Reader TTS

ABSTRACT Lifshitz transition (LT) refers to an abrupt change in the electronic structure and Fermi surface and is associated to a variety of emergent quantum phenomena. Amongst the LTs

observed in known materials, the field-induced LT has been rare and its origin remains elusive. To understand the origin of field-induced LT, it is important to extend the material basis

beyond the usual setting of heavy fermion metals. Here, we report on a field-induced LT in PrAlSi, a magnetic Weyl semimetal candidate with localized 4_f_ electrons, through a study of

magnetotransport up to 55 T. The quantum oscillation analysis reveals that across a threshold field _B_* ≈ 14.5 T the oscillation frequency (_F_1 = 43 T) is replaced by two new frequencies

(_F_2 = 62 T and _F_3 = 103 T). Strikingly, the LT occurs well below the quantum limit, with obvious temperature-dependent oscillation frequency and field-dependent cyclotron mass. Our work

not only enriches the rare examples of field-induced LTs but also paves the way for further investigation of the interplay among topology, magnetism, and electronic correlation. SIMILAR

CONTENT BEING VIEWED BY OTHERS SIGNATURES OF A MAGNETIC-FIELD-INDUCED LIFSHITZ TRANSITION IN THE ULTRA-QUANTUM LIMIT OF THE TOPOLOGICAL SEMIMETAL ZRTE5 Article Open access 01 December 2022

THE DISCOVERY OF THREE-DIMENSIONAL VAN HOVE SINGULARITY Article Open access 14 March 2024 ABNORMALLY ENHANCED HALL LORENZ NUMBER IN THE MAGNETIC WEYL SEMIMETAL NDALSI Article Open access 26

November 2024 INTRODUCTION The Lifshitz transition (LT) has received renewed attention in condensed matter physics. An LT1 is an electronic topological transition of the Fermi surface (FS)

driven by the variation of the band structure and/or the Fermi energy. Since such a transition does not necessarily require simultaneous symmetry breaking, and meanwhile, it can occur at _T_

 = 0, and be tuned by parameters other than temperature (such as pressure, strain, doping, magnetic field, etc.)1,2, it, therefore, can be deemed as a topological quantum phase transition.

In the vicinity of Lifshitz transitions, many peculiar emergent phenomena may appear, such as van-Hove singularity, non-Fermi-liquid behavior, unconventional superconductivity, and so on

(e.g. refs. 3,4). Compared with a number of cases tuned by doping or pressure that have been widely seen in topological systems5,6, cuprate superconductors7,8, iron pnictides

superconductors9,10, and other strongly correlated materials3,11, the examples of LT driven by a magnetic field are rare. This is because the energy scale of a laboratory magnetic field, in

the order of 1–10 meV, is much smaller than the characteristic energy scale of most metals (~102−103 meV). Only in a few cases, mostly limited in heavy-fermion (HF)

metals12,13,14,15,16,17,18,19,20, the hybridization between conduction electrons and localized _f_ electrons leads to narrow renormalized bands with a small Fermi energy and thus the Zeeman

term can be sufficiently strong to shift the spin-split FS15. Recently, field-induced LTs were also observed in some low Fermi energy non-magnetic semimetals, such as bismuth21, TaP22, and

TaAs23, wherein magnetic field beyond the quantum limit can empty a Dirac or Weyl pocket with small Fermi energy. However, in these cases, no additional Fermi pocket emerges and the carriers

of the empty pocket were transferred to other pockets (previously existing). Here we present a new example of field-induced LT beyond heavy-fermion systems in the magnetic Weyl semimetal

candidate PrAlSi, by a systematic study of quantum oscillation (QO) effect with the magnetic field extending up to 55 T. We observe a single frequency (_F_1 = 43 T) below a critical field of

_B_* = 14.5 T, in agreement with what was previously reported24. Above _B_*, we see clearly the emergence of two new frequencies (_F_2 = 62 T and _F_3 = 103 T) and the disappearance of the

original _F_1. We exclude the possibility of magnetic breakdown and identify _B_* as a critical point where the field-induced LT occurs. By comparing the reported Fermi surface of NdAlSi and

the theoretical calculation of PrAlSi, we conclude that the LT occurs in the hole-like Weyl pockets along the direction of Γ−X of the Brillouin zone (BZ, hereafter). Our work not only

enriches the rare examples of field-induced LTs but also paves the way for further investigation on the interplay among topology, magnetism, and electronic correlation. The _R_Al_X_ family

(_R_ = rare earth and _X_ = Si or Ge) compounds have recently been proposed to host ideal candidates of magnetic Weyl semimetals25,26, and provide a platform to investigate the interaction

between magnetism and Weyl physics27,28,29,30,31. They crystallize in a tetragonal structure with the noncentrosymmetric space group symmetry of I41/md (No. 109). One advantage of this

family is that Weyl nodes generated by inversion breaking are robust and can be shifted by the Zeeman coupling in the _k_ space25. Several intriguing physical properties have been observed

in this family. The list includes the coexistence of type-I and type-II Weyl fermion in LaAlSi32 and LaAlGe33, topological Hall effect in CeAlGe34, anisotropic anomalous Hall effect in

CeAlSi35, and Weyl-driven collective magnetism in NdAlSi36. The compound PrAlSi studied here is a ferromagnetic semimetal with Curie temperature _T_C ~ 18 K. A recent work based on static

field (9 T) transport measurements by Lyu et al. revealed a large anomalous Hall conductivity ~2000 Ω−1 cm−1 and an unusual temperature dependence of QO with a single frequency24. RESULTS

EXPERIMENTAL RESULTS AND ANALYSIS High-quality single crystals of PrAlSi were synthesized using the flux method. The inset of Fig. 1a shows the crystal structure of PrAlSi with the magnetic

moments of Pr easily orientated along the _c_-axis after the application of a small field24. In our transport measurements, the magnetic field was along the _c_-axis and the electrical

current was along the _b_-axis (more details are presented in the “Methods” section and Supplemental Material). Figure 1a shows magnetoresistance measured in the static field at 2 K (red

curve) and pulsed field at 1.8 K (black curve). Normalized magnetoresistance (_ρ_(_B_)−_ρ_(0))/_ρ_(0) reaches 116 at 55 T and remains non-saturating. The purple dashed line corresponds to

_B_1.7. Figure 1b presents the oscillatory part of the longitudinal resistivity Δ_ρ_(_B_), obtained by subtracting a smooth background from the measured _ρ_(_B_) (see Supplementary Fig. 2

for more raw data). At low temperatures, oscillations are visible above the field as low as 3 T, indicating the good quality of the sample. The rough Dingle mobility of 1/_B_c = 0.33 T−1 is

close to the average mobility of 0.26 m2/V s yielded from the amplitude of the quadratic low-field magnetoresistance (see the inset of Supplementary Fig. 2a). The single-frequency QO for

static field measurements retains until temperature down to 80 mK. A more complex pattern emerges when the larger magnetic field is applied, as seen in Fig. 1c. Figure 2a and b show the

results of the fast Fourier transformation (FFT) of the oscillatory part of the magnetoresistance Δ_ρ_ as a function of 1/_B_. The SdH frequencies extracted from low-field (_B_ < 14.5 T)

and high-field (_B_ > 14.5 T) data display a dramatic difference. Note that, since this compound is ferromagnetic, we took into the demagnetization factor to correct the applied field in

all the analyses of SdH effect (see Section 9 of the Supplemental Material). We identified _B_* = 14.5 T as a critical field, after checking several fields close to _B_*. As shown in

Supplementary Fig. 3, we have intercepted a field with different values, 10, 14, 14.5, 15, and 20 T for the segmented FFT analyses. We can see the crossover from the lower QO frequency to

the two higher QO frequencies as the segment changes between the 5.7 T and the selected field. Two higher QO peaks emerge when we segment the field at 20 T and we note that the low QO peaks

persist because of the inclusion of the low-field QOs below 14.5 T. From the comparison of the segmented FFT analyses, 14.5 T was determined as the field of the LT. There is only one

fundamental frequency in the FFT spectrum until down to 80 mK below _B_* (see Fig. 2a). It should be noted that _F_1 gradually decreases with temperature, changing from 43 T at 80 mK to 32 T

at 35 K, as shown in the inset. Similar temperature dependence in _F_1 was also reported in earlier work on PrAlSi24, whereas the values of _F_1 are relatively smaller than ours. We

attribute this discrepancy to the difference in stoichiometry19. Figure 2b shows that above _B_* there are two new QO frequencies (_F_2 = 62 T, _F_3 = 103 T) and their high-order harmonics.

Such a change in the Fermi surface is also manifested in the effective cyclotron mass _m_*. The value of _m_* for each frequency can be deduced from the fitting of FFT amplitude according to

the temperature damping factor, and this yields the small _m_* = 0.08_m_e for _F_1 (with field range 5.7–14.5 T), and 0.23_m_e and 0.28_m_e for _F_2 and _F_3, respectively, where _m_e is

the mass of a free electron. Interestingly, a careful look into the temperature dependence of the amplitude of the oscillatory peak leads to the fact that the effective mass is enhanced

2-fold between 2.8 T and _B_*, as shown in Fig. 2c. This feature is reminiscent of HF systems displaying an LT and will be discussed more later on. The effective masses of _F_2 and _F_3 as

the function of a field higher than _B_* are absent here, mainly because it is rather difficult to extract the exact amplitude of entangled peaks in the oscillatory part from two frequencies

and their harmonic terms. More explanation about the effective mass mentioned above is exhibited in Supplementary Fig. 5. The Fermi energy of the band corresponding to _F_1 is then

estimated _ε_F ~ 125 meV. To further demonstrate the field-induced Fermi surface change near _B_* = 14.5 T, we performed Lifshitz–Kosevich (LK) fitting on Δ_ρ_(_B_) measured under the pulsed

field. We notice that all the analyzed FFT data are from the pulsed fields. More details can be found in Section 4 of the Supplementary Material. As is shown in Fig. 3a, the Δ_ρ_ for the

field below _B_* can be well reproduced by the LK fitting with a single _F_1 (cf. the red dot line). However, such a fitting collapse when the field exceeds _B_*. This problem can be fixed

in an alternate fitting by employing both _F_2 and _F_3, seeing the blue dot line in Fig. 3b. Noteworthy that this 2-frequency LK fitting fails in the low-field window, implying that _F_2

and _F_3 appear only in the high-field range. Thus, the variation of QO frequencies with the disappearance of 43 T and the emergence of 62 and 103 T clearly point to the change in Fermi

surface topology, viz an LT. Firstly, we can rule out magnetic breakdown as the origin, because there is no extra QO frequency (19 T and 60 T) in the low-field range even for temperature as

low as 80 mK. Moreover, the peak with the frequency of 43 T does not persist under a high magnetic field, either. Secondly, we can also exclude a metamagnetic transition as the driver of

this process. Figure 4a shows the field dependence of magnetization at 2 K with the magnetic field applied along the _c_-axis. One clearly finds that the magnetization saturates to

~3.1_μ_B/Pr at a small field 0.48 T, and no additional transition can be resolved nearby 14.5 T except for some traces of de Haas–van Alphen oscillations (inset of Fig. 4a). This is

different from the case of NdAlSi, where a magnetic transition to the final Weyl-mediated helical magnetism leads to a change in QO frequency36. In order to further clarify this

field-induced LT, it is helpful to estimate the density of carriers of each Fermi pocket. According to the Lifshitz–Onsager relation, _F_ = (ℏ/2_π__e_)_A_F, where ℏ is Planck’s constant and

\({A}_{{\rm {F}}}=\pi {k}_{{\rm {F}}}^{2}\) is an extremal cross-sectional area of the Fermi surface perpendicular to the field with Fermi wave vector _k_F. The bands become non-degenerate

due to spin–orbit coupling36. Assuming these Fermi pockets are spheres, we find that the LT wipes out \({n}_{{{\rm {F}}}_{1}}\)= 3.2 × 1018 cm−3 and produces \({n}_{{{\rm {F}}}_{2}}\)= 5.5 ×

 1018 cm−3 and \({n}_{{{\rm {F}}}_{3}}\)= 1.2 × 1019 cm−3 per four pockets. Note that the total number of pockets would be a multiple of 4, due to the symmetric requirement (see below). The

total carrier density of the hole and electron can be also extracted by fitting the Hall resistivity with the two-band model, $${\rho }_{xy}(B)=\frac{B}{{{{\rm{e}}}}}\frac{({n}_{h}{\mu

}_{h}^{2}-{n}_{e}{\mu }_{e}^{2})+{\mu }_{h}^{2}{\mu }_{e}^{2}({n}_{h}-{n}_{e}){B}^{2}}{{({n}_{h}{\mu }_{h}+{n}_{e}{\mu }_{e})}^{2}+{\mu }_{h}^{2}{\mu

}_{e}^{2}{({n}_{h}-{n}_{e})}^{2}{B}^{2}}.$$ (1) Here, _n_ and _μ_ represent carrier density and mobility, and the subscripts h and e denote hole and electron, respectively. We obtain _n_h = 

4.3 × 1019 cm−3, _n_e = 5.3 × 1019 cm−3, _μ_h = 0.18 m2/V s and _μ_e = 0.22 m2/V s. These values fit both Hall resistivity and magnetoresistivity reasonably well up to _B_* (see Fig. 4c and

Supplementary Fig. 7). The deduced mobilities are also close to the value obtained from quantum oscillations and magnetoresistance. The average zero-field mobility 〈_μ_〉 extracted from the

residual resistivity _ρ_0 = 15 μΩ cm is about 0.5 m2/V s, slightly larger than the finite-field mobility. Such a discrepancy has been observed in other semimetals37,38 and attributed to the

field-induced mobility reduction. The carrier densities of hole and electron are within 10% of the compensation 2[_n_e_n_h/(_n_e + _n_h)], compared to ~4% in bismuth39 and WTe240. This near

compensation would explain the observed unsaturated magnetoresistance. The slight excess in the hole may result from uncontrollable doping which could be also the reason for the sample

dependence of _F_1 as discussed above. This fit, which properly works up to _B_* (shown by a black arrow in Fig. 4c), fails above _B_*. The change occurring at _B_* is evident in Fig. 4b,

which shows the first derivative of the longitudinal and Hall resistivities. The violet dotted lines demonstrate the apparent change of slope in MR and Hall resistivities at 14.5 T. We let

∣_n_h−_n_e∣ to stay constant across _B_*, in order to respect the Luttinger theorem41. We infer that _F_2 and _F_3 should correspond to carriers of opposite signs with a density difference

of \(| {n}_{{{F}}_{3}}-{n}_{{{F}}_{2}}| =6.5\times 1{0}^{18}\) cm−3. Assuming that there are 8 pockets for _F_1 (\(2{n}_{{F}_{1}}\)= 6.4 × 1018 cm−3), would be compatible with the Luttinger

theorem. Both types of carriers increase by about 0.6 × 1019 cm−3 (\({n}_{{F}_{3}}-2{n}_{{F}_{1}}\) and \({n}_{{F}_{2}}\), respectively). By fitting the Hall resistivity curve with _n_h = 

4.9 × 1019 cm−3 and _n_e = 5.9 × 1019 cm−3, we obtain _μ_h = 0.05(1) m2/V s and _μ_e = 0.16(1) m2/V s. This is shown in Fig. 4c with a blue line. The mobility (\(\mu =\frac{e\tau }{{m}^{*

}}\)) of holes drop (~72%) more than that of electron (~27%), implying the sign of _F_1 with a small mass should be hole-like, since its mass increases by 2.5 times by assuming the same

scattering time _τ_. We conclude that _F_2 has an electron-like sign and _F_3 is a hole-like one. Thus, each hole pocket (_F_1) evolves into a larger hole pocket (_F_3) and an additional

electron pocket (_F_2). This indicates the existence of a van-Hove singularity (saddle point) in this system. To get more information about the Fermi surface of PrAlSi, we performed the

measurements of angular-dependent MR with a pulsed magnetic field at _T_ = 1.8 K. Figure 5a shows the oscillatory component extracted by subtracting the smooth background from the MR

measured at different _θ_, which is defined as the angle between the _c_-axis and the magnetic field, and the current was along _b_-axis as shown in the inset (see the Supplementary Fig. 10

for the raw MR data). The SdH oscillations evolve systematically and can be observed in all angles as the magnetic field is rotated from _θ_ = 0° to _θ_ = 87°. Figure 5b and c present the

segmented FFT spectra for different angles _θ_. The inset of Fig. 5b shows the critical fields at various angles, which indicates that the LT also envolves with _θ_. We determined the _B_*

as the same method mentioned above and the detail is shown in Supplementary Fig. 4. The oscillation frequency _F_1 shown in Fig. 5b is weakly dependent on the angle, indeed indicating a

nearly spherical Fermi surface of this band and the evolution of angle-dependent oscillation frequencies _F_2, _F_3 and their harmonic terms shown in Fig. 5c. According to the experimental

results, Fig. 5d presents the angle dependence of the quantum oscillation _F_1 which is shown as black symbols as well as _F__α_, _F__β_, _F__γ_ and _F__η_ are the calculated frequencies

obtained from the SKEAF program42. The Fermi level was shifted with 3 meV in the calculation because of the uncertain doping. The _F__α_ is quite close to the observed _F_1. Whereas the

higher frequencies obtained from the calculation are not been observed by experiment in our case, may be due to the low mobility of these bands. Next, we tried to locate these pockets in the

BZ, and our similar calculation results (see Supplementary Fig. 11). The electronic structure also resembles that of NdAlSi36. Since the center of the BZ is not occupied, symmetry imposes

four-fold degeneracy of each pocket. According to the calculation, the schematic of the positions of pockets _F_1, which are represented by orange spheres along the Γ−X direction of the BZ

in Fig. 5e. The pockets along Γ−S are large and cannot be easily modified, hence for clarity they are not shown here and the Fermi pockets are plotted in Supplementary Fig. 9. Instead, the

bands along Γ−X are shallow and host Weyl points and they should be susceptible to the magnetic field. The new _F_2 and _F_3 pockets appear after the disappearance of _F_1. So it is a

reasonable assumption that they locate on the Γ−X line as well where the pockets _F_1 lie on, as shown in Fig. 5f. Indeed, some Weyl signatures were observed for the pockets _F_1. All the

values extracted from the peak and valley positions of SdH oscillation fall on a line with an intercept of ~−0.01 in the Landau fan diagram, indicating a non-trivial _π_ phase (see

Supplementary Fig. 6b). Its cyclotron mass is a very small and changes with a magnetic field. Note that a normal parabolic band (\(E=\frac{\hslash {A}_{{\rm {F}}}}{2\pi m}\)) would not

change its cyclotron mass (\({m}_{{\rm {CR}}}=\frac{{\hslash }^{2}}{2\pi }\frac{\partial {A}_{{\rm {F}}}(E,{k}_{\parallel })}{\partial E}\))43 as the Fermi energy changes. The increasing of

the effective mass may imply the increase of spin fluctuation of the pockets with LT transition, similar to the early report14 instead of the response from a normal parabolic band. In order

to better understand the Weyl nature of the Fermi pockets, it is indispensable for confirming the Weyl points along the direction of Γ−X line of the BZ. As shown in Fig. 5e, we obtained two

pairs of Weyl points along the Γ−X line by band structure calculation of selected paths of the BZ and the details are listed in the table of Supplementary Fig. 11. The results agree with the

prior work on Weyl points and Fermi surface of PrAlSi44. DISCUSSION Take together, three prominent features of the LT in PrAlSi can be found: (i) the QO frequencies are strongly temperature

dependent, (ii) the quasiparticle effective mass increases gradually when approaching _B_*, and (iii) the critical field for such LT is far below the quantum limit. In conventional metals,

only a small change in QO frequency of the order of (_k_B_T_/_E_F)2 is expected upon warming45. Temperature-dependent QO frequency was observed in some HF metals, which is typically ascribed

to the sensitivity of the _f_–_c_ (_c_-conduction electrons) hybridization and the corresponding Kondo resonance state with a variation of temperature12,13,46. In this framework, the change

of _m_* was also attributed to an itinerant-localized transition of 4_f_ electrons14. However, in PrAlSi, DFT calculations manifested that the Pr-4_f_ bands locate well below the Fermi

level (see Supplementary Fig. 8), notable _f_–_c_ hybridization is unlikely. Furthermore, PrAlSi is a low-carrier density semimetal, the Kondo screening is also expected to be weak according

to Nozières exhaustion idea47,48. Therefore, it is unlikely that the observed LT in PrAlSi originates from a competition between the Zeeman term and a characteristic Kondo coherence energy

as in HF systems. In the cases of bismuth21, TaP22, and TaAs23, the quantum limits have been reached to empty a Dirac or Weyl pocket and caused a field-induced LT. In our case, however, a

rough estimate yields the quantum limit field in the range of 40–100 T, much larger than the critical field _B_* ~ 14.5 T. Another possibility for the observed LT in PrAlSi might be related

to the crystal-electric-field (CEF) effect. This arises because the nine-fold-degenerate _j_ = 4 multiplet of Pr3+ in a _D_2_d_ (\(\bar{4}\)2m) point symmetry CEF splits into two non-Kramers

doublets and five singlets49. A recent analysis based on specific heat measurements revealed that the ground state is probably a doublet, while the magnetic entropy gain reaches \(R\ln 3\)

at about 20 K, \(R\ln 4\) at about 30 K, and saturates to \(R\ln 9\) at a temperature as low as ~95 K24. This suggests that at least one excited state sitting not far above the ground

doublet, potentially in the order of 10 K. It is reasonable to speculate that a magnetic field of ~ 10 T might be sufficient to modify the CEF energy levels and the orbital characters, which

possibly changes the Fermi surface topology. In addition, this field-induced evolution of CEF levels is also qualitatively consistent with the temperature-dependent QO frequency and

field-dependent _m_* as observed experimentally. Actually, this scenario was also proposed recently for the field-induced Fermi surface reconstruction in CeRhIn550. To further address this

possibility, more experiments like inelastic neutron scattering are needed to figure out the diagram of the CEF splitting. In summary, we grew high-quality single crystals and observed

pronounced SdH oscillations in PrAlSi with a magnetic field up to 55 T. A LT transition occurs around 14.5 T. The change in carrier densities and Fermi pockets revealed by QO and the Hall

effect are consistent with each other. By comparison with theoretical calculations, we propose that LT occurs along the Γ–X orientation and involves the Weyl pockets. One hole pocket becomes

an electron pocket and a hole pocket, which indicates the existence of a van-Hove singularity. PrAlSi, therefore, represents a unique case of field-induced LT beyond the HF systems. METHODS

SAMPLE GROWTH AND CHARACTERIZATIONS Single crystals of PrAlSi used in our studies were synthesized using the flux method. The starting materials are high-purity chunks of praseodymium,

silicon, and aluminum, mixed into an alumina crucible. Then, the alumina crucible and quartz wool were placed in a quartz tube, which was sealed under a high vacuum, and heated to 1100 °C at

3 °C/min. And holding for 12 h and then the tube was cooled down to 750 °C in 100 h and dwelt for 2 days. The excess Al flux was removed by centrifuging. Powder and single crystal x-ray

diffraction (XRD) have been used to obtain the XRD pattern and confirm the structure and the orientation. The atomic proportion was determined by energy-dispersive x-ray spectroscopy (EDS).

MEASUREMENTS The low-field magnetic transport measurements were performed on an Integra AC (Oxford Instruments) with a 16 T superconducting magnet and a Leiden dilution refrigerator with a

14 T superconducting magnet. Temperature- and field-dependent resistivity measurements were made in the standard four-probe method with a pair of the current source (Keithley 6221) and

DC-Nanovoltmeter (Keithley 2182A). The high-field magnetic transport measurements were carried out under a pulsed magnetic field at Wuhan National High Magnetic Field Center (WHMFC). Golden

wires were attached using silver paste on the rectangular sample and every contact resistance was maintained to be <2 Ω in the measurements. ACKNOWLEDGEMENTS We thank Kamran Behina for

insightful discussions. This work is supported by the National Key Research and Development Program of China (Grant No. 2022YFA1403503), the National Science Foundation of China (Grant Nos.

12004123, 51861135104, and 11574097), the Fundamental Research Funds for the Central Universities (Grant no. 2019kfyXMBZ071), the open research fund of Songshan Lake Materials Laboratory

(2022SLABFN27) and National Key R&D Program of China (2022YFA1602602). DATA AVAILABILITY The data supporting the present work are available from the corresponding authors upon request.

REFERENCES * Lifshitz, I. Anomalies of electron characteristics of a metal in the high pressure region. _Sov. Phys. JETP_ 11, 1130–1135 (1960). Google Scholar  * Varlamov, A. A., Galperin,

Y. M., Sharapov, S. G. & Yerin, Y. Concise guide for electronic topological transitions. _Low Temp. Phys._ 47, 672–683 (2021). Article  ADS  Google Scholar  * Steppke, A. et al. Strong

peak in _T_c of Sr2RuO4 under uniaxial pressure. _Science_ 355, 145 (2017). Article  Google Scholar  * Luo, Y. et al. Normal State 17O NMR Studies of Sr2RuO4 under Uniaxial Stress. _Phys.

Rev. X_ 9, 021044 (2019). Google Scholar  * Yang, H. F. et al. Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs. _Nat. Commun._ 10, 3478 (2019). Article 

ADS  Google Scholar  * Liu, Y. et al. Bond-breaking induced Lifshitz transition in robust Dirac semimetal VAl3. _Proc. Natl Acad. Sci. USA_ 117, 15517 (2020). Article  ADS  Google Scholar  *

Benhabib, S. et al. Collapse of the normal-state pseudogap at a Lifshitz transition in the Bi2Sr2CaCu2O8+_δ_ cuprate superconductor. _Phys. Rev. Lett._ 114, 147001 (2015). Article  ADS 

Google Scholar  * Norman, M. R., Lin, J. & Millis, A. J. Lifshitz transition in underdoped cuprates. _Phys. Rev. B_ 81, 180513 (2010). Article  ADS  Google Scholar  * Ren, M. et al.

Superconductivity across Lifshitz transition and anomalous insulating state in surface K-dosed (Li0.8Fe0.2OH)FeSe. _Sci. Adv._ 3, e1603238 (2017). Article  ADS  Google Scholar  * Liu, C. et

al. Evidence for a Lifshitz transition in electron-doped iron arsenic superconductors at the onset of superconductivity. _Nat. Phys._ 6, 419–423 (2010). Article  Google Scholar  * Kwon, J.

et al. Lifshitz-transition-driven metal-insulator transition in moderately spin–orbit-coupled Sr2−_x_La_x_RhO4. _Phys. Rev. Lett._ 123, 106401 (2019). Article  ADS  Google Scholar  *

Kozlova, N. et al. Magnetic-field-induced band-structure change in CeBiPt. _Phys. Rev. Lett._ 95, 086403 (2005). Article  ADS  Google Scholar  * Aoki, D. et al. Field-induced Lifshitz

transition without metamagnetism in CeIrIn5. _Phys. Rev. Lett._ 116, 037202 (2016). Article  ADS  Google Scholar  * Aoki, H., Uji, S., Albessard, A. K. & Ōnuki, Y. Transition of f

electron nature from itinerant to localized: Metamagnetic transition in CeRu2Si2 studied via the de Haas–van Alphen effect. _Phys. Rev. Lett._ 71, 2110–2113 (1993). Article  ADS  Google

Scholar  * Bastien, G. et al. Lifshitz transitions in the ferromagnetic superconductor UCoGe. _Phys. Rev. Lett._ 117, 206401 (2016). Article  ADS  Google Scholar  * Yelland, E. A.,

Barraclough, J. M., Wang, W., Kamenev, K. V. & Huxley, A. D. High-field superconductivity at an electronic topological transition in URhGe. _Nat. Phys._ 7, 890–894 (2011). Article 

Google Scholar  * Niu, Q. et al. Fermi-surface instability in the heavy-fermion superconductor UTe2. _Phys. Rev. Lett._ 124, 086601 (2020). Article  ADS  Google Scholar  * Pfau, H. et al.

Interplay between Kondo suppression and Lifshitz transitions in YbRh2Si2 at high magnetic fields. _Phys. Rev. Lett._ 110, 256403 (2013). Article  ADS  Google Scholar  * Pfau, H. et al.

Cascade of magnetic-field-induced Lifshitz transitions in the ferromagnetic Kondo lattice material YbNi4P2. _Phys. Rev. Lett._ 119, 126402 (2017). Article  ADS  Google Scholar  * Gourgout,

A. et al. Collapse of ferromagnetism and Fermi surface instability near reentrant superconductivity of URhGe. _Phys. Rev. Lett._ 117, 046401 (2016). Article  ADS  Google Scholar  * Zhu, Z.

et al. Emptying Dirac valleys in bismuth using high magnetic fields. _Nat. Commun._ 8, 15297 (2017). Article  ADS  Google Scholar  * Zhang, C.-L. et al. Magnetic-tunnelling-induced Weyl node

annihilation in TaP. _Nat. Phys._ 13, 979–986 (2017). Article  Google Scholar  * Ramshaw, B. J. et al. Quantum limit transport and destruction of the Weyl nodes in TaAs. _Nat. Commun._ 9,

2217 (2018). Article  ADS  Google Scholar  * Lyu, M. et al. Nonsaturating magnetoresistance, anomalous Hall effect, and magnetic quantum oscillations in the ferromagnetic semimetal PrAlSi.

_Phys. Rev. B_ 102, 085143 (2020). Article  ADS  Google Scholar  * Chang, G. et al. Magnetic and noncentrosymmetric Weyl fermion semimetals in the _R_AlGe family of compounds (R = rare

earth). _Phys. Rev. B_ 97, 041104 (2018). Article  ADS  Google Scholar  * Puphal, P. et al. Bulk single-crystal growth of the theoretically predicted magnetic Weyl semimetals RAlGe (R = Pr,

Ce). _Phys. Rev. Mater._ 3, 024204 (2019). Article  Google Scholar  * Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room

temperature. _Nature_ 527, 212–215 (2015). Article  ADS  Google Scholar  * Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. _Nat. Mater._ 16, 1090–1095 (2017).

Article  ADS  Google Scholar  * Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. _Nat. Phys._ 14, 1125–1131 (2018). Article  Google Scholar  * Morali,

N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. _Science_ 365, 1286–1291 (2019). Article  ADS  Google Scholar  * Sakai, A. et al. Giant

anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. _Nat. Phys._ 14, 1119–1124 (2018). Article  Google Scholar  * Su, H. et al. Multiple Weyl fermions in the

noncentrosymmetric semimetal LaAlSi. _Phys. Rev. B_ 103, 165128 (2021). Article  ADS  Google Scholar  * Xu, S.-Y. et al. Discovery of Lorentz-violating type II Weyl fermions in LaAlGe. _Sci.

Adv._ 3, e1603266 (2017). Article  ADS  Google Scholar  * Puphal, P. et al. Topological magnetic phase in the candidate Weyl semimetal CeAlGe. _Phys. Rev. Lett._ 124, 017202 (2020). Article

  ADS  Google Scholar  * Yang, H.-Y. et al. Noncollinear ferromagnetic Weyl semimetal with anisotropic anomalous Hall effect. _Phys. Rev. B_ 103, 115143 (2021). Article  ADS  Google Scholar

  * Gaudet, J. et al. Weyl-mediated helical magnetism in NdAlSi. _Nat. Mater._ 20, 1650–1656 (2021). Article  ADS  Google Scholar  * Ding, L. et al. Intrinsic anomalous Nernst effect

amplified by disorder in a half-metallic semimetal. _Phys. Rev. X_ 9, 041061 (2019). Google Scholar  * Fauqué, B. et al. Magnetoresistance of semimetals: the case of antimony. _Phys. Rev.

Mater._ 2, 114201 (2018). Article  Google Scholar  * Bhargava, R. N. de Haas–van Alphen and galvanomagnetic effect in Bi and Bi–Pb alloys. _Phys. Rev._ 156, 785–797 (1967). Article  ADS 

Google Scholar  * Zhu, Z. et al. Quantum oscillations, thermoelectric coefficients, and the fermi surface of semimetallic WTe2. _Phys. Rev. Lett._ 114, 176601 (2015). Article  ADS  Google

Scholar  * Luttinger, J. M. Fermi surface and some simple equilibrium properties of a system of interacting fermions. _Phys. Rev._ 119, 1153–1163 (1960). Article  ADS  MathSciNet  MATH 

Google Scholar  * Julian, S. Numerical extraction of de Haas–van Alphen frequencies from calculated band energies. _Comput. Phys. Commun._ 183, 324–332 (2012). Article  ADS  Google Scholar 

* Singleton, J. _Band Theory and Electronic Properties of Solids_, Vol. 2 (Oxford University Press, 2001). * Yang, H.-Y. et al. Transition from intrinsic to extrinsic anomalous Hall effect

in the ferromagnetic Weyl semimetal PrAlGe1−_x_Si_x_. _APL Mater._ 8, 011111 (2020). Article  ADS  Google Scholar  * Shoenberg, D. _Magnetic Oscillations in Metals_ (Cambridge University

Press, 2009). * Goll, G. et al. Temperature-dependent fermi surface in CeBiPt. _EPL (Europhys. Lett.)_ 57, 233 (2002). Article  ADS  Google Scholar  * Nozières, P. Some comments on Kondo

lattices and the Mott transition. _Eur. Phys. J. B_ 6, 447–457 (1998). Article  ADS  Google Scholar  * He, X. et al. PrBi: topology meets quadrupolar degrees of freedom. _Phys. Rev. B_ 101,

075106 (2020). Article  ADS  Google Scholar  * Dhar, S. The heat capacity of PrSi2. _J. Magn. Magn. Mater._ 132, 149–152 (1994). Article  ADS  Google Scholar  * Lesseux, G. G. et al.

Orbitally defined field-induced electronic state in a Kondo lattice. _Phys. Rev. B_ 101, 165111 (2020). Article  ADS  Google Scholar  Download references AUTHOR INFORMATION AUTHORS AND

AFFILIATIONS * Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China Lei Wu, Shengwei Chi, Huakun Zuo, Gang Xu,

 Yongkang Luo & Zengwei Zhu * Department of Physics, Southern University of Science and Technology, 518055, Shenzhen, China Lingxiao Zhao Authors * Lei Wu View author publications You

can also search for this author inPubMed Google Scholar * Shengwei Chi View author publications You can also search for this author inPubMed Google Scholar * Huakun Zuo View author

publications You can also search for this author inPubMed Google Scholar * Gang Xu View author publications You can also search for this author inPubMed Google Scholar * Lingxiao Zhao View

author publications You can also search for this author inPubMed Google Scholar * Yongkang Luo View author publications You can also search for this author inPubMed Google Scholar * Zengwei

Zhu View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS Z.Z. and L.Z. conceived and oversaw this work. L.W., H.Z., and L.Z. performed the

experiments. Z.Z., G.X., L.W., and S.C. performed band structure calculations. L.W., L.Z., Y.L., and Z.Z. wrote the manuscript with inputs from co-authors. CORRESPONDING AUTHORS

Correspondence to Lingxiao Zhao, Yongkang Luo or Zengwei Zhu. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. SUPPLEMENTARY INFORMATION SUPPLEMENTAL MATERIAL RIGHTS AND PERMISSIONS

OPEN ACCESS This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or

format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or

other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in

the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the

copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Wu, L., Chi, S., Zuo, H.

_et al._ Field-induced Lifshitz transition in the magnetic Weyl semimetal candidate PrAlSi. _npj Quantum Mater._ 8, 4 (2023). https://doi.org/10.1038/s41535-023-00537-y Download citation *

Received: 09 February 2022 * Accepted: 02 January 2023 * Published: 10 January 2023 * DOI: https://doi.org/10.1038/s41535-023-00537-y SHARE THIS ARTICLE Anyone you share the following link

with will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt

content-sharing initiative