含Fe/sub 3/C磁性顆粒之非晶質碳膜之製作與研究

Magnetic proper ties of Fe

C nanogr ains embedded in car bon matr ix Y. H. Lee

, T. C. Han, and J . C. A. Huang

Physics Department, National Cheng-Kung University, Tainan 70101, Taiwan, Republic of China

ABSTRACT

Magnetron dc co-sputtering of a composite target of graphite disk plus iron rods was used in manufacturing carbon films with Fe ₃ C nanograin inclusions. Both temperature and field dependent magnetizations, M(T) and M(H), were measured for samples of various carbon concentrations ( from 37% to 85%). M(T) were measured in both conditions of zero field cooling and a field cooling at H = 100 Oe.

Experimental results of χ (T), obtained from M(T), of zero field cooling, were theoretically fitted by using Wolhfarth’s model of non-interacting particles with log-normal distribution function of particle size. Only the films containing pure Fe ₃ C grains are well fitted theoretically. Blocking temperature, grain size, and dispersion of grain size distribution are obtained from fitting results. Saturation magnetization, and coercivity are obtained from the results of M(H) measurements. Films, as deposited, are superparamagnetic and show zero room temperature coercivity. The largest room temperature coercivity of 965 Oe is obtained for the sample of 72 at.% C made at the sputtering pressure of 4 mtorr and annealed at the temperature of 550 ^o C for 60 min.

High-density magnetic recording medium, on the order of 100 Gb/in ² , is a target that many investigators are striving for. Although many different materials and techniques ^1~7 have been proposed to reach the goal, there are common important features existing among these proposals. They are fine magnetic particles/grains on the order of nanometer and well magnetically insulated in order to have high enough density and signal to noise ratio. Besides, due to ultra-fine magnetic particles, thermal stability is especially important. Thus, high coercivity or high magneto-crystalline anisotropy of a material is concerned. Basing on our long-term research on the topic of diamond-like carbon (DLC) films, we chose making Fe-C composite films for the application of high-density recording media. We have succeeded in making pure Fe 3 C nanograins embedded in amorphous carbon films possessing room temperature coercivity of 965 Oe, which is higher than the reported values among other works on Fe-C composites ^8~10 .

Amorphous carbon films containing Fe ₃ C nanograins were made by sputtering a two-inch diameter graphite target with several pieces of iron rods, 2 mm diameter and 4 mm long, on top of it. Figure 1 shows carbon concentration of films changing with the sputtering pressure and the number of pieces of iron rods. Dashed line in Fig.1, obtained by referring to the results of TEM studies ¹¹ , is used to identify a region of lower pressures and higher carbon concentrations, in which pure Fe ₃ C grains are produced.

Temperature dependent magnetizations, M(T), were measured in a field of H =

100 Oe in both conditions of zero field cooling (ZFC) and a field cooling (FC). The

results of χ (T) = M(T)/H of the samples made at a constant pressure of 8.5 mtorr with

carbon concentrations of 42%, 65%, and 85%, respectively, are selected and displayed

in Fig.2. The films with 42 and 65 at.% C contain both Fe and Fe ₃ C grains but the

film with 85 at.% C contains only Fe 3 C grains. In Fig.2, all ZFC curves of susceptibilities, χ (T), show an increasing behavior with temperature until a

maximum is reached at T = T B , temporarily called "blocking temperature", after which decreasing with temperature. The susceptibilities of FC curves, χ (T),

increase with decreasing temperature until reaching a maximum. The maximum is maintained in Fig. 2(a) at low temperatures. However, a low temperature minimum appears, additionally, in both χ (T) of Fig. 2(b) and (c), but it is much weaker in (c).

An additional low temperature minimum in χ (T) is observed only in Fig. 2(b). It is

also found that χ (T) deviates from

χ (T) at T = T

irr ≠ T B as temperature decreases. Both the difference between χ (T) and

χ (T) at T

irr ≤ T ≤ T B and the temperature range between T irr and T B are getting smaller from Fig. 2(a) to (c) with carbon concentration getting larger. These characteristic behaviors of χ (T) and

χ (T) can be understood in the framework of superparamagnetism

¹² . On considering a system of single domain magnetic particles, relaxation time τ is important in determining how quickly the remanence M r relaxes to its equilibrium value at temperature T. The relaxation time τ is derived and expressed as ¹² :

τ ^-1 = f o exp(-K a V/k B T) (1)

K _a is the magnetic anisotropy constant, V the particle volume, k _B the Boltzman constant, T the absolute temperature and f o the frequency factor which has a value of 10 ⁹ ~ 10 ¹¹ sec ^-1 . Obviously, the value of τ depends on both V and T. For a typical time of experiment, τ = 100 sec is a reasonable value to mark the transition to a stable behavior. At temperature T, an upper limit of particle volume V _m = 29.9k _B T/K _a is estimated for being superparamagnetic. Because τ < 100 sec for particles with V

< V m , it shows paramagnetism and gives zero coercivity. For particles of constant size

V, there exists a temperature T _B = K _a V/29.9k _B . When T < T _B ( τ > 100 sec), paramagnetism disappears and hysteresis appears. T B is thus called blocking temperature. In Fig.2, all curves of χ (T) increase gradually from low temperature to

a maximum at T = T B indicating a non-constant size of grains existing in the films. T B

is thus more proper to be called "most probable blocking temperature" and V m , calculated from T _B , is "most probable maximum grain volume". For simplicity, we still call T B as "blocking temperature" and V m as "maximum grain volume". By assuming the grain as a spherical ball, the maximum grain diameter, D _m , is used, instead.

The curve of χ (T) changes with temperature is governed by the grain size

distribution. By fitting χ (T) theoretically, we can obtain anisotropy constant K

a

together with T _B , V _m and grain size distribution function f(x), from which the mean grain volume <V>, and thus the mean grain diameter,<D>, can be calculated. A model of Wohlfarth’s non-interacting magnetic particles is adopted in the process of fitting. According to Wohlfarth ¹³ , we get

xf(x) = (3K a / ε M s 2

ln(2 π f o τ ) ^-1 ) dT

d ( χ T) (2)

ε the volume fraction occupied by ferromagnetic particles and is approximated as one, M _s the saturation magnetization and is obtained separately from M(H) measurements. In fitting the experimental results of

dT

d ( χ T), f(x) was assumed a

log-normal distribution function as f(x) = (1/ 2 π σ x)exp[-

2

2 ) (ln

σ

x ] (3)

x = V/<V> = T B /<T B > and <T B > is the mean blocking temperature; σ , a fitting

parameter which is related with the dispersion of grain size distribution. Eq. (3) is

then used in calculating χ (T)

¹⁴ of the films with non-constant grains as

χ (T) =

^{< >} ∫

0 2

) 3 (

T V

B s

m

dx x T xf

k V ε M

+ ∫

) ( 2

) 3

(

s

m

dx x K f

ε M

(4)

The results of calculations are shown as solid lines in Fig.2. A very good fit is observed only in Fig. 2(c) where the film contains pure Fe ₃ C grains. However, discrepancies are observed in Fig. 2(a) and (b), which are attributed to Fe grains existing in these films. The discrepancy decreases with increasing carbon concentration (or decreasing iron concentration). From TEM images ¹¹ of the film with 42 at.% C, some specially large Fe grains were observed near the edges of the film, which result in not only a large deviation between the results of calculation and experiment but also a shoulder-like behavior in χ (T) at the high temperature. From fitting, results of T _B , D _m , <D>, σ and K a of the films used in Fig. 2 are obtained.

Only those related to the discussion here, like T B , D m and σ are listed in table I.

Also included in table I are the results of the films being made at lower pressures and containing pure Fe 3 C grains with carbon concentration of 78, 75 and 72%, respectively. For the films made at the constant pressure of 8.5 mtorr, σ decreases when carbon concentration increases from 42% to 85%. Smaller σ implies more uniform grain size distribution, therefore, less difference between χ (T) and

χ (T).

Thus, both the deviation between χ (T) and

χ (T) and the range between T

irr and

T B are getting smaller from Fig. 2(a) to (c). The additional low temperature minimum

in both χ (T) and

χ (T) in Fig. 2(b) is due to the very fine grains, which are not

blocked at very low temperatures. Comparing to D m = 6.4 nm of 65 at.% C, grains of

85 at.% C are much smaller with D _m = 4.9 nm. Thus, a much weaker low temperature

minimum of χ (T) is observed in Fig. 2(c) and that of

χ (T), which is assumed

occurring at the temperature lower than our measuring temperature, is not observed.

Field dependent magnetization measurements, M(H), were taken at both temperatures of 298 K and 5 K. All films as deposited are paramagnetic at room temperature. Coercivity, Hc, and saturation magnetization, Ms, obtained from M(H) are the values at T = 5 K and listed in table I. Focusing at the films with pure Fe 3 C grains in table I, D m increases slightly with decreasing carbon concentration from 85% to 72% and both H _C and M _S increase with increasing D _m . It implies Fe ₃ C grains are single magnetic domain. In order to obtain coercivity at room temperature, the film with 72 at.% C and the largest D _m was chosen for post deposition annealing at temperatures T a = 250 ~ 600 ^o C for 60 min. In Fig. 3(a), χ (T) of T a = 250 ^o C and 550 ^o C, measured at H = 100 Oe, are displayed. T B , thus D m , increases strongly with increasing T a . M(H) measured at T = 298 K for T a = 350 ^o C, 450 ^o C, and 550 ^o C, respectively, is displayed in Fig. 3(b). At T _a ≥ 450 ^o C, none zero room temperature coercivity is observed and increasing with T a . M S increases also with T a . At T a = 600

o C, Fe ₃ C grains decomposed. The largest M _s = 585 emu/cm ³ and H _c (298K) = 965 Oe are obtained at T a = 550 ^o C. The averaged grain size for T a = 550 ^o C is estimated, from TEM images ¹¹ , to be about 18 nm..

In summary, pure Fe ₃ C nanograins embedded in amorphous carbon films are obtained. Films, as deposited, are superparamagnetic and show zero room temperature coercivity. After annealing at the temperature of 550 ^o C for 60 min., the largest room temperature coercivity of 965 Oe is obtained for the sample of 72 at.% C made at the pressure of 4 mtorr.

The authors like to thank the financial support of this work by the Republic of

China's National Science Council under Grant No. NSC90-2112-M006-031.

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FIGURE CAPTONS

Fig. 1. Relation of carbon concentration changes with sputtering pressure and number of pieces of iron rods. Dashed line is used to indicate a region of low pressure and high carbon concentration, in which pure Fe ₃ C grains are obtained.

Fig. 2. Temperature dependence of susceptibility, χ (T), for samples of (a) 42 at.% C, (b) 65 at.% C, and (c) 85 at.% C and for conditions of zero-field cooling (ZFC) and field cooling (FC). Solid line shows results of calculation by using Wohlfarth’s model of non-interacting magnetic particles.

Fig. 3. (a) Temperature dependence of susceptibility χ (T); triangle and circle are for

T a =250 ^o C and T a = 550 ^o C, respectively; and (b) field dependence of magnetization

M(H) for sample of 72 at.% C made at pressure of 4 mtorr and annealed at

temperature of 550 ^o C.

TABLE CAPTION

TABLE I. Most probable blocking temperature and grain diameter, T _B and D _m ,

fitting parameter σ , coercivity and saturation magnetization at the temperature of 5K,

H c (5K) and M s (5K), are listed for the films containing both Fe and Fe 3 C grains and

only Fe 3 C grains.

Figure 1, Y. H. Lee

0 5 10 15 20 25

30 40 50 60 70 80 90 100

(7) (5) (2) (3)

(0.5) (1)

C arb on con ce n trat ion (at . % )

Pressure (mtorr)

Figure 2, Y. H. Lee

0 50 100 150 200 250 300 350 400 0.0

0.1 0.2 0.3 0.4 (c)

T

= 13 K

T irr = 270 K χ (e m u /c m 3 O e)

T (K)

0 50 100 150 200 250 300 350 400

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (b)

T B = 32 K

T irr = 310 K χ ( em u/cm

Oe )

T (K)

0 50 100 150 200 250 300 350 400

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 (a)

T B = 52 K

T irr = 340 K

ZFC FC Calculation

χ ( em u/ cm 3 Oe )

T (K)

42 at. % C D

= 6.5 nm σ = 1.20

65 at. % C D

= 6.4 nm σ = 0.52

85 at. % C

D

= 4.9 nm

σ = 0.47

Figure 3, Y. H. Lee

0 50 100 150 200 250 300 350 400

0.0 0.2 0.4 0.6 0.8 1.0 1.2 (a)

ZFC FC

T

T

= 340 K T

= 220 K

χ (e m u /c m 3 O e)

T (K)

-15 -10 -5 0 5 10 15

-8 -6 -4 -2 0 2 4 6 8

(b)

Ta = 350

C Ta = 450

C Ta = 550

C

M ( 100 em u/ cm 3 )

H (KOe)

Sample at. % C Pressure

( mtorr ) T B

(K)

D m

(nm)

ó H C (5K) (Oe)

M S (5K) (emu/cm ³ )

42 ^a) 85 52 6.5 1.20 402 400

65 ^a) 8.5 32 6.4 0.52 208 227

85 ^b) 8.5 13 4.9 0.47 170 148

78 ^b) 6 15 5.1 0.50 400 365

75 ^b) 6 15 5.1 0.51 410 380

72 ^b) 4 20 5.2 0.55 503 395

a) The sample contains both Fe and Fe 3 C grains.

b) The sample contains only Fe 3 C grains.

Table I, Y. H. Lee