Magnetic exchange induced Weyl state in a semimetal EuCd2Sb2

Magnetic Weyl semimetals (WSMs) bearing long-time pursuing are still very rare. We herein identified magnetic exchange induced Weyl state in EuCd2Sb2, a semimetal in type IV magnetic space group, via performing high magnetic field (B) magneto-transport measurements and ab initio calculations. For the A-type antiferromagnetic (AFM) structure of EuCd2Sb2, external B larger than 3.2 T can align Eu spins to be fully polarized along the c-axis and consequently drive the system into a ferromagnetic (FM) state. Measurements up to B ~ 55 T revealed a striking Shubnikov-de Hass oscillation imposed by a nontrivial Berry phase. We unveiled a phase transition from a small-gap AFM topological insulator into a FM WSM in which Weyl points emerged along the {\Gamma}-Z path. Fermi arcs on (100) and (010) surfaces are also revealed. The results pave a way towards realization of various topological states in a single material through magnetic exchange manipulation.


(B) magneto-transport measurements and ab initio calculations. For the A-type antiferromagnetic (AFM) structure of EuCd 2 Sb 2 , external B larger than 3.2 T can align Eu spins to be fully polarized along the c-axis
Once the spin degeneracy is lifted by either breaking the time-reversal symmetry (T) or spatial inversion symmetry (P), the Dirac point (DP) characterized by chiral symmetry will split into a pair of Weyl points (WPs) which behave as the monopoles of Berry curvature [5][6][7] . The WPs emerged in pairs are well separated in momentum space under the conservation of the opposite chirality of the Berry curvature, which consequently are topologically stable and will not be annihilated unless they could be moved to the same ĸ-point in the Brillouin zone (BZ). The existence of WPs can produce extraordinary intriguing properties, such as chiral anomaly effect, gravitational effect, strong intrinsic anomalous and spin Hall effect, large magnetoresistance (MR), etc. [19][20][21][22][23] .
The P-breaking Weyl fermions, which is realized entirely by crystal structure, have been established in a number of Weyl semimetals (WSMs) such as TaAs family 6,7,26 , (W/Mo)Te 2 27, 28 , and photonic crystals 29  The temperature (T) dependent longitudinal resistivity ρ xx measured at various B presented in Figure S2(b) demonstrate not only a semi-metallic behavior but also the influences from the AFM ordering and the localized Eu 2+ . Since the easy alignment of Eu spins along the c-axis in the AFM structure by B, it naturally reminds us of the magneto-transport measurements on EuCd 2 Sb 2 with B//c to experimentally map out the FS in the FM structure. The B dependence of ρ xx measured up to 55 T in pulsed magnetic fields applied along the c-axis with current (I) in the ab-plane (B//c⊥I) and at T = 2 -30 K is depicted in Figure 1 gives A F1 = 1.11(4) nm -2 and A F2 = 0.028(5) nm -2 , corresponding to the frequencies of 117 T and 30 T, respectively. However, theoretical calculations exposed two hole and two electron bands in the FM structure of EuCd 2 Sb 2 rather than only two hole bands crossing E F , seen in Figure  To provide more evidences for demonstrating the nontrivial topological state in in EuCd 2 Sb 2 at high B, the Berry phase φ B accumulated along cyclotron orbits was examined. Generally speaking, the pseudo-spin rotation under a magnetic field in a Dirac/Weyl system will produce a non-trivial φ B which could be accessed from the Landau level (LL) index fan diagram or a direct fit of SdH oscillations by using the L-K formula [42][43][44] . The phase shift is generally a sum φ i = −γ+δ, where γ is the phase factor expressing as 1/2-φ B /2π and δ represents the dimension-dependent correction to the phase shift 39 . In a 2D case, this parameter amounts zero, while in a 3D case δ is equal to ±1/8 where the sign depends on type of charge carriers and kind of cross-section extremum 45,46 . The inset in Figure 1 The nontrivial band structure and susceptible magnetism in EuCd 2 Sb 2 are intimately related to the transport properties. For Dirac/Weyl semimetal, when B//I, the negative MR can appear due to a population imbalance between Weyl fermions of different charities, which can produce a net electric current 21 . At relatively low magnetic field (< 2 T), the magnetic structure is A-type AFM with tiny gaps which is rather close to be a DSM (Figures 2(b) and 2(c)). Thus, as seen in Figure 3 Note added: During preparation of this paper, we became aware of two related work appeared on arXiv. One is a theoretical predication of single pair of WPs in EuCd 2 As 2 but lacks of experiments 56 . The other one reported the theoretical and experimental studies on our EuCd 2 As 2 crystals, which claimed the discovery of an ideal Weyl state induced by magnetic exchange 57 . The information about the Fermi arcs that are crucial for a WSM was not found. Moreover, our investigation on the different system EuCd 2 Sb 2 was totally independent and we have no private communications about our work during the whole process.

Single-crystal growth, compositions and single crystal x-ray diffraction
chracterizations. The EuCd 2 Sb 2 single crystals were grown by using tin as the flux.

Magnetization and magneto-transport measurements.
Magnetic properties of EuCd 2 Sb 2 were characterized on a commercial magnetic

ARPES measurements and the Hubbard U determination.
High-resolution angle-resolved photoemission spectroscopy (ARPES) was used to directly measure the band structure of the paramagnetic EuCd 2 Sb 2 . ARPES data was mainly acquired at BL4 and BL10 of ALS, USA, at 20 K. The overall energy and angle resolutions were 15 meV and 0.2°, respectively. Fresh EuCd 2 Sb 2 surfaces for ARPES measurements were obtained by in-situ cleaving the crystals at low temperatures (20 K).

The ab initio calculations
The first-principles electronic structure calculations on EuCd 2 Sb 2 were carried out by using the projector augmented wave (PAW) method 58 as implemented in the VASP package 59 . The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof 60 was employed for the exchange-correlation functional.
The kinetic energy cutoff of the plane-wave basis was set to be 340 eV. The experimental lattice constants and atomic positions of EuCd 2 Sb 2 were adopted 36  Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

b. Magnetization and resistivity measurements.
The temperature dependent magnetization (M(T)) along the out-of-plane (B//c) direction is shown in Figure S2 The temperature dependence of longitudinal resistivity ρ xx at various B presented in Figure S2(b) shows several prominent features: above 40 K ρ xx displays an almost linear temperature dependence with the residual resistivity ratio ρ xx (300K)/ρ xx (40K) being approximately 1.5, indicative of an essential semi-metallic behavior. Below 40 K, ρ xx starts to gradually increase upon cooling till it reaches a peak at T N , and subsequently exhibits a sudden drop with further decreasing the temperature to 2 K.
The low temperature behavior of ρ xx , totally resembling that of the sister compound EuCd 2 As 2 , could be reasonably understood in connection with the scattering of conduction electrons by the localized Eu 2+ which is coupling with the Cd and As orbitals and the gradual spin alignment in external magnetic field. The disappearance of such peak at B > 3.2T which is the critical magnetic field (B c ) at which the spins are completely aligned along c axis, also supports this argument.

e. ab initio calculations
The first-principles electronic structure calculations on EuCd 2 Sb 2 were carried out by using the projector augmented wave (PAW) method 3  To further validate the choice of the Hubbard interaction parameters, we further studied the magnetic properties of EuCd 2 Sb 2 in several typical magnetic configurations of Eu spins as in Figure S6. Depending on the Hubbard interaction strength between Eu f-electrons, three different types of collinear magnetic states can be stabilized. The A-type AFM configuration was found to be the most energetic favorable state for U between 3 and 8 eV, which validates the choice of effective U value (4.5 eV) chosen from the comparison to ARPES measurement ( Figure S5). The magnetic ground state of EuCd 2 Sb 2 in A-AFM configuration with weak coupling of inter-layer Eu spins also agrees with the experimentally measured Neel temperature of 7.4 K 1 and is similar to the case of EuCd 2 As 2 3, 4 . Further calculations with different easy axis of magnetization show that Eu spins prefer to lie in the ab-plane.
Nevertheless, the magnetic anisotropy energy (MAE), i.e., the energy difference ( ) between the in-plane and out-of-plane spin directions, is very small ( 0.2 meV/Eu). The weak inter-layer interaction as well as the small MAE indicate that EuCd 2 Sb 2 is prone to the external magnetic field, which is in good accordance with above low saturation field in the magnetization measurements, seen by the inset in Figure S2(a).