Effects of magnetic field, strain, and size on the Morin temperature of spherical α-Fe2O3particles
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IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-18, NO. 6, NOVEMBER 1982 1583 Effects of Magnetic Field, Strain, and Size on the Morin Temperature of Spherical a-Fe2O3 Particles* George J. Muench, Sigurds Arajs, and Egon Matijevic? Clarkson College of Technology Potsdam, New York 13676 ABSTRACT New studies of the effects of the magnetic field, strain, and size on the Morin temperature, Tu, of spherical a-Fe203 particles of narrow size dlstribu- tion with the mean diameters varying between 30 to 320 nm have been made using a vibrating sample mag- netometer. Our particle data have been compared, using certain approximations, with the data from ear- lier single crystal studies. Possible role of defects on the observed magnetic behavior of small and/or strained a-FezO3 particles is emphasized. The magnetic structure of a-FezO3 is essentially that of a uniaxial antiferromagnet. In this case, the uniaxial anisotropy is the sum of a dipolar term favoring the (111) plane and a fine structure term favoring the [111] axis. [1]1 Since these two con- tributions have different signs and temperature de- pendences, an antiferromagnetic axis reorientation is expected at the temperature where the total aniso- tropy changes sign. This phase transition is called the Morin temperature TM, and in single crystals it occurs at about 260 K. exchange term D-MlxM2,where MI and M2 arc the sub- lattice magnetizations and 8 is the Dzialoshinsky- Moriya antisymmetric exchange vector, the sublattice magnetizations in the (111) plane are slightly canted. [2j This give rise to a weak ferromagnetic config- uration (WF). When the sublattice magnetizations are along the [ill] direction, the canting is absent, and the magnetic configuration is purely antiferromag- net ic (AF) . An important consequence of the Dzialoshinsky- Moriya term is the possibility of converting the low temperature AF configuration into the high iempera- ture WF phase by external magnetic fields, H either parallel or perpendicular to the [11&] axis. The necessary critical magnetic fields, H , depend on their orientation with respect to the'crystal lattice. When the external field is applied parallel or perpen- dicular to the 11111 direction, the corresponding ex- pressions for their critical vales are [2], respec- tively Because t$e+fr$e energy Eontainz an antisymmetric 0 In the above equations HE and HD are effective fields defined bv Jacobs eta1 [21, and H.., and H.,, are the two anisotropy fields. ~ .. KL hL Both the zero field transition, T,(H = 0) and the transitions caused by have been extegsively studied in single crystals but not in small particles. The latter case provides an interesting complication. It is well known that the quantity TM(H = 0) is decreased in submicron a-Fe203 particles. [3] This decrease is usually ascribed to the reduction of the dipolar part at the magnetic anisotropy due to the lattice dilation. The corresponding decrease in T (H = 0) qrovides an altered state which can be infyuenced by H. For this reason we have undertaken the present study. :.Clarkson College of Technology, Potsdam, New York 9:Supported by the Electric Power Research Institute, Contract RP. 966-3 The samples of a-Fep03 were prepared using tech- niques described elsewhere. [4,5] The particle sizes were determined by the methods of electron microscopy and x-ray line broadening. The mean particle diameters ranged from 30 to 320 nm with a standard deviation less than 20%. An impurity level of under 5% was estab- lished by x-ray diffraction. Magnetization measurements were made using a vi- brating sample magnetometer. The values of H ranged from 100 to 20,000 Oe. The temperature TM was obser- ved from the increase in the magnetization as the sample was warmed up through the transition region. Specifically, T was chosen to be the temperature at which the strai&t line through the magnetization data before the transition intersected the straight line through the steepest part of the transition. each size sample were fitted to a least squares straight line. Quadratic fitting was found to be un- necessary. The results are given in Table I. The TM data as a function of magnetic field for Table I Sample Diameter(nm) TM(H = O)(K) ATM/GH(K 0e-l) 10 30 196.1 1.03 x 14 73 215.3 1.19 x 13 74 208.8 1.28 x 11 93 221 .o 1.25 x 16 98 226.2 1.17 x 15* ** 248 6.33 x 9v 320 201.6 1.42 x 9v* 320 256.3 a .49 x "Sample was annealed at 5OO0C for 24 hours n*Sample shape was elipsoidal with axes of 410 nm and 240 nm Lattice strains were determined using X-ray dif- fraction methods by averaging the,deviations from the bulk sample data associated with the eight most in- tense reflections. The temperature, T, dependence of H is due to [2] the T dependences of the anisotropy gields $1 and HKZ. It is assumed that the T dependence of the ratio AT~/AH', where AT irs fhe change in TM due to the change in magnetic fiel8, AH, is also due to the variation of anisotropy withT. Therefore, the calculated ATM/AH is plotted (Fig. 1) against TM(H = 0). This fiBure shows that there is a fair correlation between AT-/AH and T (H = 0). Since the lowest T point is for tge smallest particles,it is tempting to postulate the existence of a size as well as .a T effect. However, for the Sample 9, the virgin and the annealed particles possess very different values of T (H = 0) which still follow the observed trend of other size particles. Since the annealing did not affect the particle size, it must be concluded that, likely, the size is not significant . showing in Flg 2. the dependence of AT /AH on the relative strain, Ga/a, where a is the yattice constant. M M Since Tu is often related to strain [3], we are 0018-9464/82/1100-1583$00.7501982 IEEE
Transcript of Effects of magnetic field, strain, and size on the Morin temperature of spherical α-Fe2O3particles
IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-18, NO. 6, NOVEMBER 1982 1583
Effects of Magnetic Field, Strain, and Size on the Morin Temperature of Spherical a-Fe2O3 Particles*
George J. Muench, Sigurds Arajs, and Egon Matijevic? Clarkson College of Technology
Potsdam, New York 13676
ABSTRACT
New studies of the effects of the magnetic field, strain, and size on the Morin temperature, Tu, of spherical a-Fe203 particles of narrow size dlstribu- tion with the mean diameters varying between 30 to 320 nm have been made using a vibrating sample mag- netometer. Our particle data have been compared, using certain approximations, with the data from ear- lier single crystal studies. Possible role of defects on the observed magnetic behavior of small and/or strained a-FezO3 particles is emphasized.
The magnetic structure of a-FezO3 is essentially that of a uniaxial antiferromagnet. In this case, the uniaxial anisotropy is the sum of a dipolar term favoring the (111) plane and a fine structure term favoring the [111] axis. [1]1 Since these two con- tributions have different signs and temperature de- pendences, an antiferromagnetic axis reorientation is expected at the temperature where the total aniso- tropy changes sign. This phase transition is called the Morin temperature TM, and in single crystals it occurs at about 260 K.
exchange term D-MlxM2, where MI and M2 arc the sub- lattice magnetizations and 8 is the Dzialoshinsky- Moriya antisymmetric exchange vector, the sublattice magnetizations in the (111) plane are slightly canted. [ 2 j This give rise to a weak ferromagnetic config- uration (WF). When the sublattice magnetizations are along the [ill] direction, the canting is absent, and the magnetic configuration is purely antiferromag- net ic (AF) .
An important consequence of the Dzialoshinsky- Moriya term is the possibility of converting the low temperature AF configuration into the high iempera- ture WF phase by external magnetic fields, H either parallel or perpendicular to the [11&] axis. The necessary critical magnetic fields, H , depend on their orientation with respect to the'crystal lattice. When the external field is applied parallel or perpen- dicular to the 11111 direction, the corresponding ex- pressions for their critical vales are [2], respec- tively
Because t$e+fr$e energy Eontainz an antisymmetric
0
In the above equations HE and HD are effective fields defined bv Jacobs et a1 [21, and H.., and H.,, are the two anisotropy fields.
~ .. KL hL
Both the zero field transition, T,(H = 0) and the transitions caused by have been extegsively studied in single crystals but not in small particles. The latter case provides an interesting complication. It is well known that the quantity TM(H = 0) is decreased in submicron a-Fe203 particles. [3] This decrease is usually ascribed to the reduction of the dipolar part at the magnetic anisotropy due to the lattice dilation. The corresponding decrease in T (H = 0) qrovides an altered state which can be infyuenced by H. For this reason we have undertaken the present study.
:.Clarkson College of Technology, Potsdam, New York 9:Supported by the Electric Power Research Institute, Contract RP. 966-3
The samples of a-Fep03 were prepared using tech- niques described elsewhere. [ 4 , 5 ] The particle sizes were determined by the methods of electron microscopy and x-ray line broadening. The mean particle diameters ranged from 30 to 320 nm with a standard deviation less than 20%. An impurity level of under 5% was estab- lished by x-ray diffraction.
Magnetization measurements were made using a vi- brating sample magnetometer. The values of H ranged from 100 to 20,000 Oe. The temperature TM was obser- ved from the increase in the magnetization as the sample was warmed up through the transition region. Specifically, T was chosen to be the temperature at which the strai&t line through the magnetization data before the transition intersected the straight line through the steepest part of the transition.
each size sample were fitted to a least squares straight line. Quadratic fitting was found to be un- necessary. The results are given in Table I.
The TM data as a function of magnetic field for
Table I
Sample Diameter(nm) TM(H = O ) ( K ) ATM/GH(K 0e-l)
10 30 196.1 1.03 x
14 73 215.3 1.19 x 13 74 208.8 1.28 x
11 93 221 .o 1.25 x
16 98 226.2 1.17 x 15* ** 248 6.33 x
9v 320 201.6 1.42 x
9v* 320 256.3 a .49 x "Sample was annealed at 5OO0C for 24 hours n*Sample shape was elipsoidal with axes of 410 nm and 240 nm
Lattice strains were determined using X-ray dif- fraction methods by averaging the,deviations from the bulk sample data associated with the eight most in- tense reflections.
The temperature, T, dependence of H is due to [2] the T dependences of the anisotropy gields $1 and HKZ. It is assumed that the T dependence of the ratio AT~/AH', where AT irs fhe change in TM due to the change in magnetic fiel8, AH, is also due to the variation of anisotropy with T. Therefore, the calculated ATM/AH is plotted (Fig. 1) against TM(H = 0) . This fiBure shows that there is a fair correlation between AT-/AH and T (H = 0). Since the lowest T point is for tge smallest particles,it is tempting to postulate the existence of a size as well as .a T effect. However, for the Sample 9, the virgin and the annealed particles possess very different values of T (H = 0) which still follow the observed trend of other size particles. Since the annealing did not affect the particle size, it must be concluded that, likely, the size is not significant . showing in Flg 2. the dependence of AT /AH on the relative strain, Ga/a, where a is the yattice constant.
M
M
Since Tu is often related to strain [ 3 ] , we are
0018-9464/82/1100-1583$00.7501982 IEEE
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Fig. 1. AT /AH v s T (H = 0) f o r d i f f e r e n t s i z e a-Pe2O3 p a r t l c l e s . M . P o i n t s (x) have been ca l cu la t ed from p l o t s i n Ref. 2 . Curve (---I i s the approximated curve through the cal- c u l a t e d p o i n t s .
F igu re 2 add i t iona l ly con f i rms t ha t AT /AH i s no t s i g n i f i c a n t l y a f f e c t e d by t h e p a r t i c l e ' s l z e . Y .
s i n g l e c r y s t a l s is d i f f i c u l t . The major complication i s t h a t H depends on o r i e n t a t i o n . But a l l o r i e n t a - t i ons a r e ' poss ib l e i n a powdered sample. Therefore, a n " e f f e c t i v e " c r i t i c a l f i e l d , H e f f , must be de- termined by a v e r a g i n g o v e r a l l o r l e n t a t i o n s . Un- f o r t u n a t e l y , t h i s i s q u i t e d i f f i c u l t t o do.
the average of Hcl and HcL.. This i s e q u i v a r e n t f f is t o assuming that I, v a r i e s l l n e a r l y w i t h t h e a n g l e between 8 and t h e €1111 axis . Fur thermore , it a l s o then must be assumed that H changes with T a s t h e average of T dependences ofCH and Hcl.
of the angle between 8 and t h e [ill] a&. This dependence i s s igmoida l wi th a f a i r l y f l a t s e c t i o n near 45". Therefore , ATM/AH was determined from the average of AT /H and @i/HcA. The l a t t e r q u a n t i t i e s were t%ce$"from t h e p l o t s ( F i g u r e s 4 and 5) i n J a c o b s e t a l . [Z] The c a l c u l a t e d p o i n t s ( c r o s s e s ) are shown i n F i g . 1.
t u r e (T > 220 K) p a r t i c l e p o i n t s a r e i n r e a s o n a b l e ag reemen t w i th t he ave raged s ing le c rys t a l da t a . However, for lower va lues of T , t he re a r e cons ide rab le d e v i a t i o n s f r o m t h e s i n g l e c r y s t a l b e h a v i o r . Thus, i t appea r s t ha t w e a r e obse rv ing a change i n t h e H dependence of T when TH is depressed. However, t h i s depression by i v s e l f is a complicated process; L a t -
Comparison of p a r t i c l e r e s u l t s w i t h t h o s e on
A naive approximation is t o assume t h a t H
Morrison e t all [6] have c a f h a t e d H a s a func t ion
It can be seen from Fig. 1 tha t the h igh tempera-
t i c e d i l a t i o n w i t h d e c r e a s i n g s i z e h a s b e e n o f t e n observed. Artman [l] has ca l cu la t ed t ha t such a d i l a t ion shou ld r educe t he d ipo la r an i so t ropy and thus lower T (H = 0 ) . However, a c c o r d i n g ' t o t h e ca l cu la t ion ,Mthe above dep res s ion does no t a f f ec t t he H dependence.
-- t
10 e
.+ '
i- 15
Fig. 2. ATM/AH v s Aa/a f o r d i f f e r e n t s i z e a-Fe2O3 p a r t i c l e s . Curve (---) is t h e b e s t s t r a i g h t l ine through the measured points .
Our sugges t ion for the observed d ivergence in F ig . 2 i s t h e l i k e l y " d e f e c t i v e " n a t u r e of our samples. It i s well known t h a t s m a l l p a r t i c l e s o f a-Fe203 have higher total magent ic anisotropy than the bu lk ma te r i a l . Th i s i nc reased an i so t ropy is u s u a l l y a s c r i b e d t o l a t t i c e i m p e r f e c t i o n s i n t h e p a r t i c l e a n d / o r a t i t s s u r f a c e . In a d d i t i o n , d e f e c t s o f t e n c o n t r i b u t e [ 7 ] t o a "defect magnetic moment" below T . L a s t l y , l a t t i c e d e f e c t s a l s o h a v e b e e n observeg [8] to lower TM. Therefore , i t can be ex- pec ted tha t the s imple magnet ic an iso t ropy descr ibed by Artman [l] i s augmented by d e f e c t a n i s o t r o p i e s w h i c h a r e p a r t i c u l a r l y s i g n i f i c a n t i n s m a l l a n d / o r h igh ly s t r a ined s amples .
REFERENCES
[l] J . O . Artman, J . C . Murphy, and S . Foner, "Magnetic Aniso t roov in Ant i fe r romagnet ic Corundum-Type A I - Sesquioxides", Phys. Rev., V o l . 138, PP. b.912- A917, May 1965.
.~
[2 ] I . S . Jacobs, R .A. Beyerlein, S . Foner, and J . P . Remeika, "Field Induced Magnetic Phase Transi- t ions in Ant i fe r romagnet ic Hemat i te (a -Fe20g) ," I n t . J . Magnetism, Vol.1 pp. 193-208, 1971.
[31 Robert C . Mininger, J r . and Dietr ich Schroeer , ~~
"Massbauer S tud ie s of t h e Morin T r a n s i t i o n i n Bulk and Microcrystalline a-Fe203," J . Phys. Chem. S o l i d s , Vol. 39, pp. 137-144, 1978.
[4] E . Ma t i j ev i6 and P. Scheiner, "Ferric Hydrous Oxide S o l s 111. Prepa ra t ion of Uniform P a r t i - c l e s by Hydrolysis of Fe ( I I1 ) - Chloride, - N i t r a t e , a n d - Perch lo ra t e So lu t ions , " J. Coll. I n t e r f a c e S c i . , Vol. 63(3) pp. 509-524, March 1978.
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[5] George J . Muench, S . Arajs, and E. MatijeviE, "Magnetic Properties of Monodispersed Submicronic a-Fe2Og P a r t i c l e s , " J. Appl. Physics, Vol. 52(3) PP. 2493-2495. March 1981. ..
[6] B.R. Morrison, A.H. Morrish, and G . J . Troup, "High-Field Antiferromagnetic Resonance i n a-Fe2O3," Phys. Stat . Sol . (b), Vol. 56(1) pp. 183-195, 1973.
[7] D,J. Dunlop; "Magnetic Properties of F ine-Par t i - cle Hematite," Ann. dc. CeSophysique, Vol. 27(3) pp. 269-293, 1971.
[8] V.A. P o v i t s k i i , A.N. Salugin, and E.E. Makarov, "Defec t ive S t ruc ture of Hematite and Morin Transi- t i o n , " Sov. .Phys. S o l i d S t a t e , Vol. 17(12) pp. 2372-2374, Dec. 1975.
