Multiple Phase Transitions Research Articles

Delayed phase switching field and improved capacitive energy storage in Ca2+-modified (Pb,La)(Zr,Sn)O3 antiferroelectric ceramics

Antiferroelectric ceramics have captured great attention on capacitive energy storage because of their giant power density and fast discharge speed, which is highly desirable for high- and pulsed-power devices. Nevertheless, the conflict between breakdown electric field and phase switching field of antiferroelectric ceramics blocks to achieve the optimum energy storage capability. In present letter, Ca2+-modified (Pb0.97La0.02)(Zr0.6Sn0.4)O3 ceramics achieved improved breakdown electric field, delayed phase switching field and multiple phase transition under high electric field simultaneously, giving rise to an ultrahigh recoverable energy density of 10.04 J/cm3 and a high energy storage efficiency of 83.95%. Furthermore, the ceramics also displayed excellent thermal reliability as temperature increased to 150 °C, and superior discharge behavior, characterized by Wdis of 5.17 J/cm3 and t0.9 of 5.18 μs. This work not only demonstrates the promising applications of PbZrO3-based antiferroelectric ceramics in energy storage capacitors, but also supplies an effective route to explore high-performance antiferroelectric materials.

Impact of strain on the magnetocaloric effect of oxide heterostructures

We report a detailed study of the magnetocaloric effect in heterostructures of La2NiMnO6 and La2/3Sr1/3MnO3. The shape, width and magnitude of the temperature dependence of the magnetic entropy change (ΔSm) for these multilayer samples are affected by their layout with a clear impact from epitaxial strains on each layer. A large ΔSm over a wide temperature range which goes beyond room temperature is observed in all samples. We observe a temperature-independent table-top-like ΔSm over a temperature range as large as 100K in the trilayer samples. La2NiMnO6 double perovskite with multiple magnetic phase transitions sensitive to strain is the key to tuning and shaping the temperature dependence of the magnetic entropy changes to suit the requirements of several cooling cycles.

Built-in electric field and strain tunable valley-related multiple topological phase transitions in VSiXN4(X=C,Si,Ge,Sn,Pb) monolayers

Valley-related multiple topological phase transitions have attracted significant attention because they provide significant opportunities for fundamental research and practical applications. Unfortunately, however, there is no real material as of yet that can realize valley-related multiple topological phase transitions. Here, through first-principles calculations and model analysis, we investigate the structural, magnetic, electronic, and topological properties of ${\text{VSi}X\text{N}}_{4}(X=\mathrm{C},\mathrm{Si},\mathrm{Ge},\mathrm{Sn},\mathrm{Pb})$ monolayers. ${\text{VSi}X\text{N}}_{4}$ monolayers are stable and intrinsically ferrovalley materials. Intriguingly, we found that built-in electric field and strain can induce valley-related multiple topological phase transitions in materials from valley semiconductor to valley half-semimetal, to valley quantum anomalous Hall insulator, to valley half-semimetal, and to valley semiconductor (or to valley metal). The nature of the topological phase transition is the built-in electric field and strain-induced band inversion between the ${d}_{xy}/{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals at $K$ and ${K}^{\ensuremath{'}}$ valleys. Our findings not only reveal the mechanism of multiple topological phase transitions, but they also provide an ideal platform for the multifield manipulating the spin, valley, and topological physics. This will lead to alternative perspectives for spintronic, valleytronic, and topological nanoelectronic applications based on these materials.

Multiple Electronic Phase Transitions of NiO via Manipulating the NiO6 Octahedron and Valence Control

AbstractWhile the multiple Mottronic and electronic phase transitions as recently discovered in nickelates (e.g., ReNiO3) open up a new paradigm in correlated electronic applications, these applications are largely impeded by the intrinsic material metastability of the perovskite nickelates. Herein, the study demonstrates the analogous multiple electronic phase transition properties in the thermodynamically stable NiO, compared to ReNiO3, from both perspectives of band gap regulation and orbital filling regulation. The adjustment in band gap of NiO with t2g6eg2 orbital configuration is achieved via establishing biaxial tensile or compressive interfacial strains that increase or reduce the material resistivity, respectively. The relaxor ferroelectricity of 0.7Pb(Mg2/3Nb1/3)O3‐0.3PbTiO3 (PMNPT) further enables an electric field adjustable resistance switch (ΔR/R) within NiO/PMNPT heterostructure with higher performances (e.g., ΔR/R of 82% upon a bias voltage of 20 V) than the reported oxides/PMNPT heterostructure. Furthermore, the magnitude in resistance switch of the tensile strained NiO via hydrogenation associated Mottronic process reaches ≈1011 that exceeds the previously reported ones. This study highlights the higher material stability and easier growth of NiO, compared to ReNiO3, with analogous multiple Mottronic and electronic phase transition properties that pave the way to its practical applications in correlated electronics.

Multiple Magnetic Phase Transitions and Critical Behavior in Single-Crystal SmMn2Ge2

Magnetic materials with noncollinear spin configurations have engendered significant interest in condensed matter physics due to their intriguing physical properties. We direct our attention towards the magnetic properties and critical behavior of single-crystal SmMn2Ge2, an itinerant magnet with numerous temperature-dependent magnetic phase transitions. Notably, SmMn2Ge2 displays significant magnetic anisotropy with easy magnetization direction switching from the c axis to the ab plane as temperature decreases. The critical behavior of the ferromagnetic transition occurring above room temperature is thoroughly examined. Reliable and self-consistent critical exponents, including β = 0.292(2), γ = 0.924(8), and δ = 4.164(6), along with the Curie temperature T c = 347 K, are extracted through various methods, which provide evidence for the coexistence of multiple magnetic interactions in SmMn2Ge2. Further analysis reveals that the magnetic interaction of SmMn2Ge2 is a long-range type with the interaction distance decaying as J(r) ∼ r −4.35.

Single-cell intracellular pH dynamics regulate the cell cycle by timing the G1 exit and G2 transition.

Transient changes in intracellular pH (pHi) regulate normal cell behaviors, but roles for spatiotemporal pHi dynamics in single-cell behaviors remain unclear. Here, we mapped single-cell spatiotemporal pHi dynamics during mammalian cell cycle progression both with and without cell cycle synchronization. We found that single-cell pHi is dynamic throughout the cell cycle: pHi decreases at G1/S, increases in mid-S, decreases at late S, increases at G2/M and rapidly decreases during mitosis. Importantly, although pHi is highly dynamic in dividing cells, non-dividing cells have attenuated pHi dynamics. Using two independent pHi manipulation methods, we found that low pHi inhibits completion of S phase whereas high pHi promotes both S/G2 and G2/M transitions. Our data also suggest that low pHi cues G1 exit, with decreased pHi shortening G1 and increased pHi elongating G1. Furthermore, dynamic pHi is required for S phase timing, as high pHi elongates S phase and low pHi inhibits S/G2 transition. This work reveals that spatiotemporal pHi dynamics are necessary for cell cycle progression at multiple phase transitions in single human cells.

Complex phase transitions and phase engineering in the aqueous solution of an isopolyoxometalate cluster

Inorganic salts usually demonstrate simple phasal behaviors in dilute aqueous solution mainly involving soluble (homogeneous) and insoluble (macrophase separation) scenarios. Herein, we report the discovery of complex phase behavior involving multiple phase transitions of clear solution – macrophase separation – gelation – solution – macrophase separation in the dilute aqueous solutions of a structurally well-defined molecular cluster [Mo7O24]6− macroanions with the continuous addition of Fe3+. No chemical reaction was involved. The transitions are closely related to the strong electrostatic interaction between [Mo7O24]6− and their Fe3+ counterions, the counterion-mediated attraction and the consequent charge inversion, leading to the formation of linear/branched supramolecular structures, as confirmed by experimental results and molecular dynamics simulations. The rich phase behavior demonstrated by the inorganic cluster [Mo7O24]6− expands our understanding of nanoscale ions in solution.

Microscopic Imaging Homogeneous and Single Phase Superfluid Density in UTe_{2}.

Odd-parity superconductor UTe_{2} shows spontaneous time-reversal symmetry breaking and multiple superconducting phases, which imply chiral superconductivity, but only in a subset of samples. Here we microscopically observe a homogeneous superfluid density n_{s} on the surface of UTe_{2} and an enhanced superconducting transition temperature near the edges. We also detect vortex-antivortex pairs even at zero magnetic field, indicating the existence of a hidden internal field. The temperature dependence of n_{s}, determined independent of sample geometry, does not support point nodes along the b axis for a quasi-2D Fermi surface and provides no evidence for multiple phase transitions in UTe_{2}.

The modulation of magnetism and charge carrier in magnetic topological insulator MnBi4Te7 by Pb and Sb co-doping

The intrinsic magnetic topological insulator (MTI) MnBi2Te4 family containing magnetic order and nontrivial topology are fantastic materials for studying exotic topological states, such as quantum anomalous Hall effect, but the strong antiferromagnetic (AFM) coupling hinders potential practical applications. Here, we carry out magnetic and transport measurements on (Mn(1−x)Pbx)Bi4Te7 (0 ≤ x ≤ 0.52) single crystals. As x increases from 0 to 0.45, the AFM exchange interaction is gradually weakened by the dilution of magnetic moments. When x reaches up to 0.52, the AFM coupling is completely suppressed and it turns into a ferromagnetic -like ground state. Additionally, Sb substitutions on Bi sites in this system can not only alter the charge carriers but also further influence the magnetism and bring multiple magnetic phase transitions under low temperatures. Our results demonstrate a MTI candidate with adjustable magnetic ground state and charge carriers in Pb and Sb co-doped MnBi4Te7, which provides a promising platform to study rich topological quantum phases and benefits the potential applications in the future.

Anisotropic thermal property characterizations and optical phonon contribution analysis of ZnO under high pressure

Zinc oxide (ZnO) is a wide band-gap semiconductor material with versatile applications in high-tech fields. Under high pressure, ZnO exhibits multiple phase transitions, which are of great significance for the development of photocatalysts, micro-devices with stress-controlled elements, and the investigation of relevant structure-activity relationships. However, previous studies have reported only theoretical calculations of its thermal transport properties under high pressure due to the challenges of experimental methodology. In this work, we employed a combination of the time-domain thermoreflectance technique and diamond anvil cell to characterize the anisotropic thermal properties of ZnO crystal under 0–20 GPa. Simultaneously, we studied the micro-structure of ZnO in the same pressure range by Raman spectra. Our proposed modified Leibfried-Schlomann equation adequately explained the non-monotonic trend of the thermal conductivity within 10 GPa observed in measurement results. Additionally, we report the ZnO thermal conductivity during the decompression process for the first time. Our experimental results and theoretical analysis advance the understanding of the thermal transport mechanism of wide-gap semiconductors under high pressure and pave the way for their high-pressure modification.

Magnetic and Magnetotransport Properties of the Magnetic Topological Nodal‐Line Semimetal TbSbTe

AbstractThe magnetic properties, magneto‐resistivity, Hall resistivity, Seebeck coefficient, and heat capacity are investigated for a magnetic topological nodal‐line semimetal TbSbTe. The calculated energy‐band structures of TbSbTe show two nodal rings on the kx‐ky planes, and the Fermi surface possesses one electron pocket with an enclosure of one hole pocket around the Γ point. The multiple magnetic phase transitions are induced at critical magnetic fields of Hc1 ≈ 10.5 kOe, Hc2 ≈ 20.8 kOe, and Hc3 ≈ 38.2 kOe at 2 K for the H // ab plane. Temperature dependence of electrical resistivity displays a hump‐like feature around 240 K, a general positive slope above TN = 6 K but a negative slope below TN. The magnetoresistance exhibits a conversion from the semi‐classical H2 dependence at weak fields to the linear‐field dependence at high fields, indicating the presence of a Dirac linear energy dispersion. TbSbTe may provide an ideal platform for studying topological physics and designing devices based on topological quantum materials.

Optimal estimation and computational limit of low-rank Gaussian mixtures

Structural matrix-variate observations routinely arise in diverse fields such as multilayer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the fundamental questions like its statistical optimality and computational limit are largely under-explored. In this paper, we propose a low-rank Gaussian mixture model (LrMM) assuming each matrix-valued observation has a planted low-rank structure. Minimax lower bounds for estimating the underlying low-rank matrix are established allowing a whole range of sample sizes and signal strength. Under a minimal condition on signal strength, referred to as the information-theoretical limit or statistical limit, we prove the minimax optimality of a maximum likelihood estimator which, in general, is computationally infeasible. If the signal is stronger than a certain threshold, called the computational limit, we design a computationally fast estimator based on spectral aggregation and demonstrate its minimax optimality. Moreover, when the signal strength is smaller than the computational limit, we provide evidences based on the low-degree likelihood ratio framework to claim that no polynomial-time algorithm can consistently recover the underlying low-rank matrix. Our results reveal multiple phase transitions in the minimax error rates and the statistical-to-computational gap. Numerical experiments confirm our theoretical findings. We further showcase the merit of our spectral aggregation method on the worldwide food trading dataset.

Low-temperature and elastic properties of the 1/1 Tsai-type quasicrystal approximant GdCd6 investigated by ultrasonic measurements

Low-temperature and elastic properties of the quasicrystal approximant GdCd6 have been investigated by means of an ultrasonic measurement. Salient elastic anomalies were observed in the temperature and magnetic field dependence of the principal elastic constants, most probably being associated with the successive multiple magnetic phase transitions showing up at low temperatures. Based on the experimental data, a magnetic field vs temperature phase diagram was constructed. In a zero magnetic field, at least four phases appear to exist. However, the phase diagram both for the magnetic field applied for H// and H// is richer, and interestingly some phase boundaries correspond to the development of field-induced phases, leading to the intricate magnetic phase diagram possibly with multiple ordered phases. We discuss the elastic and electronic properties at low temperatures, and also the nature of the multiple magnetic phase transitions of GdCd6.

Multiple phase transitions and anomalous non-Hermitian skin effect

Non-Hermiticity is revolutionizing the common understanding in the Hermitian scope by interfacing with topological physics. A single non-Hermitian band can host nontrivial topology that is defined over the nonzero windings of the system's eigenvalues, but not the eigenvectors, as opposed to the Hermitian topological systems. This unique non-Hermitian band topology is responsible for the intriguing non-Hermitian skin effect. Here, we show that the band topology of non-Hermitian one-band models can experience multiple phase transitions. Each transition is identified by a change of the eigenvalue winding. Such an interesting phenomenon is enabled by strategically manipulating the long-range couplings. Associated with the multiple phase transitions, the non-Hermitian skin effect exhibits anomalous behaviors, i.e., in different phases, the skin modes take on different forms of wave localizations. At the transition points, the skin modes evolve into Bloch-wavelike extended states, as if the Hermiticity is restored. For demonstration, we consider a modified Hatano-Nelson model with nonreciprocal next-nearest neighbor couplings. Therein, two phase transitions are identified, corresponding to a stationary and a dynamic one (with respect to the reciprocal nearest-neighbor coupling). Exact analytical derivations are performed to analyze the phase transitions and the associated anomalous non-Hermitian skin effect, which show consistency with the numerical results based on the generalized Brillouin zone method. Our work reveals rich non-Hermitian topological physics in one-band systems, which are considered to be topologically trivial in Hermitian systems. By further showing the anomalous non-Hermitian skin effect, intriguing wave manipulations may inspire experiments in classical realms such as photonics and phononics where versatile non-Hermitian controls are feasible.

Multiple phase transitions shape biodiversity of a migrating population.

In a wide variety of natural systems, closely related microbial strains coexist stably, resulting in high levels of fine-scale biodiversity. However, the mechanisms that stabilize this coexistence are not fully understood. Spatial heterogeneity is one common stabilizing mechanism, but the rate at which organisms disperse throughout the heterogeneous environment may strongly impact the stabilizing effect that heterogeneity can provide. An intriguing example is the gut microbiome, where active mechanisms affect the movement of microbes and potentially maintain diversity. We investigate how biodiversity is affected by migration rate using a simple evolutionary model with heterogeneous selection pressure. We find that the biodiversity-migration rate relationship is shaped by multiple phase transitions, including a reentrant phase transition to coexistence. At each transition, an ecotype goes extinct and dynamics exhibit critical slowing down (CSD). CSD is encoded in the statistics of fluctuations due to demographic noise-this may provide an experimental means for detecting and altering impending extinction.

Magnetic and electrical properties of a heavy-fermion compound EuRh2Al8

We report the magnetic, thermodynamic, and electrical properties of ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$, a Eu-based heavy fermion member in the ${\mathrm{RT}}_{2}{\mathrm{X}}_{8}$ families with an orthorhombic $Pbam$ structure. Magnetization studies reveal multiple phase transitions in the single crystals, including two successive antiferromagnetic transitions at ${T}_{N1}\ensuremath{\sim}12.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{N2}\ensuremath{\sim}8.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. These two transitions are closely related to competing magnetic interactions in the Shastry-Sutherland lattice, which further give rise to another in-plane spin-flop transition at 1/3 of the full magnetization below 5 K when the applied magnetic field is higher than 6 T within the $ab$ plane. In addition to these, specific heat measurements in ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$ demonstrate a heavy fermion state with a large Sommerfeld coefficient $\ensuremath{\gamma}=393\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{mol}}^{\ensuremath{-}1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{K}}^{\ensuremath{-}2}$. Electrical transport measurement shows that its resistivity exhibits a ${T}^{2}$-dependence below ${T}_{N2}$ and a robust linear $T$-dependence above ${T}_{N1}$, which is also typical of a heavy fermion metal. Our work provides fundamental physical properties of ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$ and promotes understanding of the complex magnetic interactions and unusual spin correlations in the ${\mathrm{RT}}_{2}{\mathrm{X}}_{8}$ families.

Sawtooth lattice multiferroic BeCr2O4 : Noncollinear magnetic structure and multiple magnetic transitions

Noncollinear magnetic structures and multiple magnetic phase transitions in a sawtooth lattice antiferromagnet consisting of ${\mathrm{Cr}}^{3+}$ are experimentally identified in this work, thereby proposing the scenario of magnetism-driven ferroelectricity in a sawtooth lattice. The title compound, ${\mathrm{BeCr}}_{2}{\mathrm{O}}_{4}$, displays three magnetic phase transitions at low temperatures---at ${T}_{N1}\ensuremath{\approx}7.5$ K, at ${T}_{N2}\ensuremath{\approx}25$ K, and at ${T}_{N3}\ensuremath{\approx}26$ K---revealed through magnetic susceptibility, specific heat, and neutron diffraction in this work. These magnetic phase transitions are found to be influenced by externally applied magnetic fields. Isothermal magnetization curves at low temperatures below the magnetic transitions indicate the antiferromagnetic nature of ${\mathrm{BeCr}}_{2}{\mathrm{O}}_{4}$ with two spin-flop-like transitions occurring at ${H}_{c1}\ensuremath{\approx}29$ kOe and ${H}_{c2}\ensuremath{\approx}47$ kOe. Our high-resolution x-ray and neutron diffraction studies, performed on single crystal and powder samples, unambiguously determined the crystal structure as orthorhombic $Pbnm$. By performing the magnetic superspace group analysis of the neutron diffraction data at low temperatures, the magnetic structure in the temperature range ${T}_{N3,N2}<T<{T}_{N1}$ is determined to be the polar magnetic space group $P21nm.{1}^{\ensuremath{'}}(00g)0s0s$ with a cycloidal magnetic propagation vector ${\mathbf{k}}_{1}=(0,0,0.090(1))$. The magnetic structure in the newly identified phase below ${T}_{N1}$ is determined as $P21/b.{1}^{\ensuremath{'}}[b](00g)00s$ with the magnetic propagation vector ${\mathbf{k}}_{2}=(0,0,0.908(1))$. The cycloidal spin structure determined in our work is usually associated with electric polarization, thereby making ${\mathrm{BeCr}}_{2}{\mathrm{O}}_{4}$ a promising multiferroic belonging to the sparsely populated family of sawtooth lattice antiferromagnets.

Quasi-two-dimensional magnetic properties in atomic layer resolved La0.7Sr0.3MnO3/LaAlO3 superlattices

Materials in low dimensions show interesting physics and excellent potential in practical applications. The atomic-level control of two-dimensional (2D) behavior in a traditional three-dimensional (3D) system is quite hard, and the ${({\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3})}_{n}/{(\mathrm{LaAl}{\mathrm{O}}_{3})}_{n}$ (LMSO/LAO) superlattice on a (001) $\mathrm{SrTi}{\mathrm{O}}_{3}$ substrate was investigated to explore its quasi-2D behavior. The number of magnetic phase transitions has a close relationship with the number of unit cells ($n$): only one phase transition for $n=2$ and four phase transitions for $n=8$. It was found that the local structure of each ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3}$ atomic layer is responsible for the multiple phase transitions: the gradual change of the tetragonal ratio and the in-plane tensile strain-induced $3d$ electronic orbital occupancy control the magnetic properties of 2D-LSMO atomic layers. For the outmost 2D-LSMO atomic layer contacting $\mathrm{LaAl}{\mathrm{O}}_{3}$ directly, interface-related factors reduce the intensity of magnetic interaction significantly. With the increase of $n$, the properties around the LSMO/LAO interface changes, which demonstrates that the superlattice configuration and the lattice-mismatch strain could be employed to explore the quasi-2D behavior of a traditional 3D system.

Phonon dynamics in lead free perovskite (1-x)KNN-xBAN (x = 0.0–0.1): a temperature dependent raman study

K0.5Na0.5NbO3 (KNN) has been under extensive focus in recent times due to it being an alternative to lead-free multifunctional materials and properties like room temperature ferroelectricity, stability in air and technology friendly applications. In this work, we report a comprehensive temperature dependent, compositional change induced structural variation and polarization dependent Raman spectroscopy on BaAl0.5Nb0.5O3 (BAN) doped KNN in the spectral range of 10–1000 cm−1. Multiple phase transitions are marked by the strong renormalization of the phonon self-energy parameters, i.e. mode frequencies and linewidths, in the temperature range of 83 K to 623 K. Change in the phase transition temperature is tracked via phonon anomalies with varying doping concentration, x = 0.0, 0.02, 0.05, 0.07 and 0.1, and is found to be as large as ∼100 K for orthorhombic to tetragonal phase transition for x = 0.1. Raman extracted phase diagram shows that the stability of the ferroelectric orthorhombic phase in the vicinity of room temperature increases with the increasing doping concentration. Also, from our polarization-dependent measurements we could decipher the symmetry of the observed phonon modes for KNN system.

Orthorhombic Na2/3Cu0.1Mn0.9O2 cathode: Enhanced Na storage performances with the suppressed Mn–O bond anisotropy

Orthorhombic Mn-based layered oxides (P′2) have drawn much attention as promising cathode materials for sodium ion batteries (SIBs) with high specific capacities and rich resources. However, P′2-NaxMnO2 cathode suffers from inferior rate capability and poor cycling performances, owing to the complicated phase transition during de-/sodiation process. Herein, Cu-substitution P′2-Na2/3Cu0.1Mn0.9O2 is successfully prepared to mitigate the multiple phase transition by reducing the distortion of the MnO6 octahedron. Mn–O bond anisotropy is decreased and the spacing distance of Na layer is constricted by the modulation of the CuO6 octahedron, giving enhanced electronic conduction, validated by theoretical calculations and X-ray diffraction refinement. P′2-OP4 phase transition is replaced by reversible P′2-Z phase transition with slighter volume change, leading to the lower lattice strain in both c-axis direction and a-b plane, as probed by Operando/ex situ X-ray diffraction and synchrotron X-ray absorption spectra, which strengthens the stability of lattice skeleton. Consequently, P′2-Na2/3Cu0.1Mn0.9O2 exhibits outstanding rate capabilities (102 mAh/g at 750 mA g−1) and enhanced cycle performances (91 % at 150 mA g−1 after 100 cycles). This Cu-substitution strategy provides an effective method to design the structure-stable layered oxide cathodes for SIBs.