Exchange Constants Research Articles

All-optical measurement of interlayer exchange coupling in Fe/Pt/FePt thin films

Time Resolved Magneto Optic Kerr Effect spectroscopy was used to all-optically study the dynamics in exchange coupled Fe(10 nm)/Pt(x = 0–5 nm)/FePt (10 nm) thin films. As the Pt spacer decreases, the effective magnetization of the layers is seen to evolve towards the strong coupling limit where the two films can be described by a single effective magnetization. The coupling begins at x = 1.5 nm and reaches a maximum exchange coupling constant of 2.89 erg/cm2 at x = 0 nm. The films are ferromagnetically coupled at all Pt thicknesses in the exchange coupled regime (x ≤ 1.5 nm). A procedure for extracting the interlayer exchange constant by measuring the magnetic precession frequencies at multiple applied fields and angles is outlined. The dynamics are well reproduced using micromagnetic simulations.

Topological Hall effect in ferromagnetic/non-ferromagnetic metals heterojunctions

In a magnetic system, the spin orbit coupling can combine with the exchange interaction to generate an anisotropic exchange interaction that favors a chiral arrangement of the magnetization. This is known as the Dzyaloshinskii-Moriya interaction (DMI). Contrary to the Heisenberg exchange interaction, which leads to collinear alignment of lattice spins, the form of DMI is therefore very often to cant the spins by a small angle. If DMI is strong enough to compete with the Heisenberg exchange interaction and the magnetic anisotropy, it can stabilize chiral domain wall structure such as skyrmion. When a conduction electron passes through a chiral domain wall, the spin of the conduction electron will experience a fictitious magnetic field (Berry curvature) in real space, which deflects the conduction electrons perpendicular to the current direction. Therefore, it will cause an additional contribution to the observed Hall signal that is termed topological Hall effect (THE). The THE has attracted much attention since it is a promising tool for probing magnetic skyrmions. Recent extensive experiments have focused on the the THE in the ferromagnetic/non-ferromagnetic metal heterojunctions due to the inherent tunability of magnetic interactions in two dimensions. We firstly review the THE in ferromagnetic multilayers, in which the domain wall energy with interfacial DMI can be written as =4AK-D, where Dis the effective DMI energy constant, A the exchange constant, K the anisotropy constant. For the most favorable chirality, it lowers the energy. The limit of this situation is when goes to zero, which defines the critical DMI energy constant Dc=4AK/. Therefore, the domain wall energy would be negative and the chiral domain walls should proliferate if D Dc, and the methods that can modulate D and Dc to reduce have been explored. We have also reviewed the THE in MnGa/heavy metal bilayers. The largest THE signals have been found based on the MnGa films with smallest Dc, which correspondingly results in the smallest . The large topological portion of the Hall signal from the total Hall signal has been extracted in the whole temperature range from 5 to 300 K and the magnitude of fictitious magnetic field has been determined.

Magnetic domain chirality and tuning of skyrmion topology

Owing to the topologically protected properties, magnetic skyrmions possess high stability and small critical driving current, thus making them potentially applied to future racetrack memory devices. Skyrmions have been identified in several material systems. One large class contains the centrosymmetric materials, where skyrmions emerge as the competition between perpendicular magnetic anisotropy and magnetic dipolar interactions. The recently reported skyrmion host includes La-Sr-Mn-O, hexagonal MnNiGa, Fe3Sn2, etc. In these systems, due to the isotropic characteristic of the dipolar interaction, magnetic bubble can exhibit various topologies and helicities. The common types of bubbles existing in the materials are the trivial one with n=0 (n is the topological charge) and the non-trivial one with n=1, and the latter is taken to be equivalent to magnetic skyrmion. In this article, we investigate the formation of skyrmions under various magnetic parameters and the role of stripe domain chairity in tuning the bubble topology. The main method we use here is micromagnetic simulation with the Object Oriented MicroMagnetic Framework (OOMMF) code. Also some recent experimental results on MnNiGa and Fe3Sn2 are exhibited and compared with the simulation prediction. Under a fixed magnetization (Ms), by tuning the exchange constant A and magnetic anisotropy Ku, we find that the domains can evolve into a bubble state under a moderate anisotropy value, and to some extent, large anisotropy favors the formation of n=1 topological skyrmion. In the case of the stripe domains, it is found that different initial configuration can lead to different domain wall charity and further change the process of skyrmion formation. When the magnetization in the domain wall orients in the same direction, n=0 bubble will form upon applying magnetic field. While the magnetization in the wall orients alternatively up and down, a topological skyrmion is directly formed. In the stripe domains with inversed 180 Bloch wall, in-plane magnetization dominates and no bubble or skyrmion can form. In addition, the tilt of the magnetic field and uniaxial anisotropy can also change the morphology and topology of the skyrmions, which has been verified in our experiments. According to the above results, we propose to tune the topology of skyrmions in centrosymmetric material through adjusting the ground magnetic state, magnetic anisotropy and in-plane components, which can be realized by element doping at different sites and appropriately designing the sample.

Evidence of magnetoelectric coupling in 0.9BiFeO3-0.1Ba[Ti0.95(Yb0.5Nb0.5)0.05]O3 ceramic

The physical properties of the Multiferroïc lead-free 0.9BiFeO3-0.1Ba[Ti0.95(Yb0.5Nb0.5)0.05]O3 ceramic were investigated by in-situ Mössbauer spectroscopy, X-ray diffraction (XRD), dielectric measurements and Raman scattering. Both BiFeO3 and 0.9BiFeO3-0.1Ba[Ti0.95(Yb0.5Nb0.5)0.05]O3 ceramics underwent in-situ Mössbauer spectroscopy in the temperature range of 300 K to 653 K and the parameters of hyperfine interactions were determined. The magnetic transition temperature TN of our doped sample was of 568 K, which was lower than that of BiFeO3. This reduction of TN originated from the presence of different exchange constants resulting from the weakening of JFe-Fe. The deviation of the reduced magnetic hyperfine field H(T)/H(0) as a function of the reduced temperature T/TN from the Brillouin curve of Fe3+ (S = 5/2) for the three sextets and the determination of the critical exponent β, of 0.375 ± 0.022 in the range of 0.01 < 1-T/TN < 0.5 revealed a 3D magnetic long range order phase transition. The complexity of the spatial spin structure was a result of the canting of antiferromagnetically ordered spins of BiFeO3. Our findings revealed the effect of the non-magnetic substituents Ba and Yb/Nb/Ti in A and B sites, respectively on the magnetic properties. Around the magnetic transition temperature, both isomer shift evolution and quadruple splitting distribution showed pronounced anomalies associated with the onset of magnetic ordering. The Debye temperature (θD) was deduced to be of 257 ± 21 K. These results revealed 0.9BiFeO3-0.1Ba[Ti0.95(Yb0.5Nb0.5)0.05]O3 as a promising material for piezoelectric devices. XRD analyses were performed for temperatures from 300 K up to 750 K. Gradual structural evolution, as temperature increased, exhibited an isostructural phase transition and an anomaly in the evolution of lattice parameters and the unit cell volume as well as a significant shift in the atomic positions near the magnetic transition temperature TN. These behaviors indicate magnetoelastic coupling. The temperature dependence of the real part of dielectric permittivity and dielectric loss (tan δ) was investigated over a wide range of temperatures at 1 kHz. During its evolution, an anomaly was observed at 568 K; which corresponded to the magnetic transition temperature TN. Raman scattering spectra were measured in the temperature range from 303 K to 728 K. Drastic changes, especially that of the three two-phonon modes centered at around 1000-1500 cm−1, were the results of magnetic rearrangement and atomic displacement leading to both modulating magnetic exchange interaction and polarization state. All these results prove the magnetoelectric coupling of 0.9BiFeO3-0.1Ba[Ti0.95(Yb0.5Nb0.5)0.05]O3 ceramic.

Magnetization reversal, exchange interaction, and switching behavior studies on Ru doped GdCrO3

A systematic study on the crystal structure and magnetic properties of GdCr1−xRuxO3 (where 0 ≤x≤ 0.15) was carried out by powder x-ray diffraction along with low temperature magnetization measurements. Lattice parameters and cell volume continuously increase with doping due to the incorporation and formation of higher ionic radius Ru4+ and Cr2+ ion, respectively. Pure GdCrO3 shows the antiferromagnetic (AFM) ordering at 170 K and a spin-reorientation transition around 8 K. Surprisingly, the AFM ordering temperature does not show any variation with the tetravalent Ru doping; while, spin-reorientation completely disappears with 5% Ru doping within the investigated temperature region. All these compounds exhibit magnetization reversal under low applied fields in field-cooled (FC) protocol. Highly delocalized 4d orbitals and occupation number of Ru4+ result in a decrease of antisymmetric exchange constant (D) with doping. Additionally, the formation of high-spin Cr2+ in weak octahedral field increases the effective magnetic moment for doped samples. Magnetic relaxation study in FC mode reveals the memory effect of pure GdCrO3. Magnetic field-assisted switching behavior study corroborates that magnetic state (positive or, negative) can easily be switched by the application of magnetic field.

Study of Cationic and Nonionic Mixed Micelles with NaBr and 3,5-Cl2C6H3CO2Na by Use of Probe Nucleophilic Reaction of Piperidine with Ionized Phenyl Salicylate.

Behaviors of cationic and nonionic mixed micelles in the form of hexadecyltrimethylammonium bromide (HDABr) and hexadecyltrimethylammonium bromide-Polyethylene glycol hexadecyl ether (C16E20), in the presence of inert salts (NaBr and 3,5-dichlorosodium benzoate), by the use of reaction probe between Pp and ionized PhSH (Pp = piperidine and PhSH = phenyl salicylate), has been reported in this work. The values of RXBr (RXBr denotes ion exchange constants obtained in the presence of micelles of different structural features) or KXBr (KXBr denotes ion exchange constants obtained in the presence of micelles of the same structural features) for 3,5-Cl2C6H3CO2- were almost the same at three different [HDABr]T (0.006, 0.010 and 0.015 M). The average value of RXBr or KXBr determined, in the presence of pure HDABr micelles, using semi empirical kinetic (SEK) method appeared to be almost 2½-fold larger (RXBr or KXBr = 198) than that in the presence of mixed HDABr-C16E20 micelles (RXBr or KXBr = 78). Rheological measurements indicated the existence of wormlike/twisted micelles and vesicle at 0.015 M pure HDABr, various [3,5-Cl2C6H3CO2Na], and 25 and 35℃ whereas there were evidence of only spherical micelles in the presence of mixed HDABr-C16E20 ([HDABr]T = 0.015 M and [C16E20]T = 0.006 M) at both temperatures.

Ab Initio Theoretical Prediction of Structural, Electronic, and Magnetic Properties in the 3d (Mn)-Doped Zinc-Blende MgSe: A DFT-mBJ Approach

In this paper, we have investigated the structural, electronic, and magnetic properties of magnesium selenium (MgSe) doped with transition metal manganese (Mn) impurity in the cubic diluted magnetic semiconductor (DMS) zinc blende structure. The compounds which we are interested are as Mg1−x Mn x Se where x change between 0 and 1 by step 0.25. All properties are studied, using first-principles calculation of density functional theory under the framework of the full-potential linearized augmented plane waver (FP-LAPW). In our study, we employed the Wu-Cohen generalized approximation (WC-GGA) to optimize the crystal structure, whereas Tran-Blaha modified Becke-Johnson potential (TB-mBJ) as a new functional was applied to compute the electronic and magnetic properties in order to get some better degree of precision. The electronic band structures and density of state plots reveal ferromagnetic semiconducting behavior in these compounds, and the exchange constants N 0 α and N 0 β are calculated to validate the effects resulting from exchange splitting process. Moreover, for each concentration x, the value of total magnetic moment has been estimated to equal to 5 μ B. The important magnetic moments values obtained in these compounds indicate the potential for their use in spintronic devices.

Ab Initio Study of Structural, Electronic, and Magnetic Properties of A 1 − x III $\mathrm {A}_{1-x}^{\text {III}}$ Mn x BVI: In1−x Mn x S-Diluted Magnetic Semiconductor

First-principles density functional calculations on the new class of diluted magnetic semiconductor $A_{1-x}^{III}{Mn}_{x}B^{VI}$ In1−x Mn x S for x = 0.25 and 0.5 are investigated to study the structural, electronic, and magnetic properties, employing the full-potential linearized augmented plane wave method. Electronic band structures and density of states revealed a half-metallic character of In1−x Mn x S and show the stability of anti-ferromagnetic states as compared with ferromagnetic states. The calculated exchange constants J dd are in good agreement with experimental and theoretical results on magnetic properties of single crystalline $\mathrm {A}_{1-x}^{\text {III}}{\text {Mn}}_{x}\mathrm {B}^{\text {VI}}$ in the anti-ferromagnetic case. Our predicated calculations on the s,p-d exchange constants N 0 α and N 0 β show that they are lower than in $\mathrm {A}_{1-x}^{\text {II}}{\text {Mn}}_{x}\mathrm {B}^{\text {VI}}$ DMS. The local environment is found tetrahedral as in the II–VI DMS and other (III,Mn) VI compounds. The total magnetic moment for In1−x Mn x S for different concentrations is in accordance with the exact value 5 μ B and comes mainly from impurity Mn. The local magnetic moments of Mn ions are reduced from their free space charges values due to the p-d hybridization which produces small magnetic moments on the nonmagnetic In and S sites. The Curie temperature of In1−x Mn x S is calculated within the mean field approximation and compared with other DMS systems.

DFT-Mbj Study of Electronic and Magnetic Properties of Cubic Cecro3 Compound: An Ab-Initio Investigation

By considering density functional theory (DFT) in terms of ab-initio investigation, we have explored the structural, electronic and magnetic properties of cubic CeCrO3 for the first time. In order to determine the structural stability of cubic CeCrO3 compound, we optimized the structure of CeCrO3 in non-magnetic (NM), ferromagnetic (FM) and Anti-ferromagnetic (AFM) phases by using PBE generalized gradient approximation (GGA) functional to find the exchangecorrelation potential. From structural optimization, the FM phase of CeCrO3 is observed to be stable. For computing electronic and magnetic properties, thelately advanced modified Becke and Johnson local (spin) density approximation (mBJLDA) is used. Calculated band structures and density of states plots with an integer magnetic moment of 4 μB and reveal half-metallic character. In addition, s–d exchange constants (N0α) and p–d exchange constant (N0β) are determined, which are in agreement with a distinctive magneto-optical experiment.

Heisenberg model analysis on inelastic powder neutron scattering data using parent and K doped BaMn2As2 samples

Low temperature powder inelastic neutron scattering measurements were performed on three different powder samples; parent BaMn2As2,12.5% K-doped Ba0.875K0.125Mn2As2 and 25% K-doped Ba(0.75)K0.25Mn2As2. The Heisenberg Model involving J1‐J2‐Jz coupling constants were compared to the data by a powder integration routine using Monte Carlo integration methods. The best magnetic parameters were selected using a chi-square test where model intensities were compared to the full (q,E) dependence of magnetic scattering. A key step to this analysis is the characterization of the background which is formed mostly by phonon scattering intensities along with other sources including the magnetic impurity scattering events. The calculated powder magnetic intensities added to the estimated background obtained from the non-magnetic high momentum transfer region. The agreement between the simulated and the raw data enabled us to perform quantitative analysis of the unreacted MnO impurities. Overall, this is another confirmation along with earlier studies using this technique, that magnetic exchange constants can be calculated within an acceptable range with a very quick inelastic neutron powder experiment without need for a single crystal sample.

Spin-Current Manipulation of Photo-Induced Magnetization Dynamics in Heavy Metal/Ferromagnet Double Layer-Based Nanostructures

Spin currents offer a way to control static and dynamic magnetic properties, and therefore they are crucial for next-generation MRAM devices or spin-torque oscillators. Manipulating the dynamics is especially interesting within the context of photo-magnonics. In typical $3d$ transition metal ferromagnets like CoFeB, the lifetime of light-induced magnetization dynamics is restricted to about 1 ns, which e.g. strongly limits the opportunities to exploit the wave nature in a magnonic crystal filtering device. Here, we investigate the potential of spin-currents to increase the spin wave lifetime in a functional bilayer system, consisting of a heavy metal (8 nm of $\beta$-Tantalum (Platinum)) and 5 nm CoFeB. Due to the spin Hall effect, the heavy metal layer generates a transverse spin current when a lateral charge current passes through the strip. Using time-resolved all-optical pump-probe spectroscopy, we investigate how this spin current affects the magnetization dynamics in the adjacent CoFeB layer. We observed a linear spin current manipulation of the effective Gilbert damping parameter for the Kittel mode from which we were able to determine the system's spin Hall angles. Furthermore, we measured a strong influence of the spin current on a high-frequency mode. We interpret this mode an an exchange dominated higher order spin-wave resonance. Thus we infer a strong dependence of the exchange constant on the spin current.

A2MnXO4 Family (A = Li, Na, Ag; X = Si, Ge): Structural and Magnetic Properties.

Four new manganese germanates and silicates, A2MnGeO4 (A = Li, Na) and A2MnSiO4 (A = Na, Ag), were prepared, and their crystal structures were determined using the X-ray Rietveld method. All of them contain all components in tetrahedral coordination. Li2MnGeO4 is orthorhombic (Pmn21) layered, isostructural with Li2CdGeO4, and the three other compounds are monoclinic (Pn) cristobalite-related frameworks. As in other stuffed cristobalites of various symmetry (Pn A2MXO4, Pna21 and Pbca AMO2), average bond angles on bridging oxygens (here, Mn-O-X) increase with increasing A/X and/or A/M radius ratios, indicating the trend to the ideal cubic (Fd3̅m) structure typified by CsAlO2. The sublattices of the magnetic Mn2+ ions in both structure types under study (Pmn21 and Pn) are essentially the same; namely, they are pseudocubic eutaxy with 12 nearest neighbors. The magnetic properties of the four new phases plus Li2MnSiO4 were characterized by carrying out magnetic susceptibility, specific heat, magnetization, and electron spin resonance measurements and also by performing energy-mapping analysis to evaluate their spin exchange constants. Ag2MnSiO4 remains paramagnetic down to 2 K, but A2MnXO4 (A = Li, Na; X = Si, Ge) undergo a three-dimensional antiferromagnetic ordering. All five phases exhibit short-range AFM ordering correlations, hence showing them to be low-dimensional magnets and a magnetic field induced spin-reorientation transition at T < TN for all AFM phases. We constructed the magnetic phase diagrams for A2MnXO4 (A = Li, Na; X = Si, Ge) on the basis of the thermodynamic data in magnetic fields up to 9 T. The magnetic properties of all five phases experimentally determined are well explained by their spin exchange constants evaluated by performing energy-mapping analysis.

Ground state and magnetic properties of the Cr-doped Ni-Mn-(Ga, Ge, In, Sn) alloys: Insights from ab initio study

By using first-principles calculations in combination with supercell approach a series of Ni8Mn2Cr2Z4 (Z = Ga, Ge, In, Sn) are studied with partial replacing of Mn by Cr to investigate the effect of such substitution on their structural and magnetic properties. Two 16-atom supercells with different distribution of Cr in the Mn sublattice and magnetic ordering are considered. Crystal structure optimization shows that the magnetic ground state of Ni8Mn2Cr2Z4(Z = Ga, In) alloys is the state with pairwise antiparallel magnetic moments of Cr atoms. While for Ni8Mn2Cr2Z4 (Z = Ge, Sn) alloys is it ferromagnetic state with parallel magnetic moments of Cr and Mn atoms. Based on ground state energies it is shown that martensitic phase can be realized only in Ni8Mn2Cr2Z4 (Z = Ga, Ge) alloys. For the stable crystal structures with associated magnetic order magnetic exchange constants are calculated, to estimate Curie temperatures with the help of mean-field approximation. Obtained results are in qualitative agreement with experimental and theoretical data.

Electronic structure and magnetism of epitaxial Ni–Mn–Ga(-Co) thin films with partial disorder: a view across the phase transition

The influence of Co-doping in off-stoichiometric Ni–Mn–Ga and Ni–Mn–Ga–Co thin films on the magnetic coupling of the atoms is investigated with x-ray magnetic circular dichroism in both the martensitic as well as austenitic phase, respectively. Additionally, first principles calculations were performed to compare the experimentally obtained absorption spectra with theoretical predictions. Calculated exchange constants and density of states for the different atomic sites underline the large influence of chemical and magnetic order on the magnetocaloric properties of the material.

Interlayer exchange coupling in perpendicularly magnetized Pt/Co/Ir/Co/Pt structures

The occurrence of both interlayer exchange coupling and perpendicular magnetic anisotropy is evidenced in Pt/Co/Ir/Co/Pt magnetron sputtered structures. We point out the effect of lattice strains on stabilizing the perpendicular magnetic anisotropy. The surface magnetic anisotropy constant is around 1.76 erg cm−2 and around 1.5 erg cm−2 for the Co layers, depending on their positioning within the stack. We demonstrate a relatively high interlayer exchange constant of −2.5 erg cm−2 at the first antiferromagnetic coupling maximum corresponding to an exchange field larger than 12 kOe. The interlayer exchange coupling shows remarkable annealing endurance being preserved for annealing temperatures up to 400 °C.

Magnetization Process of the S = 1/2 Two-Leg Organic Spin-Ladder Compound BIP-BNO

We have measured the magnetization of the organic compound BIP-BNO (3,5'-bis(N-tert-butylaminoxyl)-3',5-dibromobiphenyl) up to 76 T where the magnetization is saturated. The S = 1/2 antiferromagnetic Heisenberg two-leg spin-ladder model accounts for the obtained experimental data regarding the magnetization curve, which is clarified using the quantum Monte Carlo method. The exchange constants on the rung and the side rail of the ladder are estimated to be J(rung)/kB = 65.7 K and J(leg)/kB = 14.1 K, respectively, deeply in the strong coupling region: J(rung)/J(leg) > 1.

Critical and compensation behavior of a mixed spin-5/2 and spin-3/2 Ising antiferromagnetic system in a core/shell nanowire

In this work, Monte Carlo simulations based on metropolis algorithm were performed to study the critical and compensation temperatures of a core–shell nanowire with spins and , respectively, considering an Ising antiferromagnetic system. The influence of nearest neighbors exchange interactions and crystal field anisotropy on the critical and compensation behaviors of the system has been analyzed. The effects of the nanowire height in the critical and compensation temperatures were evaluated. The results show that, for a system with given values of exchange interaction constants and crystal field anisotropy, a compensation point only appears if two requirements are satisfied. First, the weight of the core magnetization in the total magnetization must be greater than the weight of the shell magnetization at zero temperature. And second, the exchange constant of shell ions must be greater than a certain value. This value is, at the same time, greater than the exchange constant of core ions. The critical and compensation temperatures are very sensitive to variations in the exchange constant of the shell ions and core ions, respectively, while the crystal field anisotropy affects both temperatures.

High-temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high-temperature series expansion study

We develop high temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity and entropy as a function of temperature for different values of the Kitaev coupling $K$ and Heisenberg exachange coupling $J$ (with $|J|\le |K|$) are presented. These expansions show good convergence down to a temperature of a fraction of $K$ and in some cases down to $T=K/10$. In the Kitaev exchange dominated regime, the inverse susceptibility has a nearly linear temperature dependence over a wide temperature range. However, we show that already at temperatures $10$-times the Curie-Weiss temperature, the effective Curie-Weiss constant estimated from the data can be off by a factor of 2. We find that the magnitude of the heat capacity maximum at the short-range order peak, is substantially smaller for small $J/K$ than for $J$ of order or larger than $K$. We suggest that this itself represents a simple marker for the relative importance of the Kitaev terms in these systems. Somewhat surprisingly, both heat capacity and susceptibility data on Na$_2$IrO$_3$ are consistent with a dominant {\it antiferromagnetic} Kitaev exchange constant of about $300-400$ $K$.

Contribution to Spin Tubes Study

In this work, we aim to study both analytically and numerically the behavior of triangular spin tubes made by three chains which are connected to one another by exchange, in the presence of single-ion anisotropy. By diagonalizing the spin Hamiltonian, the partition function was exactly calculated within the transfer matrix approach and several relevant physical quantities were derived and analyzed. Depending on the sign and strengths of the exchange and anisotropy constants, the system reveals a rich variety of features such as frustration and steplikes in the magnetization curves arising from both geometry and conflicting interactions.

Tailored material properties using textile composites

Lightweighting is essential for the reduction of energy consumption in transportation. The most common approach is through the application of high specific strength and stiffness materials, such as composites and high performance aluminum alloys. One of the challenges associated with the use of advanced materials is the high cost. This paper explores the opportunities of using hybrid composites (glass and carbon, for example) with selective fiber placement to optimize the weight subject to price constraints for given components.Considering the example of a hat-section for hood reinforcement, different material configurations were modeled and developed. The required thickness of the hat section to meet the same bending stiffness as an all carbon composite beam was calculated. It was shown that selective placement of fiber around the highest moments results in a weight savings of around 14% compared to a uniformly blended hybrid with the same total material configuration. From this it is possible to estimate the materials cost of the configurations as well as the weight of the component. To determine which is best it is necessary to find an exchange constant that converts weight into cost – the penalty of carrying the extra weight. The value of this exchange constant will depend on the particular application.