Transport studies on relaxation behavior in spin-glass phase of itinerant magnetic intercalate FexTiS2

60

Journal

of Magnetism

Transport studies on relaxation behavior of itinerant magnetic intercalate Fe,TiS, M. Inoue, K. Sadahiro Department Received

of Materials

6 August

and Magnetic

in spin-glass

Materials

98 (1991) 60-64 North-Holland

phase

and H. Negishi

Science, Faculty of Science, Hiroshima

1990; in revised form 1 February

Universiiy, Hiroshima

730, Japan

1991

Hall resistivity pH and magnetoresistance. Ap/pc in the spin-glass phase of a 3d transition-metal intercalation compound Fe,Tiq (x = 0.20) have been measured over the temperature range 1.5-4.2 K and the time range 0.1-1000 s under pulsed magnetic fields up to 16 T. The pH - H and Ap/po- H curves show a hysteresis corresponding to the magnetization curve, and these quantities decay with time t after the pulsed field is switched off, obeying the algebraic dependence or power-law of the form, pH = At-” and 1Ap/p,,) = Bt-“, where the exponents m and n are found to be temperature dependent, in good agreement with those found for other spin-glass systems

1. Introduction Fe,TiS, is one of the 3d transition-metal intercalation compounds, formed by insertion of Fe atoms into octahedral sites in the weakly coupled Van der Waals gaps of the host lT-CdI, type TiS, layered crystal, where the intercalated Fe 3d orbitals are hybridized with the neighboring host S 3p and Ti 3d atomic orbitals, giving rise to various magnetic ordered states, such as spin-glass (SG, x I 0.20) cluster-glass (CG, 0.20 < x I 0.40) and ferromagnetic phases (x > 0.40) with the easy axis parallel to the c-axis of the crystal [1,2]; these magnetic properties can be reasonably understood in terms of an itinerant electron (band) model rather than a rigid band picture [3-51. Characteristic features of the SG and CG phases of this material are summarized as follows [6,7]: (i) In the SG phase, the linear component of ac magnetic susceptibilities X0 has a cusp, the nonlinear components X1 and xZ showing an enhanced peak, at the freezing or glass temperature Tg.(ii) In the CG phase, X0, X, and xZ have nearly the same behavior as those in the SG phases at Tg,but X2 has an additional small peak at a higher temperature than 0304-8853/91/$03.50

0 1991 - Elsevier Science Publishers

Ts. Some of these results are apparently in qualitative agreement with those found in localized electron spin systems (Ising, XY and Heisenberg types) [8,9], but some are not; an excellent overview of general SG behaviors in various magnetic systems has been reported by Binder and Young DOI. For further understanding of the SG behavior in our material system Fe,TiS, (x = 0.20), in the present work we have studied the relaxation phenomena by measuring the time decay profiles of the transport quantities such as Hall resistivity and magnetoresistance, rather than conventional magnetization measurements, after a pulsed magnetic field is switched off.

2. Experimental Single crystals of Fe,TiS, with x = 0.20 (SG phase with the freezing temperature Tg= 41 K) were grown by a chemical vapor transport technique as done in previous works. The transport measurements were carried out by a conventional dc potentiometric method with an electrical cur-

B.V. (North-Holland)

A4. Inoue et al. / Relaxation behavior in Fe,TiS,

rent applied in the plane of a layered crystal (or along the a-axis) and a pulsed magnetic field (half-wave pulse with duration of 50 ms; maximum field intensity available up to 16 T) applied perpendicular to the plane or along the c-axis of the crystal. The Hall and magnetoresistive voltages were detected by a digital storage oscilloscope through a home-made preamplifier over the time range O-50 ms and by a micro- or nano-voltmeter over the time range 50 ms-1000 s, whose output signals were fed to a personal computer for record and analysis. The time decay profiles of the voltages were obtained by the following procedure; first the sample is zero-field cooled, then a pulsed field is applied, and the resultant voltages are measured by the above method; both sample current and magnetic field directions are reversed to average out any spurious signals, as done usually in galvanomagnetic measurements. As we shall see later, the decay curves are dependent on the number of repetitions of the field-application N; the repeated pulse application was made every 30 min, well after a long lapse of time compared to the time scales of the relaxation behaviors of concern here.

3. Results Fig. 1 shows the recorder traces of the magnetic field dependence of (a) Hall resistivity pn and (b) transverse magnetoresistance Ap/p, at 4.2 K up to the field intensity of 8 T. These pn-H and Ap/p,,-H curves show an appreciable hysteresis, corresponding to the magnetization curve measured previously [ll]; here only the 1st and 4th quadrants of one complete cycle are depicted. Here we should note that the values of both quantities at H = 0 after the field cycle decayed with time t, as shown by dotted arrows, indicating the existence of a relaxation process in the transport quantities, which reflect remanent magnetization M, as we shall see below. At higher magnetic fields H > 8 T well above the saturation of magnetization, the pH-H curve is almost linear with H having a negative slope, though not shown

I

‘p 0

61 1

4

-Z 0 I Q-4 -

I

1

I

a _

,* 2.’ _LC .%:’ ./ -9’

+&j _8 .,.::;....:n~

I

I I

I

H (T) Fig. 1. Recorder traces of (a) the Hall resistivity pH and (b) the transverse magnetoresistance Ap/po at 4.2 K for F%.2,,Ti& plotted against a pulsed magnetic field up to 8 T (pulse duration; 50 ms); here the curves are shown in the 1st and 4th quadrants. Dotted arrows indicate the relaxation behaviors after the magnetic field is switched off.

here. In magnetic materials, a Hall resistivity pn is conventionally written by pH = R,H + ~TR,M,

(1)

where M is a magnetization, R, a normal Hall coefficient and R, an extraordinary Hall coefficient; this is what is called an anomalous Hall effect [12]. Using eq. (1) and the observed magnetization curve [ll], we can estimate the values of R, and R,; R, = -2.2 X lo-’ cm3/C and R, = 0.65 cm3/C at 4.2 K. These experimental results indicate that the dominant conduction carriers are electrons and the density of states at the Fermi level for the down-spin band is expected to be higher than that for the up-spin band, according to existing theories of anomalous Hall effect [12,13]. Fig. 2 shows the time decay curves of (a) pH and (b) Ap/p,, at 4.2 K after the magnetic field is

62

M. Inoue et al. / Relaxation behavior in Fe,TiS, 8.2

Table 1 Representative functional forms for relaxation process of remanent magnetizations M in various spin glass systems

I”“““‘1

Functional forms

Material systems

1. Logarithmic

AuFe [14],

M=A,-B,lnr 2. Algebraic M=A,i-”

(F%.~Mn0.s&sR16$Als Rb,MnO.sCrO.sCl, WI, F%.5Mn0.5Ti4 [171, theories [18,19]

3. Stretched exponential M = A, exp[ -(t/r)l--n] (Oincl)

WI

Euc,Sr,,,S [20] -AgMn, -CuMn [21]

Note: The exponent n used in this table is different from that of the present studies [ours is defined for the transport quantity; see eq. (2)J.

&jl , , , , , , , 1 20

h0 t

Fig. 2.

of (a)

80

100

(s) pH and at 4.2 K shown in is switched s.

1 by

sulating random mixtures like Rb, Mn,, Cr,,Cl 4 [16] and Fe,,sMn,,,TiO, [17], as predicted by theories [18,19], and a stretched exponential type for Eu,,,Sr0.4S [20], AgMn and CuMn [21]. Here one notes that when% exponeza in the algebraic dependence, M = A2tea, is much less than unity, then it can be approximated by a logarithmic dependence, M = A, - B, In r.

lOor

completely zero, traced over the time ranges up to 100 s. The value of pn decreases drastically within a few seconds and continues to decrease further even at time t = 100 s, showing a relaxation behavior; such a behavior is also seen for Ap/pO. Since the magnetic field H is now zero and pr, is proportional to the remanent magnetization M according to eq. (l), the observed decay curve for pn is regarded as the relaxation curve for M.

8.051

4. Discussion Thus far various functional forms have been known for a relaxation process of remanent magnetizations in a variety of spin glasses (e.g., see ref. [lo]). As listed in table 1 for representative forms, a logarithmic dependence is found for a dilute alloy like AuFe [14] for amorphous magnetic . mater-ml of (F%,,Mn,,,),,P,,$Al, [15], an algebraic dependence or a power-law found for in-

6.0' IO4

I too

10'

1 IO2

I 103

t (s) Fig. 3. Log-log plots of (a) -d In p,/dt and (b) pH vs. time t at 4.2 K over the time range 0.1-1000 s; the slope of (a) is - 1.0 and that of (b) is m = 0.0258 [the exponent in eq. (2)].

M. Inoue et al. / Relaxation behavior in Fe,TiS,

63

An empirical check for the validity or the applicability of the above three forms to the present case can be made by plotting M vs. t in semilogarithmic scales or by comparing the slope of log-log plots of ( - d In M/dt) vs. t, according to the well-known method [17,20]; the slope of the latter plot is - 1 for the algebraic dependence and --n (0 < n < 1) for the stretched exponential one. In fig. 3a is shown one of the typical results for in at 4.2 K, where the experimental data lie well on a straight line with the slope - 1.0; this is also the case for the decay curves of the magnetoresistances Ap/p,. Thus in our case, at least the algebraic (or power-law) dependence is valid for the time decay curves of pu and Ap/p,,, obeying the following forms, T / Ts

and n are the exponents for the Hall resistivity and magnetoresistance, respectively (A, B: constants). As shown in fig. 3b for the pH-t curve at 4.2 K plotted in logarithmic scales, the data points actually lie well on a straight line over a wide time range 0.1-1000 s with the best-fit values of A = 7.58 X 10e8 Q m and m = 0.0258. We see that since m -=z 1, the logarithmic dependence could also be applicable, as noted above. The exponents m and n in eq. (2) obtained for our SG system over the temperature range 1.5-4.2 K are found to be proportional to temperature, as given in the inset of fig. 4, where these values, together with those obtained in other SG materials, are also plotted against the reduced temperature T/T, (T,: freezing or glass temperature) for comparison. We see that far below Tg (or T/T, < l), these values increase with increasing temperature, regardless of the nature of magnetism (itinerant or localized electron systems), in good agreement with theoretical predictions of Monte Carlo calculations for the Ising SG model by Binder and Schriider [20]. According to their result, at low temperatures (T + 0) the exponent m for a remanent magnetization M [to which pu is proportional, according to eq. (2)] is given by m = k,T/2

AJ

with AJ=

k,T,,

(3)

Fig. 4. Compiled data for the exponents o (or m in our case) in the algebraic or power-law dependence of relaxation phenomena (measured by mostly remanent magnetizations, except for ours) in various spin glass systems plotted against the reduced temperature T/T, (Tg: freezing or glass temperature); 0 present work, 0 Fee,Mn,,Ti03 (IRM), n Fe,,sMn,sTiO, (TRM) CrcJZl, [16], A Monte Carlo simulation by 1171, v RW%., Binder and Schroder [18]. The inset shows the enlarged temperature dependence of the exponents m (solid circles) and n (open circles) obtained from the Hall resistivity and magnetoresistance measurements, respectively.

where A J is the width of the Gaussian distribution of the exchange interactions between the spins. Thus with this relation we have m = 0.5(T/T,), which is about twice as large as our observed value m = 0.23(T/T,) (see fig. 4). At any rate, the relaxation phenomena for this SG system obey the power-law over the time range 0.1-1000 s. Further studies over the longer time range will be required to clarify whether there is a cross-over from the short time regime to the long time regime, as found for the insulating Eu,,Sr,,,S system [22]. Furthermore, we have found that the exponents m and n are sensitive to “magnetic history”, as shown in fig. 5, where as a typical example we show the values of m at 4.2 K obtained under the pulsed magnetic fields applied up to 4 and 8 T plotted against the number of repetitions of fieldapplication N. At a higher field, m is less dependent on N, while at a lower field it is strongly

64

A4. Inoue et al. / Relaxation

behauior in Fe,TiS,

Acknowledgements We thank M. Sasaki and M. Koyano for valuable discussions and Y. Hara for his assistance in taking the present data.

References

Fig. 5. The exponent m at 4.2 K obtained, after a pulsed magnetic field up to 4 or 8 T is switched off, plotted against the number of repetitions of the field application N.

dependent, which means that the magnetic states are in a metastable state characteristic of SG phases [lo]. Finally, we would like to note that the ratio of the exponent for the magnetoresistance to that for the Hall resistivity, n/m, is about 2.2-2.7 in the temperature range studied. As mentioned above, the Hall resistivity pH is proportional to M and thus using eq. (2) we have AP/P,

0: M”/“,

(4)

which indicates that in our SG system the magnetoresistance is proportional to the power of the remanent magnetization M with the exponent n/m (= 2.2-2.7) which is a little larger than the reported value of 2 found for some spin glasses 1231. In conclusion, we would like to emphasize that the present work contains the first experimental data to show the presence of a relaxation behavior in the transport properties, measured over the time range from 0.1 to 1000 s, and to confirm the validity of the power-law (or logarithmic dependence) for the itinerant magnetic system of Fe, TiS,. Such relaxation phenomena seem to be common to various spin glasses, regardless of itinerant or localized electron systems.

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