Synergistic Strain Engineering Effect of Hybrid Plasmonic, Catalytic

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Letter pubs.acs.org/NanoLett

Synergistic Strain Engineering Effect of Hybrid Plasmonic, Catalytic, and Magnetic Core−Shell Nanocrystals Maogang Gong,† Xin Jin,‡ Ridwan Sakidja,§ and Shenqiang Ren*,† †

Department of Mechanical Engineering, Temple University, Philadelphia, Pennsylvania 19122, United States Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, Kansas 66047, United States § Department of Physics Astronomy and Materials Science, Missouri State University, Springfield, Missouri 65897, United States ‡

S Supporting Information *

ABSTRACT: Hybrid core−shell nanocrystals, consisting of distinct components, represent an emerging functional material system, which could facilitate synergistic coupling effects via integrating drastically different functionalities. Here we report a unique strain engineering effect induced by phase transformation between plasmonic core and magnetic shell materials, which leads to a facile surface reconstruction of bimetallic core−shell nanocrystals to enhance their synergistic magnetic and catalytic properties. This advancement dramatically results in two orders of magnitude enhancement in magnetic coercivity and significant improvement in catalytic activity. Mechanistic studies involving the kinetic measurement and theoretical modeling uncover a structural distortion and surface rearrangement mechanism during the core−shell phase transformation pathway. This facile methodology could potentially open up the new design of multifunctional artificial hybrid nanostructures by the combination of phase transformation and surface engineering for emerging technological applications. KEYWORDS: Hybrid nanocrystals, core−shell, nanomagnetism, catalysis

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control, and chemical incompatibility before and after the disorder/order transition. Here we report a unique strain engineering method induced by a phase transformation that enables a facile control of surface atomic rearrangement and a favorable structural distortion of the functional core−shell hybrid nanocrystals. By combining the experimental kinetic studies with the density functional theory (DFT) based atomistic modeling, we have been able to elucidate the mechanisms of the phase transformation that governs the surface atomic rearrangement for the control of magnetic anisotropy and plasmonic-enhanced photocatalysis. The AuCu bimetallic structures have long been considered as an ideal candidate material to study a structural deformation that is facilitated by a thermally triggered phase transformation.11−13 Figure 1a shows a representative scanning transmission electron microscopy (STEM) image of the facecentered cubic (fcc) AuCu dendritic nanostructures, where each dendrite/branch has an average 40 nm in width and 250 nm in length. To reveal the crystalline structure of the asprepared AuCu branched nanostructures, high-resolution TEM

urface atomic arrangement is the main factor governing the functionality of metallic nanoparticles in energy-critical catalysis, magnets, and surface plasmonics.1−4 While the shape and size determine the intrinsic characteristics of monometallic nanocrystals, the lattice arrangement and site segregation have been shown to greatly influence the functionality of bimetallic materials.5,6 By engineering surface atomic structures of hybrid nanocrystals, novel plasmonic, magnetic, catalytic, and electronic properties can be rationally tuned as to selectively promote their functionalities.7−10 While the nanocrystals from organic ligand-guided growth often exhibit a thermodynamically unstable surface caused by the ligand residues, which ultimately results in blocking on the functional sites, the full utility of lattice engineering and phase transformation of hybrid core−shell nanostructures, on the other hand, could lead to a novel and robust monocrystalline epitaxial arrangement. More importantly, such an arrangement can be even further engineered to trigger disorder-to-order transition under certain conditions.2 Up until now, however, the use of phase transformation of complex core−shell hybrid nanocrystals under lattice-matching constraint to promote new functionalities has not yet been fully explored. Indeed, one of the major obstacles for the phase transformation design is the latticematching requirement, which is typically very difficult to achieve due to the large differences in crystal structure, material © XXXX American Chemical Society

Received: October 4, 2015 Revised: November 1, 2015

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Figure 1. Branched structure of AuCu nanocrystals. (a) TEM image of AuCu nanocrystals. (b) HRTEM images of single nanocrystal. (c,d) The HRTEM images marked by the dashed box in b, the inset of c shows the corresponding FFT pattern selected from the core region. (e) STEM and EDX elemental mapping of elements of Au (green) and Cu (red) and their superimposed image.

Figure 2. AuCu−FeMn core−shell structures of pristine (a−c) and annealed at 380 °C (d−f). (a,b) TEM and HRTEM images of AuCu−FeMn core−shell pristine nanocrystal at the Fe/Mn ratio of 50 to 50. (c) STEM elemental mapping images of AuCu−FeMn core/shell nanocrystals, AuCu (red), FeMn (green) and their superimposed image. (d,e) TEM and HRTEM images of AuCu−FeMn core−shell annealed nanocrystal at the Fe:Mn ratio of 50 to 50. (f) STEM elemental mapping images of AuCu−FeMn core−shell nanocrystals, AuCu (red), FeMn (green), and their superimposed image.

(HRTEM) analysis is conducted on one such nanostructures (Figure 1b). Figure 1c,d exemplifies the regions marked by the dashed boxes in Figure 1b, where the lattice fringes can be clearly identified in both images. The lattice distance of 0.23 nm in both inner (Figure 1c) and outer layers of branch (Figure 1d) suggests the (111) surface plane of fcc-AuCu. The terrace traces on the edge of the branched structure (marked with the dashed line in Figure 1d) indicate the high-index nature of the surface facets.12 The Fast fourier transform (FFT)

pattern selected from the core region (Figure 1c) further confirms the crystalline nature of AuCu branched nanocrystals. In particular, Figure 1e shows the energy dispersive X-ray (EDX) elemental mapping of Au and Cu elements. The elemental overlapping of Au and Cu species with a fairly similar intensity throughout pointed to a uniform chemical distribution within these branched nanocrystals. In addition, the crystallographic indexes of X-ray diffraction (XRD) spectrum verify the fcc-AuCu crystal structure (Supporting Information Figure S1). B

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Figure 3. Magnetic characteristics and phase transformation of AuCu−FeMn core−shell branched nanocrystals. (a) Magnetic-hysteresis loops of L10-AuCu−FeMn core−shell nanocrystals with an overall Fe/Mn ratio at 50 to 50 under different annealing conditions. The inset indicates the annealing temperature-dependent coercivity of L10-AuCu−FeMn. (b) XRD patterns of AuCu−FeMn core−shell nanocrystals: pristine and after 380 °C annealing. The labeled peaks represent AuCu (black) and FeMn (Red) diffraction peaks. (c,d) The coercivity of crystals depend on FeMn shell thickness and stoichiometry.

Earth-abundant FeMn alloys have long attracted significant research interest primarily due to their structure-controlled magnetocrystalline anisotropy (Ku).14,15 Their hard magnetic and catalytic properties, however, have not yet been fully studied possibly due to the complexity of its antiferromagnetic characteristics and cubic atomic arrangement.16 It will be critical in this case to change its atomic packing and lattice structure via the epitaxial growth, which dictates surface functional properties such as catalysis, magnetism, and plasmonics. The epitaxial artificial superlattice can transform a disorder to an order state as a result of phase transition, and consequently convert an originally cubic phase into a tetragonal phase upon reaching a critical thickness.17 Thus, we postulated a prototypical system following this mechanism should be observed when we grew a magnetic FeMn shell onto a plasmonic AuCu nanocore structure, where the common (111) plane from each phase is resided at the interface of these two cubic structures. Figure 2a shows a typical TEM image of the AuCu−FeMn (core−shell) branched nanocrystals with an overall 50/50 (Fe/ Mn) atomic ratio (as shown in the EDX analysis of Supporting Information Figure S2). The thickness of FeMn shell has been tuned from 3.0 to 15.2 nm by controlling the shell growth time (Supporting Information Figure S3). In addition to the growth time, the stoichiometry of Fe/Mn in the shell can be controlled by the amounts of Fe and Mn precursors used in the synthesis (The synthetic details are shown in the experimental section and Supporting Information Table S1). The HRTEM images (Figure 2b) of one single AuCu−FeMn nanocrystal clearly show that each nanocrystal is composed of the AuCu core and FeMn shell. The interfringe distance of the AuCu core is 0.230 nm, corresponding to (111) lattice constant of fcc-AuCu, while the interplanar distance of the FeMn shell is 0.227 nm,

corresponding to the (110) surface plane of body-centered cubic (bcc) FeMn shell. Figure 2c shows the scanning TEM (STEM) and elemental mapping images of a single AuCu− FeMn nanocrystal, which further confirm its core−shell hybrid nanostructure. The STEM image shows that the compositionally graded color gradually fades from the core to the edge of branches and a faint-color shell can be located around the braches. The Au and Cu elements are centered in the core region of each branched crystal. The composition image confirms a uniform coating of FeMn shell on the AuCu core. Figure 2d,e shows the TEM and HRTEM images of AuCu− FeMn nanocrystals that were annealed at 380 °C for 20 h. Although no obvious structural change is observed, we do detect a subtle change of the lattice constant after annealing (Figure 2e). The elemental mapping and STEM images confirm the core−shell structural intactness after the thermal annealing treatment (Figure 2f). There are two distinguishable nanoscale domains that can be identified with the lattice constant of 0.218 and 0.215 nm. These constants were originated from the (111) plane of L10-AuCu and (110) plane of tetragonal FeMn. It is important to note that the tetragonal distortion of FeMn shell is initiated by the AuCu phase transition from fcc to L10 phase, which is controlled by the annealing temperature. Thus, to systematically study tetragonal distortion effect on magnetic properties of FeMn shell, we carried on an additional series of magnetic measurements to elucidate the FeMn shell thickness and annealing temperature dependence. Figure 3a shows the magnetic hysteresis (M-H) loops of the AuCu−FeMn nanocrystals (the mass contribution from the nonmagnetic AuCu core has been deducted). The coercivity of AuCu−FeMn nanocrystals is 7 Oe before thermal annealing, while the sample annealed at 380 °C reached to as high as 1150 Oe. This C

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Figure 4. Structural transformation and related modeling. (a) Heteroepitaxial interfacial structure of AuCu−FeMn core−shell systems: pristine (left) and after 380 °C annealing (right). (b−d) The phase transformation process of AuCu−FeMn core−shell nanostructures from x- and y-directions. (e) The total energy per atom for the bct supercells relative to that of relaxed bcc supercells (the aspect ratio =1).

thickness exceeds the critical thickness, the outer atomic layers of FeMn shell would return to its equilibrium cubic structure, thus leading to a reduced Hc. By tuning the concentration of Mn from 0% to 100% at a constant shell thickness (3.0 nm), the Hc value first increases and reaches a maximum value at 50%, consistent with the predicted value in a similar tetragonal systems.2 The epitaxial growth relationship between the (111) AuCu core and (110) FeMn shell suggests a Bain distortion relationship between two phases.19,20 To quantify the distortion and the strain, the lattice mismatch (m) expression has been selected, m = (a2 − a1)/a1, defined as the difference of the lattice parameters between the two phases, where a1 and a2 are the lattice constant of (111) AuCu core and (110) FeMn shell, respectively. The calculated mismatch between the L10 AuCutetragonal FeMn and L10-AuCu/bcc-FeMn are 2.7% and 4.1%, respectively, indicating that the interface of L10-AuCu/ tetragonal-FeMn with a potentially lower misfit should be more stable than that of L10-AuCu/bcc-FeMn. Figure 4a−d shows a schematic interfacial structure of heteroepitaxially grown AuCu−FeMn nanocrystals. Because the strain distortion energy increases proportionally to the epitaxial growth thickness,21 as the epitaxial layers thickness and associated strain energy increases, the epitaxial layer structure would relax gradually to its natural bulk structure. There exists a critical

coercivity change of FeMn shell originates from the phase evolution from cubic to tetragonal during thermal annealing, which is attributed to the disorder/order transition of the AuCu core from fcc to L10 phase. To further understand the phase transformation effect on tetragonal distortion, an increase of the annealing temperature to 500 °C was employed, resulting in a coercivity decrease from 1150 to 206 Oe. Although a higher annealing temperature can improve the crystallinity, the AuCu could phase transform back to the fcc phase at 500 °C,11 leading to a reduced tetragonal distortion of FeMn shell with a lower coercivity. The XRD patterns (Figure 3b) further verify the phase transformation of the AuCu−FeMn (core−shell) nanocrystals upon annealing at 380 °C. Particularly, the diffraction peak (200) in the pristine XRD pattern confirms the existence of fcc-AuCu phase while (002) and (201) peaks after annealing at 380 °C represent the L10-AuCu structure.11,18 The changes in XRD patterns are consistent with the structural characterization from the HRTEM image (Figure 2e). Moreover, the shell thickness and composition dependent magnetic characteristics of annealed AuCu−FeMn nanocrystals are shown in Figure 3c,d. As the shell thickness of FeMn tuned from 3.0 to 15.2 nm at a composition of Fe50Mn50, the coercivity (Hc) of the annealed samples decreases, indicating the existence of the critical shell thickness beyond which the tetragonal distortion become fully relaxed. When the shell D

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Figure 5. Catalysis and mechanism of AuCu−FeMn nanocrystals. (a,b) The absorption versus time spectra and activity of FeMn (annealed), AuCu (annealed), AuCu−FeMn pristine (AuCu−FeMn-p), and AuCu−FeMn annealed (AuCu−FeMn-a) catalysts for the hydrogenation of p-nitrophenol in aqueous phase. (c) Absorption versus time spectra of annealed AuCu−FeMn catalysts under dark and different light intensity. (d) Effect of local surface plasmonic effect on hydrogenation activity of AuCu−FeMn catalyst. (e) Nitrophenol adsorbed onto (e1) (001) Au terminating surface, (e2) (001) Cu terminating surface, and (e3) (Fe, Mn) (001) surface. (f) Adsorption energy of one nitrophenol on to a supercell slab (81 atoms) of catalysts. Note: while we sampled a number of slab configurations with higher Mn content, we fixed the binding sites to one Fe and one Mn atoms on the terminating surface. In all (Fe, Mn) terminating surface, we employ an ideal c/a ratio (1.0).

thickness Tc for such a recovery mechanism which is determined by the crystal interface misfit m and elastic constant22 ⎡1 + ln (1 − v)x + ln ⎣ Tc 2π d = x 8π (1 + v)m

procedures in VASP was utilized: (1) an internal atomic relaxation with no change in the cell volume followed by (2) an cell volume relaxation with a constant c/a ratio. These two processes were alternated until the total energy convergence of 10−5 eV was achieved. Figure 4e shows the energy difference between these supercells (normalized per atom) relative to the total energy of the “pure bcc” with an aspect ratio of c/a of 1. Two important findings that we can point out here: (1) With an increasing deviation of aspect ratio (c/a) to the ideal bcc (c/ a = 1), as expected, there is a corresponding increase in the total energy difference between bcc and bct structures. (2) There is an accompanying reduction with respect to the total energy difference between bcc and bct structures with a higher Mn substitution. The second finding suggests that Mn could lower the energy barrier for the transition from bcc to bct structures. Not surprisingly, the minimum point in terms of the most favorable energetics for an ideal bcc with a low content of Mn should be expected to favor a stable bcc, not bct phase to be consistent with the Fe−Mn phase diagram.26 With a higher content of Mn, however, the energy landscape is more complicated. For one, the total energy difference between bcc and bct can apparently be significantly reduced relative to those at lower Mn content. This lowering of the energy difference is consistent and further explain the experimental results that indicated the ready phase transformation into a bct structure for the (Fe, Mn) solid solution phase. The reduction of the energy barrier for such a phase transition suggests that Mn does play

4hc ⎤ x ⎦

where x is intermediate lattice constant x = 2ab/(a + b), d is the spacing between atomic planes on each side of the interface, and v is Poisson’s ratio of FeMn. The calculated critical thickness Tc of L10-AuCu/tetragonal-FeMn is 3.8 nm, which further confirms the results shown in Figure 3c,d. To further support the experimental analysis on the Baintype phase transition, we performed electronic structure calculations within the DFT approximation as implemented in VASP code21,23 to assess the energetics associated with the formation of body-centered tetragonal (bct) structures with a various aspect ratio and the influence of Mn substitution to Fe as a result of the Bain phase transition. We applied a super cell approach using 3 × 3 × 3 unit cells (54 atoms) with various level of Mn substitution (0−50%). For the supercell calculations, we employed gamma centered k-point grids and the recommended projected augmented wave24 potentials with the GGA-PBE25 exchange and correlation approximations. A relatively high and constant energy cutoff of 350 eV was used to ensure a high precision. To relax the atomic positions for a given aspect ratio of c/a, alternating modes of atomic relaxation E

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and Mn atomic positions could affect their catalytic activity. From the classic volcano shape curve in catalysis, it can be inferred that the presence of Mn (a large lattice constant) would increase the metal−oxygen binding energy on Fe (relatively small lattice constant) surfaces, d-band center shifts away from Fermi level as a result.29 Therefore, hydrogenation reactions are facilitated by the adsorbed oxygen groups due to the enhanced binding energy, which is more significant on the annealed FeMn surface. A recent systematic theoretical evaluation on the mechanisms for the nitrophenol reduction33 suggested that the binding energy can be linked reasonably to the reaction rates of the reduction process following the Brønsted−Evans−Polanyi (BEP) relation.34,35 The binding energy associated with the chemisorption of p-nitrophenol onto a number of catalyst candidates were evaluated: (1) the Cu-terminating and (2) Au-terminating (001) surface of ordered Au50Cu50, and (3) (001) surface of (Fe, Mn) solid solutions with various contents of Mn (Figure 5e). Four different slab configurations for higher Mn content cases were sampled to assess the potential variation in the energetics due to the varied Mn distributions. For each case, two oxygen atoms are orientated normal to the slab’s surface and the molecule and the catalyst are allowed to fully relaxed. The adsorption energy is calculated by the following: Eadsorption = E t o t o f r e l a x e d ( c a t a l y s t + n i t r o p h e n o l ) −E t o t o f r e l a x e d c a t a l y s t − Etot of isolated nitrophenol. Figure 5f shows the adsorption energy for one p-nitrophenol molecule onto the surface. It shows that the adsorption of p-nitrophenol is higher with the Cu terminating surface compared to that of Au. This is quite expected considering the relatively higher bonding strength expected by the Cu terminating atoms and consistent with the previous work.33 We also noted that there is a general increase with respect to the adsorption energy when the Mn is present. There is, however, a larger variation with respect to the binding energy with increasing Mn content presumably due to the varied Mn distributions. Nevertheless, the Mn substitution for Fe in general does enhance the chemisorption of nitrophenol onto the catalyst and thus, following the BEP relation, it may accordingly enhance the catalytic reaction rates as also observed in the experimental findings. The results of our study may potentially open up a new opportunity to control functional hybrid core−shell nanocrystals by taking advantage of the phase transformation-induced strain engineering. The core−shell structure utilizes a unique surface strain facilitated by the lattice mismatch between the core and shell materials to exploit both magnetically and catalytically active phases of bimetallic nanocrystals. As a model system, we have demonstrated that the FeMn shell coating on the plasmonic AuCu core structures exhibit the surface strain controlled magnetic (164-fold enhancement of magnetic coercivity) and outstanding catalytic performances (9-fold enhancement of TOF values for the hydrogenation of pnitrophenol). Insights generated in this work allow us to design novel and cost-effective materials and such a new catalytic approach can potentially have a greater implication in addressing some of our current energy and environment concerns, such as renewable fuels and pollution controls.

an important role in securing a nonequilibrium structure at the vicinity of the AuCu−FeMn interface. Furthermore, there appears to be a slight deviation from c/a = 1 of the minimum point with a higher Mn content that further gives a further credence to the ease in the bct phase formation (Figure 4e). This is consistent with the previous theoretical analysis on the energetics of fcc (Fe50Mn50) solid solution, showing that indeed a small tetragonal distortion (c/a = 1.01) was obtained after atomic and cell relaxations.27 Because the energy difference is similarly too small, further work will be needed to verify the effect, but the experimental evidence does suggest such a distortion is energetically feasible. In order to understand the structural distortion effect on the surface atomic rearrangement of FeMn shell, a series of catalytic activity tests for the hydrogenation of p-nitrophenol to paminophenol were carried out. It is important to mention that numerous previous reports on catalytic activities have been primarily focused on the use of noble metal based catalysts, such as Au,28 Pd,29 Ru,30 and Pt,31,32 but there have been no such results exist that we are aware of on non-noble materials (such as Fe and Mn). Preliminary hydrogenation results on individual FeMn and AuCu nanoparticles show that the latter display a relatively higher activity for p-nitrophenol conversion as expected. Particularly, the FeMn and AuCu catalysts show the turnover frequency (TOF) values of 0.028 and 0.042 mmol/mg·h, respectively. However, the AuCu−FeMn hybrid nanostructures exhibit an enhanced hydrogenation activity under an identical condition yielding TOF values of 0.093− 0.168 mmol/mg·h. Specifically, the pristine and annealed AuCu−FeMn hybrid nanostructures (Figure 5a,b) demonstrate approximately 0.093 and 0.168 mmol/mg·h activity, respectively. The annealed AuCu−FeMn nanocrystals display a remarkably six-fold activity for the hydrogenation of pnitrophenol in the aqueous phase in comparison with that obtained from the FeMn catalyst (based on the FeMn content in nanocrystals). The template effect induced by the presence of AuCu core was further studied by controlling the shell thickness of FeMn materials, the results of which are shown in the inset of Figure 5b. We should however note that as the thickness of FeMn shell increases from 5.95 to 7.37 nm, the hydrogenation catalytic activity of p-nitrophenol does decrease significantly from 0.168 to 0.084 mmol/mg·h. The reduction in TOF values may indicate that as more FeMn layers are added to the surface, there is a corresponding reduction in the influence of the atomic rearrangement triggered by the phase transformation of AuCu core toward the catalytic activity (Supporting Information Figure S4). Nevertheless, we can still observe the benefits of a synergistic activity on the hybrid materials which surpasses the TOF values achieved by the individual FeMn or AuCu nanocrystals. Interestingly, as the thickness of FeMn shell further increases to 19.2 nm, the observed TOF value becomes fairly constant similar to the value produced by the 7.37 nm shell structure. It should be noted that the presence of electromagnetic field also cause a local surface plasmonic effect on AuCu phase,12 which in turn, could enable the plasmon-dependent photocatalytic activity (Figure 5c,d). A light illumination enhances the catalytic activity for p-nitrophenol conversion, where 2.5 mW/cm2 light illumination for 10 s display a superior activity (0.26 mmol/mg· h), which shows nine times higher activity for the p-nitrophenol hydrogenation than that of FeMn nanocrystals. We further analyze the effect of bimetallic FeMn formulation on the hydrogenation activity as a surface reorganization of Fe

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b04036. F

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(23) Kresse, G.; Furthmüller, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (24) Blöchl, P. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (25) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (26) Kubaschewski, O. Iron-Binary Phase Diagrams; Springer-Verlag: Berlin Heidelberg Gmbh, 1982; pp 61−63. (27) Ekholm, M.; Abrikosov, I. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 104423. (28) Lee, J.; Park, J. C.; Song, H. Adv. Mater. 2008, 20, 1523−1528. (29) Pozun, Z. D.; Rodenbusch, S. E.; Keller, E.; Tran, K.; Tang, W.; Stevenson, K. J.; Henkelman, G. J. Phys. Chem. C 2013, 117, 7598− 7604. (30) Antonels, N. C.; Meijboom, R. Langmuir 2013, 29, 13433− 13442. (31) Komatsu, T.; Hirose, T. Appl. Catal., A 2004, 276, 95−102. (32) Vaidya, M. J.; Kulkarni, S. M.; Chaudhari, R. V. Org. Process Res. Dev. 2003, 7, 202−208. (33) Pozun, Z. D.; Rodenbusch, S. E.; Keller, E.; Tran, K.; Tang, W.; Stevenson, K. J.; Henkelman, G. J. Phys. Chem. C 2013, 117, 7598− 7604. (34) Bronsted, J. N. Chem. Rev. 1928, 5, 231−338. (35) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 11−24.

Materials and Methods, Table S1, Figures S1−S4, and lattice mismatch calculations. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

M.G. carried out experiments and wrote the manuscript. X.J. participated in the catalytic analysis and manuscript preparation. R.S. did the modeling calculation. S.R. guided the project and edited the paper. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.R. thanks the financial support from the U.S. National Science Foundation (NSF) under the CAREER Award No: NSF-DMR1551948 (magnetically hard nanocrystals) and NSF-CMMI1553986 (nanomanufacturing).

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