Observation of transition from semiconducting to metallic ground state in high-quality single crystalline FeSi
OObservation of transition from semiconducting to metallic ground state inhigh-quality single crystalline FeSi
Y. Fang , , S. Ran , , W. Xie , and M. B. Maple , , ∗ Materials Science and Engineering Program, University of California, San Diego, La Jolla, California 92093, USA Center for Advanced Nanoscience, University of California, San Diego, La Jolla, California 92093, USA Department of Physics, University of California, San Diego, La Jolla, California 92093, USA Department of Materials Science and Engineering,University of Maryland, Collage Park, 20742, USA and Department of Chemistry, Louisiana State University, Baton Rouge, LA, 70803, USA (Dated: October 15, 2018)We report anomalous physical properties of single-crystalline FeSi over a wide temperature range1.8-400 K. X-ray diffraction, specific heat, and magnetization measurements indicate that the FeSicrystals synthesized in this study are of high quality with a very low concentration of magnetic impu-rities ( ∼ ρ ( T ) can be described by activated behavior with an energygap ∆ = 57 meV between 67 K and 150 K. At temperatures below 67 K, ρ ( T ) is significantly lowerthan an extrapolation of the activated behavior, and the Hall coefficient and magneto-resistivityundergo a sign change in this region. At ∼
19 K, a transition from semiconducting to metallic-likebehavior is observed with deceasing temperature. Whereas the transition temperature is very robustin a magnetic field, the magnitude of the resistivity below ∼
30 K is very sensitive to magnetic field.There is no indication of a bulk phase transition or onset of magnetic order in the vicinity of either67 K or 19 K from specific heat and magnetic susceptibility measurements. These measurementsprovide evidence for a conducting surface state in FeSi at low temperatures.
I. INTRODUCTION
The transition metal silicides FeSi, MnSi, CoSi, andCrSi, have the B20 crystal structure, which is the onlygroup in the cubic system without an inversion cen-ter. These compounds exhibit rich physical phenom-ena that are of great interest for fundamental under-standing and potential applications. For example, the d -electron compound FeSi shows a remarkable similarityto f -electron Kondo insulators, and the electrical resis-tivity ρ ( T ) evolves continuously with decreasing temper-ature from metallic behavior (d ρ /d T >
0) to stronglycorrelated semiconducting behavior (d ρ /d T <
0) [1 ? –4]. A considerable amount of theoretical effort [5–10] hasbeen expended to explain the strong temperature depen-dence of the magnetic susceptibility χ ( T ) of FeSi whichreaches a maximum value at around 500 K [1] that is notrelated to magnetic order [11, 12].The ground state of FeSi is considered to be non-magnetic; however, experimental investigations of FeSiat low temperature reveal features that are sample de-pendent and are not well understood [4, 13, 14]. Thepublished results are consistent in terms of the smallsemiconducting energy gap of 50-60 meV in the tem-perature range of 70-170 K. However, further decreaseof the temperature results in either saturation steps [4],a hump (shoulder) at 70 K [14, 15] or ∼
35 K [16], amoderate increase of ρ with decreasing temperature be-low 40 K [17] or 50 K [18], or a saturation below about5 K [19] of ρ ( T ). Besides, the values of ρ below 70 K re-ported by these references are also very different, indicat- ∗ Corresponding Author: [email protected] ing strong sample dependence of the electrical transportbehavior. It has been well established in experimentsthat the electrical properties of semiconductors can bevery sensitive to external dopants. [20–22] To investigatethe intrinsic physical properties of FeSi, we prepared highquality single-crystal samples of FeSi and performed var-ious physical property measurements over a wide tem-perature range of 1.8-400 K. Anomalous electrical trans-port behavior associated with a change in primary chargecarriers and negative magneto-resistivity at low tempera-tures were observed in all of the samples. We also reportmetallic conducting behavior of FeSi single crystals be-low ∼
19 K, yielding evidence for a conducting surfacestate, consistent with specific heat, magneto-resistivity,and magnetization measurements.
II. EXPERIMENTAL DETAILS
Single-crystalline samples of FeSi were grown in high-temperature Sn flux with Fe: Si molar ratio of 1: 1.The quality of the FeSi samples was assessed by meansof single crystal X-ray diffraction at room temperature.A Bruker Apex II X-ray diffractometer with Mo K α ( λ = 0.71073 ˚A) radiation was used to measure the scat-tering intensity. The crystal structure was refined withSHELXTL package [23]. Electrical resistivity, magneto-resistivity, Hall effect, and specific heat measurementswere performed in a Quantum Design Physical PropertyMeasurement System (PPMS) DynaCool. The magne-tization and magnetic susceptibility measurements werecarried out in a Quantum Design Magnetic PropertyMeasurement System (MPMS) [24]. a r X i v : . [ c ond - m a t . m t r l - s c i ] A p r FIG. 1. (a) The crystal structure of FeSi (Red: Fe; Blue:Si). (b) Single crystal X-ray diffraction precession image ofthe ( h l ) plane in the reciprocal lattice of FeSi at 300 K. Allof the resolved spots correspond to the cubic chiral crystalstructure P
3. (c) 3D Fourier map showing the electrondensity in B z -axis. III. RESULTS AND DISCUSSION
The FeSi single crystals grow along the [111] directionin the Sn flux, resulting in bar-shaped samples. The re-sults of single-crystalline X-ray diffraction on FeSi areshown in Fig. 1. Consistent with previous studies, stoi-chiometric FeSi crystallizes in the cubic chiral structurewith space group P B a = 4.4860(5) ˚A. No vacancies were observed according tothe refinement. The resulting profile residual Rp is 1.79%with weighted profile residual Rwp 4.11%. No electrondensity residual was detected, indicating the high qualityof the FeSi crystals.Because of their bar-shape and high quality, the FeSisingle crystals are very suitable for electron transportmeasurements along the [111] direction. Upon coolingfrom 400 K, metallic-like behavior can be observed downto 336 K, below which the resistivity increases with de-creasing temperature, resulting in a minimum in ρ ( T )at T min = 336 K (see the inset of Fig. 2(a)). Similarfeatures can also be found in other references with val-ues of T min mostly in the range 150-300 K) [4, 25–27].Decreasing the temperature further results in a gradualenhancement of semiconducting behavior down to 152 K,which has been reported to be related to the opening ofa semiconducting energy gap [28–30].A plot of ln( ρ ) vs. (1/ T ) for FeSi shown in Fig. 2(b) FIG. 2. (a) Electrical resistivity ρ vs. temperature T for FeSiwith the current flowing along the [111] direction below 200K. (b) ln( ρ ) vs. 1/ T . The insets of (a) and (b) show theresistivity at high temperatures and a picture of the samplewith the four-wire electrical lead configuration, respectively. is linear in the temperature range 152 K ( T ) to 67 K( T ), consistent with standard activated behavior withan energy gap ∆ = 57.1 meV; this value of ∆ is com-parable to previously reported gap values of 50-60 meV[1, 3, 15, 18]. From 54-30 K, where the relation ln( ρ )vs. 1/ T is also linear, the value of d ln( ρ )/d(1/ T ) corre-sponds to am energy gap of 35 meV. Below 30 K ( T ), the ρ ( T ) curve cannot be described by a standard activationmodel. Further decrease of the temperature below 19 K( T ) results in a decrease of ρ with decreasing tempera-ture as shown in Fig. 2(a). As the phenomena observedin ρ ( T ) below T are quiet different from the electricaltransport behavior of FeSi reported in other references,we repeated the measurements on five different FeSi sin-gle crystals which yielded the same results.For a better understanding of the temperature depen-dence of the observed electrical transport behavior, es-pecially the metallic conducting behavior, we performedspecific heat C p ( T ) measurements on the samples downto 1.8 K, the results of which are shown in Fig. 3. Thespecific heat C p ( T ) can be reasonably well described bythe sum of electronic and lattice contributions at low FIG. 3. Specific heat C p ( T ) of FeSi at low temperatures from1.8 to 80 K. A plot of C p / T vs T below 20 K is shown in theinset. The dashed line in the inset is a fit of the expression C p / T = γ + βT to the data with the values of γ , β , and θ D given in the inset of the figure. temperatures C p = γT + βT . No anomalies at T = 67K, T = 30 K, and T = 19 K can be observed, indicat-ing the absence of any bulk phase transitions in FeSi atthese temperatures. The estimated value of the Debyetemperature θ D of 457 K lies within the range of 377-515K previously reported [4, 31, 32]. On the other hand, theelectronic specific heat coefficient γ is estimated to be0.41 mJ.mol − .K − , which is only about 8-30% of pre-viously reported values [4], suggesting that the samplesstudied in this work have a lower concentration of elec-tron donor impurities, as the value of γ is proportionalto the density of electronic states at the Fermi level. Themetallic-like conduction below T = 19 K exhibited bythe FeSi samples in this work is dramatically differentfrom the semiconducting behavior observed in other FeSisamples which have higher concentrations of charge car-riers. The seemingly contradictory phenomena suggestthat the metallic conduction observed in this study is un-likely to be a bulk phenomenon, which is also supportedby the absence of phase transition features in the C p ( T )data.The temperature dependence of the magnetic suscep-tibility χ ( T ) for FeSi is shown in Fig. 4. Above 100 K,the value of susceptibility increases with increasing tem-perature, which is similar to the behavior of χ ( T ) foran antiferromagnet at temperatures below the N´eel tem-perature. In the temperature range 20-100 K, χ ( T ) isvery small ∼ − .T − , indicating a very weakresponse of FeSi to external magnetic field and a non-magnetic ground state for FeSi. Below 15 K, χ ( T ) of FeSihas a Curie-Weiss like upturn with decreasing tempera-ture, which is believed to be associated with magneticimpurities [1, 11]. In this study, however, the magnitude FIG. 4. Magnetic susceptibility χ vs. temperature T for FeSisingle crystals. The corresponding magnetization curve at3.5 K is shown in the inset. The dashed curve is a fit of theLangevin function to the M ( H ) data and the onset temperature of the χ ( T ) upturn is signif-icantly smaller and lower, respectively, than previouslyreported values [15, 16, 33], indicating lower magneticimpurity concentration for the present samples. The kinkobserved in the M ( H ) curve at around 2 T indicated bythe arrow in the inset of Fig. 4 is also consistent withthe paramagnetic impurity scenario. Above 2 T, it seemsthat the magnetic field does not dramatically affect themagnetization of the samples, which also suggests the ab-sence of magnetic order at low temperatures. The resultsof the magnetic measurements reveal that the samples areof high quality and the transitions observed around T =67 K and T = 19 K in the ρ ( T ) curve are not related toany bulk magnetic transitions.In this study, the magnetization of FeSi can be welldescribed by using the following Langevin functions: M = M S [ coth ( µH/k B T ) − k B T /µH ] (1)in which µ is the magnetic moment of the impurity clus-ters and M S is the saturation magnetization. The corre-sponding fitting of M ( H ) at 3.5 K gives M s = 2.433 × µ B /mol and µ = 7.95 µ B . If we assume that the mag-netic moment per impurity atom is 3 µ B as in pure iron,the concentration of impurity Fe atoms is only about130 ppm per Fe atom, which is significantly lower thanthe impurity concentration previously estimated for sin-gle crystal specimens of FeSi [11, 33]. The fitting resultsalso show that, on average, there is only about 2-3 mag-netic impurity atoms in each cluster, indicating atomicsize magnetic clusters.Figure 5 shows ρ ( T ) data for FeSi under external mag-netic field. At high temperatures, the values of ρ arealmost independent of the applied magnetic field; how-ever, a negative magneto-resistivity ( M R ), where
M R = FIG. 5. Electrical resistivity ρ vs. temperature T in magneticfields up to 9 T. The applied field is perpendicular to thecurrent. Shown in the upper inset is ρ vs. H at several anglesbetween the direction of the applied field and the current.Displayed in the lower inset is the temperature dependenceof the magneto-resistance (MR). The definition of the MR isgiven in the lower inset. ( ρ - ρ )/ ρ , can be observed around 70 K as indi-cated by the arrow in the inset of Fig. 5. that becomesvery significant below 30 K, which is very close to thetemperatures T = 67 K and T = 30 K, respectively. Itshould be mentioned that previous studies of the M R arenot consistent: A negative
M R was reported by Paschen et al. below 30 K and attributed to quantum interfer-ence effects [4]; however, a change of sign at around 70K (close to T = 67 K in this study) was reported laterbelow which the M R is positive [14]. In this study, thenegative
M R reaches a minimum value at T = 19 K.The peak in the absolute value of the M R in this studyis about 20%, which is obviously higher than the peakin the absolute value of the
M R reported in Refs. [4]and [14], revealing the dependence of the
M R on sam-ple quality. While ρ ( T ) is very sensitive to the appliedfield at low temperatures, the value of T seems indepen-dent of H , which provides additional evidence that thetransition observed in ρ ( T ) around T is not related tomagnetic order.The evolution of ρ as a function of H at several anglesof H with respect to the long axis of the FeSi crystal at10 K is shown in the upper inset of Fig. 5. The value of ρ is suppressed with increasing field, but the evolution of ρ ( H ) deviates slightly from a linear relation. The anglebetween the directions of the applied field and the current( α ) has only a slight effect on the values of ρ ( H ). How-ever, the negative M R is still very remarkable in the casethat the applied field is parallel to the current (parallelto the surface of the sample), which is inconsistent withthe behavior of topological insulators. This behavior can
FIG. 6. Evolution of the Hall coefficient R H with temperature T . The Hall resistivity ρ H vs. H at 65 and 75 K is shown inthe inset. be qualitatively understood by considering both bulk andsurface electron conduction for FeSi. The negative M R can be observed at temperature T which is far above T ,suggesting that the negative M R is a bulk phenomenon.If we assume that the response of surface resistivity toexternal field is positive due to the additional scatteringof free electrons by the Lorentz force, increasing α willincrease the effective applied field on the sample’s surfaceand thus slightly enhance the M R .The main results of the Hall effect measurements attemperatures down to 30 K are displayed in Fig. 6. Un-like the results of previous reports [4], linear relations ofthe Hall resistivity vs. applied external field can be seenup to 9 T over a wide temperature range above 30 K (seethe inset of Fig. 6). At high temperatures, the Hall coeffi-cient R H is positive and increases slightly with decreasingtemperature, indicating that the dominant charge carri-ers are electrons (which is understandable as the mobilityof electrons in intrinsic semiconductors are usually muchhigher than that of holes). However, a change of sign of R H is observed at ∼
68 K, which is very close to T =67 K and to the temperature of the sign change of the M R . The phenomena observed in the R H ( T ), M R ( T ),and ρ ( T ) measurements are consistent with one another,indicating that there is a electronic phase transition ataround T = 67 K below which the resistivity is dom-inated by hole conduction and is sensitive to externalfield. IV. SUMMARY
In summary, the following conclusions can be drawnfrom this study:(1) The electron transport behavior of FeSi is highlysensitive to sample quality. High quality of the sin-gle crystal samples in this study is supported by X-raydiffraction, specific heat, and magnetization measure-ments.(2) In the temperature range 150-67 K, the semicon-ducting energy gap is 57 meV. Below 67 K, a muchsmaller energy gap and a sign change of magneto-resistance and Hall coefficient are observed.(3) Further decrease of the temperature results in asharp reversible transition from a negative slope to apositive slope of ρ ( T ) at 19 K. Corresponding magnetiza-tion and magneto-resistivity measurements suggest thatthere is no magnetic order associated with this transi-tion. Furthermore, no feature can be observed in specificheat measurements. The results indicate that the metal-lic conduction behavior below T is probably a surfacephenomenon.(4) We should also emphasize that the intrinsic re-sponse of FeSi to an external magnetic field is almostzero below 100 K; however, a significantly large negativemagneto-resistivity which reaches its maximum value at T = 19 K is observed in the resistivity measurements.Considering the possibility that a trivial signal can notbe observed in the MPMS, the contradictory phenom- ena also suggests the existence of a special surface statethat contributes additional electronic conductivity to thesamples.(5) This study cannot provide a clear picture of thesurface state of FeSi and the possibility that FeSi as atopological insulator cannot be ruled out. Further inves-tigations of the electronic states on the surface are neededto explore this possibility. V. ACKNOWLEDGEMENTS
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