Table Of ContentInterplay of iron and rare-earth magnetic order in rare-earth iron pnictide
superconductors under magnetic field
Lei-Lei Yang1, Da-Yong Liu1, Dong-Meng Chen2, and Liang-Jian Zou1,3∗
1 Key Laboratory of Materials Physics, Institute of Solid State Physics,
Chinese Academy of Sciences, P. O. Box 1129, Hefei, Anhui 230031, China
2 College of Science, China University of Petroleum, Qing Dao, 266580, China
3 Department of Physics, University of Science and Technology of China, Hefei, 230026, China
(Dated: January 13, 2017)
The magnetic properties of iron pnictide superconductors with magnetic rare-earth ions under
7
strong magnetic field are investigated based on the cluster self-consistent field method. Starting
1
0 from an effective Heisenberg model, we present the evolution of magnetic structures on magnetic
2 field in RFeAsO (R=Ce, Pr, Nd, Sm, Gd and Tb) and RFe2As2 (R=Eu) compounds. It is found
that spin-flop transition occurs in both rare-earth and iron layers under magnetic field, in good
n
agreement with the experimental results. The interplay between rare-earth and iron spins plays a
a
key role in the magnetic-field-driven magnetic phase transition, which suggests that the rare-earth
J
layers can modulate the magnetic behaviors of iron layers. In addition, the factors that affect the
2
critical magnetic field for spin-flop transition are also discussed.
1
PACSnumbers: 74.70.Xa,74.25.Ha,61.30.Gd
]
l
e
- INTRODUCTION sition temperatures T are very different, indicating a
r c
t possiblydistinctmagneticinteractionbetweenrare-earth
s
. and Fe layers in different compounds, and these distinct
t Since the iron-based superconductors were discov-
a magnetic coupling is crucial in promoting the supercon-
m ered [1], the families of iron pnictides and chalcogenides
ducting transition temperature.
displayveryrichphasediagrams,includingantiferromag-
-
d netism or spin-density wave [2, 3], superconductivity [1], Especially, these magnetic rare-earth ions exhibit dif-
n structural/magnetic phase transitions [3], orbital order- ferent magnetic interactions, resulting in a more compli-
o
ing [4–7] and nematic ordered phase [8], etc.. The prox- cated magnetic behaviors. For example, in 1111 system,
c
[ imity of magnetism and superconductivity suggests the therareearthionsofRFeAsOareAFM,andundergoan
spin degree of freedom plays a key role in understanding AFM-paramagnetic phase transition at TN [19]. While
v1 the basic low-energy physics of the iron-based supercon- in 122 system, such as in EuFe2As2, Eu2+ ions display
8 ductors. And spin fluctuations have been proposed as a ferromagnetic (FM) ordering [12], etc.. A series of ex-
5 the unconventional superconducting mechanism of iron- periments had been performed to investigate the role of
2 basedsuperconductors[9]. Thus,tounderstandthemag- themagneticrare-earthionsontheFe-3dmagnetismand
3 netic properties is a primary task in uncovering the mi- superconductivity. Meanwhile, the influence of magnetic
0
croscopicmechanismoftheiron-basedsuperconductivity. field on these complicated magnetic orderingare also in-
.
1 vestigated using static and pulsed field techniques. It
Through many magnetic measurements, mainly with
0 is found when a magnetic field is applied in EuFe2As2, a
7 the help of the neutron scattering techniques, var-
spinfloptransitionoccursinrear-earthEulayerobserved
1 ious antiferromagnetic (AFM) structures in different
experimentally at a very low magnetic field [20–22]. In
v: ironpnictide compounds have been determined; the 1111
addition,inSmFeAsO,atahighpulsedmagneticfield, a
i (RFeAsO with R=rare-earthions), the 111 (AFeAs with
X spin-flop like transition is also observed [23].
A=alkali metal ions, e.g. Na) and the 122 phases
ar (AFe2As2 with A=alkaline earth metal ions, e.g. Ba, These experiments have demonstrated that in
and RFe2As2 with R=rare-earth ions, e.g. Eu), possess ironpnictidesuperconductorsthemagneticstructuresun-
striped AFM (SAFM) order [3, 10–12], while FeTe is bi- dermagneticfielddisplayacomplexphenomenon. Thus,
collinear AFM (BAFM) [13], etc.. Among these com- a question naturally arises: what role do the magnetic
pounds, the parentcompounds withmagnetic rare-earth rare-earthionsandmagneticfieldplayonthemagnetism
ions, such as RFeAsO (R=Ce, Pr, Nd, Sm, Gd and Tb) and superconductivity of the FeAs layers in these rare-
andEuFe2As2,havedemonstratedparticularinteresting. earth compounds? To address this question, a detail
SmFeAsO1−xFx shows the maximum Tc with about 55 theoretical investigation is expected. In this paper, we
K [14], in other iron-pnictides with magnetic rare-earth present the effect of magnetic rare-earth ions and mag-
ions, the T is about 41 K for Ce [15], 52 K for Pr [16], netic field on the magnetism of iron pnictide compounds
c
and 51 K for Nd [17]. However, in EuFe2As2, the Tc is and investigate the interplay of magnetic rear-earthand
only about 29.5 K [18]. Since the basic FeAs units are Fe ions. This paper is organized as follows: a model
very similar in these systems, the superconducting tran- Hamiltonianandtheclusterself-consistentfield(Cluster-
2
SCF)methodaredescribedinSec.II;thentheresultsand layer as
discussions are presented in Sec. III; the last section is
devoted to the remarks and conclusions. HS =J1S X S~i·S~j +JcS X S~i·S~j
<ij> <ij>c (2)
+JSX(Siα)2,
i
MODEL HAMILTONIAN AND METHOD
where S~ is the rare-earth spin, JS is the NN magnetic
1
exchange constants of intralayer rare-earth spins, JS is
c
IthasbeenshownthattheeffectiveHeisenbergmodels the interlayer coupling along the c-axis, J is the single-
S
provide a reasonable description for the magnetic struc- ion anisotropy energy of rare-earth ions, and α=x for
ture and spin wave behaviors in the iron-based super- Eu spins in EuFe2As2 and α=z (i.e. c direction) for Sm
conductors [24]. The J1-J2 frustrated Heisenberg model spins in SmFeAsO. And we also consider the interlayer
was firstly proposed to describe the magnetic properties coupling between the rare-earth (R) and FeAs layers:
of the iron-based superconductors. While, the inelas-
ticneutronscatteringexperimentsfoundalargein-plane HsS =JcsS X ~si·S~j, (3)
anisotropy in the magnetic interactions [25], suggesting <ij>c
themagneticexchangeconstantsJ1a >J1b withadenot- where JsS is the coupling between R and Fe ions.
ing the AFM direction and b the FM direction. Thus an c
Itisknownthattheexternalmagneticfieldisaneffec-
effectiveJ1a-J1b-J2 modelcouldwelldescribethestriped tive tool to modulate the spin degree of freedom. In this
AFM(SAFM) orderiniron-basedcompounds [26]. Here
paperwemainlyconsidertwokindsofmagneticfield,one
we start from the J1a-J1b-J2 Heisenberg model. (B ) is applied along the direction of a or b axis of the
//
magneticunit cell, andanother(B⊥) is perpendicularto
it (i.e. along the direction of c axis). In general, the
1.0
Short range correlation external magnetic field is described as
0.8
)
B(M0.6 HB =−gµBBX(sαi +Siα) (4)
0.4 NØel Stripe i
0.2
where α=x/z depends on the direction of the magnetic
0.00.0 0.2 0.4 0.6 0.8 1.0 field, where x (z) along a (c) axis of the magnetic unit
J2/J1 cell. Thus the total Hamiltonian of the system is H =
FIG.1. (a)Sketchofthesquare-latticeclusteradoptedinour H +H +H +H .
s S sS B
Cluster-SCFapproach,and(b)phasediagramofJ1-J2spin-21 In order to treat with the spin correlations and fluc-
Heisenberg model obtained by ourCluster-SCF method.
tuations including short-rangeones accurately,we adopt
theclusterself-consistentfield(Cluster-SCF)methodde-
velopedbyustosolvethisanisotropicHeisenbergmodel.
An effective J1a-J1b-J2 Heisenberg model for iron-
The main idea of this method as follows: we divide the
based compounds is described as,
latticeintoacentralclusterplussurroundingspins,treat
the magnetic interactions of the spins inside the cluster
Hs =J1sa X ~si·~sj +J1sb X ~si·~sj exactly, and the couplings of surrounding spins outside
<ij>a <ij>b theclusteristreatedasself-consistent”molecular”fields.
+J2s X ~si·~sj +Jcs X ~si·~sj (1) The details could be found in Refs. [27–29]. Here we ex-
tend our method to deal with the Heisenberg model in-
<<ij>> <ij>c
+JsX(sαi)2, cJl2umdiondgetlsh,eeNtcN..NAisnatnereaxcatimonp,lesutochvearsifyJ1o-uJr2aapnpdroJa1cah-J,w1be-
i
calculated the phase diagramof J1-J2 Heisenberg model
with spin s = 1/2 on a square lattice, and the result is
whereJs ,Js andJs arethenearest-neighbor(NN)and
1a 1b 2 shown in Fig. 1. It is clearly shown that our phase di-
next-nearest-neighbor (NNN) magnetic exchange con-
agram is good agreement with these obtained by other
stants with spin ~s of Fe ions, respectively; Js is the in-
c methods,suchasseriesexpansions[30]andcoupledclus-
terlayer coupling along the c-axis and J is the single-
s ter[31]methods,demonstratingtheeffectivenessandva-
ion anisotropy energy of Fe ions. Notice that α is given
lidity of our Cluster-SCF method.
according to the experimental results, α=x (i.e. a di-
TosolvethisHeisenbergmodel,themagneticexchange
rection) for Fe spins in both EuFe2As2 and SmFeAsO parameters should be given firstly. In order to com-
compounds.
pare the different rare-earth layers, we use the same pa-
We consider the magnetic couplings in the rare-earth rameters for Fe layers in both RFe2As2 and RFeAsO
3
systems. Here we adopt the parameters for Fe layers RFe As case
2 2
with Js =59.9 meV, Js =−9.2 meV, Js=13.6 meV and
1a 1b 2
Js=1.8 meV according to the inelastic neutron scatter-
c We find that in the stable magnetic ground state of
ing experiments [25, 32]. And we estimate the single-ion
anisotropy energy parameter J =0.07 meV. Note that RFe2As2 with R=Eu, the Fe spins in FeAs layer are
s SAFM with interlayer AFM; meanwhile, the Eu2+ spins
we estimate the single-ion anisotropy energy parame-
in the rare-earthlayers are ferromagnetic (FM) with the
ters within spin-wave theory with a relationship ∆ =
interlayer AFM. Notice that the spin directions of both
2sp2Js(J1a+2J2+Jc), where ∆ is spin gap [33, 34] in Eu2+ and Fe2+ ions align in the a-b plane. According
thispaper. ForRFe2As2case,consideringNe´eltransition
to the analysis of the symmetry of the magnetic struc-
temperatureTRN=19KforEulayerinEuFe2As2 [19,35], ture, the influence of rare-earth ions on Fe ions is can-
wechooseJS=−0.8meV,JS=0.4meVandJ =0.2meV.
1 c S celed in the absence of magnetic field within the present
Due to the large magnetic moment M =6.9 µ [12],
Eu B meanfieldapproximation. Oncethemagneticfieldisap-
the spinS =7/2forEuionistreatedinaclassicallevel.
plied, the magnetic rare-earth ions would contribute an
Meanwhile the spin s = 1 for Fe ion is considered in a
effective molecular field on Fe spins. Our results show
quantum level. The interlayer coupling between Eu and
that when a magnetic field (H//a or H//c) is applied,
Fe ions JsS=0.4 meV [37]. For RFeAsO (R=Ce, Pr,Nd,
c the system undergoes a series of complicated magnetic
Sm, Gd and Tb) case, we choose JS=4 meV, JS=0.4
1 c phase transitions. As shown in Fig. 3(a) and (b), the
meV, J =0.2 meV and JsS=0.4 meV [37]. In compari-
S c magneticfielddependenceoftotalmagnetizationperfor-
son with RFe2As2 case, the spin for R=Ce, Pr, Nd, Sm, mula (Mtot and Mtot) globally displays similar behavior
Gd and Tb ions is also calculated with a classical value a c
for H//a and H//c. With the increase of the magnetic
S =1/2[36]duetoasmallmagneticmoment(e.g. about
field,Mtot andMtot firstundergoaliftsteeply,andthen
0.83 µ for CeFeAsO) for rear-earth ions in RFeAsO a c
B almost linearly increase to a saturated value.
compounds [37]. The clusters and magnetic exchange
couplings of RFe2As2 (R=Eu) and RFeAsO (R=Ce, Pr, However, the detail of Matot displays a lot of differ-
Nd, Sm, Gd and Tb) compounds are shown in Fig. 2. encefromthatofMctot. ThetotalmagnetizationMatot of
EuFe2As2 displaystwosharpphasetransitionsunderthe
parallel magnetic filed H//a: the first one corresponds
to the spin flop transition of Eu2+ spins and the sec-
ond one to that of Fe2+ spins, as seen in the two insets
of Fig. 3(a). The critical magnetic field of the spin-flop
transition for Eu2+ ions, Hc(Eu), is about 0.02J1a (∼9
T). In fact, due to the low critical magnetic field, the
spin-flop transition for Eu2+ ions is observed in the ex-
periments [20–22]. While for a perpendicular magnetic
field (H//c), no spin-flop transition is observed, only
a successive AFM-FM transition corresponds a canted
magnetism of rare-earth ions. When the magnetic field
becomes strong enough, the total magnetization ferro-
magnetically saturates in both cases.
FIG. 2. Schematic clusters of (a) RFe2As2 (R=Eu) and (b)
RFeAsO (R=Ce,Pr, Nd, Sm,Gd and Tb). All themagnetic The atom-resolved magnetization contributed from
exchange couplings are denoted. Eu2+ and Fe2+ ions are plotted for H//a and H//c in
Fig. 4. From Fig. 4(a), one can see that when applied
parallelmagneticfield(H//a)becomeslargerthanacrit-
ical field HR, the magnetization components M and
c a
M of Eu ions suffer a sharp change, corresponding to
b
a spin flop transition. With the further increase of H,
the magnetic Eu ions enter into a canted phase, until
RESULTS AND DISCUSSIONS
into a saturated FM phase. In contrast, for a perpen-
dicular magnetic field (H//c), once the magnetic field is
Utilizing the cluster-SCF method, we study the influ- applied,the systemgraduallytransitsto a cantedphase,
ence of magnetic field and the coupling between Fe and as seen in Fig. 4(b). One notices that at HR, there is no
c
rare-earthspinsonthe magneticgroundstatesandmag- influenceofFeionsontherare-earthionsduetothecan-
netic phase transition both in RFe2As2 (R=Eu) and in cellation of the AFM molecular fields within the present
RFeAsO (R=Ce, Pr, Nd, Sm, Gd and Tb) systems. In mean field approximation. As a comparison with rare-
the following, we address the detailed results for these earth 4f spins, the magnetic phase transitions of Fe-3d
two systems for comparison. magnetism are similar, but occurs at a relatively large
4
6 (a) 6 (b)
B) EuFe2As2 (H//a) B) EuFe2As2 (H//c)
Eu (M4 Eu (M4
2 Ma 2 Ma
Mb Mc
0 0
0.00 0.04 0.08 0.12 0.00 0.04 0.08 0.12
H/J1a H/J1a
2.0 2.0
1.6 (c) 1.6 (d)
Fe B()M 1.2 EuFe2As2 (H//a) Fe B()M1.2 EuFe2As2 (H//c)
0.8 0.8
Ma Ma
0.4 Mb 0.4 Mc
0.0 0.0
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
H/J1 a H/J1a
FIG. 4. Dependence of magnetization components, Ma and
Mb, of Eu2+ ions and of Fe2+ ions on magnetic field (a) and
(c) H//a and (b) and (d) H//c in EuFe2As2.
(7)Eu(FM-FM)-F-Fe(FM-FM),asseeninFig.5(a),from
which one observes that the spin-flop transitions of Eu
spins and Fe spins occur at the second and fifth stage,
respectively;andunderperpendicularfieldH//c,thesys-
temevolvesfrom(1)Eu(FM-AF)-AF-Fe(SAFM-AF),(2)
FIG.3. Totalmagnetizationdependenceonmagneticfield(a) Eu(FM-canted)-AF-Fe(canted-canted),(3)Eu(FM-FM)-
H//a and (b) H//c in EuFe2As2. The left and right insets AF-Fe(canted-canted), to (4) Eu(FM-FM)-F-Fe(FM-
in (a) present the spin-flop transition, and the inset in (b) FM), as seen in Fig. 5(b).
corresponds a successive AFM-FM transition.
magnetic field. From Fig. 4(c) with H//a, it is clearly
foundthatthecriticalparallelmagneticfieldofspin-flop
forFe2+ ion(Hc(Fe)) isabout0.288J1a (∼130T),which
is not observed experimentally due to its large H (Fe).
c
ThusFe-spinflopphenomenonmayonlybeobservedex-
perimentally in a strong pulsed magnetic field. In fact,
the effect of R ions on Fe ions is equivalent to an effec-
tive molecular field, about 0.11J1a at HcFe. This shows
that the 4f-magnetism could considerably affect the Fe-
3d magnetic properties under magnetic field.
To further uncover the influence of magnetic field on
FIG.5. Evolutionofmagneticstructureonthemagneticfield
the magnetic structures in EuFe2As2, we display the H//a(a)andH//c(b)inEuFe2As2. Theredandbluearrows
evolution of magnetic structure on the magnetic field representthespinsofEuandFe,respectively. Thelongarrow
H in Fig. 5, where we denote the magnetic config- indicates the increasing direction of magnetic field strength.
uration of each stage in such a form: R(intralayer-
interlayer coupling between R-R ions)-RFe(interlayer In simple systems, it is known that the critical mag-
couplingbetweenR-Feions)-Fe(intralayer-interlayercou- netic field of the spin-flop transition is proportional to
pling between Fe-Fe ions). With the increasing the single-ion anisotropy energy. In the present compli-
magnetic field, the system undergoes the follow- cated magnetic systems, however, due to the interlayer
ing configurations: under parallel field H//a, the coupling between Eu2+ and Fe2+ ions, the variation of
system evolves from (1) Eu(FM-AF)-AF-Fe(SAFM- the critical magnetic field is very complex, as seen in
AF), (2) Eu(spin-flop-FM-AF)-AF-Fe(SAFM-AF), (3) Fig.6. ItshowsthattheFMinterlayercouplingbetween
Eu(FM-canted)-AF-Fe(SAFM-AF), (4) Eu(FM-FM)- rare-earth and Fe ions (JsS <0) favors the occurrence
c
AF-Fe(SAFM-AF), (5) Eu(FM-FM)-AF-Fe(spin-flop- of the Fe-spin flop transition; however, the AFM inter-
SAFM-AF), (6) Eu(FM-FM)-AF-Fe(canted-canted), to layer coupling (JsS >0) is unfavorable of the transition.
c
5
Furthermore, the interlayer coupling between rare-earth
ions,JS,alsostronglyaffectsthespin-floptransition;for
c
the FM (AFM) interlayer coupling between rare-earth
and Fe ions, JS, i.e. the AFM coupling between mag-
c
netic rare-earthions, unfavors (favors)the occurrence of
the Fe spin-flop transition. In addition, the intralayer
coupling ofrare-earthions, JS, does notaffect this tran-
1
sition.
0.7
JscS= -1.0 meV
(a)
0.6 JscS= -0.6 meV
)
Fe0.5 EuFe2As2 JscS= -0.2 meV
(
1a
J/0.4
cH
0.3
JscS= 0 meV JscS= 0.6 meV
0.2
JscS= 0.2 meV JscS= 1.0 meV
0.1
0 2 4 6 8 10
S
Jc (meV)
FIG. 6. Critical magnetic field of the spin-flop transition
(Hc(Fe)) for Fe2+ ion depends on the interlayer coupling JcS
in EuFe2As2 with magnetic field H//a.
FIG.7. Dependenceoftotalmagnetization onmagneticfield
(a) H//a and (b) H//c of SmFeAsO.
RFeAsO case
wasobservedinastrongpulsedmagneticfieldinarecent
Actually, the magnetism of 4f electrons in RFeAsO experiment [23]. In contrast to Eu ions in 122 system,
(R=Ce, Pr, Nd, Sm Gd and Tb) is very different from the influence of the molecular field of Fe spins on Sm
that in RFe2As2. In order to investigate the magnetic spins is significant due to different magnetic polarized
interplay between 4f and 3d electrons, we also calcu- axis of Fe and Sm ions, which contributes to a weak ef-
late the magnetic properties of RFeAsO (R=Sm). For fective field about 0.0007J1a on Sm spins. Meanwhile,
RFeAsO (R=Sm), the calculated magnetic ground state
of the rare-earthlayer is Ne´el-AFM (NAFM) with inter- 1.0 1.0
layer AFM, and that of Fe layer is SAFM with an AFM (a) (b)
0.8 0.8
) )
interlayer Fe spins. In the present case, the spin direc- B SmFeAsO (H//a) B SmFeAsO (H//c)
tions of Sm2+ and Fe2+ ions align along the c axis and Sm (M00..46 Sm (M00..46
in the a-b plane, respectively. As a consequence, when Ma Ma
a magnetic field (H//a or H//c) is applied, the system 0.2 Mc 0.2 Mc
undergoes a complex magnetic phase transition and is 0.0 0.0
0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8
different from EuFe2As2. As shown in Fig. 7, the total H/ J1a H/ J1a
magnetization of SmFeAsO displays only one spin-flop FIG. 8. Dependence of sublattice magnetization
transitionundertheparallelmagneticfiled(H//a)inthe components(Ma and Mb) of Sm2+ ion on magnetic field (a)
FeAs layer. While for the perpendicular magnetic filed H//a and (b) H//c in SmFeAsO.
(H//c), the spin flop transition occurs in the rare earth
layers. This is very different from the EuFe2As2 shown we find that the critical magnetic field of spin-flop for
above. Fe2+ ions (Hc(Fe)) is relatively large, about 0.364J1a
The atom-resolved magnetizations of Sm2+ and Fe2+ (∼164T).Thiscriticalvalueisslightlylargerthanthatof
ions in SmFeAsO are also plotted in Fig. 8. From EuFe2As2. The reason is that the magnetic field should
Fig.8(b), itis obviouslyfoundthatthe criticalmagnetic firstlyovercometheintralayerAFMcouplingbetweenSm
fieldofspin-flopforSm2+ ions(Hc(Sm))isabout0.08J1a ions before the spin-flop transition occurs. And the ef-
(∼36 T), considerably larger than the critical value in fectivefieldcontributedfromSmionsonFeionsisabout
EuFe2As2. In fact, this spin-floptransitionof Sm2+ ions 0.035J1a.
6
The evolution of magnetic structure in SmFeAsO on
applied magnetic field H is displayed in Fig. 9. With (a) JscS= -1.0 meV JscS= -0.2 meV
the same definition to last section, one finds that with 0.5 JscS= -0.6 meV JscS= 0 meV
the increase of the magnetic field, the system under- ) SmFeAsO JscS= 0.2 meV
e
goes the following stages: under H//a case, the system F
(
undergoes from (1) R(NAFM-AF)-AF-Fe(SAFM-AF), 1a
J
/
(2) R(canted-canted)-AF-Fe(SAFM-AF), (3) R(canted- cH0.4
canted)-AF-Fe(spin-flop-SAFM-AF), (4) R(FM-FM)-
AF-Fe(canted-canted),to(5)R(FM-FM)-F-Fe(FM-FM); JscS= 0.6 meV
and under H//c case, the system undergoes from (1) JscS= 1.0 meV
R(NAFM-AF)-AF-Fe(SAFM-AF), (2) R(NAFM-AF)- 0.3
0 2 4 6 8 10
AF-Fe(canted-canted), (3) R(spin-flop-NAFM-AF)-AF-
S
Fe(canted-canted), (4) R(canted-canted)-AF-Fe(canted- Jc (meV)
0.6
canted), (5) R(FM-FM)-AF-Fe(canted-canted), to (6) (b) JscS= -1.0 meV
R(FM-FM)-F-Fe(FM-FM), obviously different from SmFeAsO JscS= -0.6 meV
these in EuFe2As2 compounds. e) 0.5 JscS= -0.2 meV
F
(
1aJ 0.4
/
cH
JscS= 0.2 meV
0.3
JscS= 0.6 meV
JscS= 0 meV JscS= 1.0 meV
0.2
0 2 4 6 8 10
S
J1 (meV)
FIG.10. Dependenceofthecriticalmagneticfieldofthespin-
floptransitionforFe2+ ionsontheinterlayercouplingJcS (a)
and JS (b) in SmFeAsO underH//a.
1
FIG.9. Evolutionofmagneticstructureonappliedmagnetic
field H//a (a) and H//c (b) in SmFeAsO. CeFeAsO is stronger than those in SmFeAsO, showing
thattheweakinterlayercouplinginSmFeAsOfavorsthe
InSmFeAsO,thedependence ofcriticalmagneticfield spin fluctuations in FeAs layers, hence more high super-
oftheFe-spinflop(H (Fe))ontheinterlayercouplingJsS conducting transition temperature. Also we expect that
c c
andJS underH//aisshowninFig.10(a),whichexhibits a small magnetic anisotropic energy of rare-earth spins,
c
similar tendency of EuFe2As2 case. The only difference JS,favorsthespinfluctuationsofFespins,thusenhances
isthatnoaneffectivemagneticfieldlikeFMofEuionsis the pairing force and Tc.
neededtoovercomeduetothe AFMconfigurationinthe
rare-earthlayers. IncontrasttothecaseofEuFe2As2,the
intralayercouplingofrare-earthionsJS alsosignificantly
1
affects the critical magnetic field value of the Fe spin-
flop transition, since additional magnetic field is needed CONCLUSIONS
to overcome the AFM coupling between R spins. In the
caseofCeFeAsO,alargepositivevalue,JsS∼3.79meV,
c
is found in the µSR experiment [37], implying a very In summary, we investigate the magnetic phase tran-
large coupling between Ce and Fe ions. sition behavior in both 1111 and 122 systems with 4f-
In the series of RFeAsO, the experiments found that electrons. Our results demonstrate that the interplay of
the Ne´el transition temperatures for R=Ce, Pr and Sm, 3dand4f spinsplaysakeyroleinthe magneticfieldde-
Gd and Tb layers as well as Fe layers, are TR=4.4, 11, pendence ofthese iron-basedsuperconductorswithmag-
N
4.66, 4.11 and 2.54 K, and TFe=137, 123, 138, 128 and netic rare-earth ions. The magnetic rare-earth layers,
N
122 K [37, 38], respectively. These indicate that the in- like magnetic intercalated layers, can tune the spin flop
tralayer magnetic exchange couplings are only slightly transition of the square Fe lattice in iron-based com-
different in these rare-earthcompounds. Meanwhile, the pounds. We expect that further experiments of strong
neutron scattering experiments find that the interlayer static or pulsed magnetic field could verify these field-
magnetic coupling between R and Fe spins (i.e. JsS) in induced magnetic phase transitions.
c
7
ACKNOWLEDGMENT Dai P. C 2008 Phys. Rev. B 78 132504
[17] Ren Z A, Yang J, Lu W, Yi W, Shen X L, Li Z C, Che
G C, Dong X L, Sun L L, Zhou F and Zhao Z X 2008
This work was supported by the National Sciences
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