Kohler's Scaling Research Articles

Extremely large magnetoresistance and anisotropic transport in the multipolar Kondo system PrTi2Al20

Multipolar Kondo systems offer unprecedented opportunities to design astonishing quantum phases and functionalities beyond spin-only descriptions. A model material platform of this kind is the cubic heavy fermion system PrT2Al20 (T=Ti, V), which hosts a nonmagnetic crystal-electric-field ground state and substantial Kondo entanglement of the local quadrupolar and octopolar moments with the conduction electron sea. Here, we explore the magnetoresistance (MR) and Hall effect of PrTi2Al20, which develops ferroquadrupolar (FQ) order below TQ∼2 K, and compare their behavior with that of the MR and Hall effect of the non-4f analog, LaTi2Al20. In the FQ ordered phase, PrTi2Al20 displays extremely large magnetoresistance (XMR) of ∼103%. The unsaturated, quasilinear field (B) dependence of the XMR violates Kohler's scaling and defies description based on carrier compensation alone. By comparing the MR and the Hall effect observed in PrTi2Al20 and LaTi2Al20, we conclude that the open-orbit topology on the electron-type Fermi surface sheet is key for the observed XMR. The low-temperature MR and the Hall resistivity in PrTi2Al20 display pronounced anisotropy in the [111] and [001] magnetic fields, which is absent in LaTi2Al20, suggesting that the transport anisotropy ties in with the anisotropic magnetic field response of the quadrupolar order parameter. Published by the American Physical Society 2024

Signature of filamentary superconductivity in centrosymmetric silicide LuScSi

Discovery of new superconductors with different crystal structure and exotic physics provides a great prospect for better understanding of superconducting mechanism. In this context, a detailed investigation of the structural, magnetic and electrical transport properties of a new superconducting alloy, LuScSi have been reported. Temperature (T) and magnetic field (H) dependent magnetisation (M) analysis reveals the onset of filamentary superconductivity below TC ∼ 4.2 K, which is among the highest value of TC that has been reported for LuTX (T = transition element, X = p block element) systems. This is corroborated with T and H dependent resistivity (ρ) and heat capacity (C) studies. Interestingly, in normal state, ρ exhibits a non-Fermi liquid behaviour (ρ (T) ∝ T2.38) in the range 5 < T < 50 K and Bloch-Gruneisen–type T dependence for 50 K < T < 250 K. The Kohler scaling is also employed on the magnetoresistance (MR) data indicating a single scattering rate across the Fermi surface in the normal state. Our studies reflect the conventional nature of moderately coupled superconducting state of this alloy.

Violation of Kohler's rule at the charge density wave transition in 1T-TiSe2

The Kohler scaling of magnetoresistance (MR) is examined across the charge-density-wave (CDW) transition of 1T-TiSe2 microflakes. The normalized MR value vs (B/ρ0)2 showed linear dependence, where B is the magnetic field and ρ0 is the resistivity at zero magnetic field. However, all MR-(B/ρ0)2 curves at various temperatures were not coincident with each other, demonstrating the violation of Kohler's rule. The Kohler slope, K = dMR/d[(B/ρ0)2], and the MR value reached a minimum at the CDW transition temperature, TCDW. The nonmonotonous relationship between the Kohler slope and the Hall coefficient was observed, indicating a nonuniform electron scattering rate on the Fermi surface. The MR value satisfied the scaling laws of ∼|T − TCDW|1.35 and ∼|T − TCDW|0.62 below and above TCDW, respectively. Our results highlight magnetotransport properties of the 1T-TiSe2 microflakes in the critical region of the CDW phase transition.

Magnetotransport studies of the Sb square-net compound LaAgSb2 under high pressure and rotating magnetic fields

Square-net-layered materials have attracted attention as an extended research platform of Dirac fermions and of exotic magnetotransport phenomena. In this study, we investigated the magnetotransport properties of $\mathrm{La}\mathrm{Ag}{\mathrm{Sb}}_{2}$, which has Sb-square-net layers and shows charge density wave (CDW) transitions at ambient pressure. The application of pressure suppresses the CDWs, and above a pressure of 3.2 GPa a normal metallic phase with no CDWs is realized. By utilizing a mechanical rotator combined with a high-pressure cell, we observed the angular dependence of the Shubnikov--de Haas (SdH) oscillation up to 3.5 GPa, and we confirmed the notable two-dimensional nature of the Fermi surface. In the normal metallic phase, we also observed a remarkable field-angular-dependent magnetoresistance (MR), which exhibited a ``butterflylike'' polar pattern. To understand these results, we theoretically calculated the Fermi surface and conductivity tensor at the normal metallic phase. We showed that the SdH frequency and Hall coefficient calculated based on the present Fermi surface model agree well with the experiment. The transport properties in the normal metallic phase are mostly dominated by the anisotropic Dirac band, which has the highest conductivity due to linear energy dispersions. We also proposed that momentum-dependent relaxation time plays an important role in the large transverse MR and negative longitudinal MR in the normal metallic phase, which is experimentally supported by the considerable violation of Kohler's scaling rule. Although quantitatively complete reproduction was not achieved, the calculation showed that the elemental features of the butterfly MR could be reasonably explained as the geometrical effect of the Fermi surface.

Chiral anomaly induced negative magnetoresistance and weak anti-localization in Weyl semimetal Bi0.97Sb0.03 alloy

Experimental access to massless Weyl fermions through topological materials promises substantial technological ramifications. Here, we report magneto-transport properties of Bi1−x Sb x alloy near the quantum critical point x = 3% and 3.5%. The two compositions that are synthesized and studied are single crystals of Bi0.97Sb0.03 and Bi0.965Sb0.035. We observe a transition from semimetal to semiconductor with the application of magnetic field in both specimens. An extremely large transverse magnetoresistance (MR) 1.8 × 105% and 8.2 × 104% at 2.5 K and 6 T is observed in Bi0.97Sb0.03 and Bi0.965Sb0.035, respectively. Kohler scaling of transverse MR reveals the crossover from low field quadratic MR to a high field linear MR at low temperatures in both samples. A decrease in longitudinal MR is observed only in Bi0.97Sb0.03 that implies the presence of chiral anomaly associated with the Weyl state at the crossover point (x = 0.03) in Bi1−x Sb x system. The chiral anomaly is absent for the sample Bi0.965Sb0.035. A sharp increase in longitudinal resistivity for Bi0.97Sb0.03 close to zero magnetic fields indicates the weak anti-localization effect in Bi0.97Sb0.03. Extremely high carrier concentrations and high mobilities have been recorded for both the samples.

Magnetoresistance and scaling laws in type-II Weyl semimetal WP2

Topological materials with extremely large magnetoresistance exhibit a prognostic feature of resistivity turn-on behaviour. This occurs when the temperature dependence of resistivity ρ(T) changes from metallic to semiconducting characteristics on application of external magnetic field above a threshold value. Here, we study the magneto-transport properties of type-II Weyl Semimetal WP2. The zero field electrical resistivity in the low temperature region indicates the dominant electron-phonon scattering. The saturation in ρ(T) curves under all applied magnetic fields are observed at low temperatures. A minimum in resistivity at ~40K is revealed in the temperature derivative of resistivity curves, which implies onset of field induced turn-on effect. Furthermore, a non-saturating linear magnetoresistance (MR) is observed above ~ 5 T which is generally assigned to linear energy dispersion near the Weyl nodes. However, Kohler's scaling fits the data well with resistivity ρ~(B/ρ0)m that implicitly explains the turn-on behaviour and the resistivity minimum. Thus, semi-classical theories of magnetoresistance are consistent with our data without the need to invoke topological surface states. Our findings in this work provides an alternative basis to understand the temperature dependence of magnetoresistance in topological materials.

Structural and Magnetotransport Studies of Iron‐Intercalated Bi2Se3 Single Crystals

A detailed investigation on the structural and magnetotransport properties of iron‐intercalated Bi2Se3 single crystals is presented. The X‐ray diffraction and Raman studies confirm the intercalation of Fe in the van der Waals gaps between the layers. The electrical resistivity of the compounds decreases upon intercalation, and Hall resistivity shows the enhancement of the charge carriers upon intercalation. The magnetoresistance (MR) shows the non‐saturating linear behavior at higher magnetic field and low temperature. Intercalation of Fe increases the onset of the linear MR behavior, indicating the reduction in quantum effects. The Kohler scaling used on the MR data indicates single scattering process for all these compounds in the measured temperature range of 3–300 K.

Validity of Kohler's rule for the magneto-resistance in pristine and irradiated NbAs2

The synthesis, characterization and magneto-transport investigations on the single crystals of semimetal NbAs2 in a temperature range varying from 300 K to 2.5 K with a magnetic field up to 14 T are reported. The temperature dependence of resistivity that exhibits a metallic behavior without a magnetic field is seen to show an upturn as the magnetic field is applied resulting in a very large magneto-resistance. The upturn temperature displays a systematic increase with increasing fields. It is shown that this behavior of magneto-resistance can be understood in terms of the Kohler's scaling relation rather than in terms of the existence of a critical magnetic field inducing a metal to insulator transition. Through careful experiments, including angular dependence of magneto-resistance, it is verified that NbAs2 does not show negative longitudinal magneto-resistance, a characteristic of Weyl semimetal.

Fermions and bosons in nonsymmorphic PdSb2 with sixfold degeneracy

PdSb2 is a candidate for hosting 6-fold-degenerate exotic fermions (beyond Dirac and Weyl fermions).The nontrivial band crossing protected by the nonsymmorphic symmetry plays a crucial role in physical properties. We have grown high-quality single crystals of PdSb2 and characterized their physical properties under several stimuli (temperature, magnetic field, and pressure). While it is a diamagnetic Fermi-liquid metal under ambient pressure, PdSb2 exhibits a large magnetoresistance with continuous increase up to 14 T, which follows the Kohler's scaling law at all temperatures. This implies one-band electrical transport, although multiple bands are predicted by first principles calculations. By applying magnetic field along the [111] direction, de Haas-van Alphen oscillations are observed with frequency of 102 T. The effective mass is nearly zero (0.045m0) with the Berry phase close to {\pi}, confirming that the band close to the R point has a nontrivial character. Under quasihydrostatic pressure (p), evidence for superconductivity is observed in the resistivity below the critical temperature Tc. The dome-shaped Tc versus p is obtained with maximum Tc~2.9 K. We argue that the formation of Cooper pairs (bosons) is the consequence of the redistribution of the 6-fold-degenerate fermions under pressure.

Magnetoresistance in LuBi and YBi semimetals due to nearly perfect carrier compensation

Monobismuthides of yttrium and lutetium are shown as new representatives of materials which exhibit extreme magnetoresistance and magnetic-field-induced resistivity plateau. At low temperatures and in magnetic field of 9T the magnetoresistance attains the order of magnitude of 10,000% and 1,000%, on YBi and LuBi, respectively. Our thorough examination of electron transport properties of both compounds show that observed features are the consequence of nearly perfect carrier compensation rather than of possible nontrivial topology of electronic states. The field-induced plateau of electrical resistivity can be explained with Kohler scaling. Anisotropic multi-band model of electronic transport describes very well the magnetic field dependence of electrical resistivity and Hall resistivity. Data obtained from the Shubnikov-de Haas oscillations analysis also confirm that Fermi surface of each compound contains almost equal amounts of holes and electrons. First-principle calculations of electronic band structure are in a very good agreement with the experimental data.

Extremely large magnetoresistance in the topologically trivial semimetal α−WP2

Extremely large magnetoresistance (XMR) was recently discovered in many non-magnetic materials, while its underlying mechanism remains poorly understood due to the complex electronic structure of these materials. Here, we report an investigation of the $\alpha$-phase WP$_2$, a topologically trivial semimetal with monoclinic crystal structure (C2/m), which contrasts to the recently discovered robust type-II Weyl semimetal phase in $\beta$-WP$_2$. We found that $\alpha$-WP$_2$ exhibits almost all the characteristics of XMR materials: the near-quadratic field dependence of MR, a field-induced up-turn in resistivity following by a plateau at low temperature, which can be understood by the compensation effect, and high mobility of carriers confirmed by our Hall effect measurements. It was also found that the normalized MRs under different magnetic fields has the same temperature dependence in $\alpha$-WP$_2$, the Kohler scaling law can describe the MR data in a wide temperature range, and there is no obvious change in the anisotropic parameter $\gamma$ value with temperature. The resistance polar diagram has a peanut shape when field is rotated in $\textit{ac}$ plane, which can be understood by the anisotropy of Fermi surface. These results indicate that both field-induced-gap and temperature-induced Lifshitz transition are not the origin of up-turn in resistivity in the $\alpha$-WP$_2$ semimetal. Our findings establish $\alpha$-WP$_2$ as a new reference material for exploring the XMR phenomena.

Magnetotransport properties and evidence of a topological insulating state in LaSbTe

In this report, we present the magnetotransport and magnetization properties of LaSbTe single crystals. Magnetic field-induced turn-on behavior and low-temperature resistivity plateau have been observed. By adopting both metal-semiconductor crossover and Kohler scaling analysis, we have discussed the possible origin of the temperature and magnetic field dependence of resistivity. At 5 K and 9 T, a large, non-saturating transverse magnetoresistance (MR) $\sim$ 5$\times$10$^{3}$ \% has been obtained. The MR shows considerable anisotropy, when the magnetic field is applied along different crystallographic directions. The non-linear field dependence of the Hall resistivity confirms the presence of two types of charge carriers. From the semiclassical two-band fitting of Hall conductivity and longitudinal conductivity, very high carrier mobilities and almost equal electron and hole densities have been deduced, which result in large MR. The Fermi surface properties have been analyzed from de Haas-van Alphen oscillation. From the magnetization measurement, the signature of non-trivial surface state has been detected, which confirms that LaSbTe is a topological insulator, consistent with the earlier first-principles calculations.

Giant magnetoresistance, three-dimensional Fermi surface and origin of resistivity plateau in YSb semimetal

Very strong magnetoresistance and a resistivity plateau impeding low temperature divergence due to insulating bulk are hallmarks of topological insulators and are also present in topological semimetals where the plateau is induced by magnetic field, when time-reversal symmetry (protecting surface states in topological insulators) is broken. Similar features were observed in a simple rock-salt-structure LaSb, leading to a suggestion of the possible non-trivial topology of 2D states in this compound. We show that its sister compound YSb is also characterized by giant magnetoresistance exceeding one thousand percent and low-temperature plateau of resistivity. We thus performed in-depth analysis of YSb Fermi surface by band calculations, magnetoresistance, and Shubnikov–de Haas effect measurements, which reveals only three-dimensional Fermi sheets. Kohler scaling applied to magnetoresistance data accounts very well for its low-temperature upturn behavior. The field-angle-dependent magnetoresistance demonstrates a 3D-scaling yielding effective mass anisotropy perfectly agreeing with electronic structure and quantum oscillations analysis, thus providing further support for 3D-Fermi surface scenario of magnetotransport, without necessity of invoking topologically non-trivial 2D states. We discuss data implying that analogous field-induced properties of LaSb can also be well understood in the framework of 3D multiband model.

Electron carriers with possible Dirac-cone-like dispersion inFeSe1−xSx(x=0and 0.14) single crystals triggered by structural transition

We report detailed study of the transport properties of FeSe$_{1-x}$S$_x$ ($x$ = 0 and 0.14) single crystals grown by vapor transport method. 14\% S doping is found significantly suppress the structural transition from $T_s$ $\sim$ 86 K in FeSe to $\sim$ 49 K, although the superconducting transition temperature, $T_c$, is only slightly affected. A pronounced linear magnetoresistance (MR) is observed in both FeSe and FeSe$_{0.86}$S$_{0.14}$ single crystals, which is found to be triggered by the structural transition. The linear MR and related discussion indicate the possible existence of Dirac-cone-like state, which may come from the band shift induced by ferro-orbital order. The mobility of the Dirac-cone-like band is found to decrease after S doping. Besides, the invalid Kohler's scaling of MR is found for temperature below $T_s$ in both crystals, however the re-establishment of the Kohler's scaling at temperatures below 30 K is observed in FeSe, but not in FeSe$_{0.86}$S$_{0.14}$. All these observations above support that the orbital ordering causes the band reconstruction in FeSe, and also that the orbital ordering in FeSe is suppressed by the chemical pressure from S doping.

Multiband effects and possible Dirac fermions inFe1+yTe0.6Se0.4

We investigated the transport properties of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ single crystals with different amounts of excess Fe prepared by O$_2$ annealing. The O$_2$ annealing remarkably improves transport properties. In particular, a strongly nonlinear Hall resistivity was observed only in the fully-annealed crystal, and the magnetoresistance (MR) is drastically enhanced after annealing, reaching a value larger than 17% at 16 K and 14 T. The obvious change of transport properties after the annealing indicates that the band structure of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ is affected by the excess Fe. The nonlinear Hall resistivity and violation of (modified) Kohler's scaling of the large MR prove the multiband effects in the Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ single crystal. The MR for the fully-annealed crystal develops linearly against magnetic field from intermediate field (e. g. 2 T at 16 K) to the measurement limit of 14 T. This phenomenon is interpreted by the existence of Dirac cone state, in which all the Dirac fermions occupy only the lowest Landau level in the quantum limit.

Precursor state to superconductivity inCeIrIn5: Unusual scaling of magnetotransport

We present an analysis of the normal-state Hall effect and magnetoresistance in the heavy-fermion superconductor ${\text{CeIrIn}}_{5}$. It is demonstrated that the modified Kohler's scaling---which relates the magnetoresistance to the Hall angle---breaks down prior to the onset of superconductivity due to the presence of a precursor state to superconductivity in this system. A model-independent single-parameter scaling of the Hall angle governed solely by this precursor state is observed. Neither the Hall coefficient nor the resistivity exhibits this scaling, implying that this precursor state preferentially influences the Hall channel.

Hall effect and magnetoresistance in single crystals ofNdFeAsO1−xFx(x=0and 0.18)

Hall effect and magnetoresistance have been measured on single crystals of ${\text{NdFeAsO}}_{1\ensuremath{-}x}{\text{F}}_{x}$ with $x=0$ $({T}_{c}=0\text{ }\text{K})$ and $x=0.18$ $({T}_{c}=50\text{ }\text{K})$. For the undoped samples, strong Hall effect and magnetoresistance with strong temperature dependence were found below about 150 K. The magnetoresistance was found to be as large as 30% at 15 K at a magnetic field of 9 T. From the transport data we found that the transition near 155 K was accomplished in two steps: first one occurs at 155 K which may be associated with the structural transition, the second one takes place at about 140 K which may correspond to the spin-density-wave-like transition. In the superconducting sample with ${T}_{c}=50\text{ }\text{K}$, it is found that the Hall coefficient also reveals a strong temperature dependence with a negative sign. But the magnetoresistance becomes very weak and does not satisfy Kohler's scaling law. These dilemmatic results (strong Hall effect and very weak magnetoresistance) prevent understanding of the normal-state electric conduction by a simple multi-band model by taking into account the electron and hole pockets. Detailed analysis further indicates that the strong temperature dependence of ${R}_{H}$ cannot be easily understood with the simple multi-band model either. A picture concerning a suppression to the density of states at the Fermi energy in lowering temperature is more reasonable. A comparison between the Hall coefficient of the undoped sample and the superconducting sample suggests that the doping may remove the nesting condition for the formation of the spin-density wave order, since both samples have very similar temperature dependence above 175 K.

Magnetotransport and superconductivity of α-uranium

We have measured the electrical resistivity, magnetoresistance and Hall effect on several new single-crystal samples and one polycrystalline sample of α-U. The residual resistivity ratios of these samples vary from 13 to 315. Matthiessen's law appears to hold above the onset of the charge-density wave phase transitions that begin near 43 K, but not below this temperature. Sharp features at all three charge-density wave transitions are observed and the effects of high magnetic fields on them are presented and discussed. The magnetoresistance is anisotropic, reaches 1000% at 2 K and 18 T and does not exhibit Kohler scaling. The Hall coefficient is positive, independent of magnetic field and slightly temperature dependent above about 40 K in agreement with earlier studies. Below 40 K the Hall coefficient changes sign as the temperature falls, varies with field and becomes much more strongly negative at the lowest temperatures than has been reported. Some of our results suggest that a spin-density wave may coexist with the charge-density wave states. Superconductivity is observed in two of our samples; we argue that it is intrinsic to α-U and suggest that it is consistent with a two-band model. Several parameters characterizing the transport and superconductivity of α-U are estimated.

Angular dependence of the magnetoresistance of TiSi 2 single crystals

We measured the transverse magnetoresistance Δϱ ϱ of good quality TiSi 2 single crystals at low temperatures (4.2≤ T≤112 K) in magnetic fields up to 7.8 Tesla. Single crystals were produced by a modified Czochralski pulling technique and they have low residual resistivity (typically ϱ(4.2 K) = 0.15 μΩ· cm ) and high residual resistance ratio (typically RRR > 50). The angular dependence of magnetoresistance shows either minima or maxima when the magnetic field is parallel to the principal crystallographic axes. At high fields ( B > 1 T). we found that the magnetoresistance has a magnetic field dependence weaker than the B 2 law expected for compensated metals. At 7.8 T, the values of ω c τ obtained are of the order of unity. The Kohler scaling rule is observed within three orders of magnitude of the reduced parameter B ϱ (where ϱ is the zero field resistivity measured between 4.2 and 112 K).