The search for candidate Kitaev materials has largely focused on $4d$ and $5d$ transition-metal compounds with various lattice geometries. In contrast, investigations of rare-earth $4f$ systems have thus far been restricted mainly to honeycomb and triangular lattices. In this work, we investigate the rare-earth-based double perovskites ${\mathrm{Ba}}_2{\mathrm{YbNbO}}_6$ and ${\mathrm{Ba}}_2{\mathrm{NdNbO}}_6$, which crystallize in a face-centered cubic structure. Magnetization and heat-capacity measurements establish isolated $j_{\mathrm{eff}}=1/2$ Kramers doublet ground states arising from strong spin-orbit coupling (SOC) and crystal electric-field effects, which are further supported by density functional theory calculations. Millikelvin-temperature thermodynamic measurements reveal long-range magnetic order with moderate frustration in both compounds. The emergence of magnetic order may be understood within an order-by-disorder scenario, as theoretically proposed for rare-earth fcc lattices with finite Kitaev interactions. Our results thus identify ${\mathrm{Ba}}_2{\mathrm{YbNbO}}_6$ and ${\mathrm{Ba}}_2{\mathrm{NdNbO}}_6$ as promising rare-earth spin-orbit-entangled magnets and motivate further experimental and theoretical investigations aimed at determining the complete exchange tensor to elucidate the microscopic origin of the underlying magnetic interactions.

We compare extensive ab initio simulations and embedded-atom-model molecular dynamics for analysis of collective dynamics in liquid Fe at several experimental pressures and temperatures of 2200 and 2700 K [Y. Kuwayama et al., Phys. Rev. Lett. 124, 165701 (2020)]. Dynamic eigenmodes of the generalized Langevin equation were calculated based on simulation data and analyzed in a wide range of wave numbers with a focus on dispersion of collective excitations. We analyze the origin of positive dispersion of sound excitations in connection with contributions from different types of hydrodynamic and nonhydrodynamic fluctuations to the corresponding eigenvectors. Dispersion of collective excitations and adiabatic speed of sound, estimated from the simulation data at three pressures, is compared to the values obtained from the inelastic x-ray scattering experiments.

MAX phase $\mathrm{T}{\mathrm{i}}_2\mathrm{SC}$ comes under the category of hexagonal ternary carbides whose room-temperature (RT) total thermal conductivity $\left({\kappa }_{\mathrm{T}}={\kappa }_{\mathrm{e}}+{\kappa }_{\mathrm{ph}}\right)$ is experimentally reported to be the highest amongst all in the 211 category and one of the highest values across the broader MAX-phase family. It shows anomalous temperature $\left(\mathrm{T}\right)$ dependence of ${\kappa }_{\mathrm{T}}$ at high $T$ over a broad range of temperatures. In this study, employing first-principles-based phonon-electron calculations, we quantify the contributions of both electron (${\kappa }_{\mathrm{e}}$) and phonon (${\kappa }_{\mathrm{ph}})$ separately to its thermal conductivity without considering the Sommerfeld value as the decoupling factor. We demonstrate that the weak temperature dependence of ${\kappa }_{\mathrm{T}}$ above RT arises from the comparable phonon-electron interaction relative to the phonon-phonon interaction, and the room-temperature contribution of ${\kappa }_{\mathrm{ph}}$ is 50% of the total thermal conductivity. The phonon-electron interaction is found to be higher throughout the whole frequency range compared to the anharmonic phonon-phonon interaction because of the large density of states around the Fermi energy, hence high metallicity, arising from two opposing types of interactions, antibonding $\mathrm{Ti}d\text{−}\mathrm{S}p$ and bonding $\mathrm{Ti}d\text{−}\mathrm{Ti}d$. The anharmonic phonon-phonon scattering rate is also noted to be higher in $\mathrm{T}{\mathrm{i}}_2\mathrm{SC}$ than in other group-d carbides due to significant cross-plane phonon-phonon coupling and an asymmetric bonding environment. At temperatures below 400 K, the electronic Lorenz number significantly deviates from its conventional Sommerfeld value. Despite the strong structural anisotropy in $\mathrm{T}{\mathrm{i}}_2\mathrm{SC}$, its electrical transport is isotropic, while thermal transport shows only weak anisotropy. This behavior originates from the compensation between group velocities and scattering rates either across different electronic bands and phonon modes, or between their energy-dependent directional averages.

We develop a self-energy-dressed Green's function framework for terahertz-induced phonon angular momentum in polar crystals. The rectified angular-momentum response is formulated as a second-order response and, within a dressed-bubble approximation, is expressed in terms of retarded phonon propagators weighted by mode-resolved polarization and angular-momentum matrix elements. Anharmonic self-energies enter through the dressed propagators, incorporating finite-temperature frequency renormalization and linewidth broadening directly into the response kernel. Applying this framework to wurtzite GaN, we show that the terahertz propagation direction and polarization select distinct rotational phonon channels: a nondegenerate ${\mathrm{E}}_1\left(\mathrm{TO}\right)\text{−}{\mathrm{A}}_1\left(\mathrm{TO}\right)$ channel with phase- and frequency-tunable angular momentum, and a degenerate ${\mathrm{E}}_1\left(\mathrm{TO}\right)$ channel with helicity-selected response. Anharmonic broadening suppresses and smooths the resonant structures while preserving the characteristic phase dependence of each channel. An order-of-magnitude estimate based on the phonon inverse Faraday-effect framework gives an mT-scale effective magnetic field for representative electron-phonon coupling strengths. This work places coherent terahertz-driven circular-phonon physics in a first-principles-based response framework and provides a starting point for going beyond constant-damping driven-mode descriptions.

The essence of the quantum anomalous Hall (QAH) effect is that, in the absence of an external magnetic field, the bulk of a material remains insulating while its boundaries host a quantized number of dissipation-free chiral edge channels determined precisely by the Chern number. A high Chern number signifies multiple parallel dissipationless transport pathways, dramatically boosting the efficiency of charge and information transfer. Here, we adopt stacking engineering to implement layer-degree-of-freedom-programmable QAH effects in the A-type antiferromagnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. A perpendicular electric field drives the system reversibly between topologically nontrivial and trivial regimes and further induces a high-Chern-number quantum Hall state accompanied by a multilayer Hall effect, i.e., a robust bilayer current redistribution between surface and middle layers, extending tunability from single to dual layers. Floquet calculations show that circularly polarized light can suppress layer-resolved Hall response; the QAH state depends markedly on the light's helicity, with AB and BA stackings exhibiting opposite responses to left- and right-handed circular polarization. This work establishes a framework for electric- and optical-field control of layer Hall effects, offering materials-compatible theoretical routes and experimental protocols for ultra-low-power topological electronics, layer-resolved memory, and reconfigurable quantum devices.

We investigate the interplay between superconductivity and nematic order in a two-dimensional electron gas with competing pairing and quadrupolar forward-scattering interactions. The model includes both $s$-wave and $d$-wave superconducting channels. We compute the mean-field free energy density and determine the phase diagrams as functions of interaction strengths and temperature by solving a set of coupled self-consistent equations. At zero temperature, we find that the nematic order competes strongly with $d$-wave superconductivity, leading to a direct first-order phase transition, while its interplay with $s$-wave pairing allows for a coexistence phase characterized by an anisotropic Fermi surface with a uniform superconducting gap. At finite temperatures, quadrupolar interactions promote the emergence of additional superconducting components, giving rise to regimes where $s$-wave, $d$-wave, and nematic orders coexist. Our results highlight the role of symmetry and interaction strength in shaping the phase structure and provide a minimal framework to describe intertwined nematic and superconducting phases in correlated electron systems.

Unidirectional magnetoresistance, or electric magnetochiral anisotropy (eMChA), is a nonlinear magnetotransport effect emerging in noncentrosymmetric conductors. This phenomenon manifests as a resistance $R$ change proportional to the first power of both the electric current $\mathbf{I}$ and applied magnetic field $\mathbf{B}$. The eMChA contribution $\mathrm{\Delta }R\left(B\right)/R\left(0\right)$ takes distinct forms: (i) a chiral term, $2\chi \mathbf{I}·\mathbf{B}$, and (ii) a polar term, $2\gamma \mathbf{I}·(\mathbf{P}\times \mathbf{B})$, where $\mathbf{P}$ denotes the electric polarization and $\chi$ and $\gamma$ represent the respective eMChA coefficients. In Fontana et al. [Phys. Rev. Lett. 135, 106602 (2025)], we provided empirical evidence that the eMChA in the conduction band of tellurene is polar $(\chi =0,$ $\gamma \ne 0)$ and showed that it emerges from the quantum metric dipole associated with its Weyl node and from the lone pair polarization $\mathbf{P}$. Here, we extend this study to the valence band of tellurene, where the eMChA is commonly assumed to be chiral $(\chi \ne 0,\gamma =0)$. We show that a finite polar coefficient $\gamma \ne 0$ also emerges naturally through a downfolding procedure, in which remote Weyl-node-containing bands induce momentum-space gradients of the quantum metric in the low-energy levels, activating finite metric dipoles. Combining semiclassical Boltzmann transport with a $\mathbf{k}·\mathbf{p}$ description of tellurene, our numerical calculations agree quantitatively with doping $\left(\mu \right)$ dependent second-harmonic measurements of the longitudinal voltage $V_{\parallel }^{2\omega }\left(\mu \right)$ in perpendicular field. The combined chiral and polar characters $(\chi \ne 0,\gamma \ne 0)$ of the eMChA in tellurene also explains the shift in the angular $\left(\varphi \right)$ dependence of $V_{\parallel }^{2\omega }\left(\varphi \right)$ for in plane fields. Our results demonstrate that the polar eMChA can arise in topologically trivial bands through multiband effects and establish tellurene as a platform for quantum-geometric rectification in both electron and hole regimes.

We show that a hybrid moiré one-dimensional (moiré-1D) superlattice gives electrical control over whether a Dirac-Dirac momentum resonance opens a charge-neutrality gap, and through which mass channel. In twisted bilayer graphene subject to a layer-dependent unidirectional scalar potential, the charge-neutrality gap is controlled by the Fourier parity of the resonance-selected dressed interlayer harmonic: odd selected harmonics gap same-chirality Dirac-cone pairs, whereas even selected harmonics gap opposite-chirality pairs. A dressed-harmonic two-cone theory shows that this rule follows from two ingredients: the selected harmonic fixes the Pauli sector of the intercone matrix, and the dressed transverse velocities fix the relative chirality of the interacting cones. Because the 1D modulation can reverse the transverse velocity of one layer, it can electrically switch the relative chirality and hence the active mass channel, e.g., turning an even resonance from gapless to gapped. Full-wave continuum miniband calculations confirm both the exact-resonance rule and a finite near-resonant gapped window with quantitative fabrication tolerances. Far away from resonance, the same dressing yields strongly anisotropic but gapless Dirac bands. Hybrid moiré-1D superlattices therefore provide a route to programmable mass selection in coupled Dirac systems.

Orbital-free density functional theory (OFDFT) is a promising route to large-scale first-principles simulations, but its application to second-row covalent systems remains limited by the inaccurate description of localized, highly inhomogeneous densities and by the lack of angular-momentum dependence in conventional local pseudopotentials. Here, we develop a unified tight-binding orbital-free density functional theory framework that incorporates both nonlocal kinetic energy and nonlocal pseudopotential energy terms within the same reference-density expansion. In this formulation, a frozen reference density constructed from scaled atomic densities captures the dominant localized atomic contributions, while the self-consistent density variation accounts for bonding and environment-dependent effects. Meanwhile, the nonlocal pseudopotential energy density functional restores the angular-momentum-dependent electron-ion interactions essential for describing directional bonding. Benchmarks on representative B- and C-based covalent systems show that the proposed framework accurately reproduces the equation-of-state properties, relative energetics, and electron-density distributions of diverse boron allotropes while retaining the linear-scaling behavior of OFDFT. For carbon allotropes, the method captures the main structural and bonding trends, with remaining deviations mainly associated with the near-core kinetic energy density of dense $s{p}^3$ phases. These results establish a viable unified OFDFT framework for large-scale simulations of covalent materials and highlight the accuracy of near-core kinetic energy as a key challenge for further methodological development.

We introduce a Kapitza-like mechanism for the near-field radiative heat transfer and show that fast modulation of any parameter controlling the flux, such as the vacuum gap or a material response, produces a quadratic, time-averaged correction in the slow thermal dynamics. This correction splits into a frequency-independent static term and a low-pass dynamical term, yielding sizable modulation-induced temperature shifts and modified effective thermal conductances that can stabilize or destabilize the steady state. Applying the theory to gap modulation between SiC slabs, we derive analytical scaling laws and predict temperature shifts that are fully measurable with existing experimental platforms, requiring only readily accessible low modulation frequencies of order $\mathrm{\Omega }\approx {10}^4\mathrm{rad}/\mathrm{s}$. Our results establish a thermal analog of the Kapitza mechanism and provide a general route for controlling radiative heat flow in micro- and nanoscale platforms.

Blue phosphorene (BlueP) has attracted considerable attention, and Cu(111) has been widely explored as a potential growth substrate. However, although several experiments have interpreted phosphorus-derived phases on Cu(111) as BlueP or BlueP-related structures, the chemical identity and atomic registry of the early-stage stripe phases remain unresolved. Here, by combining first-principles calculations with systematic structural searches, we identify a ${\mathrm{Cu}}_3{\mathrm{P}}_2$ ribbonlike surface alloy as the lowest-energy candidate for these stripe phases within the explored configuration space, rather than a direct pure BlueP overlayer. The simulated scanning tunneling microscopy contrast of this model is consistent with the observed stripe features, while its registry with Cu(111) accounts for the reported orientation locking. We further show that ${\mathrm{Cu}}_3{\mathrm{P}}_2$ ribbons can be periodically stitched into longer-period Cu–P superstructures that are energetically favored among the structures considered. In contrast, direct BlueP formation on bare Cu(111) is less favorable than several low-energy Cu–P surface-alloy structures. These results clarify the atomic structure and orientation-locking mechanism of phosphorus-induced stripe phases on Cu(111) and provide an atomic-scale basis for understanding the subsequent coverage-dependent evolution of the P/Cu(111) system.

Stacking order and layer thickness exert significant influence on the physical properties of two-dimensional materials. Here, using first-principles calculations and symmetry analysis, we theoretically investigate the stacking- and layer-dependent Raman responses of InSe and infer the corresponding symmetry-based second-harmonic generation (SHG) selection rules. For bulklike InSe, the calculated low-frequency Raman spectra (below $30 {\mathrm{cm}}^{-1}$) enable direct phase-sensitive spectral fingerprints: no peak is found for $\gamma$-InSe, whereas $\epsilon$- and $\beta$-InSe exhibit peaks near 20.2 and $17.8 {\mathrm{cm}}^{-1}$, respectively. Point-group analysis further indicates that SHG response is symmetry-allowed for bulk $\gamma$- and $\epsilon$-InSe, whereas it is symmetry-forbidden for bulk $\beta$-InSe. For few-layer InSe, the frequencies of the strongest shear modes exhibit a blueshift for the AB-stacked $\epsilon$ and $\beta$ phases, but a redshift for the ABC-stacked $\gamma$ phase, as the layer number increases. SHG response is symmetry-allowed for both odd- and even-layer $\gamma$- and $\epsilon$-InSe, whereas it is allowed for odd layers and forbidden for even layers in $\beta$ phase. This layer-dependent evolution of the low-frequency Raman modes, combined with symmetry-based SHG selection rules, provide an effective route for distinguishing the three InSe polytypes in the few-layer regime. In the high-frequency region, the ${{\mathrm{A}}^{\prime }}_1^1(\sim 110$ ${\mathrm{cm}}^{-1}$) and ${{\mathrm{A}}^{\prime }}_1^2(\sim 235$ ${\mathrm{cm}}^{-1}$) modes display a blueshift and a redshift, respectively, for all three phases with increasing layer thickness. The low-frequency shear modes and the frequency difference between ${{\mathrm{A}}^{\prime }}_1^1$ and ${{\mathrm{A}}^{\prime }}_1^2$ can serve as indicators of layer number in ultrathin films. Combined with analytical lattice-dynamical models, we reveal that the competition between the surface effect and the thickness effect governs the overall evolution of the high-frequency Raman trends. This work clarifies the microscopic origin of Raman responses in InSe and provides theoretical guidance for phase identification, thickness estimation, and elastic modulus characterization of layered materials.

We theoretically study the phase-dependent thermal conductance of a short Josephson junction based on a Rashba semiconducting nanowire with proximity-induced superconductivity. We show that an in-plane Zeeman field induces a quasicontinuum of states inside the superconducting gap, leading to a strong enhancement of the low-temperature thermal conductance. The thermal conductance exhibits a sharp peak precisely at the critical field that separates the trivial and topological superconducting phases, thereby serving as a sensitive probe of the topological phase transition. Moreover, when the Zeeman field acquires a component parallel to the Rashba spin-orbit field, the Andreev bound states experience a Doppler shift, giving rise to an anomalous phase-dependent thermal conductance. This Doppler shift is directly related to an effective finite-momentum pairing of Cooper pairs. Our results establish phase-coherent heat transport as an effective and complementary tool for detecting finite-momentum pairing and topological transitions in nanowire-based Josephson junctions.

Sodium-ion batteries have gained much interest over the past years and especially layered oxides are highly considered as cathodes for the next generation of batteries. However, there are still significant challenges to overcome in these materials for practical applications mainly related to capacity degradation and voltage fading. A key influence factor for these challenges are phase transitions that occur by gliding of layers during operation of these materials. Until now there is limited atomistic-level understanding on such transitions as simulations of these processes are computationally demanding. In this work, we trained a classical pairwise Coulomb-Buckingham potential versus extensive ab initio data using a genetic algorithm to study O2-P2 phase transitions in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$. Our density functional theory (DFT) and classical potential calculations show that phase-transition barriers decrease upon desodiation and are further lowered if dynamic conditions are considered through molecular dynamics simulations. Our developed classical potential is able to capture phase transitions and its related increase in the Na-ion diffusivity under standard laboratory conditions at the $\mu \mathrm{s}$ timescale of molecular dynamics simulation. Furthermore, it is found that the phase transition occurs gradually via various $\mathrm{OP}n$ phases.

As prototypical strongly correlated materials, manganese oxides serve as key platforms for studying electronic correlations. Under high pressure, drastic changes in local coordination, bond lengths, and electronic screening modify the electron correlation strength. However, due to the difficulty in determining the Hubbard $U$ value to correctly describe the localized $d$-electron state for various structures in high-pressure simulations, previous works generally used fixed $U$ values to investigate the pressure-driven phase transition of manganese oxides, resulting in significant controversies. Here, a machine learning approach is developed to fit the Hubbard $U$ parameters for exploring the high-pressure properties of ${\mathrm{Mn}}_{\mathrm{y}}{\mathrm{O}}_{\mathrm{x}}$ and applied to construct convex hulls at pressures of 0–200 GPa. Several new high-pressure phases are found and long-standing controversies about the phase-transition sequence of MnO and ${\mathrm{Mn}}_2{\mathrm{O}}_3$ are resolved by high-throughput structure search and comparing x-ray diffraction patterns. This work provides new insights into the high-pressure behavior of the Mn-O system and contributes to advancing studies of transition metal oxides characterized by localized $d$ electrons.

It has been suggested that the anisotropic behavior of orbital transport can be distinct from that of the spin counterpart. On another front, the microscopic mechanisms underlying the anomalous Hall effect and the spin Hall effect are generally categorized into the intrinsic Berry curvature mechanism and the extrinsic mechanism induced by disorder scattering, each with distinct scaling relations. A similar analysis for orbital transport has rarely been performed. Here, we investigate both aspects of the orbital current generation in a light metal V. The orbital-to-spin conversion is achieved using a heavy metal Pt insertion layer or Ni as the ferromagnetic layer. Benefiting from the epitaxial growth of V with a low disorder strength, the orbital current generation is characterized by a large transverse conductivity and long diffusion length, consistent with the expectation for an intrinsic orbital Hall effect. Across all the heterostructures studied, we confirm the orbital current's isotropic nature, i.e., the orbital current generation is barely affected when the charge current is applied along different crystallographic directions, consistent with the high-symmetry crystal structure. Crucially, the intrinsic nature of the orbital current generation is demonstrated by the scaling analysis, showing a scattering-independent orbital Hall conductivity.

We investigated the rare-earth triangular-lattice antiferromagnet ${\mathrm{NdMgAl}}_{11}{\mathrm{O}}_{19}$ using single-crystal magnetization (1.8 K $\le T\le$ 300 K, ${\mu }_{0}H\le 7\mathrm{T}$) and specific-heat measurements down to 45 mK. The dc susceptibility confirms a well-isolated Kramers doublet ground state with pronounced Ising-type anisotropy, with $g_c\approx 3.7, g_{ab}\approx 1.45$. Curie-Weiss fits yield weak, anisotropic antiferromagnetic exchange, with ${\theta }_c=-0.54\mathrm{K}$ and ${\theta }_{ab}=-0.87\mathrm{K}$. Heat capacity measurements show no long-range magnetic order down to 40 mK. Instead, $C_m/T$ exhibits a broad maximum near 0.081 K whose magnitude and field evolution are consistent with short-range correlations in an anisotropic triangular lattice. Applied magnetic fields open a Zeeman gap where the specific-heat anomaly follows $\mathrm{\Delta }=g{\mu }_B{\mu }_{0}H$, and $M(H,T)$ is well described by a Brillouin function for a $J_{\mathrm{eff}}=\frac{1}{2}$ moment. The field tuning of the low-temperature entropy manifold allows self-cooling from 1.8 K to 53 mK by adiabatic demagnetization from a ${\mu }_{0}H=9\mathrm{T}$ field. These results identify ${\mathrm{NdMgAl}}_{11}{\mathrm{O}}_{19}$ as a nearly ideal weak-exchange triangular magnet with a field-tunable correlated ground state.

A series of Ruddlesden-Popper perovskite solid solutions, ${\mathrm{Ca}}_2{\mathrm{Mn}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_4 (0.25\le x\le 0.65)$, is examined by combining density functional theory (DFT) calculations with local-scale experimental studies conducted at ISOLDE-CERN over a broad temperature range (10–1220 K). Perturbed angular correlation (PAC) spectroscopy probes the $I4/mmm$ to $I{4}_1/acd$ structural phase transitions for all compositions between 900 and 1200 K. For $x=0.65$, measurements below 160 K show that a second structural phase condenses, coexisting with the $I{4}_1/acd$ phase down to 10 K. DFT structural models reproduce a key experimental observation: in the $I{4}_1/acd$ phase, the $c$ lattice parameter shows only a minor increase upon Ti substitution, whereas the $ab$ plane expands significantly, reducing the $c/a$ ratio linearly. This anisotropic response can be attributed to a corkscrewlike mechanism, where the enhancement of in-plane $B{\mathrm{O}}_6$ octahedral rotations induces a contraction of the rocksalt layers, thereby mitigating the expansion of the $c$ axis. PAC data, supported by DFT calculations, demonstrate that Ca sites apically connected to ${\mathrm{MnO}}_6$ octahedra exhibit experimentally distinguishable Electric Field Gradients from those connected to ${\mathrm{TiO}}_6$ octahedra.

The temperature-dependent intrinsic magnetic properties of ${\mathrm{SmCo}}_5$ and its Fe- or Cu-doped compounds are systematically investigated via atomistic spin simulations. For pristine ${\mathrm{SmCo}}_5$, Curie temperature $T_{\text{C}}$ and effective anisotropy constant $K_1^{\text{eff}}$ at 0 K are calculated as 1000 K and $35\mathrm{MJ}\text{/}{\mathrm{m}}^3$, respectively, agreeing with experimental results. The domain-wall width ${\delta }_{\text{w}}$ and exchange stiffness $A_{\text{e}}$ at 0 K are determined as 3.31 nm and 39.3 pJ/m, respectively. As temperature increases, the domain wall broadens and both $K_1^{\text{eff}}\left(T\right)$ and $A_{\text{e}}\left(T\right)$ decrease, with a scaling law as $A_{\text{e}}\propto {[M_{\text{s}}\left(T\right)/M_{\text{s}}\left(0\right)]}^{1.86}$. For the metal-doped $\text{Sm}{\left({\text{Co}}_{1-x}{M}_x\right)}_5$ compounds ($M=\text{Fe},\text{Cu}$; $x=0.2,0.4$), magnetic Fe doping is found to increase $T_{\text{C}}$ through Fe-Co exchange, while nonmagnetic Cu doping decreases $T_{\text{C}}$. Both metal dopants reduce $K_1^{\text{eff}}$ by perturbing the Sm crystal field and Co spin-orbit coupling. Magnetic Fe doping is revealed to improve the thermal stability of the magnetic anisotropy of ${\mathrm{SmCo}}_5$, while nonmagnetic Cu doping weakens it. This work could advance the understanding of ${\mathrm{SmCo}}_5$ permanent magnets and the impact of transition-metal doping through a comprehensive quantification of their temperature-dependent magnetic properties.