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Considerations on Double Exchange
Abstract
Zener has suggested a type of interaction between the spins of magnetic ions which he named "double exchange." This occurs indirectly by means of spin coupling to mobile electrons which travel from one ion to the next. We have calculated this interaction for a pair of ions with general spin S and with general transfer integral, b, and internal exchange integral J. One result is that while the states of large total spin have both the highest and lowest energies, their average energy is the same as for the states of low total spin. This should be applicable in the high-temperature expansion of the susceptibility, and if it is, indicates that the high-temperature Curie-Weiss constant theta should be zero, and 1chi vs T a curved line. This is surprising in view of the fact that the manganites, in which double exchange has been presumed to be the interaction mechanism, obey a fairly good Curie-Weiss law. The results can be approximated rather well by a simple semiclassical model in which the spins of the ion cores are treated classically. This model is capable of rather easy extension to the problem of the whole crystal, but the resulting mathematical problem is not easily solved except in special circumstances, e.g., periodic disturbances (spin waves).
... These materials have shown a great development because of their remarkable structural, magnetic, and electrical properties as well as the potential technological applications which they present in several domains from spintronic to magnetic refrigeration [1,2]. These materials present a high correlation between electronic transport and ferromagnetism based on the double-exchange interactions between Mn 3+ and Mn 4+ ions via oxygen anion [3,4]. ...
... Evolution of the real part ε 1 of the dielectric permittivity vs. λ 2 and b the variation of the imaginary part ε 2 vs λ.3 ...
In this work, we present a detailed investigation of the electrical and optical properties of Pr0.5−xGdxSr0.5MnO3 (0 ≤ x ≤ 0.1) polycrystalline compounds synthesized via a solid-state route. Impedance spectroscopy measurements were performed in the frequency and temperature ranges of 40 Hz–10 MHz and from 80 to 320 K, respectively. DC conductance (GDC) results evince the semiconductor behavior of all studied compounds in the whole temperature range of study. Doping with gadolinium causes a lowering in GDC values and an increase in the activation energies. GDC is shown to be governed by the small polaron hopping model (SPH) at high temperatures and by the variable range hopping (VRH) model at lower ones. The AC measurements show a metallic behavior which can be described by the simplified Drude model. The optical properties were characterized using UV–Vis absorption spectroscopy. By analyzing the UV absorption measurements and based on the Tauc model, we have determined the optical bandgap of each compound evaluated at around 4.5 eV which is a high value compared with those obtained in the literature. The Urbach energy, the optical extinction coefficient, and the refractive index were calculated on the basis of absorbance measurements. In addition, the skin depth, optical conductivity, and the dispersion energy parameters as a function of the wavelength of the incident photon were determined and discussed. These compounds may be interesting in optoelectronic applications.
... However, the origin of CMR is different in each material family. Among these, manganites are the most explored, where, primarily, the double-exchange interaction (DEI) between mixed valence Mn ions leads to the metallic FM state (24)(25)(26). Because of the strong dependence of resistivity in a rather small magnetic field, both GMR and CMR materials attracted extensive interests in spintronics and magnetic memory applications (1)(2)(3)(4)(5). ...
... From the obtained results, we estimate an anisotropy ratio ðρ Hka xx =ρ Hkc xx Þ of ∼2.6 at 5.4 K and a magnetic field of 9 T. The large anisotropy ratio is also a confirmation of the layered We note that the observed field-induced semiconductor metallike transition and the overall magnetotransport properties have similarities with different types of CMR materials rather than TSMs. Among these CMR systems, in doped manganites, the MR is primarily originated from the DEI between mixed valence Mn ions and or the charge/orbital ordering (24)(25)(26). However, DEI alone cannot explain the resistivity behavior in manganites (8). ...
Colossal negative magnetoresistance is a well-known phenomenon, notably observed in hole-doped ferromagnetic manganites. It remains a major research topic due to its potential in technological applications. In contrast, topological semimetals show large but positive magnetoresistance, originated from the high-mobility charge carriers. Here, we show that in the highly electron-doped region, the Dirac semimetal CeSbTe demonstrates similar properties as the manganites. CeSb0.11Te1.90 hosts multiple charge density wave modulation vectors and has a complex magnetic phase diagram. We confirm that this compound is an antiferromagnetic Dirac semimetal. Despite having a metallic Fermi surface, the electronic transport properties are semiconductor-like and deviate from known theoretical models. An external magnetic field induces a semiconductor metal–like transition, which results in a colossal negative magnetoresistance. Moreover, signatures of the coupling between the charge density wave and a spin modulation are observed in resistivity. This spin modulation also produces a giant anomalous Hall response.
... The RKKY (Ruderman-Kittel- Kasuya-Yosida) model and double exchange (DE) model are very popular models. 35,36 The RKKY model is applicable in systems where localized magnetic moments interact via the exchange of itinerant electrons. The DE model is applicable in systems where both localized magnetic moments and itinerant electrons coexist and interact strongly. ...
To understand the impact of binary doping in ZnO, nanosized Zn(Ag, Ni)O systems were synthesized by the sol–gel method.
... Manganite with an ABO 3 perovskite structure is a strongly correlated electron system with coupling between the crystal structure [13,14], spin, charge, and orbital structure. To explain the rich physics of this system, it has been proposed that double-exchange interaction [15], electron-phonon coupling [16][17][18], and super-exchange interaction [19] are simultaneously present and compete with each other, establishing a delicate balance that determines the properties of the material. One feature of this type of material is the co-existence of ferromagnetic and antiferromagnetic phases in a single layer, which can be manipulated by external stimuli. ...
... Due to the aforementioned Hund coupling between e g and t 2g electrons, the formation of the e g -band strongly depends on the arrangement of magnetic dipole moments created by t 2g electrons. Indeed, as shown by Zener back in 1950 [85], and later by Anderson et al. [86] as well as Kubo and Ohata [87], the effective transfer integral for the hop of an e g electron between Mn ions may be written as t = t max cos(θ/2), where t max is the maximal value of the transfer integral and θ is the angle between the magnetic moments of the Mn ions involved in the hopping process. This is the famous double-exchange model, according to which the maximum hopping probability occurs for parallel orientation of Mn magnetic moments (θ = 0). ...
One of the most fascinating aspects of condensed matter is its ability to conduct electricity, which is particularly pronounced in conventional metals such as copper or silver. Such behavior stems from a strong tendency of valence electrons to delocalize in a periodic potential created by ions in the crystal lattice of a given material. In many advanced materials, however, this basic delocalization process of the valence electrons competes with various processes that tend to localize these very same valence electrons, thus driving the insulating behavior. The two such most important processes are the Mott localization, driven by strong correlation effects among the valence electrons, and the Anderson localization, driven by the interaction of the valence electrons with a strong disorder potential. These two localization processes are almost exclusively considered separately from both an experimental and a theoretical standpoint. Here, we offer an overview of our long-standing research on selected organic conductors and manganites, that clearly show the presence of both these localization processes. We discuss these results within existing theories of Mott–Anderson localization and argue that such behavior could be a common feature of many advanced materials.
... This essentially extends the wave function basis used and creates some difficulties in the construction of diagram techniques. Anderson and Hasegawa [79] have calculated exactly the spectrum of electron excitations in a system of two multivalent ions Mn 3+ and Mn 4+ . De Gennes [80] studied the thermodynamics of a system of classical spins neglecting strong electron correlations. ...
... This essentially extends the wave function basis used and creates some difficulties in the construction of diagram techniques. Anderson and Hasegawa [79] have calculated exactly the spectrum of electron excitations in a system of two multivalent ions Mn 3+ and Mn 4+ . De Gennes [80] studied the thermodynamics of a system of classical spins neglecting strong electron correlations. ...
... [56][57][58][59][60][61] In the parent compound LaMnO 3 , the electronic structure of the Mn 4þ cation consists of fully occupied t 2g states and one electron in the e g states separated by the crystal field energy; the effect of doping the system with divalent cations is that of removing the electron from the e g state, i.e., of adding hole carriers to the system; at sufficiently high doping, a metallic, ferromagnetic state emerges driven by the double-exchange interaction mechanism. [62][63][64] One of the most studied manganites is the Sr-doped LaMnO 3 due to its high Curie temperature (above room temperature at 30% Sr doping). 65,66 One challenge is that its magnetic and electrical properties tend to degrade when grown as thin film, although strategies for circumventing this issue have been proposed. ...
We report the direct imaging of the magnetic response of a 4.8 nm La0.9Ba0.1MnO3 film to the voltage applied across a 5 nm BaTiO3 film in a BaTiO3/La0.9Ba0.1MnO3 multiferroic heterostructure using x-ray photoemission electron microscopy (XPEEM). Specifically, we have written square ferroelectric domains on the BaTiO3 layer with an atomic force microscope in contact mode and imaged the corresponding magnetic contrast through the x-ray circular dichroic effect at the Mn L-edge with high spatial lateral resolution using XPEEM. We find a sudden decrease in the magnetic contrast for positive writing voltages above +6 V associated with the switching of the ferroelectric polarization of the BaTiO3, consistent with the presence of a magnetoelectric effect through changes in the hole carrier density at the BaTiO3/La0.9Ba0.1MnO3 interface. Temperature-dependent measurements show a decrease in the Curie temperature and magnetic moment in the areas where a positive voltage above +6 V was applied, corresponding to the hole depletion state and suggesting the onset of a spin-canted state of bulk La0.9Ba0.1MnO3. Our results are the first direct imaging of magnetoelectric coupling in such multiferroic heterostructure.
... These materials have shown a great development because of their remarkable structural, magnetic, and electrical properties as well as the potential technological applications which they present in several domains from spintronic to magnetic refrigeration [1,2]. These materials present a high correlation between electronic transport and ferromagnetism based on the double-exchange interactions between Mn 3+ and Mn 4+ ions via oxygen anion [3,4]. ...
... Second, improved/ enhanced Mn(3d)-O(2p) orbital hybridization as the Mn-O-Mn bonds are significantly straightened. Third, the resulting enhancement of double exchange interaction [48][49][50] stabilizes ferromagnetic metallic ground state of the LPCMO/LAO/STO thin films. The fundamentally important structural control parameter 20 , i.e. octahedral tilt/ rotation angle was found to be surprisingly large (φ OOR = 166°) in the strain-engineered and relaxed LPCMO/ LAO/STO film. ...
Strain engineering beyond substrate limitation of colossal magnetoresistant thin (La0.6Pr0.4)0.7Ca0.3MnO3 (LPCMO) films on LaAlO3-buffered SrTiO3 (LAO/STO) substrates has been demonstrated using metalorganic aerosol deposition technique. By growing partially relaxed 7–27 nm thick heteroepitaxial LAO buffer layers on STO a perfect lattice matching to the LPCMO has been achieved. As a result, strain-free heteroepitaxial 10–20 nm thick LPCMO/LAO/STO films with bulk-like ferromagnetic metallic ground state were obtained. Without buffer the coherently strained thin LPCMO/STO and LPCMO/LAO films were insulating and weakly magnetic. The reason for the optimized magnetotransport in strain-free LPCMO films was found to be a large octahedral Mn–O–Mn bond angle φOOR ~ 166–168° as compared to the significantly smaller one of φOOR ~ 152–156° determined for the tensile (LPCMO/STO) and compressively (LPCMO/LAO) strained films.
... addition to our results with collinear spins, we have tested our ideas with noncollinear arrangements. We report on these results that agree with the basic picture drawn so far in the Supplemental Material [29,38,42,[44][45][46][47][48][49][50][51][52][53][54][55]. We have presented a simplified, nonrelativistic model of a multiferroic system. ...
We provide a model capable of accounting for the multiferroicity in certain materials. The model’s base is on free electrons and spin moments coupled within nonrelativistic quantum mechanics. The synergistic interplay between the magnetic and electric degrees of freedom that turns into the multiferroic phenomena occurs at a profound quantum mechanical level, conjured by Berry’s phases and the quantum theory of polarization. Our results highlight the geometrical nature of the multiferroic order parameter that naturally leads to magnetoelectric domain walls, with promising technological potential.
... Among semiconductor materials, lanthanum manganite (LaMnO 3 , LMO) shows low resistivity (< 1 Ω·cm at 25 °C), and its magnetic and electrical properties can be tuned by doping [6]. In particular, when LMO is doped with alkaline earth cations occupying La 3+ positions, the magnetic and electronic properties can be tuned by the competence between two magnetic interactions: (i) the antiferromagnetic (AFM) superexchange interaction (SE), which is mainly due to overlapping electron orbitals between the Mn 3+ and O 2− atoms [7] and (ii) the ferromagnetic (FM) double exchange interaction (DE), which is produced by Mn 4+ for charge compensation in doped lanthanum manganite [8]. This makes them interesting thermistor materials since it allows control of the electric resistivity. ...
An analysis of the sensitivity of the electrical resistance to temperature changes in cobalt-doped lanthanum-strontium manganite was carried out to provide new insight into the effects of the magnetic interactions between cobalt and manganese ions on the electric properties. Cobalt-doped lanthanum-strontium manganites, La0.7Sr0.3CoxMn1−xO3 with x ranging from 0 to 0.1 (Δx = 0.025), were synthesized by high-energy ball milling for 5 h, followed by annealing at 1673 K. X-ray diffraction showed the presence of a rhombohedral phase for all the studied compositions, indicating a decrease in the bandwidth as the cobalt content increased. The Curie temperature, determined by vibrating sample magnetometry, and the insulator-metal transition temperature, determined by electrical measurements, decrease near to room temperature with increases cobalt content up to 0.1 by weakening the double exchange magnetic interaction. The results confirmed that cobalt increased the temperature coefficient of resistance for the doped manganites by up to 15.6% for 0.1 mol of cobalt near room temperature. Therefore, these materials will prove useful for the development of specialized sensing devices such as bolometers.
... Spin-fermion model describes a scenario of itinerant electrons interacting with the local magnetic moment [1][2][3], which was first proposed to study the conductivity in ferromagnetic manganites [4]. It is also sometimes referred to as the Kondo model when only one orbital is involved for itinerant electrons. ...
The spin-fermion model was previously successful to describe the complex phase diagrams of colossal magnetoresistive manganites and iron-based superconductors. In recent years, two-dimensional magnets have rapidly raised up as a new attractive branch of quantum materials, which are theoretically described based on classical spin models in most studies. Alternatively, here the two-orbital spin-fermion model is established as a uniform scenario to describe the ferromagnetism in a two-dimensional honeycomb lattice. This model connects the magnetic interactions with the electronic structures. Then the continuous tuning of magnetism in these honeycomb lattices can be predicted, based on a general phase diagram. The electron/hole doping, from the empty $e_{g}$ to half-filled $e_{g}$ limit, is studied as a benchmark. Our Monte Carlo result finds that the ferromagnetic $T_{C}$ reaches the maximum at the quarter-filled case. In other regions, the linear relationship between $T_{C}$ and doping concentration provides a theoretical guideline for the experimental modulations of two-dimensional ferromagnetism tuned by ionic liquid or electrical gating.
... This mechanism often proceeds through direct orbital overlap of spin bearing orbitals and stabilizes high spin states and promotes valence delocalization. [13][14][15] Also, Piepho, Krausz, and Schatz (PKS) proposed an electron-nuclear coupling model that posits antisymmetric metal-ligand breathing modes induce valence localization through geometric desymmetrization of the mixed-valence bimetallic core. [16] Thus, the spectroscopic and magnetic properties of mixed-valence clusters depend on the interplay between superexchange, double exchange, and vibronic modes. ...
The carbide ligand in the iron–molybdenum cofactor (FeMoco) in nitrogenase bridges iron atoms in different oxidation states, yet it is difficult to discern its ability to mediate magnetic exchange interactions due to the structural complexity of the cofactor. Here, we describe two mixed‐valent diiron complexes with C‐based ketenylidene bridging ligands, and compare the carbon bridges with the more familiar sulfur bridges. The ground state of the [Fe2(μ‐CCO)2]⁺ complex with two carbon bridges (4) is S= 1/2 ${{ 1/2 }}$ , and it is valence delocalized on the Mössbauer timescale with a small thermal barrier for electron hopping that stems from the low Fe−C force constant. In contrast, one‐electron reduction of the [Fe2(μ‐CCO)] complex with one carbon bridge (2) affords a mixed‐valence species with a high‐spin ground state (S= 7/2 ${ 7/2 }$ ), and the Fe−Fe distance contracts by 1 Å. Spectroscopic, magnetic, and computational studies of the latter reveal an Fe−Fe bonding interaction that leads to complete valence delocalization. Analysis of near‐IR intervalence charge transfer transitions in 5 indicates a very large double exchange constant (B) in the range of 780–965 cm⁻¹. These results show that carbon bridges are extremely effective at stabilizing valence delocalized ground states in mixed‐valent iron dimers.
... [12][13][14] These intriguing events were often described using the double exchange (DE) coupling model and the Jahn -Teller (J-T) effects. [15][16][17] Even though many studies on doped manganites have been undertaken, not much focus has been given to isovalent doped manganites, in which only the A-site element's average ionic radius played an important role in determining manganite characteristics. At a moderate externally applied magnetic field, these materials also exhibit a significant magneto-caloric effect (MCE). ...
The structural, morphological, magnetic, and magnetocaloric properties of nanocrystalline Pr 0.7 La 0.3 MnO 3 (PLMO), synthesized by using a wet chemical Sol-gel method, have been investigated. The single-phase nature of nanocrystalline PLMO with orthorhombic crystal structure along with the Pbnm space group was confirmed by Rietveld analysis of the X-ray diffraction pattern. The average crystallite size and lattice microstrain were determined using the Williamson-Hall technique, and they were found to be ~ 28 nm and ~ 0.00137, respectively. Transmission electron microscopy shows the particle size and structural characteristics of the sample. Temperature-dependent magnetization data show paramagnetic to ferromagnetic transition. According to Banerjee criterion, the positive slope of Arrott's plot for nanocrystalline PLMO indicates the second-order magnetic phase transition. In a 5 T external magnetic field, the maximum magnetic entropy change was found to be 2.47 J/kg K. The refrigerant capacity and relative cooling power were calculated and the values are 193.3 and 277.57 J/kg, respectively, under a 5 T applied external magnetic field.
We analyze the effects related to the low-, intermediate-, and high-spin states in different materials such as cobaltites. In these materials, the interior of magnetic polaron is formed by low-spin state in the surrounding of high-spin states (or vice versa).
We give simple estimates for the radius of small spherical FM metallic droplets in insulating AFM matrix of CMR manganites in the framework of the double exchange model. We discuss also the droplet contribution to different transport properties of phase-separated magnetic oxides, such as resistivity, magnetoresistance, magnetic susceptibility, and the spectrum of 1/f noise.
The chemical stability effect was investigated using two perovskite compositions, La0.7Nd0.1Sr0.2MnO3 and La0.7Nd0.1Sr0.2Mn0.96In0.04O3. Synthesis of these perovskites was carried out by the sol–gel method. X-ray powder diffraction study, coupled with Rietveld refinement, revealed a rhombohedral structure with the R\(\overline{3 }\)c space group. The magnetic investigation showed that both compositions exhibit a second-order phase transition. La0.7Nd0.1Sr0.2MnO3 has a Curie temperature TC of 290 K and maximum magnetic entropy change value of 4.79 J kg−1 K−1, while La0.7Nd0.1Sr0.2Mn0.96In0.04O3 has a Curie temperature TC of 277 K and maximum magnetic entropy change value of 6.2 J kg−1 K−1. The critical properties of these compositions were analyzed and found to obey the mean-field model for La0.7Nd0.1Sr0.2 Mn0.96In0.04O3 and the Heisenberg model for La0.7Nd0.1Sr0.2MnO3.
Achieving simultaneous control over multiple functional properties, such as magnetic anisotropy, magnetoresistance, and metal-insulator transition, with atomic precision remains a major challenge for realizing advanced spintronic functionalities. Here, we demonstrate a unique approach to cooperatively tune these multiple functional properties in highly strained La0.7Sr0.3MnO3 (LSMO) thin films. By inserting varying perovskite buffer layers, compressively strained LSMO films transition from a ferromagnetic insulator with out-of-plane magnetic anisotropy to a metallic state with in-plane anisotropy. Remarkably, atomic-scale control of the buffer layer thickness enables precise tuning of this magnetic and electronic phase transformation. We achieve a colossal magnetoresistance tuning of 10,000% and an exceptionally sharp transition from out-of-plane to in-plane magnetic anisotropy within just a few atomic layers. These results demonstrate an unprecedented level of control over multiple functional properties, paving the way for the rational design of multifunctional oxide spintronic devices.
In this paper, the magnetocaloric properties and magnetic phase transition of the (La–Ca) MnO3 system after secondary doping with the large magnetic moment rare earth element Gd are investigated. Analysis reveals that the polycrystalline material La0.65Ca0.3Gd0.05MnO3 exhibits a magnetocaloric effect superior to both the un-secondary doped and similar types of materials at the critical point of the ferromagnetic–paramagnetic phase transition (TC = 173 K). Under 7 T magnetic field, the maximum magnetic entropy change |∆SMmax|, refrigerant capacity RC, and relative cooling capacity RCP are 8.10 J kg⁻¹ K⁻¹, 350.54 J kg⁻¹, and 422.17 J kg⁻¹, respectively. The high overlap between TEC (4 K) and |∆SMmax| at the same magnetic field indicates its good utility. Landau theory yields a negative slope of the Arrott plot at TC, and the fit of Landau coefficients b (TC) obtains negative values verifying the ferromagnetic–paramagnetic first-order phase transition. Further calculation of the n value and the universal curve plot using the magnetocaloric effect confirmed this type of magnetic phase transition and revealed the origin of the large magnetocaloric effect. The material provides new ideas for applications in cryogenic magnetic refrigeration.
The Jahn-Teller distortion, by its virtue, leads to intriguing electronic properties in transition metal oxides. The charge disproportionation (CD) in Jahn-Teller active systems is a key electronic feature that drives metal-insulator transition (MIT). We demonstrate and quantify it using first-principles calculations combining density functional theory, dynamical mean-field theory, and Monte Carlo simulations. Taking Ca2FeMnO6 as a prototypical example of correlated oxide, our ab-initio study shows that MIT in Ca2FeMoO6 arises from the partial localization of Oxygen ligand holes at alternate Fe sites that controls both charge and magnetic ordering. Interestingly, the band gap was found to be fundamentally controlled by the strength of the charge-transfer energy, and not by the Mott-Hubbard interactions. The novel physics and insights presented in this work reveal promising routes to tune novel electronic functionality in transition metal oxides.
In this article, we develop a vibronic theory of clocking in molecular quantum cellular automata (QCA). The clocking mechanism is considered for a trigonal trimeric mixed-valence (MV) system with one mobile electron, which is shown to act as the dimeric unit encoding binary information (Boolean states 0 or 1) coupled to a third redox center (Null state). The model includes the electron transfer between the three centers; vibronic coupling of the mobile charge with the “breathing” modes, forming a double degenerate Jahn–Teller vibration of the molecular triangle; and two electric fields, one collinear to the dimeric unit, which controls the binary states, and the other perpendicular to this unit, performing clocking. In the framework of the adiabatic approximation, the potential surface of the trimeric system has been studied and the condition determining switching and clocking has been analyzed in terms of the two controlling fields and the vibronic and transfer parameters. A thorough understanding of the site populations is achieved through the quantum-mechanical solution of the vibronic problem, maintaining the adiabatic condition for the controlling fields. It is shown that a MV trimer can act as a molecular clocked QCA cell, with favorable conditions being a positive electron transfer parameter and sufficiently strong vibronic coupling.
Layered van der Waals ferromagnets, which preserve their magnetic properties down to exfoliated monolayers, are fueling an abundance of fundamental research and nanoscale device demonstration. CrGeTe3 is a prime example of this class of materials. Its temperature-pressure phase diagram features an insulator-to-metal transition and a significant increase in ferromagnetic Curie-Weiss temperatures upon entering the metallic state. We use density functional theory to understand the magnetic exchange interactions in CrGeTe3 at ambient and elevated pressures. We calculate Heisenberg exchange couplings, which provide the correct ferromagnetic ground state and explain the experimentally observed pressure dependence of magnetism in CrGeTe3. Furthermore, we combine density functional theory with dynamical mean-field theory to investigate the effects of electronic correlations and the nature of the high-pressure metallic state in CrGeTe3.
Field-effect transistors based on semiconductor integration technology have come to a bottleneck, while electric field-control of magnetism has great potential for applications in next-generation magnetic memory and calculators based on electron spins. Magnetic properties manipulation from a mechanism of ion migration driven by an electric field has the advantages of low energy consumption, non-volatility, reproducibility, and durability. Here, we introduce a solid-state integratable hydrogen ion storage electrolyte silicon phosphate as the gate to achieve reversible control of magnetoresistance, magnetism and magnetic interaction in La1−xSrxMnO3/SrTiO3 ferromagnetic system. The controllable double-exchange interaction and spin scattering mechanism sketch the theoretical physical picture for these results. This work is expected to open up additional opportunities in the translation of electric control of magnetism into practical applications.
We report on magnetic orderings of nanospins in self-assemblies of Fe3O4 nanoparticles (NPs), occurring at various stages of the magnetization process throughout the superparamagnetic (SPM)-blocking transition. Essentially driven by magnetic dipole couplings and by Zeeman interaction with a magnetic field applied out-of-plane, these magnetic orderings include a mix of long-range parallel and antiparallel alignments of nanospins, with the antiparallel correlation being the strongest near the coercive point below the blocking temperature. The magnetic ordering is probed via x-ray resonant magnetic scattering (XRMS), with the x-ray energy tuned to the Fe−L3 edge and using circular polarized light. By exploiting dichroic effects, a magnetic scattering signal is isolated from the charge scattering signal. We measured the nanospin ordering for two different sizes of NPs, 5 and 11 nm, with blocking temperatures TB of 28 and 170 K, respectively. At 300 K, while the magnetometry data essentially show SPM and absence of hysteresis for both particle sizes, the XRMS data reveal the presence of nonzero (up to 9%) antiparallel ordering when the applied field is released to zero for the 11 nm NPs. These antiparallel correlations are drastically amplified when the NPs are cooled down below TB and reach up to 12% for the 5 nm NPs and 48% for the 11 nm NPs, near the coercive point. The data suggest that the particle size affects the prevalence of the antiparallel correlations over the parallel correlations by a factor ∼1.6 to 3.8 higher when the NP size increases from 5 to 11 nm.
We investigate multiple-Q instability on a square lattice at particular ordering wave vectors. We find that a superposition of quadruple-Q spin density waves, which are connected by fourfold rotational and mirror symmetries, gives rise to a checkerboard bubble lattice with a collinear spin texture as a result of the geometry among the constituent ordering wave vectors in the Brillouin zone. By performing the simulated annealing for a fundamental spin model, we show that such a checkerboard bubble lattice is stabilized under an infinitesimally small easy-axis two-spin anisotropic interaction and biquadratic interaction at zero field, while it is degenerate with an anisotropic double-Q state in the absence of the biquadratic interaction. The obtained multiple-Q structures have no intensities at high-harmonic wave vectors in contrast to other multiple-Q states, such as a magnetic skyrmion lattice. We also show that the checkerboard bubble lattice accompanies the charge density wave and exhibits a nearly flat-band dispersion in the electronic structure. Our results provide another route to realize exotic multiple-Q spin textures by focusing on the geometry and symmetry in terms of the wave vectors in momentum space.
The spin-fermion model was previously successful to describe the complex phase diagrams of colossal magnetoresistive manganites and iron-based superconductors. In recent years, two-dimensional magnets have rapidly risen up as a new attractive branch of quantum materials, which are theoretically described based on classical spin models in most studies. Alternatively, here the two-orbital spin-fermion model is established as a uniform scenario to describe the ferromagnetism in a two-dimensional honeycomb lattice. This model connects the magnetic interactions with the electronic structures. Then the continuous tuning of magnetism in these honeycomb lattices can be predicted, based on a general phase diagram. The electron/hole doping, from the empty eg to half-filled eg limit, is studied as a benchmark. Our Monte Carlo result finds that the ferromagnetic TC reaches the maximum at the quarter-filled case. In other regions, the linear relationship between TC and doping concentration provides a theoretical guideline for the experimental modulations of two-dimensional ferromagnetism tuned by ionic liquid or electrical gating.
The magnetoresistance (MR) is a most fundamental transport parameter for metals and semiconductors. This chapter reviews various magnetic materials showing large MR, mainly focusing on transition metal oxides with strong electron correlations. The Boltzmann equation predicts that the classical MR is always positive and small, and the field dependence is quadratic at low fields. When one takes quantum natures into account, however, the MR can be negative, large, or nonmonotonic with fields. The chapter summarizes various types of MR. It also introduces bulk giant MR (GMR) materials with peculiar interactions between localized spins and conduction electrons. The chapter further explains why and how external magnetic fields cause a metal‐insulator transition in the colossal MR (CMR) materials.
The structural, electronic, and magnetic properties of novel functional magnetic intermetallics, in particular some of the most prominent magnetic Heusler alloys, have been reviewed with emphasis on their complex magnetic behavior and nonergodic glassy features, in contrast to the well‐known properties of Ti ‐ Ni and Ni ‐ Al shape memory alloys. Calculational procedures have been listed throughout the text and the theoretical results have been compared with experimental findings where possible. The thermodynamic properties of a few systems ( Ni – Co – Mn – In ), which undergo a structural phase transformation of displacive nature in conjunction with a metamagnetic first‐order phase transition, have been discussed in detail. The importance of such magnetostructural phase transition together with the so‐called thermodynamic (kinetic) arrest phenomenon for the appearance of a giant magnetocaloric effect has been underlined. The list of references should allow bridging the gap between shape memory alloys such as Ti – Ni (including recent ab initio calculations that explain the rapid decrease of the martensitic transformation temperature with disorder) and the “exotic properties” of the magnetic intermetallics.
The magnetic exchange interaction between metal centers in multinuclear compounds plays a defining role in their low-temperature magnetic behavior. Predicting magnetic exchange by computational methods is of high importance for the development of novel magnetic, spintronic materials, and devices that drives further the development of advanced computational methods. In this chapter, we give a brief overview of the origin of magnetic exchange and describe various microscopic theories accounting for it. Several computational approaches which allow the estimation of magnetic exchange in multinuclear compounds are reviewed. Computational challenges of the existing methods for accounting for the magnetic exchange will be discussed in detail in subsequent sections. The combination between accurate on-site eigenstates obtained in ab initio calculations (CASSCF + SOC + ANISO) and theoretical modeling of the magnetic dipole–dipole and exchange interactions within the Lines model, and the recently developed kinetic exchange model is described alongside several recent examples. The last section offers a review of several results obtained recently and gives our perspective on how to achieve an efficient interplay between strong magnetic exchange and a highly axial crystal field on metal sites for designing better exchange-coupled multinuclear single-molecule magnets.KeywordsMagnetic exchangeBroken-symmetry DFTAb initio calculationsMagnetic anisotropyMechanisms of magnetic interactionLines modelMultireference methods
The confluence between high-energy physics and condensed matter has produced groundbreaking results via unexpected connections between the two traditionally disparate areas. In this work, we elucidate additional connectivity between high-energy and condensed matter physics by examining the interplay between spin-orbit interactions and local symmetry-breaking magnetic order in the magnetotransport of thin-film magnetic semimetal FeRh. We show that the change in sign of the normalized longitudinal magnetoresistance observed as a function of increasing in-plane magnetic field results from changes in the Fermi surface morphology. We demonstrate that the geometric distortions in the Fermi surface morphology are more clearly understood via the presence of pseudogravitational fields in the low-energy theory. The pseudogravitational connection provides additional insights into the origins of a ubiquitous phenomenon observed in many common magnetic materials and points to an alternative methodology for understanding phenomena in locally-ordered materials with strong spin-orbit interactions.
A real-space observation of the distribution state of valence electrons, which is responsible for physical properties, is a key methodology to understand the relation between the structure and functions of matter. Here, we observe Mo 4d orbital electrons at subangstrom resolution in a pyrochlore-type oxide Nd2Mo2O7 based on the core differential Fourier synthesis (CDFS) analysis of high-energy x-ray diffraction data. The Mo4+ 4d2 orbital state is directly determined from the obtained valence electron density (VED) distribution. We also find a dip in the radial profile corresponding to a node of the 4d wave function. The VED distribution around the Nd site might be ascribed to the hybridization of neighboring O 2p with Nd 6s/6p/5d orbitals as well as the anisotropic Nd3+ 4f3 electrons, which cannot be reproduced by the simple j-j or LS coupling pictures. In this paper, we demonstrate the usefulness of the CDFS analysis to investigate the orbital states in crystalline materials.
The spectra of two-electron configurations in (jj) and (jl) coupling and of the configurations dn, f3, d2p, and d8p in (LS) coupling are calculated with tensor operators. The agreement with the odd terms of Ti II and Ni II is satisfactory. It is also proved that Gk(2k+1) is a positive decreasing function of k.
The theory of spin waves, leading to the Bloch T32 law for the temperature variation of saturation magnetization, is discussed for ferromagnetic insulators and metals, with emphasis on its relation to the theory of the energy of the Bloch interdomain wall. The analysis indicates that spin-wave theory is of more general validity than the Heitler-London-Heisenberg model from which it was originally derived. Many properties of spin waves of long wavelength can be derived without specialized assumptions, by a field-theoretical treatment of the ferromagnetic material as a continuous medium in which the densities of the three components of spin are regarded as amplitudes of a quantized vector field. As applications, the effects of anisotropy energy and magnetic forces are calculated; and it is shown that the Holstein-Primakoff result for the field dependence of the saturation magnetization can be derived in an elementary manner. An examination of the conditions for validity of the field theory indicates that it should be valid for insulators, and probably also for metals, independently of any simplifying assumptions. The connection with the itinerant electron model of a metal is discussed; it appears that this model is incomplete in that it omits certain spin wave states which can be proved to exist, and that when these are included, it will yield both a magnetization reversal proportional to T32 and a specific heat proportional to T. Incidental results include some insight into the relation between the exchange and Ising models for a two-dimensional lattice, an upper limit to the effective exchange integral, and a treatment of spin waves in rhombic lattices.
Recently, Jonker and Van Santen have found an empirical correlation between electrical conduction and ferromagnetism in certain compounds of manganese with perovskite structure. This observed correlation is herein interpreted in terms of those principles governing the interaction of the d-shells of the transition metals which were enunciated in the first paper of this series. Both electrical conduction and ferromagnetic coupling in these compounds are found to arise from a double exchange process, and a quantitative relation is developed between electrical conductivity and the ferromagnetic Curie temperature.
The vector model for the electrostatic interactions of a system of n electrons, as originally given by Dirac and as used by J. H. Van Vleck, suffers from the restriction that it allows the energy matrix to be set up completely only for a single spatial configuration. In the present paper this restriction is removed. It is shown how the complete energy matrix may be found by means of the vector model, whatever the number of configurations involved. As an example of the method, the energies of the two 2D states arising from the atomic configuration d3 are calculated. Calculations by this method are simpler than the corresponding calculations using Slater wave functions in that the energy matrix factors according to characteristic values of S.
DOI:https://doi.org/10.1103/RevModPhys.24.249
It is assumed (1) that the interaction between the incomplete d shells of the transition elements is insufficient to disrupt the coupling between the d electrons in the same shells, and (2) that the exchange interaction between adjacent d shells always has the same sign irrespective of distance of separation. The direct interaction between adjacent d shells then invariably leads to a tendency for an antiferromagnetic alignment of d spins. The body-centered cubic structure of the transition metals V, Cr, Cb, Mo, Ta, and W is thereby interpreted, as well as more complex lattices of certain alloys. It is demonstrated that the spin coupling between the incomplete d shells and the conduction electrons leads to a tendency for a ferromagnetic alignment of d spins. The occurrence of ferromagnetism is thereby interpreted in a much more straightforward manner than through the ad hoc assumption of a reversal in sign of the exchange integral. The occurrence of antiferromagnetism and of ferromagnetism in various systems is readily understood, and certain simple rules are deduced for deciding which type of magnetism will occur in particular alloys.
The mutual magnetic potential energy of atomic magnetic dipoles is unimportant in salts of high dilution at ordinary temperatures, but becomes important in determining the temperature scale in the new very low region obtained by magnetic cooling. This ``dipole‐dipole'' energy is not to be confused with exchange interaction which is important in concentrated magnetic materials and which is there responsible for ferromagnetism at ordinary temperatures. The partition function, and hence the entropy, specific heat, and susceptibility are calculated for a paramagnetic solid inclusive of dipole and simultaneously also feeble exchange coupling. In Sections 3–4 the computation is made for atoms otherwise free, but in Section 6 they are subjected in addition to a crystalline Stark field. Comparison with experiment is made in the following paper by Hebb and Purcell. Our method of partition functions is to be contrasted with the usual, essentially static Lorentz method of representing dipole‐dipole coupling by a local field, e.g., H+4πM/3 for a long test body. The Lorentz procedure is shown to be only a first approximation, which is really warranted if the density is so low or the temperature so high that one may neglect all terms but the first in the development of the partition function in 1/T. Otherwise the usual results of the local field method are obtained only by an extrapolation which is comparable with the assumption in Heisenberg's theory of ferromagnetism of identical energy for all states with the same crystalline spin. Two other types of extrapolation, based on a second approximation, are obtained which correspond respectively to assuming a Gaussian distribution of energies for these states and to use of the local field proposed by Onsager. The latter seems to be much the more satisfactory of the two.
Various manganites of the general formula La3+Mn3+O32−-Me2+Mn4+O32− have been prepared in the form of polycrystalline products. Perovskite structures were found, i.a. for all mixed crystals LaMnO3CaMnO3, for LaMnO3SrMnO3 containing up to 70% SrMnO3, and for LaMnO3BaMnO3 containing less than 50% BaMnO3. The mixed crystals with perovskite structure are ferromagnetic. Curves for the Curie temperature versus composition and saturation versus composition are given for LaMnO3CaMnO3, LaMnO3SrMnO3, and LaMnO3BaMnO3. Both types of curves show maxima between 25 and 40% Me2+Mn4+O32−; here all 3d electrons available contribute with their spins to the saturation magnetization. The ferromagnetic properties can be understood as the result of a strong positive Mn3+Mn4+ exchange interaction combined with a weak Mn3+Mn3+ interaction and a negative Mn4+Mn4+ interaction. The Mn3+Mn4+ interaction, presumably of the indirect exchange type, is thought to be the first clear example of positive exchange interaction in oxidic substances.
In this paper the general formalism of Kramers indicating the existence of superexchange interaction has been reduced, under simplifying assumptions, to the point where actual formulas for the interaction can be written down directly in terms of spin operators, with certain exchange and transition integrals as parameters. Two results of physical interest are the following: (a) superexchange must be expected to show the directional properties (as far as directional relations of interacting magnetic ions are concerned) of the orbitals in the outer shell of the non-magnetic connecting ions; and (b) the sign of the effective exchange integral depends upon the sign of the internal exchange coupling of an added electron on the magnetic ion.