We have studied the multicaloric properties of a Ni-Mn-Ga-Cu alloy. In this alloy, application of magnetic field and uniaxial stress shift its martensitic transition towards higher temperatures which results in synergic magnetocaloric and elastocaloric effects. By a proper numerical treatment of the calorimetric curves obtained under applied magnetic field and uniaxial stress we have obtained the entropy $S(T,{\mu }_{0}H,\sigma )$ as a function of the magnetic field, uniaxial stress, and temperature over the whole phase space under study. We have determined the different entropy contributions to the multicaloric effect in this alloy, and noticeably we have evidenced the role played by the interplay between magnetic and vibrational degrees of freedom. A comparison between single caloric and multicaloric effects shows that appropriate combinations of magnetic field and stress reduce the magnitude of the specific field required to obtain a given value of the isothermal entropy and adiabatic temperature changes. For example, at 299 K, to achieve an entropy change ($\mathrm{\Delta }S$) of $-14$ J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$, a magnetic field of $\sim 2.5$ T or a uniaxial stress of 19 MPa are required, while a combination of dual fields of (1 T, 12 MPa) yields to the same value of $\mathrm{\Delta }S$. Moreover, the maximum adiabatic temperature change is enlarged up to 9.4 K by the dual fields, higher than the value obtained by a single field ($\sim 7$ K). The advantage of multicaloric effect is particularly relevant at low magnetic fields which are achievable by permanent magnets. Our findings open new avenues for using multicaloric materials in novel refrigeration technologies.

The energy of the valence band maximum of ${\mathrm{NaNbO}}_3$ is determined from the Schottky barrier heights at the contacts with low work function Sn-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ and high work function ${\mathrm{RuO}}_2$ by means of x-ray photoelectron spectroscopy with in situ interface preparation. The measurements reveal a valence-band edge energy, which is comparable to that of ${\mathrm{SrTiO}}_3$ and ${\mathrm{BaTiO}}_3$. The energy gap of ${\mathrm{SrTiO}}_3$ and ${\mathrm{BaTiO}}_3$ is $3.2\mathrm{eV}$ and comparable to the values of $3.4\mathrm{eV}\mathrm{to}3.5\mathrm{eV}$, which are determined by means of optical and electron energy loss spectroscopy for ${\mathrm{NaNbO}}_3$. It is therefore expected that the conduction band minimum of ${\mathrm{NaNbO}}_3$ is also located at a similar energy as the conduction band minimum of ${\mathrm{SrTiO}}_3$ and ${\mathrm{BaTiO}}_3$. If this is the case, it can be expected that donor doping of ${\mathrm{NaNbO}}_3$ leads to an electrical conductivity, which is comparable to those of donor-doped ${\mathrm{SrTiO}}_3$ and ${\mathrm{BaTiO}}_3$ (up to $\sim$ $1\mathrm{S}/\mathrm{c}{\mathrm{m}}^{-1}$). In contrast, Sr- and Ca-doped ${\mathrm{NaNbO}}_3$ bulk ceramics exhibit a room temperature conductivity up to $10\times {10}^{-10}\mathrm{S}/\mathrm{c}{\mathrm{m}}^{-1}$, only slightly higher than that of ${\mathrm{NaNbO}}_3$. High-field conductivity measurements and impedance spectroscopy give no indication that the low conductivity is caused by insulating grain boundaries separating electrically conductive grains. It is therefore suggested that the energy gap of ${\mathrm{NaNbO}}_3$ is substantially higher than the gap of $3.4\mathrm{eV}\mathrm{to}3.5\mathrm{eV}$ determined from optical spectroscopy reported in literature and from electron energy loss spectroscopy within this paper, as also suggested from electronic structure calculations of ${\mathrm{LiNbO}}_3$ [Phys. Rev. B 77, 035106 (2008)].

Skyrmion stabilization in novel magnetic systems with the B20 crystal structure is reported here, primarily based on theoretical results. The focus is on the effect of alloying on the $3d$ sublattice of the B20 structure by substitution of heavier $4d$ and $5d$ elements, with the ambition to tune the spin-orbit coupling and its influence on magnetic interactions. State-of-the-art methods based on density functional theory are used to calculate both isotropic and anisotropic exchange interactions. Significant enhancement of the Dzyaloshinskii-Moriya interaction is reported for $5d$-doped FeSi and CoSi, accompanied by a large modification of the spin stiffness and spiralization. Micromagnetic simulations coupled to atomistic spin-dynamics and ab initio magnetic interactions reveal the spin-spiral nature of the magnetic ground state and field-induced skyrmions for all these systems. Especially small skyrmions $\sim 50\mathrm{nm}$ are predicted for ${\mathrm{Co}}_{0.75}{\mathrm{Os}}_{0.25}\mathrm{Si}$, compared to $\sim 148\mathrm{nm}$ for ${\mathrm{Fe}}_{0.75}{\mathrm{Co}}_{0.25}\mathrm{Si}$. Convex-hull analysis suggests that all B20 compounds considered here are structurally stable at elevated temperatures and should be possible to synthesize. This prediction is confirmed experimentally by synthesis and structural analysis of the Ru-doped CoSi systems discussed here, both in powder and in single-crystal forms.

Defect centers in solid-state materials have played an important role in the development of quantum information science as spin qubits. In recent years, many studies using optically detected magnetic resonance (ODMR) to manipulate the ground state spin of transition metal dopants have been reported. In this work, the tetrahedral $d^2$ and the octahedral $d^3$ transition metal ion systems are considered for the potential spin qubits, based on the ligand field theory and the basic requirements of general $\mathrm{\Lambda }$-type spin qubits. Then a computational scheme based on density functional theory is performed on the transition metal ligand structures $M{X}_n(M=\mathrm{V},\mathrm{Cr},\mathrm{Mn},\mathrm{Fe};X=\mathrm{N},\mathrm{O},\mathrm{C};n=4, 6)$ in several typical hosts to analyze quantitatively their feasibility. The results on the charge transition levels, excitation, and excited-state structure relaxation energies of $M{X}_n$ show that some of them have the proper valence states to form the required $d^2$ or $d^3$ electronic systems and the appropriate excited-state level structure with the spin-selective transition. The results on the spontaneous emission lifetime show that the ${\mathrm{MnO}}_4$ structure is mostly suitable for spin polarization due to the fastest optical transition rates among these systems considered. Finally, some suggestions on determining potentially feasible systems activated by transition metal ions in solids are given.

The molten salt flux method is applied as a synthetic route for the single crystals of the spin-triplet superconductor ${\mathrm{UTe}}_2$. The single crystals under an optimized growth condition with excess uranium exhibit a superconducting transition at $T_{\mathrm{c}}=2.1\mathrm{K}$, which is the highest $T_{\mathrm{c}}$ reported for this compound. The obtained crystals show a remarkably large residual resistivity ratio with respect to the room temperature value and a small residual electronic contribution in specific heat well below $T_{\mathrm{c}}$. These results indicate that the increase of $T_{\mathrm{c}}$ in ${\mathrm{UTe}}_2$ can be achieved by reducing the disorder associated with uranium vacancies. The excess uranium in the molten salt acts as a reducing agent, preventing tetravalent uranium from becoming pentavalent and suppressing creation of uranium vacancies. At the same time, the relatively low growth temperature can suppress Te volatilization.

In the course of searching for promising topological materials for applications in future topological electronics, we evaluated spin-orbit torques (SOTs) in high-quality sputtered δ-TaN/${\mathrm{Co}}_{20}{\mathrm{Fe}}_{60}{\mathrm{B}}_{20}$ devices through spin-torque ferromagnetic resonance (ST-FMR) and spin pumping measurements. From the ST-FMR characterization we observed a significant linewidth modulation in the magnetic ${\mathrm{Co}}_{20}{\mathrm{Fe}}_{60}{\mathrm{B}}_{20}$ layer attributed to the charge-to-spin conversion generated from the δ-TaN layer. Remarkably, the spin-torque efficiency determined from ST-FMR and spin pumping measurements is as large as $\mathrm{\Theta }=$ 0.034 and 0.031, respectively. These values are over two times larger than for α-Ta, but almost five times lower than for β-Ta, which can be attributed to the low room temperature electrical resistivity $\sim 74\mu \mathrm{\Omega }\mathrm{cm}$ in δ-TaN. A large spin diffusion length of at least $\sim 8\mathrm{nm}$ is estimated, which is comparable to the spin diffusion length in pure Ta. Comprehensive experimental analysis, together with density functional theory calculations, indicates that the origin of the pronounced SOT effect in δ-TaN can be mostly related to a significant contribution from the Berry curvature associated with the presence of a topically nontrivial electronic band structure in the vicinity of the Fermi level ($E_{\mathrm{F}}$). Through additional detailed theoretical analysis, we also found that an isostructural allotrope of the superconducting δ-TaN phase, the simple hexagonal structure θ-TaN, has larger Berry curvature, and that, together with expected reasonable charge conductivity, it can also be a promising candidate for exploring a generation of spin-orbit torque magnetic random access memory as cheap, temperature stable, and highly efficient spin current source.

Relaxor ferroelectrics are applied in electronic devices such as actuators and sonars. Morphotrophic phase boundaries (MPBs) with monoclinic structures are known for their high piezoelectricity and electromechanical coupling factors in solid solutions of ${\mathrm{PbTiO}}_3$ and relaxor ferroelectrics [$\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$ or $\mathrm{Pb}\left({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$]. Using transmission electron microscopy and synchrotron x-ray scattering, we present observations of coexisting monoclinic structures and polar nanoregions near the MPB in $\mathrm{Pb}\left({\mathrm{Yb}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3\text{−}{\mathrm{PbTiO}}_3$. The polar nanoregions in this material are randomly shaped, unlike the ferroelectric nanodomains of the canonical relaxor $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3\text{−}{\mathrm{PbTiO}}_3$. Furthermore, in situ observations reveal that the monoclinic polar nanoregions grow as the temperature decreases. A pair-distribution function analysis reveals a mixture of monoclinic $Pm$ and $Cm$ structures in the polar nanoregions without the rhombohedral structure of other Pb-based relaxor solid solutions. Owing to the peculiar nature of the coexistence of the relaxor property (polar nanoregions) and high piezoelectricity (monoclinic structure), this material is expected as a platform for understanding relaxor ferroelectricity.

Persistent photoresponses require optical excitations to metastable states, which are rare of ionic origin due to the indirect photon-ion interaction. In this work, we explore the photoinduced metastable proton states in the proton-transfer type molecular ferroelectric croconic acid. We observe that, after the photoexcitation, the changes of structural and ferroelectric properties relax in $\sim {10}^3\mathrm{s}$, indicating persistent photoresponses of ionic origin. In contrast, the photoconductivity relaxes within 1 s. The ${10}^3\mathrm{s}$ timescale suggests that the ionic metastable states result from proton transfer both along and out of the hydrogen bonds. This discovery unveils an ionic mechanism for the phototunability, which offers persistent opto-ferroelectric control for proton-transfer type molecular ferroelectrics.

Gapped spin orders induce electric polarization in multiferroics with strong magnetoelectric (ME) coupling. The sensitivity of terahertz (THz) radiation to the spin gaps and the dielectric medium can uniquely access this technologically relevant ME effect. Here, we implement magneto-THz time-domain spectroscopy to demonstrate the manifestation of spin-wave excitations responsible for the ME coupling in multiferroic compound ${\mathrm{Co}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$. We observed two sharp and a weak spin-gap resonance mode at 0.77, 1.58, and 0.91 THz at 5 K below the antiferromagnetic ordering in the absence of magnetic field. In an applied magnetic field, the strength of the 0.77 THz mode decreases while two field-induced modes, namely, the Goldstone mode and magnon excitation, appear at 0.27 and 1.50 THz, respectively. This THz optical evidence of a rich manifestation of field-controlled magnetic resonances, a mutual transfer of optical spectral weight between the zero-field and field-induced excitations, and associated change of complex refractive index in magnetic fields unravel a unique ME coupling in ${\mathrm{Co}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$.

This study presents a systematic assessment of the behavior of self-trapped electrons in ${\mathrm{PbTiO}}_3$, which is a prototypical ferroelectric material with a wide range of technological applications. Since modeling of polarons depends sensitively on the applied method, the goal of this work is to identify the parameters used in density functional theory (DFT), which allow to predict the properties of polarons with high accuracy. The $\mathrm{DFT}+U$ method is employed to benchmark how the choice of $k$-mesh grids, lattice parameters, and pseudopotential (PP) affects the polaron trapping energy. Then, the appropriate parameters were used to study polaron trapping energy and its optical transition using the HSE06 hybrid functional. It is shown that the magnitude of the trapping energy is highly sensitive to the choice of the PP and the applied lattice parameters. A comparison of polaron trapping energies using the two functionals indicates proximity of the $\mathrm{DFT}+U$ result to the HSE06 result. Finally, configuration coordinate diagrams for the polaron-associated absorption and luminescence peaks in ${\mathrm{PbTiO}}_3$ are presented and compared to experiments.

Understanding the short-range structure of an amorphous material is the first step in predicting its macroscopic properties. Amorphous strontium titanate (a-STO) presents a unique challenge due to contradictory experimental findings regarding the local oxygen environment of titanium, concluded to be either tetrahedral or octahedral. To elucidate the discrepancy, 72 models of a-STO with density ranging from the crystalline value 5.12 to $3.07\mathrm{g}/{\mathrm{cm}}^3$ were prepared using ab initio molecular dynamics liquid-quench simulations and characterized by extended x-ray absorption fine structure (EXAFS) for both Ti and Sr K edge. An excellent agreement between the calculated and two independent experimental EXAFS measurements demonstrates that the discrepancy in the Ti coordination stems from differences in the material's density. Next, density-dependent structural characteristics, including Ti-O and Sr-O coordination, distances, angles, polyhedral sharing, and vibrational density of states in a-STO are thoroughly analyzed and correlated with disorder-induced changes in the electronic properties that are calculated using a hybrid density functional. The obtained increase in the band gap and broadening of Ti-$d{e}_g$-orbital contributions in the conduction band are in excellent agreement with our x-ray absorption spectroscopy for Ti L-edge spectra and optical absorption measurements for crystalline and amorphous STO grown by pulsed laser deposition. The derived microscopic understanding of the structure-property relationship in amorphous “perovskite” serves as a foundation for further investigations of a-STO and related materials.

A high-symmetry ${\mathrm{D}}_{6h}$ form of graphene monoxide, labeled $\beta$-GmO, is proposed based on selected area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM) experiments and density functional theory (DFT) modeling. Joining the previously observed lower symmetry ${\mathrm{D}}_{2h}$ form of two-dimensional (2D) solid CO, now relabeled as $\alpha$-GmO, this work demonstrates that multiple solid phases are possible in 2D- and 3D-CO. A unit of the $\beta$-GmO primitive cell – 1,4,7-trioxacyclononane – is composed of three 1,3-dioxetane units of the $\alpha$-GmO primitive cell. The invariance of the SAED spots as the sample is tilted prove that $\beta$-GmO is composed of large area monolayers, randomly translated with respect to each other, as they form a multilayer stack. In contrast, $\alpha$-GmO domains rotate with respect to each other and have smaller in-plane domain areas for similar synthesis conditions. Ab initio computations demonstrate that $\beta$-GmO monolayers generally do not have preferred stacking order and thus do not form three-dimensional (3D) crystal structure. The $\beta$-GmO monolayer is predicted to be a 1.2 eV direct band-gap semiconductor and generally softer than both graphene and $\alpha$-GmO.

Ferroelectric and ferromagnetic orders rarely coexist, and magnetoelectric coupling is even more scarce. A possible avenue for combining these orders is by interface design, where orders formed at the constituent materials can overlap and interact. Using a combination of magnetotransport and scanning superconducting quantum interference device measurements, we explore the interactions between ferroelectricity, magnetism, and the two-dimensional electron system (2DES) formed at the novel ${\mathrm{LaAlO}}_3/{\mathrm{EuTiO}}_3/{\mathrm{Sr}}_{0.99}{\mathrm{Ca}}_{0.01}{\mathrm{TiO}}_3$(001) heterostructure. We find that the electrons at the interface experience magnetic scattering appearing along with a diverging Curie-Weiss-type behavior in the ${\mathrm{EuTiO}}_3$ layer. The 2DES is also affected by the switchable ferroelectric polarization at the ${\mathrm{Sr}}_{0.99}{\mathrm{Ca}}_{0.01}{\mathrm{TiO}}_3$ bulk. While the 2DES interacts with both magnetism and ferroelectricity, we show that the presence of the conducting electrons has no effect on magnetization in the ${\mathrm{EuTiO}}_3$ layer. Our results provide a first step towards realizing a new multiferroic system where magnetism and ferroelectricity can interact via an intermediate conducting layer.

Excitation of hybrid modes constituted by different material-supported polaritons is a common way to enhance the near-field radiative energy transport, which has fascinating promise in applications of thermal photonics. Here, we investigate near–field thermal radiation mechanisms in heterostructure composed of $h\mathrm{BN}$ film and black phosphorus single layer. The results show that this heterostructured system can give rise to a remarkable enhancement for photon tunneling, outperforming the near-field thermal radiation properties of its building blocks, as well as some other representative heterostructures. Moreover, we find that the anisotropic hybrid effect can induce a remarkable topological reconstitution of polaritons for $h\mathrm{BN}$ film and black phosphorus, forming a novel anisotropic hybrid polaritons. Notably, such hybrid modes show significant topological differences compared to $h\mathrm{BN}$ film and black phosphorus in the type-I Reststrahlen band due to the anisotropic anticrossing hybridization effect. Lastly, we systematically analyze the evolution of such hybrid polariton modes as a function of $h\mathrm{BN}$ film thickness and the corresponding influence on radiative properties of the heterostructure. This work may benefit the applications of near-field energy harvesting and radiative cooling based on hybrid polaritons in anisotropic two-dimensional material and hyperbolic film.

Doped ${\mathrm{HfO}}_2$ and ${\mathrm{HfO}}_2\text{−}{\mathrm{ZrO}}_2$ compounds are gaining significant interest thanks to their ferroelectric properties in ultrathin films. Here, we show that ${\mathrm{ZrO}}_2$ could be a playground for doping and strain engineering to increase the thickness in epitaxial thin films. Based on surface-energy considerations supported by ab initio calculations, we find that pure ${\mathrm{ZrO}}_2$ exhibits a ferroelectric rhombohedral phase ($r$ phase, with $R3m$ space group) more stable than for the HZO and pure ${\mathrm{HfO}}_2$ cases. In particular, for a thickness up to 37 nm we experimentally evidence a single (111)-oriented $r$ phase in ${\mathrm{ZrO}}_2$ films deposited on ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$-buffered ${\mathrm{DyScO}}_3\left(110\right)$ substrate. The formation of this $r$ phase is discussed and compared between ${\mathrm{HfO}}_2$, ${\mathrm{ZrO}}_2$ and HZO, highlighting the role of surface energy.

The coadsorption and complex formation of nitric oxide (NO) and water $\left({\mathrm{H}}_2\mathrm{O}\right)$ on Cu(111) are studied theoretically using the nonlocal van der Waals density functional method. The energetics, adsorption geometries, and vibrational properties of several $n\mathrm{NO}\text{−}{m\mathrm{H}}_2\mathrm{O}$ complexes $(n=1–4$, $m=1–3)$ on Cu(111) are reported, and the relative stabilities of those complexes are compared with their respective NO and ${\mathrm{H}}_2\mathrm{O}$ clusters on Cu(111). We find that the mixed $n\mathrm{NO}\text{−}{m\mathrm{H}}_2\mathrm{O}$ complexes on Cu(111) are more stable than separated NO and ${\mathrm{H}}_2\mathrm{O}$ clusters due to the attractive $\mathrm{NO}\text{−}{\mathrm{H}}_2\mathrm{O}$ and NO-NO interactions on the surface. The attractive $\mathrm{NO}\text{−}{\mathrm{H}}_2\mathrm{O}$ interaction originates mainly from the hydrogen bonding between ${\mathrm{H}}_2\mathrm{O}$ and the negatively charged NO upon adsorption. Moreover, hydrogen bonding also induces an additional back donation process from Cu(111), further strengthening the $\mathrm{NO}\text{−}{\mathrm{H}}_2\mathrm{O}$ coadsorption. In addition to hydrogen bonding, the NO-NO interaction originating from $2{\pi }^{*}$ orbital hybridization further stabilizes the formation of the $4\mathrm{NO}\text{−}3{\mathrm{H}}_2\mathrm{O}$ complex, which is observed in the experiment. Even though the hydrogen bonding strength in $\mathrm{NO}\text{−}{\mathrm{H}}_2\mathrm{O}$ complexes is slightly weaker than the one in ${\mathrm{H}}_2\mathrm{O}$ clusters, due to the saturation of hydrogen bonding and the NO-NO interaction, NO and ${\mathrm{H}}_2\mathrm{O}$ tends to form a mixed $\mathrm{NO}\text{−}{\mathrm{H}}_2\mathrm{O}$ complex on Cu(111), in agreement with experiment. Our findings shed light on the role of intermolecular interactions between NO and ${\mathrm{H}}_2\mathrm{O}$ in the formation of the NO complex, which is important for understanding the reaction of NO in three-way catalysts.

The excitonic states of transition metal dichalcogenide (TMD) monolayers are heavily influenced by their external dielectric environment and depend on the substrate used. In this work, various wide band gap dielectric materials, namely hexagonal boron nitride $\left(h\text{−}\mathrm{BN}\right)$ and amorphous silicon nitride $\left({\mathrm{Si}}_3{\mathrm{N}}_4\right)$, under different configurations as support or encapsulation material for ${\mathrm{WS}}_2$ monolayers, are investigated to disentangle the factors contributing to inhomogeneous broadening of exciton absorption lines in TMDs using electron energy loss spectroscopy in a scanning transmission electron microscope. In addition, monolayer roughness in each configuration was determined from tilt series of electron diffraction patterns by assessing the broadening of diffraction spots by comparison with simulations. From our experiments, the main factors that play a role in linewidth broadening can be classified, in increasing order of importance, by monolayer roughness, surface cleanliness, and substrate-induced charge trapping. Furthermore, because high-energy electrons are used as a probe, electron-beam-induced damage on bare TMD monolayers is also revealed to be responsible for irreversible linewidth increases. $h\text{−}\mathrm{BN}$ not only provides clean surfaces of TMD monolayers and minimal charge disorder, but can also protect the TMD from irradiation damage. This work provides a better understanding of the mechanisms by which $h\text{−}\mathrm{BN}$ remains, to date, the most compatible material for 2D material encapsulation, facilitating the realization of intrinsic material properties to their full potential.

Heavily carbon-doped ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ is a unique compound for spintronics applications as it meets all the requirements for spin injection and detection in group-IV semiconductors. Despite the great improvement of the magnetic properties induced by C incorporation into ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ compounds, very little information is available on its structural properties and the genuine role played by C atoms. In this paper, we have used a combination of advanced techniques to extensively characterize the structural and magnetic properties of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3{\mathrm{C}}_x$ films grown on Ge(111) by solid phase epitaxy as a function of C concentration. The increase of the Curie temperature induced by C doping up to 435 K is accompanied by a decrease of the out-of-plane $c$-lattice parameter. The Mn and C chemical environments and positions in the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ lattice have been thoroughly investigated using x-ray absorption spectroscopy techniques (x-ray absorption near-edge structures and extended x-ray absorption fine structures) and scanning transmission electronic microscopy (STEM) combined to electron energy loss spectroscopy for the chemical analysis. The results have been systematically compared to a variety of structures that were identified as favorable in terms of formation energy by ab initio calculations. For $x\le 0.5$, the C atoms are mainly located in the octahedral voids formed by Mn atoms, which is confirmed by simulations and seen for the first time in real space by STEM. However, the latter reveals an inhomogeneous C incorporation, which is qualitatively correlated to the broad magnetic transition temperature. A higher C concentration leads to the formation of manganese carbide clusters that we identified as ${\mathrm{Mn}}_{23}{\mathrm{C}}_6$. Interestingly, other types of defects, such as interstitial Ge atoms, vacancies of Mn, and their association into line defects have been detected. They take part in the strain relaxation process and are likely to be intimately related to the growth process. This paper provides a complete picture of the structure of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3{\mathrm{C}}_x$ in thin films grown by solid phase epitaxy, which is essential for optimizing their magnetic properties.

In the present work, we report the correlations among negative magnetization (NM), exchange bias (EB), and electrical properties in ${\mathrm{La}}_{1\text{−}x}{\mathrm{Pr}}_x{\mathrm{CrO}}_3$ $(x=0, 0.25, 0.5, 0.75, \mathrm{and} 1)$ compounds using dc magnetization, neutron depolarization, neutron diffraction, and impedance spectroscopy. The dc magnetization study infers the negative magnetization (NM) phenomenon in $x=0.25$, 0.5, and 0.75 compounds, where the compensation temperature $\left(T_{\mathrm{COMP}}\right)$ increases with $x$. At low temperature $(T<T_{\mathrm{COMP}})$, these compounds exhibit NM along with positive EB, indicating a correlation between the negative polarity of magnetization and the positive polarity of EB. However, the end compound $x=0$ does not show any NM and/or EB, whereas the other end compound, $x=1$, shows a negative EB without any NM. The presence or absence of magnetization reversal has been explained within the framework of Cooke's model which involves a competition between antiparallel coupled canted ${\mathrm{Cr}}^{3+}$ and polarized ${\mathrm{Pr}}^{3+}$ moments. Interestingly, maximum ac conductivity (with minimum activation energy required for conduction) at $x=0.75$ (which exhibits maximum $T_{\mathrm{COMP}}$) is found entangled with the lattice parameters’ crossover from $a<c$ to $a>c$ around $x=0.75$, as evident from the neutron diffraction study. The physics behind the polarity reversals of magnetization and EB, and its close connection with electrical properties, has been understood by employing the macroscopic, mesoscopic, and microscopic experimental techniques. Such correlated physical properties make these compounds useful for making thermomagnetic switches and thermal-assisted magnetic random access memory.