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Electron paramagnetic resonance of superparamagnetic NiO particles
Volume 53A, number 4
PHYSICS LETTERS
ELECTRON PARAMAGNETIC OF SUPERPARAMAGNETIC
30 June 1975
RESONANCE
NiO PARTICLES
J.N. HERAK and B. RAKVIN Institute "Ruder Bo~kovid", Zagreb, Croatia, Yugoslavia
Received 16 April 1975 EPR signals are observed in small NiO particles prepared in vacuo and in air. The imaginary part of the susceptibility exhibits a typical superparamagnetic behaviour. A transformation into a paramagnetic system is associated with the diffusion of nickel ions to anionic vacancies. The phenomenon of superparamagnetism of antiferromagnetic NiO particles is known from the experimental work of Richardson and Milligan [1 ] and the theoretical work of N6el [2]. According to N6el, the origin of the unusual magnetic behaviour of small antiferromagnetic particles comes from a small permanent magnetic moment resulting from an imperfect compensation of magnetic sublattices, predominantly on the surface. If the particles possessing a permanent moment are sufficiently small, the thermal energy at the temperature of the experiment may be sufficient to equilibrate the system in a time shorter than or comparable to that of the experiment. The phenomenon is very similar in nature to the superparamagnetism of fine ferromagnetic particles. It is interesting that there have been few or no electron paramagnetic resonance studies of pure NiO [ 3 - 5 ] . The reason probably lies in the difficulties in observing EPR signals. In the present paper we show that for very small NiO particles, EPR signals are readily observed. The intensity of the signals, proportional to the imaginary part of the susceptibility, K", depends on temperature in a similar way as does the real part, K', observed by the conventional methods. Nickelous oxide samples were prepared by a heat treatment of nickel hydroxide in vacuo or in air, at temperatures ranging from 200 ° to 600°C [6]. In such a way small NiO particles were obtained, being smaller when prepared at lower temperatures. The samples prepared in air at temperatures below 600°C or in vacuo at temperatures below 250°C gave EPR signals, the signals being stronger for smaller particles. Some typical spectra for a specimen prepared at 200°C in vacuo are shown in fig. 1. The shape and intensity
"~o = (3 350 MHz
I
/ I000
I 2000
# 3000 MAGNETIC
I ~000 FIELD
I 5000 (GAUSS)
I
Fig. 1. EPR spectra of NiO prepared at 200° V in vacuo. The spectra are recorded at 25°C (a), 120°C (b) and at 120° after short heating at 220°C. of the resonance patterns are dependent on the temperature of observation. The changes are reversible in a certain temperature range (spectra a and b). Upon a heating in vacuo at about 220°C, the spectrum first irreversibly changed into a narrower and symmetric one (fig. lc) and after that the sample became too ferromagnetic for any further EPR study. The relative intensity of the original signals (spectra a and b) as a function of temperature is show in fig. 2. In contrast to this behaviour, the intensity of the signals after the irreversible change (spectrum c) behaves in a typical paramagnetic manner (proportionality with
1/73. 307
Volume 53A, number 4
PHYSICS LETTERS
and K1 is the susceptibility based on the rotation of single domain particles [9]:
o _z
K1 = M 2 a N / 2 K V .
(5)
M s is the magnetization of a single particle and N is the number of particles in a unit volume, a = (sin 2 0), where 0 is the angle between the applied filed and the easy direction of magnetization. We may used a = 2/3. The Fourier transform of eq. (2) gives a complex susceptibility
5 i
,;o
,;o
2;0 2;o 36o 3;o ,;o
K* = (r 0 + iwrK1)/(1 + icor),
T EMPERA?URE (°K)
Fig. 2. Temperature dependence of the relative intensity of EPR spectra in the superparamagnetic range. The circles represent the experimental points and the solid curve the best fit of the theoretical K"(T) curve. The change of the line shape in the superparamagnetic region (spectra a and b) is brought about by the temperature-dependent effective magnetic field. We actually observe the ferrimagnetic resonance of the randomly oriented particles. The resonance condition in the microwave region is [7]: co(T) = 7eff (n0 + H A ( T ) ) .
(1)
H 0 is the external magnetic field and HA(T ) the temperature-dependent anisotropy field. The intensity variation (fig. 2) is brought about by the relaxation of the ferrimagnetic particles. In calculating the temperature dependence of K", we may adopt a procedure analogous to that of Gittleman, Abeles and Bozowski [8], originally used for small ferromagnetic particles. For simplicity, we assume that all the particles are identical. The total magnetization per unit volume of the sample is M ( t ) = H 0 [K0 - (K0 - K1) e x p ( - t / r ) ]
,
(2)
where r is the relaxation time associated with the anisotropy barrier, E B = K V (V is the particle volume and K the magnetic anisotropy energy): r = r 0 exp (lzB/k T).
(3)
TO is a constant of the order of 1010 sec. K 0 is the superparamagnetic susceptibility corresponding to thermal equilibrium: K0 = M 2 N / 3 k T ,
308
30 June 1975
(4)
(6)
whose imaginary part is K" = KlcoT(•O/K 1 -- 1)/(1 + CO2r2)
.
(7)
For our experimental conditions co2r 2 >> 1, leading to K"(co, T) ~ e - z (z - 1),
(8)
where z = K V/k T. For temperatures sufficiently below the N~el temperature, K is practically independent of temperature. Function (8) has a maximum at T m = E B / 2 k . From the experimental points in fig. 2 we obtain E B = 7 X 10-14erg/particle, which is essentially the same as calculated by N6el [2]. Function (8) does not fit well to the experimental points at higher temperatures in fig. 2, i f K is assumed constanL If we use the data for K (T) from other experimental measurements [10], the fit is quite satisfactory (fig. 2). The irreversible transition of the ferrimagnetic system into a paramagnetic one at 220°C (fig. Ic) is believed to be brought about by the diffusion of the uncompensated nickel ions from the surface to the anionic vacancies [ 11 ]. Upon a stronger heat treatment, metallic nickel is precipitated and the specimen becomes ferromagnetic. The samples prepared in air have an access of oxygen [6] and such a precipitation does not take place.
References
[ 1 ] J.T. Richarson and W.O. Milligan, Phys. Rev. 102 (1956) 1289. 121 L. N~el, in Low temperature physics, ed. C. DeWitt, B. Dreyfus and P.G. DeGennes (Gordon and Beach, 1962) p. 411.
Volume 53A, number 4
PHYSICS LETTERS
[31 L.R. Maxwell and T.R. McGuire, Rev. Mod. Phys. 25 (1953) 279. [4] P.F. Cornaz, J.H.C. Van Hooff, F.J. Pluijm and G.C.A. Shuit, Disc. Faraday Soc. 41 (1966) 290. [5] F. Gesmundo and P.F. Rossi, J. Solid State Chem. 8 (1973) 287. [6] R.B. Fahim and A.I. Abu-Shady, J. Catalysis 17 (1970) 10.
30 June 1975
[7] F. Brown and D. Park, Phys. Rev. 93 (1954) 381. [8] J.I. Gittleman, B. Abeles and S. Bozowski, Phys. Rev. B9 (1974) 3891. [9] S. Chikazumi, Physics of Magnetism (Wiley, 1964) p. 263. [10] A.J. Sievers III and M. Tinkman, Phys. Rev. 129 (1963) 1566. [ 11 ] G. Elshobaky, P.C. Gravelle and S.J. Teichner, J. Catalysis 14 (1969) 4.
309
PHYSICS LETTERS
ELECTRON PARAMAGNETIC OF SUPERPARAMAGNETIC
30 June 1975
RESONANCE
NiO PARTICLES
J.N. HERAK and B. RAKVIN Institute "Ruder Bo~kovid", Zagreb, Croatia, Yugoslavia
Received 16 April 1975 EPR signals are observed in small NiO particles prepared in vacuo and in air. The imaginary part of the susceptibility exhibits a typical superparamagnetic behaviour. A transformation into a paramagnetic system is associated with the diffusion of nickel ions to anionic vacancies. The phenomenon of superparamagnetism of antiferromagnetic NiO particles is known from the experimental work of Richardson and Milligan [1 ] and the theoretical work of N6el [2]. According to N6el, the origin of the unusual magnetic behaviour of small antiferromagnetic particles comes from a small permanent magnetic moment resulting from an imperfect compensation of magnetic sublattices, predominantly on the surface. If the particles possessing a permanent moment are sufficiently small, the thermal energy at the temperature of the experiment may be sufficient to equilibrate the system in a time shorter than or comparable to that of the experiment. The phenomenon is very similar in nature to the superparamagnetism of fine ferromagnetic particles. It is interesting that there have been few or no electron paramagnetic resonance studies of pure NiO [ 3 - 5 ] . The reason probably lies in the difficulties in observing EPR signals. In the present paper we show that for very small NiO particles, EPR signals are readily observed. The intensity of the signals, proportional to the imaginary part of the susceptibility, K", depends on temperature in a similar way as does the real part, K', observed by the conventional methods. Nickelous oxide samples were prepared by a heat treatment of nickel hydroxide in vacuo or in air, at temperatures ranging from 200 ° to 600°C [6]. In such a way small NiO particles were obtained, being smaller when prepared at lower temperatures. The samples prepared in air at temperatures below 600°C or in vacuo at temperatures below 250°C gave EPR signals, the signals being stronger for smaller particles. Some typical spectra for a specimen prepared at 200°C in vacuo are shown in fig. 1. The shape and intensity
"~o = (3 350 MHz
I
/ I000
I 2000
# 3000 MAGNETIC
I ~000 FIELD
I 5000 (GAUSS)
I
Fig. 1. EPR spectra of NiO prepared at 200° V in vacuo. The spectra are recorded at 25°C (a), 120°C (b) and at 120° after short heating at 220°C. of the resonance patterns are dependent on the temperature of observation. The changes are reversible in a certain temperature range (spectra a and b). Upon a heating in vacuo at about 220°C, the spectrum first irreversibly changed into a narrower and symmetric one (fig. lc) and after that the sample became too ferromagnetic for any further EPR study. The relative intensity of the original signals (spectra a and b) as a function of temperature is show in fig. 2. In contrast to this behaviour, the intensity of the signals after the irreversible change (spectrum c) behaves in a typical paramagnetic manner (proportionality with
1/73. 307
Volume 53A, number 4
PHYSICS LETTERS
and K1 is the susceptibility based on the rotation of single domain particles [9]:
o _z
K1 = M 2 a N / 2 K V .
(5)
M s is the magnetization of a single particle and N is the number of particles in a unit volume, a = (sin 2 0), where 0 is the angle between the applied filed and the easy direction of magnetization. We may used a = 2/3. The Fourier transform of eq. (2) gives a complex susceptibility
5 i
,;o
,;o
2;0 2;o 36o 3;o ,;o
K* = (r 0 + iwrK1)/(1 + icor),
T EMPERA?URE (°K)
Fig. 2. Temperature dependence of the relative intensity of EPR spectra in the superparamagnetic range. The circles represent the experimental points and the solid curve the best fit of the theoretical K"(T) curve. The change of the line shape in the superparamagnetic region (spectra a and b) is brought about by the temperature-dependent effective magnetic field. We actually observe the ferrimagnetic resonance of the randomly oriented particles. The resonance condition in the microwave region is [7]: co(T) = 7eff (n0 + H A ( T ) ) .
(1)
H 0 is the external magnetic field and HA(T ) the temperature-dependent anisotropy field. The intensity variation (fig. 2) is brought about by the relaxation of the ferrimagnetic particles. In calculating the temperature dependence of K", we may adopt a procedure analogous to that of Gittleman, Abeles and Bozowski [8], originally used for small ferromagnetic particles. For simplicity, we assume that all the particles are identical. The total magnetization per unit volume of the sample is M ( t ) = H 0 [K0 - (K0 - K1) e x p ( - t / r ) ]
,
(2)
where r is the relaxation time associated with the anisotropy barrier, E B = K V (V is the particle volume and K the magnetic anisotropy energy): r = r 0 exp (lzB/k T).
(3)
TO is a constant of the order of 1010 sec. K 0 is the superparamagnetic susceptibility corresponding to thermal equilibrium: K0 = M 2 N / 3 k T ,
308
30 June 1975
(4)
(6)
whose imaginary part is K" = KlcoT(•O/K 1 -- 1)/(1 + CO2r2)
.
(7)
For our experimental conditions co2r 2 >> 1, leading to K"(co, T) ~ e - z (z - 1),
(8)
where z = K V/k T. For temperatures sufficiently below the N~el temperature, K is practically independent of temperature. Function (8) has a maximum at T m = E B / 2 k . From the experimental points in fig. 2 we obtain E B = 7 X 10-14erg/particle, which is essentially the same as calculated by N6el [2]. Function (8) does not fit well to the experimental points at higher temperatures in fig. 2, i f K is assumed constanL If we use the data for K (T) from other experimental measurements [10], the fit is quite satisfactory (fig. 2). The irreversible transition of the ferrimagnetic system into a paramagnetic one at 220°C (fig. Ic) is believed to be brought about by the diffusion of the uncompensated nickel ions from the surface to the anionic vacancies [ 11 ]. Upon a stronger heat treatment, metallic nickel is precipitated and the specimen becomes ferromagnetic. The samples prepared in air have an access of oxygen [6] and such a precipitation does not take place.
References
[ 1 ] J.T. Richarson and W.O. Milligan, Phys. Rev. 102 (1956) 1289. 121 L. N~el, in Low temperature physics, ed. C. DeWitt, B. Dreyfus and P.G. DeGennes (Gordon and Beach, 1962) p. 411.
Volume 53A, number 4
PHYSICS LETTERS
[31 L.R. Maxwell and T.R. McGuire, Rev. Mod. Phys. 25 (1953) 279. [4] P.F. Cornaz, J.H.C. Van Hooff, F.J. Pluijm and G.C.A. Shuit, Disc. Faraday Soc. 41 (1966) 290. [5] F. Gesmundo and P.F. Rossi, J. Solid State Chem. 8 (1973) 287. [6] R.B. Fahim and A.I. Abu-Shady, J. Catalysis 17 (1970) 10.
30 June 1975
[7] F. Brown and D. Park, Phys. Rev. 93 (1954) 381. [8] J.I. Gittleman, B. Abeles and S. Bozowski, Phys. Rev. B9 (1974) 3891. [9] S. Chikazumi, Physics of Magnetism (Wiley, 1964) p. 263. [10] A.J. Sievers III and M. Tinkman, Phys. Rev. 129 (1963) 1566. [ 11 ] G. Elshobaky, P.C. Gravelle and S.J. Teichner, J. Catalysis 14 (1969) 4.
309