- Email: [email protected]
Two-dimensional spin ordering in YFe2O4
Solid State Communications, Vol. 32, pp. 1065—1068. Pergainon Press Ltd. 1979. Printed in Great Britain. TWO-DIMENSIONAL SPIN ORDERING IN YFe2 04 J.AkimitsuandY.Inada Department of Physics, Aoyama Gakwn University, Setagaya, Tokyo, Japan K. Siratori Department of Physics, Osaka University, Toyonaka, Osaka, Japan and I. Shindo and N. Kimizuka National Institute for Researches in Inorganic Materials, Sakura, Ibaragi, Japan (Received 31 May 1979 by 1. Kanamori) Aneutron diffraction study was performed on a single crystal of a new compound YFe2 04 below its Née! point. In a slightly oxygen deficient crystal, the elastic magnetic scattering takes the form of Bragg line along the c axis at (n13, nf3,!) (n * 3m) in the hexagonal lattice. This fact indicates the two-dimensional long range order of a commensurate sinusoidal spin structure.
SINCE Onsager’s famous theoretical paper [11 twodimensional Ising systems have occupied a unique I I I position in spin statistics. It is the only system for which an exact theory for the phase transition is available. In recent years, considerable experimental data on twodimensional spin systems have become available, II ii especiallyon compounds with the K2NiF4 structure i i , i [2]. This compound, however, eventually undergoes A I I i a phase transition to three-dimensional long range order Layer—. at the critical point. Recently, Ikeda et aL [3] observed F magnetic Bragg lines in a mixed system Rb2Co0.7Mg0~3 C -.. e F4 when the specimen was cooled rapidly through the Née! point. They argued that thermal inhomogeneity at TN was essential to form the two-dimensional long range order. In this note, we report the observation of completely two-dimensional magnetic long range order in B —. Fe an Ising system YFe2 04, a new compound synthesized -. . Fe by Kimizuka and Katsura [4]. The crystal has a hexagonal layered structure, a = 6.090 A, c = 24.788 Aat room temperature, [5]. equal amounts of 2~and Fe3~ions R~m exist in theThough stoichiometric compound, A e Fe is only one crystallographic site for Fe atoms there surroundedbyfiveo2ions.AsisshowninFig. 1,these B -. Fe Fe sites form triangular nets in planes perpendicular to the c-axis and two adjacent layers form a honeycomb A V lattice. These honeycomb nets are separated by a triangular net of Y3~ions octahedrally coordinated by Fig. 1. Crystal structure of YFe 2 04 in the hexagonal 3~ions and anions. The lattice of spins is similar to that of ilmenite unit ccli. Solid circles represent Fe~or Fe and two-dimensional spin correlation is expected [6]. the open circles represent y3~~ Oxygens are omitted mthe figure. Recently, Sugihara et aL [7] mvestigated the ,
~
___________
___________
-~
__________-,
-~
c
(>
v
_____
___________
_________
-,
—,
____
1065
TWO-DIMENSIONAL SPIN ORDERING IN YFe2O4
1066
Vol. 32, No. 11
xlO&
9 8 —
C
7
E 6
AL(200)
5 (~0)
~
(110)
!1~JhA~J~J —.29()
Fig. 2. Neutron diffraction along [Ii,h, 0] at 77K.
(010>
(010)
1
(100)
(100>
Fig. 3. (h, k, 0) reciprocal net of YFe2O4. Open and solid circles indicate the nuclear and magnetic peaks, respectively. The thick lines show regions which were explored for additional intensity peaks. magnetic properties of thiscompound and demonstrated very strong magnetic anisotropy, the easy axis being the c-axis. At the same time, they reported the appearance of a small ferromagnetic moment parallel to the spin axis which they labeled parasitic ferrimagnetism. The moment depends on the external magnetic field applied during cooling. They pointed out the possibility that this small moment2~ could ariseions fromonthe and Fe3~ thepreferential two antioccupation of Fe ferromagnetic sublattices. The present study was started to elucidate the magnetic structure and to find the
charge ordering, if any, which may be induced by the external field. Instead of an ordinary antiferromagnetism, we found a two-dimensional commensurate sinusoidal spin structure within the (001) planes. Single crystals were grown by the floating zone melting method under controlled oxygen partial pressure. Details were reported already [8]. X-ray and neutron diffraction patterns room temperature were those corresponding to theatLnFe 2 04 structure [9] and no other diffraction peaks were observed. The crystal used in the neutron scattering experiment was approximately
Vol. 32, No. 11
TWO-DIMENSIONAL SPIN ORDERING IN YFe2O4
1067
11
xlO C L~)
___ If)
I—..
•~
0 0
3
•
•
0
•~•
•0~ 0
•
0 •0
0
0
•
0
sO
0
0
0
•o••a • •
0
0
••
0 0
Z
0 •0
0 005
S
•
•
00
•0
0
000.
•
0
•
• •
0
0 02 1
BACKGROUND
0o
____
Fig. 4. (1/3, 1/3, 1) reflection scanned alongthe c-axis at 77K. The line profile shows no fine structure except the slow decrease due to the magnetic form factor. 7 x 4 x 1.5 nun in size and had a mosaic spread (full width at half maximum) of 0.4°.Measurements of elastic scattering of neutrons were performed by a double axis spectrometer at the JRR-3 reactor of JAERI, Tokal, operated at the neutron wavelength of 1.24 A. The Ge (311) reflection was used to eliminate higher order contamination. 20’ collimators were employed before and after the specimen, Measurements were carried out mainly at 77K. Figure 2 shows the appearance of magnetic Bragg peaks at (1/3, 1/3, 0) and (2/3, 2/3, 0) when measured along the [1, 1,0] line. No other peaks were observed in the (1*, k, 0) net although a careful search was made along directions in reciprocal space shown by the solid lines in Fig. 3. The temperature dependence of the intensity of the (1/3, 1/3, 0) reflection indicated TN to be about 210 K. Measurements in (h, h, 1) reciprocal plane showed that the magnetic reflections at (n/3, n/3, 0) (n * 3m) spread parallel to the c-axis. The line profile of (1/3, 1/3,1) along the c-axis is shown in Fig. 4. There is no fine structureexcept the slow decrease due to the magnetic form factor. When the measurement was made across the line, the width of the magnetic scattering was the same as that of the nuclear reflections as shown in Fig. 5. The continuous magnetic scattering spikes observed in this specimen of YFe2O4 are, thus, due to spin ordering in two dimensions, i.e. in planes perpendicular to the c-axis. No magnetic scattering other than (n/3, n/3, I) was observed by the scanning in
(h, h, 1) and (h, 0, 1) reciprocal planes. Furthermore, the ferromagnetic component of the magnetic scattering superposed on the nuclear intensity was not detected down to 4.2 K within our experimental accuracy. Strong anisotropy of spins being considered, such a diffraction pattern suggests that the spin structure in the (001) plane of YFe2 04 is commensurate sinusoidal with wave vector [1/3, 1/3, 01 and there is no spin correlation along the c-axis. Such a commensurate sinusoidal spin structure was reported in CsCoCl3 [10] and CsCoBr3 [11] with the triangular lattice, though antiferromagnetic interaction along the c-axis is the strongest in these materials and the ordering is three-dimensional. At low temperatures,a purely sinusoidal spin structure cannot be the ground state and ferrimagnetism within the (001) plane is expected. This ferrimagnetism was observed in the CsCoC13 family of compounds. In the present case, however, we could not find any evidence of fernmagnetism in the neutron diffraction study at 4.2 K. In the two-dimensional phase transition, the correlation length becomes infinite at the transition point in a layer of a perfect lattice. Since the interlayer coupling might not be considered as absolutely zero, the interaction between layers will exceed the thermal fluctuation at T~.Thus, the two-dimensional long range order without correlation perpendicularto the layer cannot be expected in a perfect three dimensional lattice. In the present case, inhomogeneities due to the non-stoichiometry seems to be responsible. As grown
TWO-DIMENSiONAL SPIN ORDERING IN YFe3O4
1068
xid
0
Vol. 32, No.11
(h,h,1.5~)
0~3
0.35
0.4
Fig. 5. Scan across the Bragg line (1/3, 1/3,!) at 1= 1.5. The instrumental resolution is shown by the horizontal bar.
single crystals of YFe2O4 are known to be slightly oxygen deficient. The crystal used in the present study as well as that used by Sugihara et aL [7] was not stoichlometnc. Studies on the effect ofthe stoicluometry are now in progress.
R. J. Birgeneau,PlrysicaB((Jtr.)86—88, 639 (1977).
~ ~: ~ 4.
5. Acknowledgements The authors would like to thank Prof. Y. Nakagawa and Dr. N. Tsuda and Dr. S. Kimura for stimulating discussions on various aspects of this work Critical reading of the manuscript by Prof Steinfink Is aisoapproclated. Two of the authors (J.A. and Y.I.) acknowledge Prof. N. Kitamura for encouragement and helpful comments throughout this experiment. —
REFERENCES 1. 2.
L. Onsager,Pliys. Rev. 65, 117 (1944). L.J. de Jongh & A.R. Mledema,Adv. Phys. 23, 1 (1974); For more recent work, see G. Shirane &
6. 7
N. Klmizuka & T. Katsura, J SolidState Chem. 15, 151 (1975). N. Kato, I. Kawada, N. Kimizuka & T. ICatsura, Z Krist. 141,314(1975). J. Akimitsu& Y. Ishlkawa,J, Phys. Soc. Japan
42,462(1977).
T Sugihara, K Siratori, I Shindo & T Katsura,
J. Phys. Soc. Japan 45, 1191(1978). 8. I. Shindo, N. ICimizuka & S. Kimura, Mit. Res. Bull. 11,637 (1976). 9. N. Kixnizuka, Y. Takenaka, Y. Sasada & T. Katsura,Solid State Commun. 15, 1321(1974). 10. M. Mekata&IC. Adachl,J. Fhy& Soc. Japan 44, 806 (1978). 11. W.B. Yelon, D.E. Cox & M. Eibschutz, Phys. Rev. B12, 5007(1975).
SINCE Onsager’s famous theoretical paper [11 twodimensional Ising systems have occupied a unique I I I position in spin statistics. It is the only system for which an exact theory for the phase transition is available. In recent years, considerable experimental data on twodimensional spin systems have become available, II ii especiallyon compounds with the K2NiF4 structure i i , i [2]. This compound, however, eventually undergoes A I I i a phase transition to three-dimensional long range order Layer—. at the critical point. Recently, Ikeda et aL [3] observed F magnetic Bragg lines in a mixed system Rb2Co0.7Mg0~3 C -.. e F4 when the specimen was cooled rapidly through the Née! point. They argued that thermal inhomogeneity at TN was essential to form the two-dimensional long range order. In this note, we report the observation of completely two-dimensional magnetic long range order in B —. Fe an Ising system YFe2 04, a new compound synthesized -. . Fe by Kimizuka and Katsura [4]. The crystal has a hexagonal layered structure, a = 6.090 A, c = 24.788 Aat room temperature, [5]. equal amounts of 2~and Fe3~ions R~m exist in theThough stoichiometric compound, A e Fe is only one crystallographic site for Fe atoms there surroundedbyfiveo2ions.AsisshowninFig. 1,these B -. Fe Fe sites form triangular nets in planes perpendicular to the c-axis and two adjacent layers form a honeycomb A V lattice. These honeycomb nets are separated by a triangular net of Y3~ions octahedrally coordinated by Fig. 1. Crystal structure of YFe 2 04 in the hexagonal 3~ions and anions. The lattice of spins is similar to that of ilmenite unit ccli. Solid circles represent Fe~or Fe and two-dimensional spin correlation is expected [6]. the open circles represent y3~~ Oxygens are omitted mthe figure. Recently, Sugihara et aL [7] mvestigated the ,
~
___________
___________
-~
__________-,
-~
c
(>
v
_____
___________
_________
-,
—,
____
1065
TWO-DIMENSIONAL SPIN ORDERING IN YFe2O4
1066
Vol. 32, No. 11
xlO&
9 8 —
C
7
E 6
AL(200)
5 (~0)
~
(110)
!1~JhA~J~J —.29()
Fig. 2. Neutron diffraction along [Ii,h, 0] at 77K.
(010>
(010)
1
(100)
(100>
Fig. 3. (h, k, 0) reciprocal net of YFe2O4. Open and solid circles indicate the nuclear and magnetic peaks, respectively. The thick lines show regions which were explored for additional intensity peaks. magnetic properties of thiscompound and demonstrated very strong magnetic anisotropy, the easy axis being the c-axis. At the same time, they reported the appearance of a small ferromagnetic moment parallel to the spin axis which they labeled parasitic ferrimagnetism. The moment depends on the external magnetic field applied during cooling. They pointed out the possibility that this small moment2~ could ariseions fromonthe and Fe3~ thepreferential two antioccupation of Fe ferromagnetic sublattices. The present study was started to elucidate the magnetic structure and to find the
charge ordering, if any, which may be induced by the external field. Instead of an ordinary antiferromagnetism, we found a two-dimensional commensurate sinusoidal spin structure within the (001) planes. Single crystals were grown by the floating zone melting method under controlled oxygen partial pressure. Details were reported already [8]. X-ray and neutron diffraction patterns room temperature were those corresponding to theatLnFe 2 04 structure [9] and no other diffraction peaks were observed. The crystal used in the neutron scattering experiment was approximately
Vol. 32, No. 11
TWO-DIMENSIONAL SPIN ORDERING IN YFe2O4
1067
11
xlO C L~)
___ If)
I—..
•~
0 0
3
•
•
0
•~•
•0~ 0
•
0 •0
0
0
•
0
sO
0
0
0
•o••a • •
0
0
••
0 0
Z
0 •0
0 005
S
•
•
00
•0
0
000.
•
0
•
• •
0
0 02 1
BACKGROUND
0o
____
Fig. 4. (1/3, 1/3, 1) reflection scanned alongthe c-axis at 77K. The line profile shows no fine structure except the slow decrease due to the magnetic form factor. 7 x 4 x 1.5 nun in size and had a mosaic spread (full width at half maximum) of 0.4°.Measurements of elastic scattering of neutrons were performed by a double axis spectrometer at the JRR-3 reactor of JAERI, Tokal, operated at the neutron wavelength of 1.24 A. The Ge (311) reflection was used to eliminate higher order contamination. 20’ collimators were employed before and after the specimen, Measurements were carried out mainly at 77K. Figure 2 shows the appearance of magnetic Bragg peaks at (1/3, 1/3, 0) and (2/3, 2/3, 0) when measured along the [1, 1,0] line. No other peaks were observed in the (1*, k, 0) net although a careful search was made along directions in reciprocal space shown by the solid lines in Fig. 3. The temperature dependence of the intensity of the (1/3, 1/3, 0) reflection indicated TN to be about 210 K. Measurements in (h, h, 1) reciprocal plane showed that the magnetic reflections at (n/3, n/3, 0) (n * 3m) spread parallel to the c-axis. The line profile of (1/3, 1/3,1) along the c-axis is shown in Fig. 4. There is no fine structureexcept the slow decrease due to the magnetic form factor. When the measurement was made across the line, the width of the magnetic scattering was the same as that of the nuclear reflections as shown in Fig. 5. The continuous magnetic scattering spikes observed in this specimen of YFe2O4 are, thus, due to spin ordering in two dimensions, i.e. in planes perpendicular to the c-axis. No magnetic scattering other than (n/3, n/3, I) was observed by the scanning in
(h, h, 1) and (h, 0, 1) reciprocal planes. Furthermore, the ferromagnetic component of the magnetic scattering superposed on the nuclear intensity was not detected down to 4.2 K within our experimental accuracy. Strong anisotropy of spins being considered, such a diffraction pattern suggests that the spin structure in the (001) plane of YFe2 04 is commensurate sinusoidal with wave vector [1/3, 1/3, 01 and there is no spin correlation along the c-axis. Such a commensurate sinusoidal spin structure was reported in CsCoCl3 [10] and CsCoBr3 [11] with the triangular lattice, though antiferromagnetic interaction along the c-axis is the strongest in these materials and the ordering is three-dimensional. At low temperatures,a purely sinusoidal spin structure cannot be the ground state and ferrimagnetism within the (001) plane is expected. This ferrimagnetism was observed in the CsCoC13 family of compounds. In the present case, however, we could not find any evidence of fernmagnetism in the neutron diffraction study at 4.2 K. In the two-dimensional phase transition, the correlation length becomes infinite at the transition point in a layer of a perfect lattice. Since the interlayer coupling might not be considered as absolutely zero, the interaction between layers will exceed the thermal fluctuation at T~.Thus, the two-dimensional long range order without correlation perpendicularto the layer cannot be expected in a perfect three dimensional lattice. In the present case, inhomogeneities due to the non-stoichiometry seems to be responsible. As grown
TWO-DIMENSiONAL SPIN ORDERING IN YFe3O4
1068
xid
0
Vol. 32, No.11
(h,h,1.5~)
0~3
0.35
0.4
Fig. 5. Scan across the Bragg line (1/3, 1/3,!) at 1= 1.5. The instrumental resolution is shown by the horizontal bar.
single crystals of YFe2O4 are known to be slightly oxygen deficient. The crystal used in the present study as well as that used by Sugihara et aL [7] was not stoichlometnc. Studies on the effect ofthe stoicluometry are now in progress.
R. J. Birgeneau,PlrysicaB((Jtr.)86—88, 639 (1977).
~ ~: ~ 4.
5. Acknowledgements The authors would like to thank Prof. Y. Nakagawa and Dr. N. Tsuda and Dr. S. Kimura for stimulating discussions on various aspects of this work Critical reading of the manuscript by Prof Steinfink Is aisoapproclated. Two of the authors (J.A. and Y.I.) acknowledge Prof. N. Kitamura for encouragement and helpful comments throughout this experiment. —
REFERENCES 1. 2.
L. Onsager,Pliys. Rev. 65, 117 (1944). L.J. de Jongh & A.R. Mledema,Adv. Phys. 23, 1 (1974); For more recent work, see G. Shirane &
6. 7
N. Klmizuka & T. Katsura, J SolidState Chem. 15, 151 (1975). N. Kato, I. Kawada, N. Kimizuka & T. ICatsura, Z Krist. 141,314(1975). J. Akimitsu& Y. Ishlkawa,J, Phys. Soc. Japan
42,462(1977).
T Sugihara, K Siratori, I Shindo & T Katsura,
J. Phys. Soc. Japan 45, 1191(1978). 8. I. Shindo, N. ICimizuka & S. Kimura, Mit. Res. Bull. 11,637 (1976). 9. N. Kixnizuka, Y. Takenaka, Y. Sasada & T. Katsura,Solid State Commun. 15, 1321(1974). 10. M. Mekata&IC. Adachl,J. Fhy& Soc. Japan 44, 806 (1978). 11. W.B. Yelon, D.E. Cox & M. Eibschutz, Phys. Rev. B12, 5007(1975).