No Arabic abstract
We present details of materials synthesis, crystal structure, and anisotropic magnetic properties of single crystals of CeAlGe, a proposed type-II Weyl semimetal. Single-crystal x-ray diffraction confirms that CeAlGe forms in noncentrosymmetric I4$_1$md space group, in line with predictions of non-trivial topology. Magnetization, specific heat and electrical transport measurements were used to confirm antiferromagnetic order below 5 K, with an estimated magnon excitation gap of $Delta$ = 9.11 K from heat capacity and hole-like carrier density of 1.44 $times$ 10$^{20}$ cm$^{-3}$ from Hall effect measurements. The easy magnetic axis is along the [100] crystallographic direction, indicating that the moment lies in the tetragonal $it{ab}$-plane below 7 K. A spin-flop transition to less than 1 $mu_B$/Ce is observed to occur below 30 kOe at 1.8 K in the $M(H)$ ($bf{H}|bf{a}$) data. Small magnetic fields of 3 kOe and 30 kOe are sufficient to suppress magnetic order when applied along the $it{a}$- and $it{c}$-axes, respectively, resulting in a complex $it{T-H}$ phase diagram for $bf{H}|bf{a}$ and a simpler one for $bf{H}|bf{c}$.
CeAlGe, a proposed type-II Weyl semimetal, orders antiferromagnetically below 5 K. Both a spin-flop and a spin-flip transitions to less than 1 $mu_B$/Ce are observed at 2 K below 30 kOe in the $M(H)$ ($bf{H}|bf{a}$ and $bf{b}$) and 4.3 kOe ($bf{H}|langle110rangle$) data, respectively, indicating a four-fold symmetry of the $M(H)$ along the principal directions in the tetragonal $it{ab}$-plane with $langle110rangle$ set of easy directions. However, anomalously robust and complex two-fold symmetry is observed in the angular dependence of resistivity and magnetic torque data in the magnetically ordered state once the field is swept in the $it{ab}$-plane. This two-fold symmetry is independent of temperature- and field-hystereses and suggests a magnetic phase transition that separates two different magnetic structures in the $it{ab}$-plane. The boundary of this magnetic phase transition can be tuned by different growth conditions.
We report the discovery of topological magnetism in the candidate magnetic Weyl semimetal CeAlGe. Using neutron scattering we find this system to host several incommensurate, square-coordinated multi-$vec{k}$ magnetic phases below $T_{rm{N}}$. The topological properties of a phase stable at intermediate magnetic fields parallel to the $c$-axis are suggested by observation of a topological Hall effect. Our findings highlight CeAlGe as an exceptional system for exploiting the interplay between the nontrivial topologies of the magnetization in real space and Weyl nodes in momentum space.
Magnetic topological materials have recently drawn significant importance and interest, due to their topologically nontrivial electronic structure within spontaneous magnetic moments and band inversion. Based on first-principles calculations, we propose that chromium dioxide, in its ferromagnetic pyrite structure, can realize one pair of type-II Weyl points between the $N$th and $(N+1)$th bands, where $N$ is the total number of valence electrons per unit cell. Other Weyl points between the $(N-1)$th and $N$th bands also appear close to the Fermi level due to the complex topological electronic band structure. The symmetry analysis elucidates that the Weyl points arise from a triply-degenerate point splitting due to the mirror reflection symmetry broken in the presence of spin-orbital coupling, which is equivalent to an applied magnetic field along the direction of magnetization. The Weyl points located on the magnetic axis are protected by the three-fold rotational symmetry. The corresponding Fermi arcs projected on both (001) and (110) surfaces are calculated as well and observed clearly. This finding opens a wide range of possible experimental realizations of type-II Weyl fermions in a system with time-reversal breaking.
Weyl semimetals, characterized by nodal points in the bulk and Fermi arc states on the surface, have recently attracted extensive attention due to the potential application on low energy consumption electronic materials. In this report, the thermodynamic and transport properties of a theoretically predicted Weyl semimetal NbIrTe4 is measured in high magnetic fields up to 35 T and low temperatures down to 0.4 K. Remarkably, NbIrTe4 exhibits a nonsaturating transverse magnetoresistance which follows a power-law dependence in B. Low-field Hall measurements reveal that hole-like carriers dominate the transport for T $>$ 80 K, while the significant enhancement of electron mobilities with lowering T results in a non-negligible contribution from electron-like carriers which is responsible for the observed non-linear Hall resistivity at low T. The Shubnikov-de Haas oscillations of the Hall resistivity under high B give the light effective masses of charge carriers and the nontrivial Berry phase associated with Weyl fermions. Further first-principles calculations confirm the existence of 16 Weyl points located at kz = 0, $pm$0.02 and $pm$0.2 planes in the Brillouin zone.
We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave function method. We consider a type-II WSM model with two Weyl nodes located on the $k_z$-axis, and the tilting of the Weyl cones are along the $k_x$ direction. Due to co-existing electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state, this behavior is distinct from that in the type-I WSMs, where the bound state is only formed when the hybridization exceeds a critical value. Meanwhile, the spin-orbit coupling and unique geometry of the Fermi surface lead to strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the $k_z$-axis, but the system remains invariant under a combined transformation $mathcal{T}R^{y}(pi)$, where $mathcal{T}$ is the time-reversal operation and $R^{y}(pi)$ is the rotation about the $y$-axis by $pi$. Largely modified diagonal and off-diagonal components of the spin-spin correlation function on three principal planes reflect this change in band symmetry. Most saliently, the tilting terms trigger the emergence of non-zero off-diagonal components of spin-spin correlation function on the $x$-$z$ principal plane.