Wigner Crystal and Colossal Magnetoresistance in InSb Doped with Mn.

We report magnetotransport investigation of nonmagnetic InSb single crystal doped with manganese at Mn concentration NMn ~ 1,5 × 10(17) cm(-3) in the temperature range T = 300 K-40 mK, magnetic field B = 0-25T and hydrostatic pressure P = 0-17 kbar. Resistivity saturation was observed in the absence of magnetic field at temperatures below 200 mK while applied increasing external magnetic field induced colossal drop of resistivity (by factor 10(4)) at B ~ 4T with further gigantic resistivity increase (by factor 10(4)) at 15T. Under pressure, P = 17 kbar, resistivity saturation temperature increased up to 1,2 K. Existing models are discussed in attempt to explain resistivity saturation, dramatic influence of magnetic field and pressure on resistivity with the focus on possible manifestation of three dimensional Wigner crystal formed in InSb by light electrons and heavy holes.

A crystalline state of low density electron gas was predicted by Wigner1 and experimentally observed in one and two dimensional structures23 and bulk magnetic semiconductor Hg1−v−xCdvFexSe with x ≤ 0,15 [Ref. 4]. Halperin and Rice5 put forward the idea that semiconductors with electrons at low density and large difference in effective masses between electrons and holes could be the appropriate environment for the realization of Wigner crystallization in semiconductors. It was proposed that in this type of system electrons and holes could be held together by Coulomb attraction and thus form excitons, which can condensate and create a periodic array of excitonic molecules analogous to solid hydrogen. In this condensate heavy holes can form a crystal in which electron movement resembles the electron motion in metals. In this sense InSb crystal having a large hole/electron masses ratio (mh/me = 0,5/0,01 ~ 50) can be a possible candidate to form 3D Wigner crystal. In case the concentration of electrons in crystal is below ne < 1014 cm−3, InSb parameters will be close to Wigner crystallization criteria, i.e. ne1/3aB < 1 [Ref. 5] and Bohr electron radius of about 600A [Ref. 6].

Our previous magnetotransport studies of InSb crystals doped with manganese78910 revealed that electrons and holes interplay modified InSb(Mn) conductivity at low temperatures and brought about unusual resistivity- temperature dependence (ρ-T) at manganese concentration of about NMn ~ 1017 cm−3. We also observed the dramatic resistivity increase under pressure (ρP/ρP=0 ~ 105 at P = 15 kbar and T ~ 1,5 K [Ref. 9] and simultaneous decrease in electrons and holes concentration which suggests that formation of electron-hole (e-h) insulating pairs or permanent (metastable) excitons can account for the unexpected InSb(Mn) behavior. This observation is in accordance with suggested features of the Wigner crystal which are conductivity metallization and low electrons concentration5. The main goal of the presented study is to verify if InSb could be an appropriate material for formation and study of Wigner crystal phase. As temperature and pressure are the critical parameters for Wigner crystallization we performed magnetotransport studies of InSb(Mn) crystal within the millikelvin temperature range and pressure up to 17 kbar.

Results and Discussion

Temperature-dependent resistivity

Figure 1a,b show the resistivity—temperature dependence for p-InSb(Mn) crystals at NMn = 1,6 × 1017 cm−3 and ambient pressure. The graphs clearly demonstrate that changes in resistivity-temperature dependence can be diverse within five different temperature ranges (I–V):

Figure 1

Specific resistivity, the Hall constant and charge carriers concentration as a function of 1/T at P = 0 kbar in p-InSb(Mn) sample at NMn = 1,6 × 1017 cm−3.

(a) Temperature- resistivity dependence of p-InSb(Mn). The vertical solid lines mark the temperature ranges I- (T = 300 ÷ 80 K), II- (T = 80 ÷ 20 K) and III- (T = 10 ÷ 1,5 K). (b) Specific resistivity as a function of temperature in the millikelvin temperature range at B = 0 and B = 4T (temperature ranges IV at 1,5 ÷ 0,3 K and V at 0,3 K ÷ 40 mK). (c) The Hall constant RH as a function of temperature at B = 0,1T and B = 10T (temperature range 300 ÷ 1,5 K). (d) Electrons and holes concentration as a function of temperature below 1,5 K at B = 0,1T and B = 10T. Concentration of electrons and holes were estimated as n, p = 6,25 × 1018/RH.

(I) 300 ÷ 80 K—with the sharp rise of resistivity to its maximum at T ~ 250 K (ρ = 0,065 Ωcm), further drop of resistivity and final resistivity minimum at T = 80 K (ρ = 0,037 Ωcm).

(II) 80 ÷ 20 K—is characterized by exponential increase of resistivity

where Δ0 = 1,72 meV and ρ0 = 0,03 Ωcm.

(III) 10 ÷ 1,5 K—within this range resistivity changes can be described with quadratic exponential expression7

at Δ1 = 0,2 meV and ρ01 = 0,07 Ωcm.

(IV) 1,5 ÷ 0,3 K—here resistivity exponentially increases

at Δ2 = 0,28 meV and ρ02 = 0,04 Ωcm.

In contrast to above results for semiconductors doped with nonmagnetic shallow acceptors like p-Ge(Ga) and p-Si(B) crystals resistivity-temperature dependence within the temperature range 1,5–0,3 K is usually described in the framework of hopping conductivity models

where T0 and ρ0 are temperature independent constants, α = 0,25 and α = 0,5 are indexes of Mott conductivity11 and Coulomb gap model12 respectively.

(V) 200 ÷ 40 mK—the range where resistivity is independent of temperature at ρsat = 3 × 103 Ωcm. This metallization of conductivity below 200 mK, which we observed in p-InSb(Mn) crystal, was dramatically different from the low temperature hopping conductivity usually revealed in doped semiconductors (Eq. 4). According to the model of exitonic insulator5 we can view the resistivity saturation ρsat at T < 200 mK as one of Wigner crystal conductivity characteristics where Tcryst = 200 mK should be denoted as the temperature of Wigner crystallization.

The Hall effect

To get information about charge carriers and their concentration we studied the Hall constant dependence on temperature and magnetic field at ambient pressure (P ≈ 0 kbar). It was revealed that the Hall constant can change its sign under variable temperature and magnetic field values as it is shown in Fig. 1c where RH-T dependence is presented within the temperature ranges (I ÷ V) observed for ρ-T dependence:

300 ÷ 80 K—RH is negative in low magnetic field (, T ≈ 300 K) while it is positive in high magnetic field (B > 1T, T = 300 K). Such behavior of RH as a function of magnetic field is typical for semiconductors with two charge carriers– electrons with small effective mass and heavy holes6.

80 ÷ 20 K—where the hole conduction dominates, the Hall coefficient is positive and becomes magnetic field independent. Conductivity in this temperature range is determined by the gap energy Δ0 = 1,72 meV between the valence and the impurity bands (Eq. 1). We note that in InSb an acceptor activation energy of manganese is Ea = EMn = 9 meV [Ref. 6].

10 ÷ 1,5 K—here we again observe mixed conductivity like conductivity at ambient temperature. In this case RH is negative for the low magnetic field and positive for the high magnetic field, which means that at low temperatures in p-type p- InSb(Mn) crystals the intrinsic electrons conduction dominates. We highlight that mixed conduction at low temperatures is a specific feature of InSb crystals doped with Mn. Neither InSb crystals doped with germanium- p-InSb(Ge) [Ref. 9] nor p-Ge(Ga) [Ref. 13] and p-Si(B) [Ref. 14], demonstrate n-type conductivity at low temperatures. The above observations of RH-B dependence in p-InSb(Mn) have given us possibility to relate the resistivity-temperature dependence described by Eq. 2 (T = 10 ÷ 1,5 K) to the input of e-h insulating pairs, or “permanent” excitons, into conductivity1516. It results in formation of permanent excitons extracting charge carries from the conductive crystal, the process which leads to the quadratic exponential increase of resistivity as temperature declines.

1,5 K ÷ 0,3 K—this temperature range is associated with the decrease of electrons and holes concentration resulting in active formation of excitonic insulator phase (Fig. 1d).

200 ÷ 40 mK—the tendency towards the decrease of charge carrier concentration can be clearly seen from the Hall effect measurements in the range 1,5 K–0,3 K (Fig. 1d), but we were not able to get information about electrons and holes concentration at low magnetic field due to the high sample resistance.

Pressure influence on transport properties

Resistivity-pressure dependence of p-InSb(Mn) crystal is shown in Fig. 2a, which demonstrates that pressure induces specific resistivity increase within the whole range of temperatures below 4 K (Fig. 2a,b). We should highlight two observations arising from ρ-T dependence investigation as a function of pressure. Firstly, within the activated conductivity range (above Tcryst.) resistance increase under pressure is induced by higher activation conduction energy Δ2 (Fig. 2c). Secondly, under pressure crystallization temperature Tcryst shifts towards the higher temperature range and reaches T = 1,2 K at P = 17 kbar (Fig. 2d).

Figure 2

Resistivity and charge carriers concentration under hydrostatic pressure in InSb(Mn).

(a) ρ-T dependence in p-InSb(Mn) at various pressure regimes. (b) Resistivity as a function of pressure at T = 1,6 K. (c) Activation conduction energy Δ2. (d) Wigner’s crystallization temperature Tcryst. (e) Charge carriers concentration vs pressure—n and p values revealed from the Hall effect measurements at B = 0,1T and B = 10T at T = 1,6 K. The dash curve indicates the transition from electron to hole conduction under pressure.

The Hall constant measurements at T = 1,6 K revealed that under hydrostatic pressure between P = 5 kbar and 8 kbar the conduction electrons “vanish” (Fig. 2e). We suggest that such behavior of the Hall constant is the result of permanent (metastable) excitonic insulator phase formation. We also propose that pressure stimulates increase of electron crystallization temperature and thus shifts Tcryst to higher levels (Fig. 2d). The similar concept of pressure induced excitonic insulator was introduced for pressure-driven semiconductor-metal transition in single-crystalline TmSe1−xTex [Ref. 17].

The artificial solid formed in InSb(Mn) in the proposed above Wigner crystallization model differs from the Wigner crystal structure discussed for Hg1−v−xCdvFexSe with x < 0.l5 and v ≤ 0,4, where Fe3+ (3d5) are ionized donors used for “charge superlattice” formation4. By contrast, according to the presented here Wigner model light electrons form 3D lattice pinned with heavy holes, but not impurity ions, thus forming crystalline excitonium518. This conclusion results from the Hall effect measurements where we observed both electrons and holes concentration decrease under cooling and pressure. We propose also that electrons in Wigner crystal at low concentration form antiferromagnetically ordered phase exhibiting insulator behavior.

Colossal Magnetoresistance

The results of transverse magnetoresistance measurements within millikelvine temperature range show that resistance decreases under magnetic field, reaches minimum at B ~ 4T and then goes up with the further increase of magnetic field (Fig. 3a). Resistance first decreases under magnetic field, reaches its minimum at B ~ 4T and then goes up with higher magnetic field (Fig. 3a). Thus magnetic field of about 4T induces transition from the insulator to quasimetal conductivity type (Fig. 1b). CMR value remains practically independent of temperature at millikelvin temperature range below 100 mK (Fig. 3a). As temperature goes above Tcryst CMR decreases and disappears at temperature below 4 K. Above B = 15T resistivity saturates (Fig. 3b) which we relate to electrons transition to ferromagnetic order. As temperature goes above Tcryst CMR decreases and disappears at T = 4 K. Maximal values of CMR in p-InSb(Mn) in millikelvin temperature range is comparable with CMR previously observed in both Magnetic and Diluted Magnetic Semiconductors (MS and DMS) like Gd1−xvxS4 [Ref. 19] and Hg1−xMnxTe [Ref. 20] as well as in Manganite Perovskite Pr0,7Ca0,26Sr0,04MnO3 [Ref. 21]. Important observation is that manganese concentration in InSb(Mn) was smaller by a factor 104 ÷ 105 compared to magnetic ions concentration in MS, DMS and Manganite Perovskites.

Figure 3

Colossal magnetoresistance in InSb(Mn).

(a) Specific resistivity in p-InSb(Mn) crystal as a function of magnetic field at temperature below Tcryst at P = 0 kbar. Arrows show antiferromagnetic orientation of electron spins at B = 0 ÷ 0,1T. (b) CMR in InSb(Mn) at T > Tcryst in magnetic field up to 25T at P = 0 kbar. Arrows show antiferromagnetic orientation of electron spins at B < 0,1T and ferromagnetic orientation at B > 20T. (c) ρ-B dependence at set of pressure P = 0; 1,5; 12 and 17 kbar at T = Tcryst.

Though a great many models have been meanwhile proposed for the explanation of CMR in magnetic and nonmagnetic materials the following seem to be of particular interest:

Phase separation model22 developed for hole–doped manganese oxides describing CMR as induced by magnetic field transition from antiferromagnetic insulator phase to conducting ferromagnetic state.

Magnetic polaron model23 proposed for MS explains declining resistance in magnetic field as the decrease in charge carries scattering on magnetic clusters.

The model proposed for DMS Hg1−xMnxTe connected with dramatic change in hole effective mass in magnetic field24.

Zeeman splitting model for nonmagnetic Ge crystal doped with Cu [Ref. 25].

Excitonic insulator (EI) model trying to describe the effect of transition from excitonic insulator phase to conducting state induced by external magnetic field and adapted to CMR in nonmagnetic InSb crystals doped with manganese8.

It is still hard to adapt above models for MS and DMS in the case of InSb crystals doped with manganese at impurity concentration within Ncr = p = NMn = 2 × 1017 cm−3 as InSb is nonmagnetic semiconductor in contrast to magnetic materials where magnetic ions concentration is about 105 times as large as Ncr for InSb(Mn). On the other hand, InSb gives us the unique possibility to compare the behavior of magnetic Mn—and nonmagnetic Ge- impurities, as Ge like Mn forms shallow acceptor level with the same energy at Ea = 9 meV6 and demonstrates exactly the same critical concentration of metal-insulator transition at Ncr = 2 × 1017 cm−3. But transport and magnetotransport characteristics of p-InSb(Ge) crystals at low temperatures radically differ from p-InSb(Mn) characteristics7. Crystals of p-InSb(Ge) do not demonstrate any resistivity features dependent on impurity concentration, temperature and magnetic field. Similar to p-Ge(Ga) and p-Si(B) the crystals of p-InSb(Ge) demonstrate the Variable Range Hopping conductivity, the ordinary Hall effect and positive magneotresistance typical for disordered localized nonmagnetic impurities. The difference in behavior of magnetic (Mn) and nonmagnetic (Ge) impurities in InSb could be related to the influence of Jahn-Teller (JT) lattice distortion caused by impurity manganese26. It was previously revealed that under uniaxial stress X ~ 3 kbar at T ~ 1,5 K both p-Ge(Ga) and p-InSb(Ge) demonstrate the decrease in specific resistivity by a factor 102 in magnetic field B = 3-5T27. In p-InSb(Mn) crystals CMR also increased under uniaxial stress by a factor 104 at T = 1,2 K28. Thus we can consider an uniaxiall stress in p-InSb(Ge) as a method to simulate JT distortion described by Bir29. The analogy between CMR in uniaxially stressed p-InSb(Ge) and unstressed p-InSb(Mn) crystals supports the idea of Jahn-Teller (JT) lattice distortion input in CMR. Both the uniaxial stress and the JT distortion in InSb(Mn) crystals splits the valence band and removes valence band degeneration boosting CMR effect.

Positive Magnetoresistance (PMR) observed at B > 4T could be also related to ferromagnetic orientation of electron spin, but alternative approach is the Anderson localization of electrons in high magnetic field. In this model PMR is the result of electron wave function diamagnetic shrinking30. On the other hand we revealed colossal decrease of resistivity in p-InSb(Mn) in magnetic field (CMR) between B = 0 and 4T at temperature below Tcryst. In observation of resistivity saturation at low and superlow temperatures the lack of PMR in the system at low magnetic field and T < Tcryst is the point in the favour of the Wigner crystallization concept rather than of electron localization disorder.

Contrary to uniaxial stress hydrostatic pressure caused the decrease of CMR in InSb(Mn). The influence of pressure on magnetoresistance is shown in Fig. 3c. It can be seen that ρ at B = 4T decreased only by a factor 102 at P = 1,5 kbar and at P > 14 kbar the influence of magnetic field on the resistance was insignificant.

In conclusion, revealed resistivity saturation, decrease in holes and electrons concentration at low temperatures, dramatic influence of magnetic field and hydrostatic pressure on resistivity we associate with the manifestation of the three-dimensional Wigner crystal formed in InSb(Mn) crystal. We propose that an external magnetic field at B ~ 4T and T ≤ Tcryst induces CMR effect as the transition from antiferromagnetic insulator state of electrons to metal state and induces metastable excitons dissociation at temperature above Tcryst.

Methods

InSb manganese doped single crystal was grown by Czochralsky method. Dimensions of the crystal was about 3 cm in diameter and 5 cm long. Impurity concentration of Mn varies along the crystal length from NMn ~ 1017 cm−3 at one end to the 4 × 1017 cm−3 at another end of the crystal. Samples for measurements were about 3 × 1 × 0,4 mm3 for measurements in the temperature range T = 300 ÷ 1,5 K and 0,3 × 0,2 × 0,12 mm3 for measurements in pressure cell at 3He cryostat and 3He–4He dilution refrigerator cryostat. Electrical conducting wires of gold were soldered to the samples with pure indium. Nonmagnetic pressure cells made of bronze provided hydrostatic pressure up to 16 ~ 17 kbar at low and super-low temperatures. The resistivity and the Hall effect at temperature ranges 300–1,6 K were measured in van der Pauw or the Hall bar geometry. The Hall resistance and transverse magnetoresistance measurements were carried out on the Hall bar samples in dilution refrigerator with 15T Oxford Instruments superconductive (SC) magnet at NHMFL, Florida. In other presented experiments with 10T and 18T Oxford Instruments SC magnets and 30T Bitter magnet of HMFL Nijmegen were used. Special attention was paid to magnetic field calibration of SC magnet used in experiments in millikelvin temperature range. Frequency measurements were done to detect 1H and 3He NMR lines, providing accurate field calibration data. Measured at 11 Tesla, repeatability in the same sweep direction was more than 5 mT. Repeatability when changing sweep direction was better than 20 mT. Absolute calibration at full field was within 1 mT on the downsweep, and field was 10 mT lower than displayed on the upsweep. The typical hysteresis of this magnet is less than 150 Oe. The lock-in measurements were carried out at the rate of 14 mT s−1. Zero magnetic field came to equilibrium when sweep was stopped. The sample was submerged in the cold 3He–4He mixture liquid, to exclude radiation factor.

Additional Information

How to cite this article: Obukhov, S. A. et al. Wigner Crystal and Colossal Magnetoresistance in InSb Doped with Mn. Sci. Rep. 5, 13451; doi: 10.1038/srep13451 (2015).