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Over the past five years, significant progress has been made in understanding the magnetism and electronic properties of CaAl$_2$Si$_2$-type Eu$M_2X_2$ ($M$ = Zn, Cd; $X$ = P, As) compounds. Prior theoretical work and experimental studies suggested that EuCd$_2$As$_2$ had the potential to host rich topological phases, particularly an ideal magnetic Weyl semimetal state when the spins are polarized along the c axis. However, this perspective is challenged by recent experiments utilizing samples featuring ultra-low carrier densities, as well as meticulous calculations employing various approaches. Nonetheless, the Eu$M_2X_2$ family still exhibit numerous novel properties that remain to be satisfactorily explained, such as the giant nonlinear anomalous Hall effect and the colossal magnetoresistance effect. Moreover, Eu$M_2X_2$ compounds can be transformed from semiconducting antiferromagnets to metallic ferromagnets by introducing a small number of carriers or applying external pressure, and a further increase in the ferromagnetic transition temperature can be achieved by reducing the unit cell volume. These features make the Eu$M_2X_2$ family a fertile platform for studying the interplay between magnetism and charge transport, and an excellent candidate for applications in spintronics. This paper presents a comprehensive review of the magnetic and transport behaviors of Eu$M_2X_2$ compounds with varying carrier densities, as well as the current insights into these characteristics. An outlook for future research opportunities is also provided.

Materials that exhibit strongly coupled magnetic order and electronic properties are crucial for both fundamental research and technological applications. However, finding a material that not only shows remarkable magnetoresistive responses but also has an easily tunable ground state remains a challenge. Here, we report successful manipulation of the magnetic and transport properties of EuCd$_2$P$_2$, which is transformed from an A-type antiferromagnet ($T_\mathrm{N}$ = 11 K) exhibiting colossal magnetoresistance into a ferromagnet ($T_\mathrm{C}$ = 47 K) with metallic behavior. The dramatic alteration results from a low hole concentration of $10^{19}$ cm$^{-3}$ induced by changing the growth conditions. Electronic structure and total energy calculations confirm the tunability of magnetism with a small carrier concentration for EuCd$_2$P$_2$. It is feasible to switch between the magnetic states by using field-effect to control the carrier density, thereby changing the magneto-electronic response. The controllable magnetism and electrical transport of EuCd$_2$P$_2$ make it a potential candidate for spintronics.

EuZn$_2$P$_2$ was reported to be an insulating antiferromagnet with $T_\mathrm{N}$ of 23.5 K. In this study, single crystals of EuZn$_2$P$_2$ exhibiting metallic behavior and a ferromagnetic order of 72 K ($T_\mathrm{C}$) are successfully synthesized via a salt flux method. The presence of hole carriers induced by the Eu vacancies in the lattice is found to be crucial for the drastic changes in magnetism and electrical transport. The carriers mediate the interlayer ferromagnetic interaction, and the coupling strength is directly related to $T_\mathrm{C}$, as evidenced by the linear dependence of $T_\mathrm{C}$ and the fitted Curie-Weiss temperatures on the Eu-layer distances for ferromagnetic Eu$M_2X_2$ ($M$ = Zn, Cd; $X$ = P, As). The ferromagnetic EuZn$_2$P$_2$ shows conspicuous negative magnetoresistance (MR) near $T_\mathrm{C}$, owing to strong magnetic scattering. The MR behavior is consistent with the Majumdar-Littlewood model, indicating that the MR can be enhanced by decreasing the carrier density. Our findings suggest that Eu$M_2X_2$ has highly tunable magnetism and charge transport, making it a promising material family for potential applications in spintronics.

Two dimensional (2D) semiconductors present unique opportunities to intertwine optical and magnetic functionalities and to tune these performances through defects and dopants. Here, we integrate exciton pumping into a quantum sensing protocol on nitrogen-vacancy centers in diamond to image the optically-induced transient stray fields in few-layer, antiferromagnetic CrCl$_3$. We discover that exciton recombination enhances the in-plane magnetization of the CrCl$_3$ layers, with a predominant effect in the surface monolayers. Concomitantly, time-resolved photoluminescence measurements reveal that nonradiative exciton recombination intensifies in atomically thin CrCl$_3$ with tightly localized, nearly dipole-forbidden excitons and amplified surface-to-volume ratio. Supported by experiments under controlled surface exposure and density functional theory calculations, we interpret the magnetically enhanced state to result from a defect-assisted Auger recombination that optically activates electron transfer between water vapor related surface impurities and the spin-polarized conduction band. Our work validates defect engineering as a route to enhance intrinsic magnetism in single magnetic layers and opens a novel experimental platform for studying optically-induced, transient magnetism in condensed matter systems., Comment: 11 pages, 8 figures

Theoretical studies predicted possible superconductivity in electron-doped chromium pnictides isostructural to their iron counterparts. Here, we report the synthesis and characterization of a new ZrCuSiAs-type Cr-based compound ThCrAsN, as well as its oxygen-doped variants. All samples of ThCrAsN$_{1-x}$O$_x$ show metallic conduction, but no superconductivity is observed above 30 mK even though the oxygen substitution reaches 75\%. The magnetic structure of ThCrAsN is determined to be G-type antiferromagnetic by magnetization measurements and first-principles calculations jointly. The calculations also indicate that the in-plane Cr--Cr direct interaction of ThCrAsN is robust against the heavy electron doping. The calculated density of states of the orbital occupations of Cr for ThCrAs(N,O) is strongly spin-polarized. Our results suggest the similarities between chromium pnictides and iron-based superconductors shouldn't be overestimated.

Mixed halide chemistry has recently been utilized to tune the intrinsic magnetic properties of transition-metal halides $-$ one of the largest families of magnetic van der Waals materials. Prior studies have shown that the strength of exchange interactions, hence the critical temperature, can be tuned smoothly with halide composition for a given ground-state. Here we show that the ground-state itself can be altered by a small change of halide composition leading to a quantum phase transition in FeCl$_{3-x}$Br$_x$. Specifically, we find a three-fold jump in the N\'{e}el temperature and a sign change in the Weiss temperature at $x= 0.08$ corresponding to only $3\%$ bromine doping. Using neutron scattering, we reveal a change of the ground-state from spiral order in FeCl$_3$ to A-type antiferromagnetic order in FeBr$_3$. Using first-principles calculations, we show that a delicate balance between nearest and next-nearest neighbor interactions is responsible for such a transition. These results support the proximity of FeCl$_3$ to a spiral spin liquid state, in which competing interactions and nearly degenerate magnetic $k$-vectors may cause large changes in response to small perturbations., Comment: 6 pages, 4 figures

EuCd$_2$P$_2$ is notable for its unconventional transport: upon cooling the metallic resistivity changes slope and begins to increase, ultimately 100-fold, before returning to its metallic value. Surprisingly, this giant peak occurs at 18K, well above the N\'{e}el temperature ($T_N$) of 11.5K. Using a suite of sensitive probes of magnetism, including resonant x-ray scattering and magneto-optical polarimetry, we have discovered that ferromagnetic order onsets above $T_N$ in the temperature range of the resistivity peak. The observation of inverted hysteresis in this regime shows that ferromagnetism is promoted by coupling of localized spins and itinerant carriers. The resulting carrier localization is confirmed by optical conductivity measurements.

Several recent studies have shown that the anisotropy in the magnetic structure of \ECA\ plays a significant role in stabilizing the Weyl nodes. To investigate the relationship between magnetic anisotropy and Weyl physics, we present a comparative study between EuZn$_2$As$_2$ and EuCd$_2$As$_2$ that are isostructural but with different magnetic anisotropy. We performed structural analysis, electronic transport, and magnetization experiments on millimeter-sized single crystals of EuZn$_2$As$_2$, and compared the results to those of EuCd$_2$As$_2$. By combining the first principle calculations and neutron diffraction experiment, we identify the magnetic ground state of EuZn$_2$As$_2$ as A-type antiferromagnetic order with a transition temperature ($T_\mathrm{N}$ = 19.6 K) twice that of EuCd$_2$As$_2$. Like EuCd$_2$As$_2$, the negative magnetoresistance of EuZn$_2$As$_2$ is observed after suppressing the resistivity peak at $T_\mathrm{N}$ with increasing fields. However, the anisotropy in both transport and magnetization are much reduced in EuZn$_2$As$_2$. The difference could be ascribed to the weaker spin-orbit coupling, more localized $d$-orbitals, and a larger contribution from the Eu $s$-orbitals in the zinc compound, as suggested by the electronic band calculations. The same band structure effect could be also responsible for the observation of a smaller non-linear anomalous Hall effect in EuZn$_2$As$_2$ compared to EuCd$_2$As$_2$.

Phonons are known to generate a thermal Hall effect in certain insulators, including oxides with rare-earth impurities, quantum paraelectrics, multiferroic materials and cuprate Mott insulators. In each case, a special feature of the material is presumed relevant for the underlying mechanism that confers chirality to phonons in a magnetic field. The question is whether a phonon Hall effect is an unusual occurrence - linked to special characteristics such as skew scattering off rare-earth impurities, structural domains, ferroelectricity, ferromagnetism - or a much more common property of insulators than hitherto believed. To help answer this question, we have turned to a simple insulator, with none of the previously encountered special features: the cubic antiferromagnet Cu$_3$TeO$_6$. We find that it has the largest thermal Hall conductivity $\kappa_{\rm{xy}}$ of any insulator so far. We show that this record-high $\kappa_{\rm{xy}}$ signal is due to phonons and it does not require the presence of magnetic order, as it persists above the ordering temperature. We conclude that the phonon Hall effect is likely to be a fairly common property of solids., Comment: 5 pages, 3 figures

We report the design, synthesis, structure, and properties of two complex layered phosphide nitrides, $Ak$Th$_2$Mn$_4$P$_4$N$_2$ ($Ak$ = Rb, Cs), which contain anti-fluorite-type [Mn$_2$P$_2$] bilayers separated by fluorite-type [Th2N2] layers as a result of the intergrowth between AkMn$_2$P$_2$ and ThMnPN. The new compounds are featured with an intrinsic hole doping associated with the interlayer charge transfer and a built-in chemical pressure from the [Th$_2$N$_2$] layers, both of which are reflected by the changes in the lattice and the atomic position of phosphorus. The measurements of magnetic susceptibility, electrical resistivity, and specific heat indicate existence of local moments as well as itinerant electrons in relation with d-p hybridizations. The expected dominant antiferromagnetic interactions with enhanced d-p hybridizations were demonstrated by the first-principles calculations only when additional Coulomb repulsions are included. The density of states at the Fermi level derived from the specific-heat analysis are 3.5 and 7.5 times of the calculated ones for Ak = Rb and Cs, respectively, suggesting strong electron correlations in the title compounds., Comment: 12 pages, 5 figures, 3 tables; Supporting information available on request

Strongly correlated electrons in layered perovskite structures have been the birthplace of high-temperature superconductivity, spin liquid, and quantum criticality. Specifically, the cuprate materials with layered structures made of corner sharing square planar CuO$_4$ units have been intensely studied due to their Mott insulating grounds state which leads to high-temperature superconductivity upon doping. Identifying new compounds with similar lattice and electronic structures has become a challenge in solid state chemistry. Here, we report the hydrothermal crystal growth of a new copper tellurite sulfate Cu$_3$(TeO$_4$)(SO$_4$)$\cdot$H$_2$O, a promising alternative to layered perovskites. The orthorhombic phase (space group $Pnma$) is made of corrugated layers of corner-sharing CuO$_4$ square-planar units that are edge-shared with TeO$_4$ units. The layers are linked by slabs of corner-sharing CuO$_4$ and SO$_4$. Using both the bond valence sum analysis and magnetization data, we find purely Cu$^{2+}$ ions within the layers, but a mixed valence of Cu$^{2+}$/Cu${^+}$ between the layers. Cu$_3$(TeO$_4$)(SO$_4$)$\cdot$H$_2$O undergoes an antiferromagnetic transition at $T_N$=67 K marked by a peak in the magnetic susceptibility. Upon further cooling, a spin-canting transition occurs at $T^{\star}$=12 K evidenced by a kink in the heat capacity. The spin-canting transition is explained based on a $J_1$-$J_2$ model of magnetic interactions, which is consistent with the slightly different in-plane super-exchange paths. We present Cu$_3$(TeO$_4$)(SO$_4$)$\cdot$H$_2$O as a promising platform for the future doping and strain experiments that could tune the Mott insulating ground state into superconducting or spin liquid states., Comment: 29 pages

Materials with strong magnetoresistive responses are the backbone of spintronic technology, magnetic sensors, and hard drives. Among them, manganese oxides with a mixed valence and a cubic perovskite structure stand out due to their colossal magnetoresistance (CMR). A double exchange interaction underlies the CMR in manganates, whereby charge transport is enhanced when the spins on neighboring Mn3+ and Mn4+ ions are parallel. Prior efforts to find different materials or mechanisms for CMR resulted in a much smaller effect. Here we show an enormous CMR at low temperatures in EuCd2P2 without manganese, oxygen, mixed valence, or cubic perovskite structure. EuCd2P2 has a layered trigonal lattice and exhibits antiferromagnetic ordering at 11 K. The magnitude of CMR (104 percent) in as-grown crystals of EuCd2P2 rivals the magnitude in optimized thin films of manganates. Our magnetization, transport, and synchrotron X-ray data suggest that strong magnetic fluctuations are responsible for this phenomenon. The realization of CMR at low temperatures without heterovalency leads to a new regime for materials and technologies related to antiferromagnetic spintronics.

In this paper, curved fronts are constructed for spatially periodic bistable reaction-diffusion equations under the a priori assumption that there exist pulsating fronts in every direction. Some sufficient and some necessary conditions of the existence of curved fronts are given. Furthermore, the curved front is proved to be unique and stable. Finally, a curved front with varying interfaces is also constructed. Despite the effect of the spatial heterogeneity, the result shows the existence of curved fronts for spatially periodic bistable reaction-diffusion equations which is known for the homogeneous case.

Recently, An electron-doped 12442-type iron-based superconductor BaTh$_2$Fe$_4$As$_4$(N$_{0.7}$O$_{0.3}$)$_2$ has been successfully synthesized with high-temperature solid-state reactions on basis of a structural design. The inter-block-layer charge transfer between the constituent units of "BaFe$_2$As$_2$" and "ThFeAsN$_{0.7}$O$_{0.3}$" was found to be essential to stabilize the target compound. Dominant electron-type conduction and bulk superconducting transition at ~22 K were demonstrated., Comment: 16 pages in total. 5 figures, 1 table (main article); 6 figures, 3 tables (Supporting Information)

This paper is concerned with the asymptotic behavior of solutions of time periodic reaction-diffusion equation \begin{equation*}\label{aaa} \begin{cases} u_{t}(x,t)=u_{xx}(x,t)+f(t,u(x,t)),\quad \,\,\forall x\in\mathbb{R},\,t>0,\\ u(x,0)=u_{0}(x), \quad \quad\quad\quad\quad\quad\quad\quad\quad \forall x\in\mathbb{R}, \end{cases} \end{equation*} where $u_{0}(x)$ is the Heaviside type initial function and $f(t,u)$ satisfies $f(T+t,u)=f(t,u)$. Under certain conditions, we prove that there exists a minimal propagating terrace (a family of pulsating traveling fronts) in some specific sense and the solution of the above equation converges to the minimal propagating terrace., Comment: 32pages

CsCa$_2$Fe$_4$As$_4$F$_2$ is a newly discovered iron-based superconductor with $T_\mathrm{c}\sim$ 30 K containing double Fe$_2$As$_2$ layers that are separated by insulating Ca$_2$F$_2$ spacer layers. Here we report the transport and magnetization measurements on CsCa$_2$Fe$_4$As$_4$F$_2$ single crystals grown for the first time using the self flux of CsAs. We observed a huge resistivity anisotropy $\rho_c(T)/\rho_{ab}(T)$, which increases with decreasing temperature, from 750 at 300 K to 3150 at 32 K. The $\rho_c(T)$ data exhibit a non-metallic behavior above $\sim$140 K, suggesting an incoherent electronic state at high temperatures due to the dimension crossover. The superconducting onset transition temperature in $\rho_{ab}$ is 0.7 K higher than that in $\rho_c$, suggesting two-dimensional (2D) superconducting fluctuations. The lower and upper critical fields also show an exceptional anisotropy among iron-based superconductors. The $H_{c1}^\bot(T)$ data are well fitted using the model with two $s$-wave-like superconducting gaps, $\Delta_1(0)=6.75$ meV and $\Delta_2(0)=2.32$ meV. The inter-plane coherence length $\xi_c(0)$ is $3.6$ \AA, remarkably smaller than the distance between conducting layers (8.6 \AA), consolidating the 2D nature in the title material., Comment: 8 pages, 5 figures, 1 Table

Sr2Cr3As2O2 is composed of alternating square-lattice CrO2 and Cr2As2 stacking layers, where CrO2 is isostructural to the CuO2 building-block of cuprate high-Tc superconductors and Cr2As2 to Fe2As2 of Fe-based superconductors. Current interest in this material is raised by theoretic prediction of possible superconductivity. In this neutron powder diffraction study, we discovered that magnetic moments of Cr(II) ions in the Cr2As2 sublattice develop a C-type antiferromagnetic structure below 590 K, and the moments of Cr(I) in the CrO2 sublattice form the La2CuO4 -like antiferromagnetic order below 291 K. The staggered magnetic moment 2.19(4){\mu} B /Cr(II) in the more itinerant Cr2As2 layer is smaller than 3.10(6){\mu}_B/Cr(I) in the more localized CrO2 layer. Different from previous expectation, a spin-flop transition of the Cr(II) magnetic order observed at 291 K indicates a strong coupling between the CrO2 and Cr2As2 magnetic subsystems., Comment: 7pages, 4 figures, 2 tables

ThFeAsN$_{1-x}$O$_x$ ($0\leq x\leq0.6$) system with heavy electron doping has been studied by the measurements of X-ray diffraction, electrical resistivity, magnetic susceptibility and specific heat. The non-doped compound exhibits superconductivity at $T_\mathrm{c}^\mathrm{onset}=30$ K, which is possibly due to an internal uniaxial chemical pressure that is manifested by the extremely small value of As height with respect to the Fe plane. With the oxygen substitution, the $T_\mathrm{c}$ value decreases rapidly to below 2 K for $0.1\leq x\leq0.2$, and surprisingly, superconductivity re-appears in the range of $0.25\leq x\leq0.5$ with a maximum $T_\mathrm{c}^\mathrm{onset}$ of 17.5 K at $x=0.3$. For the normal-state resistivity, while the samples in intermediate non-superconducting interval exhibit Fermi liquid behavior, those in other regions show a non-Fermi-liquid behavior. The specific heat jump for the superconducting sample of $x=0.4$ is $\Delta C/(\gamma T_\mathrm{c})=0.89$, which is discussed in terms of anisotropic superconducting gap. The peculiar phase diagram in ThFeAsN$_{1-x}$O$_x$ presents additional ingredients for understanding the superconducting mechanism in iron-based superconductors., Comment: 10 pages, 7 figures

The superconducting properties of the recently discovered double Fe$_2$As$_2$ layered high-$T_c$ superconductor RbCa$_2$Fe$_4$As$_4$F$_2$ with $T_c\approx$ 30~K have been investigated using magnetization, heat capacity, transverse-field (TF) and zero-field (ZF) muon-spin rotation/relaxation ($\mu$SR) measurements. Our low field magnetization measurements and heat capacity (C$_p$) reveal an onset of bulk superconductivity with $T_{\bf c}\sim$ 30.0(4) K. Furthermore, the heat capacity exhibits a jump at $T_{\bf c}$ of $\Delta$C$_p$/$T_{\bf c}$=94.6 (mJ/mole-K$^2$) and no clear effect of applied magnetic fields was observed on C$_p$(T) up to 9 T between 2 K and 5 K. Our analysis of the TF-$\mu$SR results shows that the temperature dependence of the magnetic penetration depth is better described by a two-gap model, either isotropic $s$+$s$-wave or $s$+$d$-wave than a single gap isotropic $s$-wave or $d$-wave model for the superconducting gap. The presence of two superconducting gaps in RbCa$_2$Fe$_4$As$_4$F$_2$ suggests a multiband nature of the superconductivity, which is consistent with the multigap superconductivity observed in other Fe-based superconductors, including ACa$_2$Fe$_4$As$_4$F$_2$ (A=K and Cs). Furthermore, from our TF-$\mu$SR study we have estimated an in-plane penetration depth $\lambda_{\mathrm{ab}}$$(0)$ =231.5(3) nm, superconducting carrier density $n_s = 7.45 \times 10^{26}~ $m$^{-3}$, and carrier's effective-mass $m^*$ = 2.45\textit{m}$_{e}$. Our ZF $\mu$SR measurements do not reveal a clear sign of time reversal symmetry breaking at $T_{\bf c}$, but the temperature dependent relaxation between 150 K and 1.2 K might indicate the presence of spin-fluctuations. The results of our present study have been compared with those reported for other Fe pnictide superconductors., Comment: 10 pages, 7 figures. arXiv admin note: text overlap with arXiv:1706.03641

We report the results of a muon-spin rotation ($\mu$SR) experiment to determine the superconducting ground state of the iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_{\rm c} \approx 28.3\,$K. This compound is related to the fully-gapped superconductor CaCsFe$_4$As$_4$, but here the Ca-containing spacer layer is replaced with one containing Ca$_2$F$_2$. The temperature evolution of the penetration depth strongly suggests the presence of line nodes and is best modelled by a system consisting of both an $s$- and a $d$-wave gap. We also find a potentially magnetic phase which appears below $\approx 10\,$K but does not appear to compete with the superconductivity. This compound contains the largest alkali atom in this family of superconductors and our results yield a value for the in-plane penetration depth of $\lambda_{ab}(T=0)=423(5)\,$nm., Comment: 6 pages, 2 figures

We have synthesized 10 new iron oxyarsenides, K$Ln_2$Fe$_4$As$_4$O$_2$ ($Ln$ = Gd, Tb, Dy, and Ho) and Cs$Ln_2$Fe$_4$As$_4$O$_2$ ($Ln$ = Nd, Sm, Gd, Tb, Dy, and Ho), with the aid of lattice-match [between $A$Fe$_2$As$_2$ ($A$ = K and Cs) and $Ln$FeAsO] approach. The resultant compounds possess hole-doped conducting double FeAs layers, [$A$Fe$_4$As$_4$]$^{2-}$, that are separated by the insulating [$Ln_2$O$_2$]$^{2+}$ slabs. Measurements of electrical resistivity and dc magnetic susceptibility demonstrate bulk superconductivity at $T_\mathrm{c}$ = 33 - 37 K. We find that $T_\mathrm{c}$ correlates with the axis ratio $c/a$ for all 12442-type superconductors discovered. Also, $T_\mathrm{c}$ tends to increase with the lattice mismatch, implying a role of lattice instability for the enhancement of superconductivity., Comment: 8 pages, 6 figures, 2 tables

We have synthesized four iron-based oxyarsenide superconductors Rb$Ln_2$Fe$_4$As$_4$O$_2$ ($Ln$ = Sm, Tb, Dy and Ho) resulting from the intergrowth of RbFe$_2$As$_2$ and $Ln$FeAsO. It is found that the lattice match between RbFe$_2$As$_2$ and $Ln$FeAsO is crucial for the phase formation. The structural intergrowth leads to double asymmetric Fe$_2$As$_2$ layers that are separated by insulating $Ln_2$O$_2$ slabs. Consequently, the materials are intrinsically doped at a level of 0.25 holes/Fe-atom and, bulk superconductivity emerges at $T_\mathrm{c}$ = 35.8, 34.7, 34.3 and 33.8 K, respectively, for $Ln$ = Sm, Tb, Dy and Ho. Investigation on the correlation between crystal structure and $T_\mathrm{c}$ suggests that interlayer couplings may play an additional role for optimization of superconductivity., Comment: 20 pages, 9 figures, 1 table

We have synthesized two iron fluo-arsenides $A$Ca$_2$Fe$_4$As$_4$F$_2$ with $A$ = Rb and Cs, analogous to the newly discovered superconductor KCa$_2$Fe$_4$As$_4$F$_2$. The quinary inorganic compounds crystallize in a body-centered tetragonal lattice with space group I4/mmm, which contain double Fe$_2$As$_2$ layers that are separated by insulating Ca$_2$F$_2$ layers. Our electrical and magnetic measurements on the polycrystalline samples demonstrate that the new materials undergo superconducting transitions at Tc = 30.5 K and 28.2 K, respectively, without extrinsic doping. The correlations between Tc and structural parameters are discussed., Comment: 9 pages,4 figures, 1 table

This paper mainly focus on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function $J$ may not be symmetric here. The asymmetry of $J$ has a great influence on the profile of the traveling waves and the sign of the wave speeds, which further makes the properties of the entire solution more diverse. We first investigate the asymptotic behavior of the traveling wave solutions since it plays an essential role in obtaining the front-like entire solution. Due to the impact of $f'(0)=0$, we can no longer use the common method which mainly depending on Ikehara theorem and bilateral Laplace transform to study the asymptotic rates of the nondecreasing traveling wave and the nonincreasing one tending to 0, respectively, thus we adopt another method to investigate them. Afterwards, we establish a new entire solution and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds., Comment: 20 pages