Giant negative magnetization in a layered organic magnet.

Abstract

Bimetallic oxalates are a class of layered organic magnets with transition metals M(II) and M'(III) coupled by oxalate molecules in an open honeycomb structure. Energy, structure, and symmetry considerations are used to construct a reduced Hamiltonian, including exchange and spin-orbit interactions, that explains the giant negative magnetization in some of the ferrimagnetic Fe(II)Fe(III) compounds. We also provide new predictions for the spin-wave gap, the effects of uniaxial strain, and the optical flipping of the negative magnetization in Fe(II)Fe(III) bimetallic oxalates.

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Giant Negative Magnetization in a Layered Organic Magnet
Randy S. Fishman and Fernando A. Reboredo
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6065, USA
(Received 21 May 2007; published 19 November 2007)
Bimetallic oxalates are a class of layered organic magnets with transition metals M?II? and M0?III?
coupled by oxalate molecules in an open honeycomb structure. Energy, structure, and symmetry
considerations are used to construct a reduced Hamiltonian, including exchange and spin-orbit inter-
actions, that explains the giant negative magnetization in some of the ferrimagnetic Fe(II)Fe(III)
compounds. We also provide new predictions for the spin-wave gap, the effects of uniaxial strain, and
the optical flipping of the negative magnetization in Fe(II)Fe(III) bimetallic oxalates.
DOI: 10.1103/PhysRevLett.99.217203PACS numbers: 75.50.Xx, 71.70.Ej, 75.10.Dg, 75.30.Gw
Compared with the burgeoning effort to synthesize and
characterize organic magnets [1,2], little progress has been
made in using symmetry and energy considerations to
predict the magnetic behavior of organic magnets. This
work closes that gap by developing the theoretical frame-
work to design the magnetic properties of bimetallic oxa-
lates [3], an important class of layered organic magnets.
We demonstrate that, due to the spin-orbit coupling within
each bimetallic layer, different choices of intercalated
cations can produce large changes in the magnetic
behavior.
Bimetallic oxalates are salts with the chemical formula
A?M?II?M0?III??ox?3?, where A is an organic cation that
separates the negatively-charged metallic layers. Each of
the metallic layers contains two different metal atoms in
the alternating honeycomb structure pictured in Fig. 1.
Neighboring metal atoms M?II? with valence ?2 and
M0?III? with valence ?3 are bridged by the oxalate mole-
cule ox ? C2O4 with valence ?2. Most commonly,
M?II? ? Mn, Ni, Fe, Co, Cu, or Zn and M0?III? ? Cr,
Ru, or Fe. The stacking of the bimetallic planes can be
rather complex with, depending on the metal and cation
species, from 2 to 6 bimetallic layers per unit cell [4,5]. For
different metal atoms, a single bimetallic layer can be
either ferromagnetic or ferrimagnetic (M?II? and M0?III?
moments parallel or antiparallel) with magnetic moments
pointing out of the plane. While it cannot change the sign
of the exchange coupling, the organic cation A does affect
the overall behavior of the system. With the appropriate
cation, bimetallic oxalates can be optically activated [5],
metallic [6], or disordered [7,8].
The bimetallic oxalates with the highest magnetic tran-
sition temperatures are the ferrimagnetic Fe(II)Fe(III)
compounds [9,10], where Fe(II) and Fe(III) have 3d6and
3d5electronic configurations, respectively. Surprisingly,
Fe(II)Fe(III) bimetallic oxalates with certain cations ex-
hibit giant negative magnetization (GNM) in a small field
of 100 Oe: while the magnetization lies along the field
direction just below the ferrimagnetic transition of about
45 K, it changes sign below about 28 K so that the mag-
netization lies opposite the magnetic field. Magnetic com-
pensation in ferrimagnets like the rare-earth transition-
metal intermetallics [11] is typically caused by the next-
nearest neighbor interactions between spins on the same
sublattice [12]. However, the large separation between the
metal atomsontheopen honeycombstructure suggeststhat
next-neighbor interactions should be rather weak. We
would like to understand why some cations produce mag-
netic compensation in the bimetallic oxalates while others
do not.
Since the separation between the bimetallic layers for
cation A ? N?n ? CnH2n?1?4grows from 8.2 to 10.2 A˚as
n increases from 3 to 5, the effect of layer separation can be
systematically investigated in the N?n ? CnH2n?1?4?
?Fe?II?Fe?III??ox?3? system. Unexpectedly, the transition
temperature increases from 35 to 48 K with increasing
layer separation (the n ? 4 and 5 cations are associated
FIG. 1 (color).
(blue) and M0?III? (purple) coupled by oxalate C2O4molecules,
with oxygen atoms in red and carbon atoms in green.
A portion of the bimetallic layer with M?II?
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with GNM but the n ? 3 cation is not). Additional evi-
dence comes from the observation [6,13] that a magnetic
s ? 1=2 cation has little effect on the critical temperature
and coercive field of a wide range of bimetallic oxalates.
These experiments suggest that the coupling between
layers is not responsible for the magnetic ordering of
bimetallic oxalates. But according to the Mermin-Wagner
theorem, gapless spin excitations in an isolated two-
dimensional layer will destroy long-range magnetic order
at nonzero temperatures. As shown below, the spin-orbit
coupling within each layer explains all the available ex-
perimental data.
Like many organic magnets [12,14], the Fe(II)Fe(III)
bimetallic oxalates contain three hierarchies of energies.
Because of its origin in the Pauli exclusion principle on
each transition metal, the Hund’s coupling that fixes the
spins S ? 2 and S0? 5=2 and orbital angular momentum
L ? 2and L0? 0on the Fe(II)(3d6)and Fe(III)(3d5)sites
is the dominant energy. Susceptibility measurements [9]
confirm that both Fe(II) and Fe(III) are in their high-spin
states. The C3-symmetric crystal-field potential produced
by the 6 oxygen atoms that surround each Fe atom is next
in importance. Finally, the contributions to the crystal-field
potential that violate C3symmetry, the antiferromagnetic
exchange coupling JcS ? S0between the Fe(II) and Fe(III)
spins, and the spin-orbit coupling ?L ? S on the Fe(II) site
(? < 0 because the Fe(II) shell is more than half filled) are
all considered to lie in the lowest-energy scale.
X-ray measurements [4] indicate that the oxygen atoms
around each transition metal form two triangles that lie
above and below the bimetallic plane. As sketched in
Fig. 1, one of the triangles is a bit closer to the transition
metal and a bit larger than the other triangle, which is ro-
tated by about 48?from the first. The heavily-compressed,
C3-symmetric octahedral crystal field V??;?;?? around
each Fe(II) site can be expanded in Legendre polynomials
as
X
? cos?3n0? ? ?n;n0?:
The phase ?n;n0 reflects the rotation of the two oxygen
triangles.
After integrating over the spherical coordinates, we find
that the crystal-field Hamiltonian Hcf? hm0jV??;?;??jmi
(m0, m ? ?2, ?1, 0) can be written
?
0
0
?0
00
??
0
0
???
where we have subtracted off a diagonal matrix. The n ?
2, 4 and n0? 0 terms in V??;?;?? produce the diagonal ?
and ?0terms, which are real; the n0? 1 terms produce the
off-diagonal ? terms, which couple the L ? 2 wave func-

V??;?;?? ?
n?3n0>1;n;n0?0
An;n0?n?3n0Pn?cos??
(1)
Hcf?
0
0
0
0
0
?
0
0
?0
0
0
??
0
0
?
0
BBBBB@
1
CCCCCA
;
(2)
tions with m ? m0? ?3 and may be complex due to the
phases ?n;1.
By diagonalizing Hcf, we obtain the low-energy orbital
doublet
j 1i/?2?j2i?????0?r?j?1i
2?j1i??????0?r?j?2i, with degenerate energies ?1?
?2???0??????0?=2?r=2 where r?
These eigenstates carry z orbital angular momentum
and
j 2i/
???????????????????????????????????
????0?2?4j?j2
p
.
h 1jLzj 1i ? ?h 2jLzj 2i
?2j?j2? ?? ? ?0?2? ?? ? ?0?r
4j?j2? ?? ? ?0?2? ?? ? ?0?r:
z ? jh 1jLzj 1ij depends only on the differ-
ence ?? ? ?0?=j?j and canvary from completely quenched
(Lcf
commonly called the orbital reduction factor [14].
In addition to the low-energy doublet j 1;2i, a singlet
j 3i ? j0i has energy ?3? 0 and an upper orbital doublet
j 4;5i is obtained from j 1;2i by taking r ! ?r. The solid
curve in Fig. 2 denotes the condition ??0?? 0 or ??0?
j?j2,where the singlet j 3icrossesthe low-energydoublet.
Since h 3jLzj 3i ? 0, the z orbital angular momentum is
completely quenched with Lcf
If octahedral symmetry were preserved by the crystal field,
then ??0?would vanish and the orbital doublet j 1;2i would
be degenerate with the singlet j 3i. With the assumption
T ? j??0?j, the singlet state is unoccupied below the solid
curve and the doublet is unoccupied above.
For a magnetically anisotropic material with ??0?< 0
and Lcf
(3)
In Fig. 2, Lcf
z? 0) to unquenched (Lcf
z? 2). The ratio ? ? Lcf
z=2 is
z? 0 above this solid curve.
z> 0, the magnetic moments M ? h2Sz? Lzi and
FIG. 2 (color online).
crystal-field parameters ?, ?0, and ? on Lcf
of 0.1 by the straight lines. The orbital doublet remains lower in
energy than the singlet below the solid curve, above which Lcf
0. A rough estimate [19] based on density-functional theory
gives the circular point.
A contour plot showing the effect of
z, given in increments
z?
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M0? h2S0zi on the Fe(II) and Fe(III) sites (set ?B? 1) are
solved within mean-field theory. A reduced Hamiltonian is
constructed on the Fe(II) site within the j 1;?i, j 2;?i
subspace (? ? ?2, ?1, 0) including both the exchange
and spin-orbit interactions. Since all matrix elements of L?
vanishin this subspace,the spin-orbit interaction ?L ? Son
the Fe(II) site is diagonal. So the energies of j 1;?i and
j 2;?i are ?1?? ??0?? ??Lcf
??0?? ???Lcf
M0?T? ? 2S0BS0??3S0JchSzi=T? > 0 is proportional to the
spin S0? 5=2 Brillouin function. It is then straightforward
to evaluate the critical temperature Tcand the average
magneticmoment
Mavg? ?M0? M?=2 ? ?jM0j ?
jMj?=2 as a function of T=Tc. We find that Tc=Jcmono-
tonicallyincreasesfrom
when ??Lcf
??Lcf
Slonczewski for Co-doped magnetite [16].
For a strong spin-orbit coupling constant, ? ? ?8Jc,
Mavgis plotted versus T=Tcfor various values of Lcf
Fig. 3, which takes the magnetic moment of Fe(III) to be
positive. When 0 ? Lcf
points and the average moment is always positive (jM0j >
jMj). In the narrow region 0:51 ? Lcf
two compensation temperatures. For 0:54 < Lcf
is a single compensation temperature above which the
average moment is negative. And for 1 < Lcf
average moment is always negative (jMj > jM0j due to
the Fe(II) orbital contribution).
These results are summarized in Fig. 4, which indicates
the number of compensation points ncomp
f??=Jc;Lcf
one for large spin-orbit coupling and in a range of Lcf
z? 3JcM0=2?? and ?2??
z? 3JcM0=2??, where the Fe(III) moment
???????????????????????????????????????
S?S ? 1?S0?S0? 1?
??????????????????????? ?
p
? 7:25
z=Jc? 0 [15] to
z=Jc! 1. A similar formalism was proposed by
3S0?S0? 1?
p
S ? 10:25 as
z in
z< 0:51, there are no compensation
z? 0:54, there are
z< 1, there
z? 2, the
in the
zg phase space. Two regions have ncomp? 1:
z
below 1; the other for small spin-orbit coupling and Lcf
1. In the upper-left region, the moment is negative just
below Tcwhere the Fe(II) moment dominates and positive
at low temperatures where the Fe(III) moment dominates;
in the lower-right region, the moment is positive just below
Tcand negative at low temperatures. The inset to Fig. 4
plots the compensation temperatures Tcompversus Lcf
several values of ??=Jc. Since Tc increases with
??Lcf
have higher critical temperatures [9].
The main role played by the cation in Fe(II)Fe(III)
bimetallic oxalates is to slightly modify the crystal field
potential by displacing the Fe(II) ions with respect to the
oxalate molecules. ‘‘Normal’’ Fe(II)Fe(III) bimetallic ox-
alates without magnetic compensation can fall into two
classes. The cations may reverse the distortion of the
octahedral crystal field so that ??0?> 0 with the Lcf
singlet lying lower in energy than the orbital doublet. Since
there is no magnetic anisotropy when Lcf
would be absent as well. Alternatively, the orbital doublet
may remain lower in energy but with a small Lcf
falling into the left ncomp? 0 region of Fig. 4.
Our results for Tcompand Tccan be used to estimate the
experimental parameters for bimetallic oxalates that ex-
hibit GNM. Taking the value of ? ? ?102cm?1or
?12:65 meV from paramagnetic resonance measurements
of Fe(II) [17] and the estimate Tcomp=Tc? 0:62 from ex-
periments on GNMmaterials [9] gives Jc? 0:46 meV and
Lcf
Lcf
z>
z for
z=Jc, these results explain why GNM materials
z? 0
z? 0, GNM
z> 0
z? 0:28 [18]. For ?=Jc? ?27:5, ncomp? 0 when
z< 0:23 so that GNM materials lie just inside the
FIG. 3 (color online).
T=Tcfor various Lcf
defined to be positive.
The average magnetic moment versus
z and ?=Jc? ?8. The Fe(III) moment is
FIG. 4 (color online).
havior denoting the number of compensation points ncomp? 0,
1, or 2 for ??=Jcversus Lcf
ncomp? 1. Inset is a plot of Tcomp=Tcversus Lcf
values of ??=Jc.
217203-3
A phase diagram of the magnetic be-
z. GNM occurs in regions with
z for various
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upper-left region of Fig. 4 with ncomp? 1 [19]. Mo ¨ssbauer
spectroscopy [9] confirms that the Fe(II) moment in GNM
compounds dominates just below Tc, as anticipated for this
region of Fig. 4. Additional support for Fig. 4 comes from
the recent discovery [20] of an Fe(II)Fe(III) bimetallic
oxalate with ncomp? 2.
The persistence of negative magnetization is associated
both with the finite energy barrier ?2?Lcf
hLzi once it is aligned parallel to the magnetic field and
with the small matrix element for this dipole-allowed
transition (due to the hybridization of the L ? 2 and L ?
1 wave functions by the nonspherical crystal-field poten-
tial V??;?;??). By optically exciting the higher-energy
state of the orbital doublet with far-infrared light of
frequency ?2?Lcf
it should be possible to flip the magnetic moment in a
negative-magnetization state below Tcomp. Optical control
of the magnetization has been previously demonstrated in a
Mn(II)Cr(III) bimetallic oxalate [5] and other organic
magnets [21].
Because it is associated with the non-C3symmetric
crystal-field potential Vs/ sin?cos2?, uniaxial strain in
the plane ofthe bimetallic layers will mix j 1iand j 2iand
lower the orbital angular momentum of the ground-state
orbital doublet. Consequently, uniaxial strain will decrease
Tcand increase Tcomp, eventually transforming a GNM
material into a normal one.
Finally, we have performed a Holstein-Primakoff ex-
pansion to evaluate the spin-wave (SW) frequencies of
Fe(II)Fe(III) bimetallic oxalates. In zero field, the SW
gap is given by
zS for flipping
zS ? 14 meV or wavelength 88:5 ?m,
?sw? ?Lcf
z=2 ? 3Jc?S0? S?=2 ? f9J2
? ??Lcf
which vanishes like ??Lcf
approaches 3JcS as ??Lcf
estimated above, we obtain ?sw? 1:65 meV, which
should be relatively simple to observe with inelastic
neutron-scattering techniques. The SW gap explains the
high transition temperatures of well-separated two-
dimensional layers, where gapless spin excitations would
suppress the critical temperature.
To conclude, we have derived from structure, symmetry,
and energy considerations a reduced Hamiltonian that ex-
plains all of the important observations about an important
class of layered organic magnets. We have made new
predictions, with potential technological implications, for
the optical and mechanical control of the negative-
magnetization state.
We gratefully acknowledge useful conversations with
Juana Moreno. This research was sponsored by the
Laboratory Directed Research and Development Program
of Oak Ridge National Laboratory, managed by UT-
c?S0? S?2
z?2? 6?Lcf
zJc?S0? S?g1=2=2;
zS=?S0? S? as ??Lcf
z=Jc! 1. Using the parameters
(4)
z! 0 and
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of Materials Science and Engineering of the U.S. DOE.
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z=Jc! 0.
z=Jc? 1, the presence of a spin-wave gap
z? 0:66, as indicated in Fig. 2.
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