Tailoring magnetic properties in Mn4molecules: A way to developsingle-molecule magnets Nguyen Anh Tuan,1,aNguyen Huy Sinh,1and Dam Hieu Chi1,2 1 Faculty of Physics, Hanoi University of S
Trang 1Tailoring magnetic properties in Mn4 molecules: A way to develop single-molecule magnets
Nguyen Anh Tuan, Nguyen Huy Sinh, and Dam Hieu Chi
Citation: Journal of Applied Physics 109, 07B105 (2011); doi: 10.1063/1.3545812
View online: http://dx.doi.org/10.1063/1.3545812
View Table of Contents: http://aip.scitation.org/toc/jap/109/7
Published by the American Institute of Physics
Trang 2Tailoring magnetic properties in Mn4molecules: A way to develop
single-molecule magnets
Nguyen Anh Tuan,1,a)Nguyen Huy Sinh,1and Dam Hieu Chi1,2
1
Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi 10000, Vietnam
2
School of Materials Science, Japan Advanced Institute of Science and Technologyn, 1-1, Asahidai, Nomi,
Ishikawa, 923-1292, Japan
(Presented 15 November 2010; received 24 September 2010; accepted 8 November 2010; published
online 21 March 2011)
Distorted cubane Mn4þMn3þ3single-molecule magnets (SMMs) having the general chemical formula
[Mn4þMn3þ3(l3-L2)3(l3-X)(OAc)3(dbm)3] (L¼ O; X ¼ various; dbmH ¼ dibenzoyl-methane),
have been studied using first-principles calculations It was shown in our previous paper that the
ferrimagnetic structure of Mn4þMn3þ3SMMs is dominated by the p type hybridization between the
dz2orbitals at the three high-spin Mn3þions and thet2gorbitals at the Mn4þion This result allows us
to predict that the ferrimagnetic structure of Mn4þMn3þ3molecules will be the most stable with the
Mn4þ-(l3-L2)-Mn3þ angle a 90, while synthesized Mn4þMn3þ3 molecules have a 95 To
design new Mn4þMn3þ3 molecules having a much more stable ferrimagnetic state, one following
approach is suggested: Controlling the Mn4þ-(l3-L2)-Mn3þexchange pathways by rational variations
in ligands to strengthen the hybridization between Mn ions By employed N-based ligands to form the
Mn4þ-(l3-L2)-Mn3þexchange pathways, new distorted cubane Mn4þMn3þ3molecules with a 90
have been designed These molecules have the Mn4þ-Mn3þ exchange coupling of about 2.5 times
stronger than that of the synthesized Mn4þMn3þ3molecules These results should facilitate the rational
synthesis of new SMMs.V C 2011 American Institute of Physics [doi:10.1063/1.3545812]
I INTRODUCTION
Single-molecule magnets (SMMs) are molecules that
can function as magnets below their blocking temperature
(TB) They are being extensively studied due to their
poten-tial technological applications to molecular spintronics.1
Their behavior results from a high ground-state spin (ST)
combined with a large and negative Ising type of
magnetoa-nisotropy, as measured by the axial zero-field splitting
pa-rameter (D) SMMs consist of magnetic atoms connected
and surrounded by ligands The challenge of SMMs consists
in tailoring magnetic properties by specific modifications of
the molecular units TheSTresults from local spin moments
at magnetic ions (Si) and exchange coupling between them
(Jij) Moreover,Jij has to be significant to differentiate the
ground spin state from the excited states.2 4Therefore,
seek-ing possibilities of the enhancement ofJij will be a way to
develop SMMs
In the framework of computational materials design,
dis-torted cubane [Mn4þMn3þ3(l3-L2)3(l3-X)(OAc)3(dbm)3]
(L¼ O; X ¼ various; dbmH ¼ dibenzoyl-methane) molecules5 , 6
are one of the most attractive SMMs because their interesting
geometric structure and important magnetic quantities can be
well estimated by first-principles calculations.710In our
previ-ous paper,7by using first-principles calculations within
general-ized gradient approximation, the basic mechanism of the
antiferromagnetic (AFM) interaction between the Mn4þion and
the three high-spin Mn3þions in Mn4þMn3þ3molecules was
analyzed The AFM Mn4þ–Mn3þcoupling (JAB) is determined
by the p type hybridization among thedz2orbitals at the Mn3þ sites and thet2gorbitals at the Mn4þsite through thep orbitals
at the l3-L2ions This result allows us to predict that ferrimag-netic structure of Mn4þMn3þ3molecules will be the most stable with the Mn4þ-(l3-L2)-Mn3þangle a 90, while synthesized
Mn4þMn3þ3molecules have a 95 One approach has been suggested to design new Mn4þMn3þ3 SMMs having a much more stable ferrimagnetic state This approach is controlling the
Mn4þ-(l3-L2)-Mn3þexchange pathways by rational variation
in l3-L ligands to strengthen the hybridization between Mn ions Our calculations show thatJABcan be increased by a fac-tor of 2.5 by using N-based ligands to form the exchange path-ways between the Mn4þ and Mn3þ ions Our results should facilitate the rational synthesis of new SMMs
II COMPUTATIONAL METHOD
To compute the geometric structure, electronic structure, and effective exchange coupling parameters of Mn4 mole-cules, the same reliable computational method as in our pre-vious paper7is adopted In this method, all calculations have been performed by using DMol3 code with the double nu-merical basis sets plus polarization functional (DNP).11 For the exchange correlation terms, the generalized gradient approximation (GGA) RPBE functional was used.12 All-electron relativistic was used to describe the interaction between the core and valence electrons.13 The real-space global cutoff radius was set to be 4.7 A˚ for all atoms The spin-unrestricted discrete Fourier transform (DFT) was used
to obtain all results presented in this study The atomic charge and magnetic moment were obtained by using the Mulliken population analysis.14 The charge density is
a) Author to whom correspondence should be addressed Electronic
addresses: tuanna@hus.edu.vn and tuanna@vnu.edu.vn.
0021-8979/2011/109(7)/07B105/3/$30.00 109, 07B105-1 2011 American Institute of Physics
JOURNAL OF APPLIED PHYSICS 109, 07B105 (2011)
Trang 3converged to 1 10–6a.u in the self-consistent calculation.
In the optimization process, the energy, energy gradient, and
atomic displacement are converged to 1 10–5, 1 10–4,
and 1 10–3 a.u., respectively The total energy difference
method was adopted to calculate the exchange coupling
parameters of Mn4 molecules.7 To determine exactly the
magnetic ground state of Mn4þMn3þ3molecules, all possible
spin configurations of Mn4þMn3þ3 molecules are
investi-gated; they are imposed as an initial condition of the structural
optimization procedure The number of spin configurations
should be considered depending on the charge state of
manga-nese ions In terms of the octahedral field, Mn4þions could, in
principle, have only the high-spin state with configuration
d3(t2g3,eg), in which threed electrons occupy three different
t2gorbitals The possible spin states of Mn3þion are the
high-spin (HS) state with configurationd4(t2g3, eg) and the
low-spin (LS) state with configurationd4(t2g4, eg) Additionally,
the magnetic coupling between the Mn4þion at the A site and
Mn3þions at the B site can be ferromagnetic (FM) or
antifer-romagnetic (AFM) Therefore, there are four spin
configura-tions that should be considered for each Mn4þMn3þ3
molecule, including (i) AFM–HS, (ii) AFM–LS, (iii) FM–HS,
and (iv) FM–LS
III RESULTS AND DISCUSSION
New distorted cubane Mn4þMn3þ3molecules have been
designed based on the synthesized [Mn4þMn3þ3(l3
-L2)3(l3-F)(OAc)3(dbm)3] (L¼ O)1 molecule.5,6 First,
the molecule (1) is reduced to [Mn4þMn3þ3(l3-L2)3(l3
-F)3(CH(CHO)2)3] (L¼ O) (2) by replacing each C6H5
ring of dbm groups with one H atom to improve the
compu-tational performance, and then six different L ligands are
employed to form the Mn4þ-(l3-L2)-Mn3þexchange
path-ways to design new six Mn4þMn3þ3 molecules These six
molecules have a general chemical formula [Mn4þMn3þ3(l3
-L2)3(l3-F)3(CH(CHO)2)3] with L¼ N-H, N-CH3,
N-C2H5, N-C2H3, N-C2H, or N-C6H5 They are labeled from
(3) to (8), and their chemical formulas are tabulated in
TableI Our calculated results show that the most magnetic
stable state of all eight molecules (1)–(8) is the AFM–HS It
means that the three Mn3þions at the B sites exist in the HS
state with configurationd4(t2g
3
, eg 1
), and the exchange
cou-pling between the three Mn3þions and the Mn4þion is AFM resulting in the ferrimagnetic structure in the molecules (1)– (8) with the largeSTof 9/2 The calculated geometric structure
of (1) is in good agreement with the experimental data reported in Refs 5 and 6 The geometric structures corre-sponding to the most stable states of the eight molecules (1)– (8) are displayed in Figs 1and2of which (1) has been syn-thesized before.5,6The geometric structure of (1) is depicted
in Fig.1 The molecule (1) hasC3vsymmetry with theC3axis passing through Mn4þand l3-Fions The [Mn4þMn3þ3(l3
-L2)3(l3-F)] core can be simply viewed as a “distorted cubane” in which the four Mn atoms are located at the corners
of a trigonal pyramid with a l3-L2–ion bridging each of the vertical faces and a l3-F–ion bridging the basal face Three carboxylate (OAc) groups formed three bridges between the
Mn4þion and the three Mn3þions The molecule (1) contains three dbm groups Each dbm group forms two coordinate bonds to complete the distorted octahedral geometry at each B site Our calculations show that the geometric structures of molecules (2)–(8) are similar to (1) as shown in Fig.2 They also have C3v symmetry with the C3 axis passing through
Mn4þand l3-Feven if their L ligand is different Also the
TABLE I The chemical formulas of Mn 4 molecules (1)–(8) and their L ligands.a
L Mn 4 Molecules m A (l B ) m B (l B ) J AB /k B (K) a( ) d AB (A ˚ ) (1) O Mn 4 O 3 F(OAc) 3 (dbm) 3 2.703 3.896 73.51 95.037 2.834 (2) O Mn 4 O 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.692 3.907 75.15 95.060 2.840 (3) NH Mn 4 (NH) 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.719 3.919 86.29 94.35 2.876 (4) NCH 3 Mn 4 (NCH 3 ) 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.566 3.917 161.40 91.24 2.820 (5) NC 2 H 5 Mn 4 (NC 2 H 5 ) 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.543 3.909 174.47 89.77 2.798 (6) NC 2 H 3 Mn 4 (NC 2 H 3 ) 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.615 3.990 108.46 91.30 2.860 (7) NC 2 H Mn 4 (NC 2 H) 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.809 4.018 63.23 93.05 2.944 (8) NC 6 H 5 Mn 4 (NC 6 H 5 ) 3 F(OAc) 3 (CH(CHO) 2 ) 3 2.469 3.966 163.25 88.84 2.831
a
Selected important magnetic and geometric parameters of (1)–(8), the effective exchange coupling parameter between the Mn4þand Mn3þions (J AB =k B ), the magnetic moment at Mn sites (m A and m B ), the exchange coupling angle Mn3þ-L-Mn4þ(a), and the distance between the Mn4þand Mn3þions (d AB ).
FIG 1 (Color online) The schematic geometric structure of (1) The [Mn 4 (l 3 -L) 3 (l 3 -F)] core is highlighted in the balls.
07B105-2 Tuan, Sinh, and Chi J Appl Phys 109, 07B105 (2011)
Trang 4distorted cubane geometry of the Mn4L3F core is preserved.
However, their bond angles and interatomic distances vary;
the exchange coupling angle (a) and the Mn3þ-Mn4þ
intera-tomic distance (dAB) are changed to the ranges of 88.84–
94.35 and 2.798 A˚ –2.944 A˚, respectively, as tabulated in
TableI As expected, the exchange coupling parameterJAB
also varies as shown in TableI The calculated results confirm
the expectation thatJABtends to become stronger when the a
reaches around 90as demonstrated in Fig.3(a) The molecule
(5) with L¼ NC2H5has the highestJAB=kBof174.47 K
cor-responding to a¼ 89.77 This value is about 2.5 times larger
than that of (1) Also, as shown in Fig.3(b), theJABtends to
become stronger with decrease ofdAB; this can be attributed
to increase of direct overlap between 3d orbitals at the A and
B sites The a anddABdependence ofJABdemonstrates that,
in the space of 88 a 92 anddAB 2.850 A˚ , JABof Mn4
molecules studied is at least about two times stronger than
that of (1) These results demonstrate the advantages of
employing N-based ligands (NR, R¼ various) instead of
oxy-gen to form exchange pathways between Mn atoms in
dis-torted cubane Mn4molecules Variation in the R group is an
effective way to tailor exchange couplings between Mn atoms
A comparison between (1) and (2) shows that their
Mn4L3F(OAc)3skeletons are nearly the same For example,
the difference in a anddABin these molecules is very small as
shown in TableI Also their magnetic moments at Mn sites
andJABare nearly the same It is noted that molecule (2) is
obtained from molecule (1) by replacing each C6H5ring of
dbm groups with one H atom These results demonstrate that
variation in the outer part of dbm groups is not as much of an
influence on magnetic properties of Mn4molecules
IV CONCLUSION
By employing N-based ligands to form the exchange
Mn3þ3(l3-L2)3(l3-F)3(CH(CHO)2)3] (L¼ NH, NCH3,
NC2H5, NC2H3, NC2H, or NC6H5) molecules withSTof 9/2 have been designed The calculated results demonstrate that
JAB tends to become stronger when a reaches around 90 Molecule (5) has the highest JAB=kB of 174.47 K corre-sponding to a¼ 89.77 This value is about 2.5 times larger than that of synthesized Mn4 SMMs The results provide some hints for synthesizing new SMMs
ACKNOWLEDGMENTS
We thank the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) for funding this work within Project No 103.01.77.09 The computations presented in this study were performed at the Information Science Center of Japan Advanced Institute of Science and Technology and the Center for Computational Science of the Faculty of Physics, Hanoi University of Sci-ence, Vietnam We are especially thankful for financial sup-port from TRIG project for presenting this work at the 55th Annual Conference on Magnetism and Magnetic Materials 1
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FIG 2 (Color online) The schematic geometric structures of (2)–(8).
FIG 3 (a) the a dependence of J AB and (b) the d AB dependence of J AB
07B105-3 Tuan, Sinh, and Chi J Appl Phys 109, 07B105 (2011)