Reprinted from

FULL PAPER
Magnetic Excitations in Inﬁnite-Layer Antiferromagnetic Insulator
Keisuke TOMIYASU, Hiroshi KAGEYAMA, Changhoon L EE, Mike H. WHANGBO,
Yoshihiro TSUJIMOTO, Kazuyoshi YOSHIMURA, Jon W. TAYLOR, Anna LLOBET,
Frans TROUW, Kazuhisa KAKURAI, and Kazuyoshi YAMADA
J. Phys. Soc. Jpn. 79 (2010) 034707# 2010 The Physical Society of Japan

Person-to-person distribution by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Journal of the Physical Society of Japan
Vol. 79, No. 3, March, 2010, 034707#2010 The Physical Society of Japan

Magnetic Excitations in Inﬁnite-Layer Antiferromagnetic Insulator
Keisuke TOMIYASU, Hiroshi K AGEYAMA1 , Changhoon L EE2 , Mike H. W HANGBO2 ,Yoshihiro TSUJIMOTO1 , Kazuyoshi Y OSHIMURA1 , Jon W. T AYLOR3 , Anna LLOBET4 ,Frans TROUW4 , Kazuhisa K AKURAI5 , and Kazuyoshi Y AMADA6
Department of Physics, Tohoku University, Sendai 980-8578, Japan
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan2
Department of Chemistry, North Carolina State University, Ralleigh, NC 27695-8204, U.S.A.
3
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, U.K.
4
LANSCE, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
5
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
6
WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
1(Received December 2, 2009; accepted January 7, 2010; published March 10, 2010)

The magnetic excitations of an inﬁnite-layer antiferromagnetic insulator SrFeO2 were examined bypowder inelastic neutron scattering to ﬁnd dispersive magnetic excitations from 15 up to 63 meV. The
scattering intensity distribution is well described by a spin wave model, conﬁrming that the out-of-plane
direct Fe···Fe exchange is comparable in strength to the in-plane Fe–O–Fe superexchange. SrFeO2 showsan additional magnetic excitation mode around 30 meV, which is suggestive of an orbital magnon arisingfrom small orbital moment on Fe2þ brought about by spin–orbit coupling.
KEYWORDS: spin wave, orbital wave, orbital angular momentum, Mott insulator
DOI: 10.1143/JPSJ.79.034707

1.

to an orbital magnon proposed for a Mott insulator withunquenched orbital angular momentum.9)

Introduction

Recently, a new iron-based antiferromagnetic insulator
SrFeO2 (Fe2þ : d6 , S ¼ 2) constructed from square-planar
FeO4 units was obtained.1) This material has the crystal
structure in which FeO2 layers of corner-sharing FeO4
square-planes alternate with layers of Sr as shown in
Fig. 1(a), and is isostructural with the inﬁnite layer compound (Sr1x Cax )CuO2 .2,3) SrFeO2 exhibits several unexpected structural and physical properties. Its antiferromagnetic transition temperature TN ’ 473 K is unusually highdespite its two-dimensional layered structure,1) and its
inﬁnite layer structure with P4/mmm space group is robust
against cation substitution (Sr2þ /Ca2þ ) as well as against
temperature.4) Furthermore, it undergoes a pressure-induced
spin transition into an intermediate spin state with S ¼ 1,
which is accompanied by insulator-to-metal and antiferromagnet-to-ferromagnet transitions.5) Density functional calculations for SrFeO2 6,7) showed that the down-spin of thehigh-spin Fe2þ occupies the nondegenerate dz2 , which shows
L ¼ 0 for the Fe2þ ions and explains why Jahn–Teller
instability is absent in SrFeO2 , and that the direct Fe···Fespin exchange between adjacent FeO2 layers is strong,hence accounting for the high TN 1) and the unprecedented
spin transition for a square-planar coordinate system.5,8)
However, there has been no experimental veriﬁcation of
the three-dimensional magnetic character on the basis ofmagnetic excitation energy measurements. The magnetic
susceptibility of SrFeO2 has not been reported because it isunstable at temperatures above 450 K and because asprepared samples possess ferromagnetic impurities diﬃcult
to remove.1) In this paper, we show on the basis of powder
inelastic neutron scattering measurements that the out-ofplane direct Fe···Fe exchange is comparable in strength tothe in-plane Fe–O–Fe superexchange, and SrFeO2 exhibits
an additional magnetic excitation mode similar in natureE-mail: tomiyasu@m.tains.tohoku.ac.jp

2.

Experiments and Computational Details

Neutron scattering experiments were performed using
direct geometry chopper spectrometers Mari at ISIS (UK)and Pharos at LANSCE (USA) installed at their respective
spallation neutron sources. The incident energies (Ei ) were
ﬁxed at 120 and 240 meV in the Mari and Pharos experiments, respectively. The data shown in the inset in Fig. 1(d)were obtained using Pharos, while all other data wereobtained using Mari. The energy resolution at elastic
condition was approximately 3% for Ei in both experiments.
Powder samples of SrFeO2 were synthesized in the manner
described in ref. 1. The 33 g and 36 g samples of SrFeO2
were used for the Mari and Pharos experiments, respectively.
Each sample was wrapped in a thin aluminum foil, which
was then enclosed with 4 He exchange gas in an aluminum
container, and set under the cold head of a closed-cycle 4 He
refrigerator.
To determine the preferred spin orientation in theantiferromagnetic ground state of SrFeO2 , we carried out
density-functional calculations for the crystal structure at
10 K1) using the full-potential linearized augmented plane
wave method encoded in the WIEN2k program package10)
with the generalized gradient approximation (GGA)11) forthe exchange–correlation functional, the on-site repulsion
U 12) on Fe to describe the strong electron correlation
associated with the Fe 3d states, and the spin–orbit coupling(SOC) on the Fe atom. Further details of our GGA+U+SOC
calculations (with several U values between 0.0 and 4.6 eV)
are summarized in ref. 13.
3.

Results

Figure 1(b) shows neutron scattering intensity distribution
in the (Q; E) space, SðQ; EÞ, measured at T ¼ 5 K, where Q
is the magnitude of momentum transfer and E is the energy
transfer. The magnetic excitations, whose intensity becomes

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J. Phys. Soc. Jpn., Vol. 79, No. 3

60

0
0

60

80

6
4
2
E=45 meV0
1.7 2.1 2.5 2.9-1
Wave number Q [Å ]

40

40
20

20

0

0
1
2
3
4
-1
Wavenumber Q [A ]

0

30
20
10

100
200
Energy [meV]

0

5

1
2
3
4
-1
Wavenumber Q [A ]0100(e) T=353 K

(g)
30

80

40
20
0

60

20
60
10
40

0

Intensity [a.u.]

FeO2
Fe2+ O2- planeJ//100
80 (b) T=5 K
60
40
20
0
12
8
4
0
-1
Wavenumber Q [A ]1002(d) T=300 K
T=20 K
1
80
Intensity [a.u.]

Energy [meV]

Energy [meV]

J'//

80

Energy [meV]

Sr 2+

J'

8

J =1.7J// =3.0
D =-0.5[meV](f)(c) T=5 K

10Energy [meV]

J

FeO2
plane

100

12

Intensity[mbarn/sr/Fe]

(a)

100
a

Integrated Intensity [a.u.]bEnergy [meV]cK. TOMIYASU et al.

5

J =0.7J// =3.5
D =-0.5
[meV]

20

0

1
2
3
4
Wavenumber Q [A-1]

5 0

1

2
3
4
Wavenumber Q [A-1]

0

5

0

1
2
3
4
-1
Wavenumber Q [A ]5

Fig. 1. (Color online) (a) Crystal and magnetic structures of SrFeO2 ,1) where the solid arrows on the Fe2þ ions indicate magnetic moments, which lie on
the ab plane. The magnetic structure is represented by a propagation vector ð1=2; 1=2; 1=2Þ. The dotted arrows deﬁne exchange interactions J? , Jk , J?0 ,and Jk0 . (b–e) Experimental SðQ; EÞ maps measured with Ei ¼ 120 meV. The intensity tone is shown in the inset of (e). The inset of (c) shows the Q
dependence integrated from E ¼ 42 to 48 meV, demonstrating the dispersion relation of the magnetic excitations. The inset of (d) shows the energy
spectrum integrated from Q ¼ 0 to 6 Å1 measured with Ei ¼ 240 meV. (f,g) Calculated SðQ; EÞ maps with Ei ¼ 120 meV based on a spin wave model.
(f) shows the best ﬁt and (g) shows the map for a more two dimensional case (E? =Ek ¼ 0:1). The intensity tone is shown in the inset of (g).

stronger in a lower Q range, are observed, and the phonon
density of states (nondispersive excitations), whose intensity
becomes stronger in a higher Q range, is distributed over theentire Q region. Figure 1(c) magniﬁes the low Q region in
Fig. 1(b). Clear dispersive magnetic excitations are observedon the trail of the phonon density of states around 20 meV,which open up from energy minima located at Qc ¼ 1:4
and 2.7 Å1 to energy maximum (Et ¼ 63 meV) widelydistributed in the Q range. The positions of Qc correspond
approximately to the magnetic Bragg points ð1=2; 1=2; 1=2Þand ð3=2; 1=2; 1=2Þ, consistent with the observed magnetic
structure. In general, SðQ; EÞ for a low-dimensional system
is smeared along the Q direction (e.g., see refs. 14 and 15).
Thus the observed clear pattern qualitatively suggests a
three-dimensional nature of the spin exchange interactions in
SrFeO2 . The Q dependence of the energy-integrated scattering intensity around Et [Fig. 2(a)] exhibits monotonic
decrease up to 5 Å1 .
To estimate the energy minimum at Qc , we roughly
extracted the magnetic components:
Z Qc þ0:4
Smag ðEÞ ¼SðQ; EÞ dQ
Qc 0:4
Z Qc 0:4
Z Qc þ0:6
2SðQ; EÞ dQ þSðQ; EÞ dQ :Qc 0:6

Qc þ0:4

ð1Þ
As seen in Fig. 1(b), the energy region below 40 meV
involves considerable phonon contributions. The Q inte-

grated range of the ﬁrst term consists of both the magnetic
excitations and phonons, while that of the second term canbe regarded as the phonon background, as seen in Fig. 1(c).
The ﬁrst and second terms (S1 and S2) and their diﬀerence(S1  S2) for Qc ¼ 1:4 Å1 are shown in Fig. 2(b). We
conﬁrmed that the E dependence of S2 is almost the same as
the phonon density of states obtained in the high Q range
in Fig. 1(b). In the S1  S2, the peak structure of phonons
disappears, indicating that no signiﬁcant phonon contributions remain, and the energy minimum at Qc is estimated as
15  5 meV, which corresponds to the gap energy (Eg ).
Figures 1(d) and 1(e) show SðQ; EÞ measured at T ¼ 300
and 353 K, respectively. With increasing T, the intensity ofthe magnetic excitations in the energy range higher than T(such as around Et ) decreases, while the opposite happensin the energy range lower than T because of the Bose
population factor.
4.

Discussion

The magnetic excitation energies of SrFeO2 can be
described by the Heisenberg spin Hamiltonian,X
X
H¼
Jmn Sm  Sn þ DðSmz Þ2 ;
ð2Þ
m;n

m

where m and n are Fe2þ sites, the spin exchange parameters
Jmn are deﬁned in Fig. 1(a), and D is the spin anisotropy
constant. The LDA (local density functional)+U calculations gave the estimates ðJ? ; Jk ; J?0 ; Jk0 Þ ¼ ð1:09; 3:52; 0:12;

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J. Phys. Soc. Jpn., Vol. 79, No. 3

K. TOMIYASU et al.

40

30

30
20
10
res.
0

S1
S2
S1-S2

(b)

5
Eg

3

4

Wavenumber Q [A-1]

20

10

res.
another
mode
Eg

0

0
2

(c)

Intensity [a.u.]

10

Intensity [a.u.]

Intensity [a.u.]

(a)

0

5

10 15 20 25 30

Energy [meV]

0 10 20 30 40 50 60 70 80

Energy [meV]Fig. 2. (Color online) Q dependence of the scattering intensity integrated from E ¼ 60 to 66 meV (a), Q-integrated energy spectra around Qc ¼ 1:4 Å1(b), and the comparison between with experimental magnetic energy spectrum and calculated spin-wave spectrum (c). The experimental (symbols)
and calculated (solid lines) data are obtained from the data shown in Figs. 1(c) and 1(f), respectively. The dotted lines are guide for eyes. In (a), theexperimental errors are smaller than the symbol sizes. In (b), S1  S2 ¼ Smag , where S1 and S2 are the ﬁrst and second terms in eq. (1), respectively. In(c), the solid and open circles correspond to S1  S2 for Qc ¼ 1:4 and 2.7 Å1 , respectively, and the solid triangles indicate the raw spectrum integrated
from Q ¼ 0 to 4 Å1 above E  40 meV. The intensity scales of these three data sets, which are diﬀerent because of a magnetic form factor, are adjusted
to smoothly connect the data points. The gray shaded area suggests the existence of another magnetic mode.

0:22Þ6) and ðJ? ; Jk ; J?0 Þ ¼ ð0:88; 3:29; 0:13Þ7) in meV units.
Xiang et al. found D ¼ 1:0 meV from their LDA+U+
SOC calculations for the ferromagnetic state of the optimized SrFeO2 structure.6) Our GGA+U+SOC calculations
for the experimental SrFeO2 structure show that D ¼ 0:45
meV for the ferromagnetic state, and D ¼ 0:39 meV for
the antiferromagnetic state.
The ratio of the
P out-of-plane exchange
P to the in-plane
energy, E? =Ek  m;n? ðJmn? Smz Sn? z Þ= m;nk ðJmnk Smz Snk z Þ ¼
ð2J?  8J?0 Þ=ð4Jk  4Jk0 Þ, where n? and nk mean the out-ofplane and in-plane Fe2þ sites for a given m site, respectively,
is 0.236) and 0.217) for each set of the theoretical J values.
E? =Ek is 0 for a completely two-dimensional system, and
0.5 for an isotropically three-dimensional system.
We analyze the SðQ; EÞ data at T ¼ 5 K [Fig. 1(c)] interms of a spin wave model by using only J? , Jk , and D
in eq. (2). Then, the spin wave dispersion h !ðqÞ for the
propagation vector q ¼ ðqa ; qb ; qc Þ can be described by theHolstein–Primakoﬀ formalism
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
h !ðqÞ ¼ 2S ½J? ð0Þ þ Jk ð0Þ  D2  ½J? ðqÞ þ Jk ðqÞ2 ; ð3Þ
where S ¼ 2, J? ðqÞ ¼ 2J? cos 2qc , and Jk ðqÞ ¼
2Jk ðcos 2qa þ cos 2qb Þ. In terms of h !ðqÞ the SðQ; EÞfunction can be written as
SðQ; EÞ

*sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ+
Ei  E¼A
jFðQÞj2 ð1 þ cos2 ÞjtðQÞj2 ½E  h !ðqÞ ;Ei
ð4Þ

where A is a scale factor of the scattering intensity,
Ei ¼ 120 meV, FðQÞ is a magnetic form factor, Q is ascattering vector,  is the angle between Q and S [thepreferred spin orientation is parallel to the a axis,1,6) asshown in Fig. 1(a)], tðQÞ is a dynamic structure factor of
the spin wave,16) and h  i represents powder orientational
averaging. For the energy scale discussed in this study, thetemperature factors are negligible at T ¼ 5 K (0:4 meV).
Equation (3) shows that, if D is nonzero, there exists an
excitation energy gap Eg given by Eg ¼ h !ð0Þ. Using theexperimentally obtained values Et ¼ 63 meV and Eg ¼ 15
meV in eq. (3), J? ¼ 7:65  2Jk meV and D ¼ 0:5 
0:3 meV are obtained; this reduces the number of freeparameters to only Jk . For FðQÞ, the Watson–Freeman form
factor is used.17) Then, by solving eq. (4), we obtain the bestﬁt shown in Fig. 1(f), which yields ðJ? ; Jk ; DÞ ¼ ð3:0  0:2;
1:7 0:3; 0:5  0:3Þ, in excellent agreement with theobserved SðQ; EÞ [Fig. 1(c)]. For a set of more two-dimensional parameters (i.e., with smaller J? =Jk ratio), the pattern
becomes smeared along the Q direction as shown in
Fig. 1(g). The Q dependence around Et is also consistent
with the experimental data [Fig. 2(a)]. Furthermore, the Et
value decreases gradually by a few meV on going from
Figs. 1(c) to 1(e). This decreasing is consistent with a spinwave, as found for MnO.18,19)
The obtained ratio J? =Jk ¼ 0:57  0:14 (E? =Ek ¼ 0:28 0:07) demonstrates that the magnetism in SrFeO2 is three
dimensional. The theoretically obtained J values6,7) also
exhibit the SðQ; EÞ pattern similar to that shown in Fig. 1(f);the experimental E? =Ek ratio agrees well with the theoretical one (0.23 and 0.21). The three dimensional magnetic
character of SrFeO2 reﬂects that the direct Fe···Fe exchange
associated with the out-of-plane magnetic orbitals (i.e., thedxz and dyz orbitals) is substantial. In contrast, the isostructural compound (Sr1x Cax )CuO2 (Cu2þ : 3d 9 , S ¼ 1=2,
kB TN =Ek  0:1)20) has no three-dimensional character because its magnetic orbital Cu 3dx2 y2 possesses no outof-plane character. The experimental value of D (i.e.,0:5  0:3 meV) is in good agreement with the theoreticalvalue estimated from the present GGA+U+SOC calculations for the antiferromagnetic state (i.e., 0:39 meV). The
nonzero D value arises from the SOC, which mixes thedown-spin dzx and dyz orbital character into the down-spin
dz2 orbital, hence leading to a small, nonzero orbital moment
on Fe2þ (of the order of 0.1 B from the present GGA+U+
SOC calculations).
Figure 2(c) shows the experimental energy spectrum ofmagnetic excitations (symbols) and the spin-wave densityof states calculated by integrating the spin-wave scattering
intensity over the whole Brillouin zone with resolution

034707-3

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J. Phys. Soc. Jpn., Vol. 79, No. 3

K. TOMIYASU et al.

correction (solid curve).21) In this calculation, the scale
factor was adjusted such that the intensity around Et
coincides with the experimental data. As expected, thecalculated spin-wave density of states is convex downward.
However, the experimental data exhibits a broad convexupward feature in the E2nd  30 meV region, which shows
the presence of an additional magnetic excitation mode
superposed on the spin wave in the E2nd region. Thisadditional excitation mode cannot be related to the excitations between the crystal-ﬁeld-split d-states, because thesmallest excitation gap (from the down-spin dz2 to the downspin dxz and dyz levels) is much greater than 0.1 eV from thedensity functional calculations.6,7)
It is of interest to consider a probable cause for the
additional magnetic excitation in the 30 meV region. The
single-crystal inelastic neutron scattering study9) of the
Mott-type antiferromagnetic insulator CoO with high-spin
Co2þ (eﬀective L ¼ 1, S ¼ 3=2) ions showed that, in
addition to the spin wave excitations with Eg  20 meV
and Et  70 meV, it exhibits excitations centered aroundE2nd  40 meV. The latter have been suggested to arise froman orbital magnon, i.e., a collective excitation in which thetilting of L is propagated like a spin wave.9) The magnetic
excitations of SrFeO2 exhibit similar features. Namely,in addition to the spin wave excitations with Eg  15 meV
and Et  63 meV, it exhibits excitations centered aroundE2nd  30 meV. This similarity leads us to suggest that theadditional excitations of SrFeO2 centered around 30 meVare due to an orbital magnon, although some phonon
contributions to the 30 meV excitations cannot be ruled out
completely because unpolarized neutrons were used in our
scattering experiments. Given that an orbital magnon mode
can occur in SrFeO2 with small orbital moment on Fe2þas well as in CoO with large unquenched orbital moment
on Co2þ , it appears that orbital magnon is a universal
phenomenon in magnetic insulators of 3d magnetic ions with
nonzero orbital moment.
5.

Conclusions

In summary, our powder inelastic neutron scattering study
conﬁrms that SrFeO2 has a three-dimensional magnetic
character, and shows a magnetic excitation mode superposedon the spin wave in the 30 meV region. The latter issuggestive of an orbital magnon, which arises from small
orbital moment on Fe2þ induced by SOC.
Acknowledgment
This work was supported by Grants-in-Aid for ScientiﬁcResearch on Priority Areas (19052004) and ScientiﬁcResearch (B) and (S), Japan–UK Collaboration Programon Neutron Scattering, Quantum Beam Technology Pro-

gram, World Premier International Research Center Initiative (WPI Initiative), the Ministry of Education, Culture,
Sports, Science and Technology, Japan. This work has
beneﬁted from the use of Pharos at the Lujan Center at
LANSCE, funded by DOE Oﬃce of Basic Energy Sciences.
Los Alamos National Laboratory is operated by Los Alamos
National Security LLC under DOE Contract DE-AC5206NA25396. M.-H. W. thanks U.S. Department of Energy
for the ﬁnancial support (Grant No. DE-FG02-86ER45259).
We thank Mr. Masaki Morita and Ms. Aya Sakaiguchi forassisting in the synthesis of samples.

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