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On the enhancement of magnetic anisotropy in cobalt clusters via non-magnetic doping
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 125303 (http://iopscience.iop.org/0953-8984/26/12/125303) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 132.239.1.231 This content was downloaded on 13/05/2017 at 01:52 Please note that terms and conditions apply.
You may also be interested in: Using graphene to control magnetic anisotropy and interaction between supported clusters Sanjubala Sahoo, M Fhokrul Islam and Shiv N Khanna Magnetic anisotropy of heteronuclear dimers in the gas phase and supported on graphene: relativistic density-functional calculations Piotr Boski and Jürgen Hafner On the interplay between geometrical structure and magnetic anisotropy: a relativistic density-functional study of mixed Pt–Co and Pt–Fe trimers and tetramers in the gas-phase and supported on graphene Piotr Boski and Jürgen Hafner Magnetic properties of transition metal Mn, Fe and Co dimers on monolayer phosphorene Imran Khan and Jisang Hong Magneto-structural properties and magnetic anisotropy of small transition-metal clusters: afirst-principles study Piotr Boski and Jürgen Hafner Cu(111) supported graphene as a substrate for magnetic dimers with a large magnetic anisotropy: relativistic density-functional calculations P Boski and J Hafner
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 125303 (7pp)
doi:10.1088/0953-8984/26/12/125303
On the enhancement of magnetic anisotropy in cobalt clusters via non-magnetic doping M Fhokrul Islam and Shiv N Khanna Department of Physics, Virginia Commonwealth University, Richmond, VA 23284-2000, USA E-mail: [email protected] Received 25 November 2013, revised 17 January 2014 Accepted for publication 22 January 2014 Published 6 March 2014
Abstract
We show that the magnetic anisotropy energy (MAE) in cobalt clusters can be significantly enhanced by doping them with group IV elements. Our first-principles electronic structure calculations show that Co4 C2 and Co12 C4 clusters have MAEs of 25 K and 61 K, respectively. The large MAE is due to controlled mixing between Co d- and C p-states and can be further tuned by replacing C by Si. Larger assemblies of such primitive units are shown to be stable with MAEs exceeding 100 K in units as small as 1.2 nm, in agreement with the recent observation of large coercivity. These results may pave the way for the use of nano-clusters in high density magnetic memory devices for spintronics applications. Keywords: nano-cluster, magnetic memory, magnetic anisotropy (Some figures may appear in colour only in the online journal)
1. Introduction
particularly important for the development of materials where the size selected clusters could serve as primitive building blocks, opening a route towards new molecular electronic materials [8–11]. Bulk Fe, Co, and Ni are all itinerant ferromagnetic elements with magnetic moments of 2.22, 1.72, and 0.61 µB /atom, respectively. The MAE at low temperatures is around 60 µeV/atom for hcp cobalt (a soft magnetic material) and is smaller for cubic Fe and Ni by a factor of 50 [12]. At small sizes, the MAE continues to be small with an upper limit of 65 µeV/atom in iron clusters containing 10 atoms [13]. For the case of cobalt, our previous studies indicate that a Co5 cluster with triangular bi-pyramidal geometry and a Co13 cluster with icosahedral geometry have MAEs of 0.1 and 0 meV/atom, respectively [14]. Recent works combining experiments and theoretical work in our group have, however, reported some interesting findings [15, 16]. In these studies, nanoassembled materials consisting of Co2 C and Co3 C nanoparticles were synthesized using wet chemical methods. The resulting material consisted of 8–10 nm nanoparticles with atomic arrangements different from bulk carbide phases. The new structures could be described as carbon atoms
The principal quantity controlling the magnetic behavior at small sizes is the magnetic anisotropy energy (MAE). Extensive research over the past three decades has shown that clusters and nanoparticles of conventional itinerant ferromagnetic solids have novel magnetic properties [1] and that clusters of Fe, Co and Ni containing a few to a few hundred atoms have magnetic moments that can be about 30% higher than the bulk [2, 3]. While these higher moments offer the promise of stronger magnets, experiments on free clusters also indicate that the reduction in size reduces the magnetic anisotropy, leading to superparamagnetic relaxations in clusters even at lower temperatures [4, 5]. This thermal instability hinders any applicability of the stronger moments in spin dependent molecular electronic transport. In addition to conventional ferromagnetic elements, small clusters of non-magnetic solids like rhodium are found to have large magnetic moments [6, 7], but such clusters also suffer from a reduction in anisotropy. In this paper, we present a rather surprising finding that the addition of a non-magnetic element like carbon to small magnetic clusters can considerably enhance the MAE. The findings are 0953-8984/14/125303+07$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
intercalating cobalt layers. Furthermore, the nanoparticles were joined together by interstitial material, believed to be carbon. Magnetic measurements indicated that the Co sites in the Co2 C and Co3 C nanoparticles had magnetic moments of around 1.0 and 1.81 µB , respectively. Co3 C also had a magnetic anisotropy of 0.1 meV/Co atom. Since the addition of a non-magnetic carbon generally quenches the magnetic moment of transition metal elements, an increase in anisotropy in these systems is unusual. Here, we adopt a bottom-up approach and examine whether the magnetic anisotropy in small Co clusters could also be enhanced by adding carbon or other group IV elements. Since it is possible to vary the particle size by controlling the experimental conditions, we first examine the smallest clusters with atomic arrangements close to those found in nanoassemblies. We also explore whether the clusters can be assembled into small units with high blocking temperatures. In this work we show that the Co4 C2 and Co12 C4 clusters exhibit large magnetic moments as well as unusually large MAEs. The role of carbon in enhancing the MAE is even more surprising than in large nanoparticles since the C states can mix freely with Co states. Upon assembly, the Co4 C2 clusters are shown to undergo coalescence, which leads to a considerable quenching of the magnetic moments as well as reduction in anisotropy. It is shown, however, that if the clusters are assembled around a central C site, the directional bonding prevents large reconstruction of the building blocks, leading to an assembly with a larger magnetic moment and a massively larger magnetic anisotropy, larger than some well known single molecule magnets (SMMs) [17–22]. Detailed theoretical analysis indicates that the increased anisotropy originates from large orbital contributions. Such units could be useful for information storage or find applications in other areas in spintronics. This is driven by the fact that single molecule magnets offer the exciting prospects of integrating memory and logic units into the same device. Note that as the information is coded into spin states, the nanoscale units discovered here can be used as memory elements as they offer large anisotropy barriers that can prevent transition from a given spin state into another spin state, thereby protecting against loss of information. Our findings also open the path towards nanoscale cluster assemblies with stable magnetic order under ordinary conditions.
was calculated using an approach proposed by Pederson and co-workers, which is based on second order perturbation theory [24]. The MAE was also calculated using an exact diagonalization method and, for the systems investigated in this work, both the perturbative and exact results agree quite well. The actual calculations were carried out within the Naval Research Laboratory Molecular Orbital Library (NRLMOL) first-principles package [24–28]. The anisotropy in small atomic clusters is largely due to magnetocrystalline anisotropy arising due to spin orbit coupling. In this paper, we have used a pragmatic approach to calculate the contribution due to spin orbit coupling as proposed by Pederson and Khanna [24]. The change in the ground state energy due to spin–orbit coupling to the second order in perturbation and for a given quantization axis is given by X
12 = α + γi j hSi i S j , (1) ij
P where α = i j (Mii12 + Mii21 ) is a constant independent of the quantization axis and the anisotropy tensor γi j is given by γi j =
1 X 11 12 21 (Mi j + Mi22 j − Mi j − Mi j ), (1N )2 ij
where Miσj σ ≡ − 0
X
X hφkσ |Vi |φk 0 σ 0 ihφk 0 σ 0 |V j |φkσ i . (2) kσ − k 0 σ 0 0
k=occ k =unocc
Here, the sums over k and k 0 involve occupied and unoccupied states, respectively and the φkσ s are Kohn–Sham orbitals. hφkσ | Vx |φk 0 σ 0 i ∂φkσ ∂φk 0 σ 0 ∂φkσ ∂φk 0 σ 0 1 8 8 − , = 2 ∂z ∂ y ∂ y ∂z 2c where 8 is the Coulomb potential. By rotating spin components along the principal axes one can show that 12 is the expectation value of the spin Hamiltonian, H = DSz2 + E(Sx2 − S y2 ).
(3)
2. Computational and theoretical details
The tensor γi j depends on the orbital character of the system and hSi i is the expectation of the ith component of the total spin of the system along the quantization axis. Clearly, the anisotropy depends on both the orbital and the spin character of the single particle levels and is largely determined by the levels close to HOMO–LUMO levels. The anisotropy can be changed by perturbing these levels, although it is not clear a priori as to what perturbation will increase the anisotropy. To obtain the anisotropy using the exact diagonalization method we calculate the total energy including the spin–orbit coupling for different magnetization directions. The anisotropy is then the difference between the largest and the smallest total energies.
The theoretical studies were carried out using a linear combination of atomic orbitals molecular orbital approach with a density functional framework. The electronic orbitals in the cluster are built out of Gaussian type orbitals centered at the atomic sites. The exchange correlation contributions are included using a generalized gradient approximation (GGA) functional as proposed by Perdew et al [23]. The calculations have been carried out at an all-electron level to avoid any uncertainties arising from the choice of pseudo potentials. For each cluster, the geometry was optimized by moving atoms in the direction of forces until the forces dropped below a threshold value of 0.001 Hartree bohr−1 . The MAE 2
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
Figure 1. Top views of the relaxed clusters (a) Co4 C2 and (b) Co12 C4 with the z-axis perpendicular to the plane. The number near each atom represents the local moment of that atom in µB . Parts (c) and (d) are the anisotropy landscapes of Co4 C2 and Co12 C4 clusters, respectively, with θ and φ being the polar and azimuthal angles, respectively. Note that the energy landscape indicates that the anisotropy at these sizes is more complex.
3. Results and discussion
However, the MAE/atom reduces as we double the size of the cluster, consistent with the fact that for very large clusters, the anisotropy should approach its value in the bulk phase. The MAE landscapes for these two systems are shown in figures 1(c) and (d). The increase of MAE of small magnetic clusters results from the combined effects of increase in the magnetic moments of the Co atoms and enhancement of the orbital moment. While in bulk, the orbital moments are largely quenched and the spin moments are also reduced due to stronger bonding with neighboring atoms, in the cluster, the presence of peripheral atoms increases the moments, which in turn increases the anisotropy. Equation (2) shows that the anisotropy energy involves the difference in energy between the occupied and unoccupied states. We found that the major contribution to the anisotropy comes from the states near the HOMO. A Mulliken population analysis indicates that while the energy levels of these CoC clusters near HOMO and LUMO levels are primarily of Co d character, there is a small contribution from p levels of C atoms. Hence, the mixing between the Co d and C p-states enhances the MAE. We would like to mention that we also have tried other atomic arrangements of Co4 C2 , which also lead to enhanced MAE. Thus, the enhancement of the MAE is a rather general feature of the carbide clusters. One simple way to perturb these levels is to replace C atoms by Si, which is the next atom in the same column of
To investigate small motifs with compositions matching the Co2 C and Co3 C phases, we construct a small cluster of Co4 C2 by adding two carbon to four cobalt atoms and a small cluster of Co12 C4 by adding four carbon to twelve cobalt atoms such that the geometries mimic unit cells of the corresponding nano-crystals. The structures are then relaxed and the resulting relaxed structures are shown in figure 1. The theoretical studies examined configurations where the local moments at the various sites were ferromagnetically or antiferromagnetically aligned. The calculated moments and the ground state structures are given in figure 1. We note from figure 1(a) that the local moments of Co atoms in Co4 C2 depend on their proximity to C atoms, with the lowest moment of 0.54 µB for the Co atom bonded to two C atoms. The remaining three Co atoms have larger moments ranging from 1.5 to 1.9 µB . Both C atoms have very small moments and they are coupled antiferromagnetically with Co atoms. It is quite remarkable that the magnetic anisotropy of a system of this small size is calculated to be about 25 K (0.54 meV/Co atom), which is about nine times larger than that in hcp Co. Similar magnetic behavior is also obtained for the Co12 C4 cluster, but because of the larger number of Co atoms in this cluster, the total moment of the system is large and the corresponding MAE is calculated to be about 61 K (0.44 meV/Co atom). 3
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
Figure 2. Relaxed structure of the Co4 C2 dimer with antiferromagnetic ground state.
Table 1. Electronic and magnetic properties of small Co based clusters.
System
HOMO LUMO (eV)
Mag. mom. (µB )
Anisotropy (K)
Anisotropy param. (K) D E
Co4 C2 Co4 Si2 Co12 C4 Co12 Si4 2 Co4 C2 2 Co4 Si2 2 Co12 C4 Co4 C2 dimer 4 Co4 C2 without C 4 Co4 C2 with C
0.28 0.32 0.13 0.17 0.19 0.11 0.06 0.11 0.13 0.09
6 6 18 18 10 10 30 8 22 18
25.70 40.34 61.36 51.69 34.44 28.80 84.65 66.21 93.16 100.61
−1.98 −2.39 −0.54 −0.43 −1.26 −0.93 −0.31 −3.05 −0.39 −0.65
−0.90 −2.07 −0.24 −0.21 −0.06 −0.23 −0.08 −0.99 −0.37 −0.62
the two units apart. Our calculations show that while the spin moment is reduced by 2 µB compared to that of a single unit of two Co4 C2 clusters, the anisotropy increases almost three times to 66 K (0.71 meV/Co atom) with an easy axis along the axis of the dimer, similar to that observed for atomic dimers. We also found a configuration with an antiferromagnetic arrangement of the spins on the two clusters to be more stable than the ferromagnetic alignment by 24 meV with an anisotropy energy of 64 K. This large increase in MAE with dimer type assembly encouraged us to study even larger structures. In an attempt to enhance the anisotropy further we examined an assembly of four Co4 C2 clusters in planar structure, as shown in figure 3(a). Previous experiments on carbide nanoparticle assemblies indicated that the space between the nanoparticles is probably filled by carbon. To examine whether similar linking via C atoms could enhance the magnetic properties, we carried out two sets of calculations, one where the cluster building blocks were linked via C atoms and the other without C at the center. We used only one C atom at the center of the assembly to keep the percentage of added C atoms close to that used in the nano-assembly experiments. All the results are summarized in table 1. It is evident from the table that the anisotropy of this small assembly of four Co4 C2 clusters, even though it has a size of only about 1.2 nm, is remarkably large. Comparing with the anisotropy of an isolated Co4 C2 cluster in table 1, we note that the anisotropy increases linearly with the size of the assembly. The average spin moment per Co atom of this assembly decreases to about 1.4 µB since the Co atoms now
the periodic table. Relaxed structures of Co4 Si2 and Co12 Si4 are slightly different from carbide clusters. The magnetic moments remain unchanged with substitution of Si but the anisotropy increases to about 40 K in Co4 Si2 (0.86 meV/Co atom) and decreases to 52 K in Co12 Si4 (0.37 meV/Co atom). It is remarkable that one can control the anisotropy by simple substitution of atoms. The effect of size on anisotropy, however, is stronger in Co4 Si2 as the anisotropy decreases faster than in Co4 C2 clusters. The results are tabulated in table 1. Since the spin moments remain unchanged with substitution of Si, the enhancement of anisotropy is due to change in orbital character in the Co4 Si2 cluster. We note from the table that the anisotropy parameters that depend on the orbital character of the single particle levels are modified significantly by Si. Our calculations show that a simple assembly of bare clusters leads to a decreases of the MAE. In an effort to enhance the anisotropy with size we have constructed an assembly of two Co2 C clusters in the form of a dimer, as shown in figure 2, motivated by recent studies of atomic dimers such as Co2 and Rh2 [29, 30], which have been shown to exhibit unusually large anisotropy. The agreement between perturbative and exact calculations of the MAE in our calculations implies that each Co4 C2 cluster may be treated as a system of giant spin moment of 6 µB . Thus, it is possible that a dimer structure of Co4 C2 may enhance the anisotropy. However, to prevent this assembly from folding back to a single unit of two Co4 C2 clusters during relaxation, we have added a C atom in the middle so that the strong directional bond of the p electrons of the C atom keeps 4
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
c Figure 3. Assembly of four Co4 C2 clusters: (a) before relaxation, (b) semi-relaxed and (c) the anisotropy landscape with the z axis
perpendicular to the plane of the assembly with θ and φ being the polar and azimuthal angles, respectively.
have more neighboring atoms to interact with. The anisotropy landscape shown in figure 3(c) clearly demonstrates easy plane anisotropy for the system, which is due to the approximate C4 symmetry of the structure, with the hard axis perpendicular to the plane of the assembly. We note from table 1 that the added C atom quenches the total spin moment by 4 µB but the anisotropy increases by about 10%, consistent with the large anisotropy observed in experiments on nanoparticles. We would like to point out that there is only one easy axis in this assembly, which lies almost in the plane of the cluster, but because of approximate C4 symmetry there are several directions of magnetization for which the energies are within 1 K of that of the easy axis. The direction of the easy axis, however, changes from [0.55 −0.83 0.08] to [0.24 0.97 −0.08] when a C atom is added at the center of the assembly. This change is due to the bonding of the p orbital of the central C atom with the d orbitals of the four neighboring Co atoms. To gain additional insight into the nature of the anisotropy we calculate the total orbital momentum of the system as a function of the quantization axis. Table 2 shows the orbital moments for easy and hard axes for clusters with and without C atoms at the center. For the hard axis, which is along the z-axis of the cluster, only the L z component contributes to the total moment, whereas for the easy axis both the L x and L y components are non-zero with very little contribution coming from the L z component, an indication that orbital current perpendicular to the plane of the system is energetically favorable.
Table 2. Total orbital moment of the 4 Co4 C2 cluster. For both cases
the hard axis is along z and the easy axis is approximately in the x–y plane but the direction of the easy axis is different. 4 Co4 C2
Quantization
Total orbital moment (µB ) Lx Ly Lz
Without C
Easy Hard Easy Hard
0.86 0.00 0.31 0.00
With C
1.33 0.00 −1.32 0.00
−0.07 −0.83 −0.05 −0.65
The anisotropy of the system can also be estimated from the orbital moments. According to Bruno’s formula [31], which is based on second order perturbation theory, the anisotropy of a system is related to the orbital moments by λ|L easy − L hard | , 4 where L easy and L hard are the orbital moments along the easy and hard axes, respectively, and λ is the spin–orbit coupling constant, which for 3d elements is about 50 meV [32]. From the orbital moments in table 2, the estimated anisotropy without a C atom is about 98 K whereas with a C atom it is about 105 K, in excellent agreement with the corresponding exact anisotropy values shown in table 1. The agreement between the exact and perturbative approaches for calculation of anisotropy implies that the spins of the individual electrons interact to form a giant spin, whose orientation dependence gives rise to the anisotropy of the system. 1=
5
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
have an in-plane easy anisotropy. It would be interesting to examine the dynamical behavior of such units under field and temperature. Note that the assembly calculation shown in figure 3 is semi-relaxed as fully relaxed structure tends to form cage-like geometry, which quenches the moment significantly, thereby reducing the anisotropy. Thus, to obtain large MAE, it is necessary to preserve the planar structure. One possible way to achieve this goal is to find an appropriate surface, e.g. a Au surface that does not interact magnetically. We are currently collaborating with an experimental group to generate size selected clusters in molecular beams and investigate their magnetic properties. This work is in progress and will form the basis of future work. Acknowledgments
The authors gratefully acknowledge financial support from ARPA-eREACT project 1574-1674 for the calculations on cobalt carbide clusters. They gratefully acknowledge support from the US Department of Energy (DOE) through grant DE-FG02-11ER16213 for the study of cluster assemblies.
Figure 4. (a) Relaxed structure of a 2 Co4 C2 cluster between two
Au leads connected via a S atom. (b) LUMO level of the system.
For the clusters to be useful in spintronic devices, it is essential that the magnetic properties of these systems remain stable under the influence of leads or surfaces. To investigate this important aspect we connected two gold (Au) leads to a 2 Co4 C2 cluster via sulfur (S) atoms as shown in figure 4(a). The leads consisted of clusters of 20 Au atoms arranged in a tetrahedral geometry to mimic a nano-electrode since such a Au cluster is shown to be very stable and chemically inert [33]. Our calculation shows that the magnetic moment remains exactly at 10 µB and the anisotropy is about 38 K, which is very close to the value of an isolated cluster. Furthermore, we have investigated the nature of the lowest unoccupied levels as they play an essential role in single electron transistor (SET) applications. Our calculations indicate that the states closer to the Fermi level are mostly localized within the cluster part of the system, as shown in figure 4(b), and are dominated by the d levels of the Co atoms.
References [1] Woodruff D (ed) 2007 Atomic Clusters: From Gas Phase to Deposited (The Chemical Physics of Solid Surfaces) vol 12 (Amsterdam: Elsevier) pp 1–626 [2] Billas I M L, Chˆatelain A and de Heer W A 1994 Science 265 1682 [3] Apsel S E, Emmert J W, Deng J and Bloomfield L A 1996 Phys. Rev. Lett. 76 1441 [4] Khanna S N and Linderoth S 1991 Phys. Rev. Lett. 67 742 [5] Xu X, Yin S, Moro R and de Heer W A 2005 Phys. Rev. Lett. 95 237209 [6] Reddy B V, Khanna S N and Dunlap B I 1993 Phys. Rev. Lett. 70 3323 [7] Cox A J, Louderback J G and Bloomfield L A 1993 Phys. Rev. Lett. 71 923 [8] Claridge S A, Castleman A W, Khanna S N, Murray C B, Sen A and Weiss P S 2009 ACS Nano 3 244 [9] Murray C B, Norris D J and Bawendi M G 1993 J. Am. Chem. Soc. 115 8706 [10] Mandal S, Reber A C, Qian M, Weiss P S, Khanna S N and Sen A 2013 Acc. Chem. Res. 46 2385–95 [11] Roy X et al 2013 Science 341 157 [12] Daalderop G H O, Kelly P J and Schuurmans M F H 1990 Phys. Rev. B 41 11919 [13] Niemeyer M et al 2012 Phys. Rev. Lett. 108 057201 [14] Kortus J, Baruah T, Pederson M R, Ashman C and Khanna S N 2002 Appl. Phys. Lett. 80 4193 [15] Harris V G et al 2010 J. Phys. D: Appl. Phys. 43 165003 [16] Carroll K J, Huba Z J, Spurgeon S R, Qian M, Khanna S N, Hudgins D M, Taheri M L and Carpenter E E 2012 Appl. Phys. Lett. 101 012409 [17] Gatteschi D, Sessoli R and Villain J 2006 Molecular Nenomagnets (Oxford: Oxford University Press) [18] Heersche H B, de Groot Z, Folk J A, van der Zant H S J, Romeike C, Wegewijs M R, Zobbi L, Barreca D, Tondello E and Cornia A 2006 Phys. Rev. Lett. 96 206801 [19] Jo M-H, Grose J E, Baheti K, Deshmukh M M, Sokol J J, Rumberger E M, Hendrickson D N, Long J R, Park H and Ralph D C 2006 Nano Lett. 6 2014
4. Conclusion
To summarize, these studies indicate that the magnetic anisotropy in cobalt clusters can be significantly enhanced by doping with carbon. In particular, Co4 C2 and Co12 C4 clusters have unusually large MAEs of 25 and 61 K respectively. The increase in anisotropy is largely due to controlled mixing between the Co d-states and the C p-states which perturbs the electronic states near the HOMO and LUMO. The MAE can be further tuned by replacing C by Si. Through studies of clusters connected to gold electrodes, we also show that the magnetic characteristics are retained when the clusters are connected to leads. In this regard, a dimer of Co4 C2 units linked by C is shown to have an antiferromagnetic ground state with a ferromagnetic configuration about 24 meV above the ground state. Both configurations have MAEs above 60 K. Such units could offer large magneto resistance as the magnetic state can be switched by applying an external field. The anisotropy can be further enhanced by forming larger assemblies of the clusters with C at the center. In addition to large anisotropy, the energy landscape of the MAE shows that the assemblies 6
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
[20] Sessoli R, Tsai H L, Schake A R, Wang S, Vincent J B, Folting K, Gatteschi D, Christou G and Hendrickson D N 1993 J. Am. Chem. Soc. 115 1804 [21] Accorsi S et al 2006 J. Am. Chem. Soc. 128 4742 [22] Michalak L, Canali C M, Pederson M R, Paulsson M and Benza V G 2010 Phys. Rev. Lett. 104 017202 [23] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 [24] Pederson M R and Khanna S N 1999 Phys. Rev. B 60 9566 [25] Pederson M R and Jackson K A 1990 Phys. Rev. B 41 7453 [26] Jackson K and Pederson M R 1990 Phys. Rev. B 42 3276
[27] Kortus J, Pederson M R, Baruah T, Bernstein N and Hellberg C 2003 Polyhedron 22 1871 [28] Postnikov A V, Kortus J and Pederson M R 2006 Phys. Status Solidi b 243 2533 [29] Strandberg T O, Canali C M and MacDonald A H 2007 Nature Mater. 6 648 [30] Bło´nski P and Hafner J 2009 Phys. Rev. B 79 224418 [31] Bruno P 1989 Phys. Rev. B 39 865 [32] van der Laan G 1998 J. Phys.: Condens. Matter 10 3239 [33] Li X L J, Zhai H-J and Wang L-S 2003 Science 299 864
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On the enhancement of magnetic anisotropy in cobalt clusters via non-magnetic doping
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 125303 (http://iopscience.iop.org/0953-8984/26/12/125303) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 132.239.1.231 This content was downloaded on 13/05/2017 at 01:52 Please note that terms and conditions apply.
You may also be interested in: Using graphene to control magnetic anisotropy and interaction between supported clusters Sanjubala Sahoo, M Fhokrul Islam and Shiv N Khanna Magnetic anisotropy of heteronuclear dimers in the gas phase and supported on graphene: relativistic density-functional calculations Piotr Boski and Jürgen Hafner On the interplay between geometrical structure and magnetic anisotropy: a relativistic density-functional study of mixed Pt–Co and Pt–Fe trimers and tetramers in the gas-phase and supported on graphene Piotr Boski and Jürgen Hafner Magnetic properties of transition metal Mn, Fe and Co dimers on monolayer phosphorene Imran Khan and Jisang Hong Magneto-structural properties and magnetic anisotropy of small transition-metal clusters: afirst-principles study Piotr Boski and Jürgen Hafner Cu(111) supported graphene as a substrate for magnetic dimers with a large magnetic anisotropy: relativistic density-functional calculations P Boski and J Hafner
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 125303 (7pp)
doi:10.1088/0953-8984/26/12/125303
On the enhancement of magnetic anisotropy in cobalt clusters via non-magnetic doping M Fhokrul Islam and Shiv N Khanna Department of Physics, Virginia Commonwealth University, Richmond, VA 23284-2000, USA E-mail: [email protected] Received 25 November 2013, revised 17 January 2014 Accepted for publication 22 January 2014 Published 6 March 2014
Abstract
We show that the magnetic anisotropy energy (MAE) in cobalt clusters can be significantly enhanced by doping them with group IV elements. Our first-principles electronic structure calculations show that Co4 C2 and Co12 C4 clusters have MAEs of 25 K and 61 K, respectively. The large MAE is due to controlled mixing between Co d- and C p-states and can be further tuned by replacing C by Si. Larger assemblies of such primitive units are shown to be stable with MAEs exceeding 100 K in units as small as 1.2 nm, in agreement with the recent observation of large coercivity. These results may pave the way for the use of nano-clusters in high density magnetic memory devices for spintronics applications. Keywords: nano-cluster, magnetic memory, magnetic anisotropy (Some figures may appear in colour only in the online journal)
1. Introduction
particularly important for the development of materials where the size selected clusters could serve as primitive building blocks, opening a route towards new molecular electronic materials [8–11]. Bulk Fe, Co, and Ni are all itinerant ferromagnetic elements with magnetic moments of 2.22, 1.72, and 0.61 µB /atom, respectively. The MAE at low temperatures is around 60 µeV/atom for hcp cobalt (a soft magnetic material) and is smaller for cubic Fe and Ni by a factor of 50 [12]. At small sizes, the MAE continues to be small with an upper limit of 65 µeV/atom in iron clusters containing 10 atoms [13]. For the case of cobalt, our previous studies indicate that a Co5 cluster with triangular bi-pyramidal geometry and a Co13 cluster with icosahedral geometry have MAEs of 0.1 and 0 meV/atom, respectively [14]. Recent works combining experiments and theoretical work in our group have, however, reported some interesting findings [15, 16]. In these studies, nanoassembled materials consisting of Co2 C and Co3 C nanoparticles were synthesized using wet chemical methods. The resulting material consisted of 8–10 nm nanoparticles with atomic arrangements different from bulk carbide phases. The new structures could be described as carbon atoms
The principal quantity controlling the magnetic behavior at small sizes is the magnetic anisotropy energy (MAE). Extensive research over the past three decades has shown that clusters and nanoparticles of conventional itinerant ferromagnetic solids have novel magnetic properties [1] and that clusters of Fe, Co and Ni containing a few to a few hundred atoms have magnetic moments that can be about 30% higher than the bulk [2, 3]. While these higher moments offer the promise of stronger magnets, experiments on free clusters also indicate that the reduction in size reduces the magnetic anisotropy, leading to superparamagnetic relaxations in clusters even at lower temperatures [4, 5]. This thermal instability hinders any applicability of the stronger moments in spin dependent molecular electronic transport. In addition to conventional ferromagnetic elements, small clusters of non-magnetic solids like rhodium are found to have large magnetic moments [6, 7], but such clusters also suffer from a reduction in anisotropy. In this paper, we present a rather surprising finding that the addition of a non-magnetic element like carbon to small magnetic clusters can considerably enhance the MAE. The findings are 0953-8984/14/125303+07$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
intercalating cobalt layers. Furthermore, the nanoparticles were joined together by interstitial material, believed to be carbon. Magnetic measurements indicated that the Co sites in the Co2 C and Co3 C nanoparticles had magnetic moments of around 1.0 and 1.81 µB , respectively. Co3 C also had a magnetic anisotropy of 0.1 meV/Co atom. Since the addition of a non-magnetic carbon generally quenches the magnetic moment of transition metal elements, an increase in anisotropy in these systems is unusual. Here, we adopt a bottom-up approach and examine whether the magnetic anisotropy in small Co clusters could also be enhanced by adding carbon or other group IV elements. Since it is possible to vary the particle size by controlling the experimental conditions, we first examine the smallest clusters with atomic arrangements close to those found in nanoassemblies. We also explore whether the clusters can be assembled into small units with high blocking temperatures. In this work we show that the Co4 C2 and Co12 C4 clusters exhibit large magnetic moments as well as unusually large MAEs. The role of carbon in enhancing the MAE is even more surprising than in large nanoparticles since the C states can mix freely with Co states. Upon assembly, the Co4 C2 clusters are shown to undergo coalescence, which leads to a considerable quenching of the magnetic moments as well as reduction in anisotropy. It is shown, however, that if the clusters are assembled around a central C site, the directional bonding prevents large reconstruction of the building blocks, leading to an assembly with a larger magnetic moment and a massively larger magnetic anisotropy, larger than some well known single molecule magnets (SMMs) [17–22]. Detailed theoretical analysis indicates that the increased anisotropy originates from large orbital contributions. Such units could be useful for information storage or find applications in other areas in spintronics. This is driven by the fact that single molecule magnets offer the exciting prospects of integrating memory and logic units into the same device. Note that as the information is coded into spin states, the nanoscale units discovered here can be used as memory elements as they offer large anisotropy barriers that can prevent transition from a given spin state into another spin state, thereby protecting against loss of information. Our findings also open the path towards nanoscale cluster assemblies with stable magnetic order under ordinary conditions.
was calculated using an approach proposed by Pederson and co-workers, which is based on second order perturbation theory [24]. The MAE was also calculated using an exact diagonalization method and, for the systems investigated in this work, both the perturbative and exact results agree quite well. The actual calculations were carried out within the Naval Research Laboratory Molecular Orbital Library (NRLMOL) first-principles package [24–28]. The anisotropy in small atomic clusters is largely due to magnetocrystalline anisotropy arising due to spin orbit coupling. In this paper, we have used a pragmatic approach to calculate the contribution due to spin orbit coupling as proposed by Pederson and Khanna [24]. The change in the ground state energy due to spin–orbit coupling to the second order in perturbation and for a given quantization axis is given by X
12 = α + γi j hSi i S j , (1) ij
P where α = i j (Mii12 + Mii21 ) is a constant independent of the quantization axis and the anisotropy tensor γi j is given by γi j =
1 X 11 12 21 (Mi j + Mi22 j − Mi j − Mi j ), (1N )2 ij
where Miσj σ ≡ − 0
X
X hφkσ |Vi |φk 0 σ 0 ihφk 0 σ 0 |V j |φkσ i . (2) kσ − k 0 σ 0 0
k=occ k =unocc
Here, the sums over k and k 0 involve occupied and unoccupied states, respectively and the φkσ s are Kohn–Sham orbitals. hφkσ | Vx |φk 0 σ 0 i ∂φkσ ∂φk 0 σ 0 ∂φkσ ∂φk 0 σ 0 1 8 8 − , = 2 ∂z ∂ y ∂ y ∂z 2c where 8 is the Coulomb potential. By rotating spin components along the principal axes one can show that 12 is the expectation value of the spin Hamiltonian, H = DSz2 + E(Sx2 − S y2 ).
(3)
2. Computational and theoretical details
The tensor γi j depends on the orbital character of the system and hSi i is the expectation of the ith component of the total spin of the system along the quantization axis. Clearly, the anisotropy depends on both the orbital and the spin character of the single particle levels and is largely determined by the levels close to HOMO–LUMO levels. The anisotropy can be changed by perturbing these levels, although it is not clear a priori as to what perturbation will increase the anisotropy. To obtain the anisotropy using the exact diagonalization method we calculate the total energy including the spin–orbit coupling for different magnetization directions. The anisotropy is then the difference between the largest and the smallest total energies.
The theoretical studies were carried out using a linear combination of atomic orbitals molecular orbital approach with a density functional framework. The electronic orbitals in the cluster are built out of Gaussian type orbitals centered at the atomic sites. The exchange correlation contributions are included using a generalized gradient approximation (GGA) functional as proposed by Perdew et al [23]. The calculations have been carried out at an all-electron level to avoid any uncertainties arising from the choice of pseudo potentials. For each cluster, the geometry was optimized by moving atoms in the direction of forces until the forces dropped below a threshold value of 0.001 Hartree bohr−1 . The MAE 2
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
Figure 1. Top views of the relaxed clusters (a) Co4 C2 and (b) Co12 C4 with the z-axis perpendicular to the plane. The number near each atom represents the local moment of that atom in µB . Parts (c) and (d) are the anisotropy landscapes of Co4 C2 and Co12 C4 clusters, respectively, with θ and φ being the polar and azimuthal angles, respectively. Note that the energy landscape indicates that the anisotropy at these sizes is more complex.
3. Results and discussion
However, the MAE/atom reduces as we double the size of the cluster, consistent with the fact that for very large clusters, the anisotropy should approach its value in the bulk phase. The MAE landscapes for these two systems are shown in figures 1(c) and (d). The increase of MAE of small magnetic clusters results from the combined effects of increase in the magnetic moments of the Co atoms and enhancement of the orbital moment. While in bulk, the orbital moments are largely quenched and the spin moments are also reduced due to stronger bonding with neighboring atoms, in the cluster, the presence of peripheral atoms increases the moments, which in turn increases the anisotropy. Equation (2) shows that the anisotropy energy involves the difference in energy between the occupied and unoccupied states. We found that the major contribution to the anisotropy comes from the states near the HOMO. A Mulliken population analysis indicates that while the energy levels of these CoC clusters near HOMO and LUMO levels are primarily of Co d character, there is a small contribution from p levels of C atoms. Hence, the mixing between the Co d and C p-states enhances the MAE. We would like to mention that we also have tried other atomic arrangements of Co4 C2 , which also lead to enhanced MAE. Thus, the enhancement of the MAE is a rather general feature of the carbide clusters. One simple way to perturb these levels is to replace C atoms by Si, which is the next atom in the same column of
To investigate small motifs with compositions matching the Co2 C and Co3 C phases, we construct a small cluster of Co4 C2 by adding two carbon to four cobalt atoms and a small cluster of Co12 C4 by adding four carbon to twelve cobalt atoms such that the geometries mimic unit cells of the corresponding nano-crystals. The structures are then relaxed and the resulting relaxed structures are shown in figure 1. The theoretical studies examined configurations where the local moments at the various sites were ferromagnetically or antiferromagnetically aligned. The calculated moments and the ground state structures are given in figure 1. We note from figure 1(a) that the local moments of Co atoms in Co4 C2 depend on their proximity to C atoms, with the lowest moment of 0.54 µB for the Co atom bonded to two C atoms. The remaining three Co atoms have larger moments ranging from 1.5 to 1.9 µB . Both C atoms have very small moments and they are coupled antiferromagnetically with Co atoms. It is quite remarkable that the magnetic anisotropy of a system of this small size is calculated to be about 25 K (0.54 meV/Co atom), which is about nine times larger than that in hcp Co. Similar magnetic behavior is also obtained for the Co12 C4 cluster, but because of the larger number of Co atoms in this cluster, the total moment of the system is large and the corresponding MAE is calculated to be about 61 K (0.44 meV/Co atom). 3
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
Figure 2. Relaxed structure of the Co4 C2 dimer with antiferromagnetic ground state.
Table 1. Electronic and magnetic properties of small Co based clusters.
System
HOMO LUMO (eV)
Mag. mom. (µB )
Anisotropy (K)
Anisotropy param. (K) D E
Co4 C2 Co4 Si2 Co12 C4 Co12 Si4 2 Co4 C2 2 Co4 Si2 2 Co12 C4 Co4 C2 dimer 4 Co4 C2 without C 4 Co4 C2 with C
0.28 0.32 0.13 0.17 0.19 0.11 0.06 0.11 0.13 0.09
6 6 18 18 10 10 30 8 22 18
25.70 40.34 61.36 51.69 34.44 28.80 84.65 66.21 93.16 100.61
−1.98 −2.39 −0.54 −0.43 −1.26 −0.93 −0.31 −3.05 −0.39 −0.65
−0.90 −2.07 −0.24 −0.21 −0.06 −0.23 −0.08 −0.99 −0.37 −0.62
the two units apart. Our calculations show that while the spin moment is reduced by 2 µB compared to that of a single unit of two Co4 C2 clusters, the anisotropy increases almost three times to 66 K (0.71 meV/Co atom) with an easy axis along the axis of the dimer, similar to that observed for atomic dimers. We also found a configuration with an antiferromagnetic arrangement of the spins on the two clusters to be more stable than the ferromagnetic alignment by 24 meV with an anisotropy energy of 64 K. This large increase in MAE with dimer type assembly encouraged us to study even larger structures. In an attempt to enhance the anisotropy further we examined an assembly of four Co4 C2 clusters in planar structure, as shown in figure 3(a). Previous experiments on carbide nanoparticle assemblies indicated that the space between the nanoparticles is probably filled by carbon. To examine whether similar linking via C atoms could enhance the magnetic properties, we carried out two sets of calculations, one where the cluster building blocks were linked via C atoms and the other without C at the center. We used only one C atom at the center of the assembly to keep the percentage of added C atoms close to that used in the nano-assembly experiments. All the results are summarized in table 1. It is evident from the table that the anisotropy of this small assembly of four Co4 C2 clusters, even though it has a size of only about 1.2 nm, is remarkably large. Comparing with the anisotropy of an isolated Co4 C2 cluster in table 1, we note that the anisotropy increases linearly with the size of the assembly. The average spin moment per Co atom of this assembly decreases to about 1.4 µB since the Co atoms now
the periodic table. Relaxed structures of Co4 Si2 and Co12 Si4 are slightly different from carbide clusters. The magnetic moments remain unchanged with substitution of Si but the anisotropy increases to about 40 K in Co4 Si2 (0.86 meV/Co atom) and decreases to 52 K in Co12 Si4 (0.37 meV/Co atom). It is remarkable that one can control the anisotropy by simple substitution of atoms. The effect of size on anisotropy, however, is stronger in Co4 Si2 as the anisotropy decreases faster than in Co4 C2 clusters. The results are tabulated in table 1. Since the spin moments remain unchanged with substitution of Si, the enhancement of anisotropy is due to change in orbital character in the Co4 Si2 cluster. We note from the table that the anisotropy parameters that depend on the orbital character of the single particle levels are modified significantly by Si. Our calculations show that a simple assembly of bare clusters leads to a decreases of the MAE. In an effort to enhance the anisotropy with size we have constructed an assembly of two Co2 C clusters in the form of a dimer, as shown in figure 2, motivated by recent studies of atomic dimers such as Co2 and Rh2 [29, 30], which have been shown to exhibit unusually large anisotropy. The agreement between perturbative and exact calculations of the MAE in our calculations implies that each Co4 C2 cluster may be treated as a system of giant spin moment of 6 µB . Thus, it is possible that a dimer structure of Co4 C2 may enhance the anisotropy. However, to prevent this assembly from folding back to a single unit of two Co4 C2 clusters during relaxation, we have added a C atom in the middle so that the strong directional bond of the p electrons of the C atom keeps 4
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
c Figure 3. Assembly of four Co4 C2 clusters: (a) before relaxation, (b) semi-relaxed and (c) the anisotropy landscape with the z axis
perpendicular to the plane of the assembly with θ and φ being the polar and azimuthal angles, respectively.
have more neighboring atoms to interact with. The anisotropy landscape shown in figure 3(c) clearly demonstrates easy plane anisotropy for the system, which is due to the approximate C4 symmetry of the structure, with the hard axis perpendicular to the plane of the assembly. We note from table 1 that the added C atom quenches the total spin moment by 4 µB but the anisotropy increases by about 10%, consistent with the large anisotropy observed in experiments on nanoparticles. We would like to point out that there is only one easy axis in this assembly, which lies almost in the plane of the cluster, but because of approximate C4 symmetry there are several directions of magnetization for which the energies are within 1 K of that of the easy axis. The direction of the easy axis, however, changes from [0.55 −0.83 0.08] to [0.24 0.97 −0.08] when a C atom is added at the center of the assembly. This change is due to the bonding of the p orbital of the central C atom with the d orbitals of the four neighboring Co atoms. To gain additional insight into the nature of the anisotropy we calculate the total orbital momentum of the system as a function of the quantization axis. Table 2 shows the orbital moments for easy and hard axes for clusters with and without C atoms at the center. For the hard axis, which is along the z-axis of the cluster, only the L z component contributes to the total moment, whereas for the easy axis both the L x and L y components are non-zero with very little contribution coming from the L z component, an indication that orbital current perpendicular to the plane of the system is energetically favorable.
Table 2. Total orbital moment of the 4 Co4 C2 cluster. For both cases
the hard axis is along z and the easy axis is approximately in the x–y plane but the direction of the easy axis is different. 4 Co4 C2
Quantization
Total orbital moment (µB ) Lx Ly Lz
Without C
Easy Hard Easy Hard
0.86 0.00 0.31 0.00
With C
1.33 0.00 −1.32 0.00
−0.07 −0.83 −0.05 −0.65
The anisotropy of the system can also be estimated from the orbital moments. According to Bruno’s formula [31], which is based on second order perturbation theory, the anisotropy of a system is related to the orbital moments by λ|L easy − L hard | , 4 where L easy and L hard are the orbital moments along the easy and hard axes, respectively, and λ is the spin–orbit coupling constant, which for 3d elements is about 50 meV [32]. From the orbital moments in table 2, the estimated anisotropy without a C atom is about 98 K whereas with a C atom it is about 105 K, in excellent agreement with the corresponding exact anisotropy values shown in table 1. The agreement between the exact and perturbative approaches for calculation of anisotropy implies that the spins of the individual electrons interact to form a giant spin, whose orientation dependence gives rise to the anisotropy of the system. 1=
5
J. Phys.: Condens. Matter 26 (2014) 125303
M F Islam and S N Khanna
have an in-plane easy anisotropy. It would be interesting to examine the dynamical behavior of such units under field and temperature. Note that the assembly calculation shown in figure 3 is semi-relaxed as fully relaxed structure tends to form cage-like geometry, which quenches the moment significantly, thereby reducing the anisotropy. Thus, to obtain large MAE, it is necessary to preserve the planar structure. One possible way to achieve this goal is to find an appropriate surface, e.g. a Au surface that does not interact magnetically. We are currently collaborating with an experimental group to generate size selected clusters in molecular beams and investigate their magnetic properties. This work is in progress and will form the basis of future work. Acknowledgments
The authors gratefully acknowledge financial support from ARPA-eREACT project 1574-1674 for the calculations on cobalt carbide clusters. They gratefully acknowledge support from the US Department of Energy (DOE) through grant DE-FG02-11ER16213 for the study of cluster assemblies.
Figure 4. (a) Relaxed structure of a 2 Co4 C2 cluster between two
Au leads connected via a S atom. (b) LUMO level of the system.
For the clusters to be useful in spintronic devices, it is essential that the magnetic properties of these systems remain stable under the influence of leads or surfaces. To investigate this important aspect we connected two gold (Au) leads to a 2 Co4 C2 cluster via sulfur (S) atoms as shown in figure 4(a). The leads consisted of clusters of 20 Au atoms arranged in a tetrahedral geometry to mimic a nano-electrode since such a Au cluster is shown to be very stable and chemically inert [33]. Our calculation shows that the magnetic moment remains exactly at 10 µB and the anisotropy is about 38 K, which is very close to the value of an isolated cluster. Furthermore, we have investigated the nature of the lowest unoccupied levels as they play an essential role in single electron transistor (SET) applications. Our calculations indicate that the states closer to the Fermi level are mostly localized within the cluster part of the system, as shown in figure 4(b), and are dominated by the d levels of the Co atoms.
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4. Conclusion
To summarize, these studies indicate that the magnetic anisotropy in cobalt clusters can be significantly enhanced by doping with carbon. In particular, Co4 C2 and Co12 C4 clusters have unusually large MAEs of 25 and 61 K respectively. The increase in anisotropy is largely due to controlled mixing between the Co d-states and the C p-states which perturbs the electronic states near the HOMO and LUMO. The MAE can be further tuned by replacing C by Si. Through studies of clusters connected to gold electrodes, we also show that the magnetic characteristics are retained when the clusters are connected to leads. In this regard, a dimer of Co4 C2 units linked by C is shown to have an antiferromagnetic ground state with a ferromagnetic configuration about 24 meV above the ground state. Both configurations have MAEs above 60 K. Such units could offer large magneto resistance as the magnetic state can be switched by applying an external field. The anisotropy can be further enhanced by forming larger assemblies of the clusters with C at the center. In addition to large anisotropy, the energy landscape of the MAE shows that the assemblies 6
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