivity curve of a semiconducting material, the aforesaid hopping conduction models are found to be reliable over a larger range of temperatures. The nature of resistivity curve as seen for the present sample is unconventional but is still semiconducting. In such cases, it seems that the conduction models have a possibility of being valid within a small range of temperature due to change in slope of the curve. The SPH model given in equation (1) elucidates hopping of small polarons (or deeply trapped electrons) to their neighbouring sites with the help of multi-phonons [24,25].
where E a is the activation energy, k B is Boltzmann constant, ρ 0 is residual resistivity. This model is dominant in the high temperature region but for our sample, the window of temperature having linear nature is very small i.e. from 265 K-300 K. It is therefore not consequential of SPH model to explain conduction mechanism in the high temperature range. Similarly, NNH model is also seen to be valid only across a narrow range of temperature. This is suggestive of a probability that transport mechanism of Fe 0.05 (SnTe) 0.97 Sb 0.03 sample consists of an amalgamation of more than one of the above models that contribute to conduction of the carriers. For representative purpose, a plot of ln(ρ/T) v/s T −1 for SPH model at different magnetic fields is shown in figure 3. From the slope of the linear fit to the graph, activation energy values E a that correspond to the polaron hopping are obtained and is given in table 1. The values are found to be decreasing with magnetic field and this is due to delocalization of charge carriers in the high temperature region [26].
In the lower regions of temperature, the viability of the VRH model, both 2D and 3D, is tested in explaining the transport mechanism [27,28]. However, 2D VRH model because of its inaptness was discarded. The 3D VRH model is therefore expressed by the equation-  where ρ 0 and T 0 are Mott parameters. T 0 represents average energy that is required for the localized charge carrier to undergo hopping to its nearest neighbouring site. In the VRH mechanism, when there is not enough thermal energy for electrons to hop and reach to their nearest neighbour, it is conducive for the electrons to hop to a site where the potential difference is small [28]. This gives rise to the process of hopping. In this case, the range of hopping is variable. A plot of ln(ρ) v/s 1/T 1/4 is shown in figure 4. The data is fitted linearly from which we understand that the VRH model holds true in the low range of temperature from 6 K-85 K. The slope of the fitted line gives the value of Mott's temperature T 0 which is given in table 1. The value of T 0 for x = 0.03 sample is found to be decreasing marginally with increasing magnetic field. Since T 0 is related to density of states N(E) at the Fermi level, its decreasing value can be correlated to an increase in the density of states. This allows hopping of charge carriers to take place between randomly distributed localized electronic states in Fe 0.05 (SnTe) 0.97 Sb 0.03 bulk alloy.

Magnetic studies
Temperature dependent DC magnetization study involving zero field cooled (ZFC) and field cooled (FC) measurements is carried out within the temperature range 10 K-300 K and in the presence of an external magnetic field of 200 Oe. From the plot in figure 5, a clear magnetic transition from one state to another can be observed. A sharp cusp observed in both ZFC and FC curves at around 132 K is suggestive of an antiferromagnetic transition in the system. Similarly, another cusp around 50 K is seen in the ZFC curve which could have its origins in the antiferromagnetic FeTe phase [29]. With further decrease in temperature, FC curve is seen to undergo a steep rise in the moment value that signifies a ferromagnetic transition in the system. Decrease in the magnetization value of ZFC curve also corresponds to the presence of ferromagnetic clusters [30]. Additionally, a large bifurcation is observed between the ZFC and FC curves at lower values of temperature. Such a bifurcation could be the characteristic trait of either a spin-glass state or cluster-glass state. These states are responsible for the freezing of random spin orientations in the sample at lower temperatures.
The magnetic hysteresis curve of Fe 0.05 (SnTe) 0.97 Sb 0.03 measured at different temperatures in the applied field range of −70 kOe to 70 kOe is shown in figure 6. For T = 10 K and 100 K, the curve develops hysteresis behaviour at low field values, reflecting ferromagnetism in the material. The curve is conspicuous by the absence of saturation and together with the presence of hysteresis suggests an interplay between antiferromagnetic and ferromagnetic phase. The S-shape of these curves which is an indicator of spin-glass or cluster-glass behavior is a consequence of this [31]. The M-H curve at 300 K also lacks saturation and on comparison with M-T curve, there is no presence of a large bifurcation between the ZFC and FC curves at 300 K. Thus, M-H curve at room temperature shows features of canted antiferromagnetism.   Our previous study on Fe 0.05 (SnTe) also demonstrated hysteresis behaviour at lower values of magnetic field for which the coercivity at 10 K was found to be 133 Oe [20]. When compared with the present sample, the coercivity value at 10 K has increased to 821 Oe. On introduction of Sb into the system, which is non-magnetic in nature, resulted in a disorder in the SnTe lattice due to Sb occupying some of the atomic sites that the parent atom previously inhabited, thereby affecting the band structure followed by creation of an impurity band in the system. A ferromagnetic coupling can exist between donor electrons and magnetic ions if the occupancy is less than half of the 3d ionic shell. Further, a breakdown of long-range order in the system occurs which signifies existence of either a spin-glass or cluster-glass state. This could be due to less number of atoms of Sb as compared to that of Fe in the system. Absence of magnetic saturation coupled with presence of a hysteresis loop at low field values directs towards possible co-existence of spin-glass/cluster-glass and ferromagnetic state. The enhanced coercivity value of Fe 0.05 (SnTe) 0.97 Sb 0.03 may seem to be the result of introduction of donor electrons of Sb into the system. Such enhanced magnetism due to donor impurity was also observed in one of our earlier work which was attributed to p-d exchange interaction process (RKKY interaction) [32]. From the hysteresis curve, we also find that the coercivity value has been decreased to 318 Oe as temperature is increased to 300 K.
The behavior of field dependent magnetization with temperature is evaluated using Arrott plot. Arrott plots are widely used for understanding of magnetic interactions and transition in the ordering [33,34]. From the Arrott plot shown in figure 7, there is a bend towards the H/M axis and no intercept is seen on the M 2 axis for 10 K and 100 K curves. In comparison to the inflection point of 100 K curve, the one for 10 K shifts to a high value of H/M. This shifting in inflection point is a signature of spin-glass/cluster-glass state. On the other hand, the curve for 300 K suggests ferromagnetic nature of the sample as it has presence of spontaneous magnetization that can be obtained by extrapolating the curve to the Y-axis. Thus, a short range ordering exists in Fe 0.05 (SnTe) 0.97 Sb 0.03 thereby supporting the transition into a spin-glass/cluster-glass state amidst ferromagnetism and the possibility of their mutual co-existence.

AC magnetization
Presence of glassy feature is usually confirmed from the ac susceptibility measurements taken at different values of frequencies. The ac magnetization study of Fe 0.05 (SnTe) 0.97 Sb 0.03 is carried out at the frequencies of 50 Hz, 100 Hz and 250 Hz at an ac field value of 5 Oe. The real part of susceptibility χ′ as a function of temperature at different frequencies is plotted in figure 8. The maximum χ′ occurs at a particular temperature which is represented as T m . This maximum is seen to have a frequency dependence, wherein the peak shifts infinitesimally to higher values of temperature from 53.91 K at 50 Hz frequency to 56.06 K at 250 Hz frequency. This is the feature that defines a magnetic glassy state [35,36]. A second peak around 130 K at all frequencies corresponds to the cusp observed in the DC magnetization measurement. Since the peaks are independent of frequency, they do not correspond to spin-glass phase.
In order to understand the origin of this frequency shift of the peak temperatures, they are fitted using three empirical models. T g is the spin-glass transition temperature which is the value of T m at zero frequency, Ea is the activation energy, k b is Boltzmann constant.
The fitted data yields zv = 1.2 and τ * = 10 −5 s using power law, τ * = 2.8 × 10 14 and E a /k b = 546 K using Arrhenius law, τ * = 10 −4 s and E a /k b = 0.29 K using Vogel-Fulcher law. The value of τ * obtained from the Arrhenius fitting is less than the range for superparamagnetic relaxation of ∼10 10 -10 13 s, thereby eliminating its possibility. However, τ * obtained from Power law and Vogel-Fulcher law identifies the sample to incorporate ferromagnetic cluster-glass behaviour. The Mydosh parameter K calculated using equation (3) also supports the presence of cluster-glass property.
The value of K for cluster-glass system falls within the range of 0.005 and 0.08 [37]. In this case, since the calculated value of K is 0.08, it confirms cluster-glass property in the sample. Cluster-glass is found to be similar to the spin-glass yet the difference lies in the presence of the cluster of spins which in turn gives rise to the glassy property. As the spins exist in clusters, the relaxation time between each spin flipping in the cluster is a slow process which could mean ferromagnetic cluster-glass behaviour of the present sample.

Conclusion
To understand the increase in magnetic ordering of the sample due to substitution of donor impurity, bulk alloy of Fe 0.05 (SnTe) 0.97 Sb 0.03 has been prepared by modified solid state technique. The effect of substituting donor impurity Sb, which is nonmagnetic in nature, on its structural, electrical resistivity, transport and magnetic properties have been investigated. Electrical resistivity is found to decrease with temperature highlighting the semiconducting nature of the material. Zero-field cooled (ZFC) and field-cooled (FC) plot and VSM measurements suggests co-existence of two magnetic states in the sample, i.e. weak ferromagnetic state and magnetic glassy state. In Fe 0.05 (SnTe) bulk alloy, we had observed only ferromagnetic ordering as a result of hole doping. In the present sample however, we also observe glassy behaviour at low temperatures. This arises due to the substitution of donor impurity Sb which results in a partial disorder in the system. At 300 K however, the sample shows canted antiferromagnetism as confirmed from the presence of unsaturated magnetization along with hysteresis curve in the M-H plot as well as presence of spontaneous magnetization in the Arrott plot. In addition to ferromagnetic order, the glassy nature of the sample is understood by the minor shifting of the peaks located at around 50 K towards higher temperatures with increasing frequency indicating the presence of cluster-glass state in the material.