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First-order-like magnetic transition in manganite oxide La0.7Ca0.3MnO3
PERGAMON
Solid State Communications 118 (2001) 377±380
www.elsevier.com/locate/ssc
First-order-like magnetic transition in manganite oxide La0.7Ca0.3MnO3 H.S. Shin a, J.E. Lee a, Y.S. Nam a, H.L. Ju a,*, C.W. Park b b
a Department of Physics, Yonsei University, Seodaemoon-gu, Seoul, South Korea 120-749 Department of Chemical Technology, Taejon National University of Technology, Yusung-Ku, Taejon, South Korea 305-710
Received 13 December 2000; accepted 29 January 2001 by S.G. Louie; received in ®nal form by the Publisher 14 March 2001
Abstract We present a dc magnetization study of the critical phenomena of a manganite oxide La0.7Ca0.3MnO3 single crystal. Based on the assumption of a continuous (second-order) magnetic transition for La0.7Ca0.3MnO3, we have determined the critical temperature TC 222 ^ 0.2 K and the critical exponents b 0.14 ^ 0.02 (b : critical exponent for the temperature dependence of spontaneous magnetization just below TC), and g 0.81 ^ 0.03 (g : critical exponent for the inverse initial susceptibility just above TC). The values of the critical exponents of La0.7Ca0.3MnO3 are different from those predicted based on various theoretical models, and even from those of higher TC manganite oxides, such as La0.7Sr0.3MnO3 (TC 354 K). In addition, Arrot and scaling plots were found to be invalid in the immediate vicinity of TC; this suggests that the magnetic transitional behaviors for La0.7Ca0.3MnO3 are different from those expected for a second-order transition. q 2001 Published by Elsevier Science Ltd. PACS: 75.30.Kz; 75.40.Cx Keywords: A. Magnetically ordered materials; D. Phase transitions
1. Introduction The recent observations of colossal magnetoresistance (CMR) close to the ferromagnetic±paramagnetic phase transition temperature TC, in R12xBxMnO3 (R La, Pr, Nd; B Ca, Sr, Ba) [1,2], have stimulated research aimed not only at reaching a better understanding of these oxide materials but also at exploring magnetic sensing devices. The most salient feature of these materials is the close relation between transport and ferromagnetism due to double exchange (DE) interaction [3] between adjacent Mn 31 and Mn 41 ions. The R12xBxMnO3 compounds have a wide range of TC, from 100 K to 380 K, depending on the average ionic radius of R and B [4]. Signi®cantly, low-TC manganite oxides behave differently from high-TC manganite oxides in many respects [5]. The low-TC (,300 K) manganite oxides have a higher resistivity, a sharper resistivity * Corresponding author. Tel: 82-2-2123-2607; fax: 82-2-3921592. E-mail address: [email protected] (H.L. Ju).
peak near TC, and a larger CMR than do those of the highTC (.300 K) manganite oxides. To better comprehend the origin of CMR, it is important to fully explore the nature of ferromagnetic phase transition. Therefore, the second-order nature of ferromagnetic transition for high-TC manganite oxides such as La0.7Sr0.3MnO3 (TC 355 K) has been examined carefully [6]. For low-TC manganite oxides, the unexpected dependence of the ferromagnetic transition on doping has been reported; the nature of transition for La0.8Ca0.2MnO3 is of a second-order type [7], while the nature of transition for La0.7Ca0.3MnO3 is of a ®rst-order type [8]. Detailed knowledge of the nature of the ferromagnetic transition for low-TC manganites is crucial in understanding CMR, unusual metal±insulator transitions, and other related phenomena. In this article, we detail an in-depth dc magnetization study of the critical phenomena for La0.7Ca0.3MnO3 low-TC manganite oxides on highquality single crystals. Assuming that the magnetic transition of La0.7Ca0.3MnO3 is of a second-order, we have determined the critical temperature TC and the critical exponents b , g , and d . Here b is the critical exponent for
0038-1098/01/$ - see front matter q 2001 Published by Elsevier Science Ltd. PII: S 0038-109 8(01)00123-5
H.S. Shin et al. / Solid State Communications 118 (2001) 377±380
2. Experimental A single crystal of La0.7Ca0.3MnO3 was grown by using a ¯oating zone furnace consisting of four mirrors and four halogen lamps, as described in detail in Ref. [7]. The X-ray diffraction result shows that La0.7Ca0.3MnO3 has a pseudo-cubic perovskite structure with a lattice constant Ê . The cation stochiometry obtained by energy of a < 0.387 A dispersive X-ray (EDX) analysis was identical with the prescribed ratio within experimental errors. The resistivity was measured by a usual four-point method. The magnetic measurements were carried out with a superconducting quantum interference device (SQUID) in ®elds up to 5 T. The sample size for magnetic measurements was 0.3 mm £ 1.5 mm £ 3.5 mm. External ®elds for magnetic measurements were applied in the longest sample direction to minimize the demagnetizing effect. In the isothermal magnetization measurements, temperature steps were 2 K. After stabilizing the temperature at each temperature, we waited 20 min before measuring the isothermal magnetization. The maximum deviation in the temperature was estimated as ^0.01 K. 3. Result and discussions Fig. 1 shows the temperature dependence of the resistivity and magnetization for a La0.7Ca0.3MnO3 single crystal. The resistivity for La0.7Ca0.3MnO3 showed a resistivity peak at a temperature TP of 225 K (which is 3 K above the TC of 222.2 K), a metal-like resistivity behavior for T , TP, and an insulator-like one for TP , T. Those resistivity behaviors are typical for single crystalline manganite oxides. The peak resistivity, r P (T 225 K), was 65 mV cm and the resistivity at 77 K, r (T 77 K), was 1 mV cm. The large residual ratio rP T 225 K=r T 77 K ,70 points to the high quality of the single crystal. For TP , T, the resistivity ®ts with r r0 exp Ea =kT, and the activation energy Ea has been found to be 70 meV. We have measured the temperature dependence of the magnetization at an external ®eld of 3000 Oe, which is above the magnetic saturation ®eld of 1000±2000 Oe. The magnetic transition was found to be very sharp and the magnetic moment at 5 K was 96 emu/g, a magnitude in agreement with the theoretical saturation magnetization. Fig. 2 shows a series of isothermal magnetization curves
0.07 100
0.06
80 M(emu/g)
the temperature dependence of spontaneous magnetization just below TC, g is the critical exponent for the inverse initial susceptibility just above TC, and d is the critical exponent at TC. In addition, we have found the scaling hypothesis for La0.7Ca0.3MnO3 is not valid for 0.98TC , T , 1.01TC. The small value of b ,0.14 and the invalidity of the scaling plots for La0.7Ca0.3MnO3 in the immediate vicinity of TC suggest that the magnetic transition of La0.7Ca0.3MnO3 is discontinuous (®rst-order-like).
r (Ωcm)
378
0.05 0.04
H=3000 Oe 60 40 20
0.03 0
0.02
0 50 100 150 200 250 300 T(K)
0.01 0.7
0.3
3
0.00 0
50
100
150
200
250
300
350
T(K) Fig. 1. Temperature dependence of the resistivity (r ) at zero ®eld and the magnetization (M) at H 3000 Oe for a La0.7Ca0.3MnO3 single crystal.
M vs. H, near TC of a La0.7Ca0.3MnO3 single crystal. The graph shows gradual magnetic transitions from the ferromagnetic to the paramagnetic state. Above TC ( 222 K), while a linear dependence is present for low ®elds, a nonlinearity is evident for high ones. In particular, it is interesting to note an upward in¯ection starting at the critical ®eld HC of about 1 T, which is possibly due to the antiferromagnetic correlation in the system [9]. In other words, this upward in¯ection, which is absent for high-TC manganite oxides such as La0.7Sr0.3MnO3 [6], can naturally be attributed to spin ¯ips in the antiferromagnetic insulating regions. Near the critical temperature for a second-order transition, a generalized Arrot's plot M 1/b vs. (H/M) 1/g [10] can be used to determine TC, the spontaneous magnetization MS (0, T ) below TC, and the initial susceptibility x 0 (i.e., dM/ dH at H 0) above TC. In the simplest case, b and g given by their mean-®eld values are 0.5 and 1, respectively [11]. Thus, in the mean-®eld theory near TC, M 2 vs H/M curves at various temperatures should be in parallel straight lines, the intercept of which on the H/M axis determines the magnetic state. The intercept is negative below TC, and positive above TC. The line for T TC passes through the origin of the M 2 vs H/M plot. As shown in Fig. 2(b), the M 2 vs. H/M curves for La0.7Ca0.3MnO3 are nonlinear and anomalous (with their apparent C-like shape in M 2 vs. H/M for H . 1 T). These features are due to upward in¯ection in the M vs. H curves above the HS ®eld. This indicates that the mean-®eld theory is not valid for La0.7Ca0.3MnO3. However, it is clear that the curves above TC extend smoothly into the H/M axis to yield the values of 1/x 0. For T , TC, a polynomial ®t of the data above H 0.5 T and an extrapolation of the data give a reliable value of MS(0, T ). From the data in Fig. 2, we have found x21 0 (T ) vs. T and MS(0, T ) vs. T, and plotted them in Fig. 3. Above TC, the inverse susceptibility x21 0 (T ) is proportional to (T 2 TC) g . Based on these data, the g
H.S. Shin et al. / Solid State Communications 118 (2001) 377±380
379
Fig. 3. Plot of x21 vs. T (closed circles) and T p vs. T (closed 0 triangles) for a La0.7Ca0.3MnO3 single crystal. Inset shows the plot of MS(0,T) vs. T.
exponent can be determined directly from our data. Using the isotherm at T TC (222 K), we ®t our magnetization with the form M(H,T TC) / H 1/d to determine d 1.22 ^ 0.02. As a further test of these values for the critical exponents and TC, our data have been compared with the prediction of the scaling hypothesis [13] M H; 1 H 2 f ^ 1b 1 g1b
Fig. 2. (a) Field dependence of the magnetization for singlecrystalline La0.7Ca0.3MnO3 at various temperatures in the range 204 K # T # 244 K. (b) Arrot plots (M 2 vs. H/M) for a La0.7Ca0.3MnO3 single crystal for 204 K # T # 244 K. The temperature step DT is 2 K.
where (1) and (2) signs represent data for T . TC and T , TC, and 1 j T 2 TC =TC j. A test of the scaling has been obtained by plotting M/1 b vs. H/1 (g 1b ). If Eq. (2) holds, then all of the data should fall on one of two curves. The data below TC should give f2, while the data above TC should give f1. Using the values of the critical exponents b , g , and the critical temperature TC obtained from our analysis
value can be obtained by using the Kouvel±Fisher method [12]: T p T
1 1 ! d d x21 21 0 ln x0 x 0 dT dT
1
Then T p T j T 2 TC j =g as T approaches TC. We have determined the value of x 0 and dx21 0 =dT for different T from the x21 vs. T plot and calculated the values of the 0 corresponding T p(T ) with Eq. (1). The T p(T ) vs. T as shown in Fig. 3 is found to be linear slightly above TC (from TC to 1.05TC), intersecting the T axis at 222.2 ^ 0.2 K. This is our estimate for TC. The slope of the T p data closest to TC gives our g value of 0.81 ^ 0.03. Below TC, spontaneous magnetization MS(0,T ) should vary with j T 2 TC j b . Using our data for MS(0,T ) from Fig. 2, MS(0,T ) has been plotted in the inset of Fig. 3 and a value of b 0.14 ^ 0.02 has been obtained. One more critical
Fig. 4. Scaling plot of M1 2b vs. H1 2 (g 1b ) for a La0.7Ca0.3MnO3 single crystal, using g 0.81 and b 0.14.
380
H.S. Shin et al. / Solid State Communications 118 (2001) 377±380
Table 1 Experimental values of the critical exponents for manganite oxides and theoretical values of the critical exponents for various models Materials
TC (K)
b
g
La0.7Sr0.3MnO3 [6] La0.67Ba0.33MnO3 [14] La0.7Ca0.3MnO3 [this work] CrO2 [15] Ni [10] MF theory [11] 3d Ising theory [11] 3d Heisenberg theory [11]
354 338.1 222.2 ^ 0.2 386.5 635.5
0.37 ^ 0.04 0.464 ^ 0.003 0.14 ^ 0.02 0.95 ^ 0.04 0.395 ^ 0.01 0.5 0.325 ^ 0.002 0.365 ^ 0.003
1.22 ^ 0.03 1.29 ^ 0.02 0.81 ^ 0.03 1.63 ^ 0.02 1.345 ^ 0.001 1 1.241 ^ 0.002 1.336 ^ 0.004
of Figs. 2 and 3, the scaled data were plotted in Fig. 4. We can see that the data points for T , TC 2 0.02TC merge into a single line as do those for TC 1 0.01TC , T. Contrastingly, for TC 2 0.02TC , T , TC, the data points are below the f2, and, for TC , T , TC 1 0.01TC, the data points are below the f1. Thus, the scaling hypothesis for La0.7Ca0.3MnO3 is not valid for TC 2 0.02TC , T , TC 1 0.01TC. The critical exponents b and g of some manganite oxides and those of various models are summarized in Table 1. We can see that the b values for manganite oxides with high-TC, such as La0.67Sr0.33MnO3 (TC 354 K) and La0.67Ba0.33MnO3 (TC 338.1 K), are close to those of conventional ferromagnets such as Ni and the Heisenberg model, while the experimental g values are not close to any values of those theoretical models listed in Table 1. In the case of La0.7Ca0.3MnO3, the b and g values are close neither to those of higher TC manganite oxides nor to those of any theoretical model in Table 1. In addition, the value of b is less than any value in the theoretical model based on second-order transitions. Therefore, the nature of the magnetic transition of La0.7Ca0.3MnO3 is completely different from that of high-TC manganite oxides and conventional ferromagnets. The nature of the magnetic transition has been found to be strongly dependent on TC even in manganite oxides having the same perovskite structure. The small value of b and the failure of the scaling hypothesis in the immediate vicinity of TC for La0.7Ca0.3MnO3 suggest that the magnetic transition for La0.7Ca0.3MnO3 may not in fact be second-order.
4. Conclusion In conclusion, we have studied the critical phenomena of the low-TC manganese oxide La0.7Ca0.3MnO3 using isothermal magnetization. Assuming a continuous (i.e. second-order) phase transition, we have determined the Curie temperature TC 222 ^ 0.2 K and the critical exponents b 0.14 ^ 0.02, g 0.81 ^ 0.03, and d 1.22 ^ 0.02 for these compounds. The values of b , g , and d are signi®cantly different from those arrived at using various previous models, and even from those yielded by
high-TC manganite oxides. Using the obtained critical exponents, the scaling hypothesis has been found to be invalid for TC 2 0.02TC , T , TC 1 0.01TC. The small values of b and the failure of the scaling hypothesis in the vicinity of TC suggest that the magnetic transition of La0.7Ca0.3MnO3 is not continuous. Acknowledgements We thank Dr B. I. Min for his helpful suggestions. The authors wish to acknowledge the ®nancial support of the Korean Research Foundation made in the program year of 1998. References [1] A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, Phys. Rev. B 51 (1995) 14103. [2] G.C. Xiong, Q. Li, H.L. Ju, S.N. Mao, L. Senapati, X.X. Xi, R.L. Greene, T. Venkatesan, Appl. Phys. Lett. 66 (1995) 1427. [3] P.G. de Gennes, Phys. Rev. 118 (1960) 141. [4] H.Y. Hwang, S.W. Cheong, P.G. Radaelli, M. Marezio, B. Batlogg, Phys. Rev. Lett. 75 (1995) 914. [5] G.C. Xiong, S.M. Bhagat, Q. Li, M. Dominguez, H.L. Ju, R.L. Greene, T. Venkatesan, J.M. Byers, M. Rubinstein, Solid State Commun. 97 (1996) 599. [6] K. Ghosh, C.J. Lobb, R.L. Greene, S.G. Karabashev, D.A. Shulyatev, A.A. Arsenov, Y. Mukovskii, Phys. Rev. Lett. 81 (1998) 4740. [7] C.S. Hong, N.H. Hur, Phys. Rev. B (2001) in press. [8] J. Mira, J. Rivas, F. Rivadulla, C. Vazquez, M. LopezQuintela, Phys. Rev. B 60 (1999) 2998. [9] K.W. Joh, C.H. Lee, C.E. Lee, Y.H. Jeong, J. Magnet. 5 (2000) 9. [10] A. Arrott, J.E. Noakes, Phys. Rev. Lett. 19 (1967) 786. [11] M. Seeger, S.N. Kaul, H. Kronmuller, Phys. Rev. B 51 (1995) 12585. [12] J.S. Kouvel, M.E. Fisher, Phys. Rev. A 136 (1964) 1626. [13] H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York, 1971, p 182. [14] N. Moutis, I. Panagiotopoulos, M. Pissas, D. Niarchos, Phys. Rev. B 59 (1999) 1129. [15] J.S. Kouvel, D.S. Rodbell, Phys. Rev. Lett. 18 (1967) 215.
Solid State Communications 118 (2001) 377±380
www.elsevier.com/locate/ssc
First-order-like magnetic transition in manganite oxide La0.7Ca0.3MnO3 H.S. Shin a, J.E. Lee a, Y.S. Nam a, H.L. Ju a,*, C.W. Park b b
a Department of Physics, Yonsei University, Seodaemoon-gu, Seoul, South Korea 120-749 Department of Chemical Technology, Taejon National University of Technology, Yusung-Ku, Taejon, South Korea 305-710
Received 13 December 2000; accepted 29 January 2001 by S.G. Louie; received in ®nal form by the Publisher 14 March 2001
Abstract We present a dc magnetization study of the critical phenomena of a manganite oxide La0.7Ca0.3MnO3 single crystal. Based on the assumption of a continuous (second-order) magnetic transition for La0.7Ca0.3MnO3, we have determined the critical temperature TC 222 ^ 0.2 K and the critical exponents b 0.14 ^ 0.02 (b : critical exponent for the temperature dependence of spontaneous magnetization just below TC), and g 0.81 ^ 0.03 (g : critical exponent for the inverse initial susceptibility just above TC). The values of the critical exponents of La0.7Ca0.3MnO3 are different from those predicted based on various theoretical models, and even from those of higher TC manganite oxides, such as La0.7Sr0.3MnO3 (TC 354 K). In addition, Arrot and scaling plots were found to be invalid in the immediate vicinity of TC; this suggests that the magnetic transitional behaviors for La0.7Ca0.3MnO3 are different from those expected for a second-order transition. q 2001 Published by Elsevier Science Ltd. PACS: 75.30.Kz; 75.40.Cx Keywords: A. Magnetically ordered materials; D. Phase transitions
1. Introduction The recent observations of colossal magnetoresistance (CMR) close to the ferromagnetic±paramagnetic phase transition temperature TC, in R12xBxMnO3 (R La, Pr, Nd; B Ca, Sr, Ba) [1,2], have stimulated research aimed not only at reaching a better understanding of these oxide materials but also at exploring magnetic sensing devices. The most salient feature of these materials is the close relation between transport and ferromagnetism due to double exchange (DE) interaction [3] between adjacent Mn 31 and Mn 41 ions. The R12xBxMnO3 compounds have a wide range of TC, from 100 K to 380 K, depending on the average ionic radius of R and B [4]. Signi®cantly, low-TC manganite oxides behave differently from high-TC manganite oxides in many respects [5]. The low-TC (,300 K) manganite oxides have a higher resistivity, a sharper resistivity * Corresponding author. Tel: 82-2-2123-2607; fax: 82-2-3921592. E-mail address: [email protected] (H.L. Ju).
peak near TC, and a larger CMR than do those of the highTC (.300 K) manganite oxides. To better comprehend the origin of CMR, it is important to fully explore the nature of ferromagnetic phase transition. Therefore, the second-order nature of ferromagnetic transition for high-TC manganite oxides such as La0.7Sr0.3MnO3 (TC 355 K) has been examined carefully [6]. For low-TC manganite oxides, the unexpected dependence of the ferromagnetic transition on doping has been reported; the nature of transition for La0.8Ca0.2MnO3 is of a second-order type [7], while the nature of transition for La0.7Ca0.3MnO3 is of a ®rst-order type [8]. Detailed knowledge of the nature of the ferromagnetic transition for low-TC manganites is crucial in understanding CMR, unusual metal±insulator transitions, and other related phenomena. In this article, we detail an in-depth dc magnetization study of the critical phenomena for La0.7Ca0.3MnO3 low-TC manganite oxides on highquality single crystals. Assuming that the magnetic transition of La0.7Ca0.3MnO3 is of a second-order, we have determined the critical temperature TC and the critical exponents b , g , and d . Here b is the critical exponent for
0038-1098/01/$ - see front matter q 2001 Published by Elsevier Science Ltd. PII: S 0038-109 8(01)00123-5
H.S. Shin et al. / Solid State Communications 118 (2001) 377±380
2. Experimental A single crystal of La0.7Ca0.3MnO3 was grown by using a ¯oating zone furnace consisting of four mirrors and four halogen lamps, as described in detail in Ref. [7]. The X-ray diffraction result shows that La0.7Ca0.3MnO3 has a pseudo-cubic perovskite structure with a lattice constant Ê . The cation stochiometry obtained by energy of a < 0.387 A dispersive X-ray (EDX) analysis was identical with the prescribed ratio within experimental errors. The resistivity was measured by a usual four-point method. The magnetic measurements were carried out with a superconducting quantum interference device (SQUID) in ®elds up to 5 T. The sample size for magnetic measurements was 0.3 mm £ 1.5 mm £ 3.5 mm. External ®elds for magnetic measurements were applied in the longest sample direction to minimize the demagnetizing effect. In the isothermal magnetization measurements, temperature steps were 2 K. After stabilizing the temperature at each temperature, we waited 20 min before measuring the isothermal magnetization. The maximum deviation in the temperature was estimated as ^0.01 K. 3. Result and discussions Fig. 1 shows the temperature dependence of the resistivity and magnetization for a La0.7Ca0.3MnO3 single crystal. The resistivity for La0.7Ca0.3MnO3 showed a resistivity peak at a temperature TP of 225 K (which is 3 K above the TC of 222.2 K), a metal-like resistivity behavior for T , TP, and an insulator-like one for TP , T. Those resistivity behaviors are typical for single crystalline manganite oxides. The peak resistivity, r P (T 225 K), was 65 mV cm and the resistivity at 77 K, r (T 77 K), was 1 mV cm. The large residual ratio rP T 225 K=r T 77 K ,70 points to the high quality of the single crystal. For TP , T, the resistivity ®ts with r r0 exp Ea =kT, and the activation energy Ea has been found to be 70 meV. We have measured the temperature dependence of the magnetization at an external ®eld of 3000 Oe, which is above the magnetic saturation ®eld of 1000±2000 Oe. The magnetic transition was found to be very sharp and the magnetic moment at 5 K was 96 emu/g, a magnitude in agreement with the theoretical saturation magnetization. Fig. 2 shows a series of isothermal magnetization curves
0.07 100
0.06
80 M(emu/g)
the temperature dependence of spontaneous magnetization just below TC, g is the critical exponent for the inverse initial susceptibility just above TC, and d is the critical exponent at TC. In addition, we have found the scaling hypothesis for La0.7Ca0.3MnO3 is not valid for 0.98TC , T , 1.01TC. The small value of b ,0.14 and the invalidity of the scaling plots for La0.7Ca0.3MnO3 in the immediate vicinity of TC suggest that the magnetic transition of La0.7Ca0.3MnO3 is discontinuous (®rst-order-like).
r (Ωcm)
378
0.05 0.04
H=3000 Oe 60 40 20
0.03 0
0.02
0 50 100 150 200 250 300 T(K)
0.01 0.7
0.3
3
0.00 0
50
100
150
200
250
300
350
T(K) Fig. 1. Temperature dependence of the resistivity (r ) at zero ®eld and the magnetization (M) at H 3000 Oe for a La0.7Ca0.3MnO3 single crystal.
M vs. H, near TC of a La0.7Ca0.3MnO3 single crystal. The graph shows gradual magnetic transitions from the ferromagnetic to the paramagnetic state. Above TC ( 222 K), while a linear dependence is present for low ®elds, a nonlinearity is evident for high ones. In particular, it is interesting to note an upward in¯ection starting at the critical ®eld HC of about 1 T, which is possibly due to the antiferromagnetic correlation in the system [9]. In other words, this upward in¯ection, which is absent for high-TC manganite oxides such as La0.7Sr0.3MnO3 [6], can naturally be attributed to spin ¯ips in the antiferromagnetic insulating regions. Near the critical temperature for a second-order transition, a generalized Arrot's plot M 1/b vs. (H/M) 1/g [10] can be used to determine TC, the spontaneous magnetization MS (0, T ) below TC, and the initial susceptibility x 0 (i.e., dM/ dH at H 0) above TC. In the simplest case, b and g given by their mean-®eld values are 0.5 and 1, respectively [11]. Thus, in the mean-®eld theory near TC, M 2 vs H/M curves at various temperatures should be in parallel straight lines, the intercept of which on the H/M axis determines the magnetic state. The intercept is negative below TC, and positive above TC. The line for T TC passes through the origin of the M 2 vs H/M plot. As shown in Fig. 2(b), the M 2 vs. H/M curves for La0.7Ca0.3MnO3 are nonlinear and anomalous (with their apparent C-like shape in M 2 vs. H/M for H . 1 T). These features are due to upward in¯ection in the M vs. H curves above the HS ®eld. This indicates that the mean-®eld theory is not valid for La0.7Ca0.3MnO3. However, it is clear that the curves above TC extend smoothly into the H/M axis to yield the values of 1/x 0. For T , TC, a polynomial ®t of the data above H 0.5 T and an extrapolation of the data give a reliable value of MS(0, T ). From the data in Fig. 2, we have found x21 0 (T ) vs. T and MS(0, T ) vs. T, and plotted them in Fig. 3. Above TC, the inverse susceptibility x21 0 (T ) is proportional to (T 2 TC) g . Based on these data, the g
H.S. Shin et al. / Solid State Communications 118 (2001) 377±380
379
Fig. 3. Plot of x21 vs. T (closed circles) and T p vs. T (closed 0 triangles) for a La0.7Ca0.3MnO3 single crystal. Inset shows the plot of MS(0,T) vs. T.
exponent can be determined directly from our data. Using the isotherm at T TC (222 K), we ®t our magnetization with the form M(H,T TC) / H 1/d to determine d 1.22 ^ 0.02. As a further test of these values for the critical exponents and TC, our data have been compared with the prediction of the scaling hypothesis [13] M H; 1 H 2 f ^ 1b 1 g1b
Fig. 2. (a) Field dependence of the magnetization for singlecrystalline La0.7Ca0.3MnO3 at various temperatures in the range 204 K # T # 244 K. (b) Arrot plots (M 2 vs. H/M) for a La0.7Ca0.3MnO3 single crystal for 204 K # T # 244 K. The temperature step DT is 2 K.
where (1) and (2) signs represent data for T . TC and T , TC, and 1 j T 2 TC =TC j. A test of the scaling has been obtained by plotting M/1 b vs. H/1 (g 1b ). If Eq. (2) holds, then all of the data should fall on one of two curves. The data below TC should give f2, while the data above TC should give f1. Using the values of the critical exponents b , g , and the critical temperature TC obtained from our analysis
value can be obtained by using the Kouvel±Fisher method [12]: T p T
1 1 ! d d x21 21 0 ln x0 x 0 dT dT
1
Then T p T j T 2 TC j =g as T approaches TC. We have determined the value of x 0 and dx21 0 =dT for different T from the x21 vs. T plot and calculated the values of the 0 corresponding T p(T ) with Eq. (1). The T p(T ) vs. T as shown in Fig. 3 is found to be linear slightly above TC (from TC to 1.05TC), intersecting the T axis at 222.2 ^ 0.2 K. This is our estimate for TC. The slope of the T p data closest to TC gives our g value of 0.81 ^ 0.03. Below TC, spontaneous magnetization MS(0,T ) should vary with j T 2 TC j b . Using our data for MS(0,T ) from Fig. 2, MS(0,T ) has been plotted in the inset of Fig. 3 and a value of b 0.14 ^ 0.02 has been obtained. One more critical
Fig. 4. Scaling plot of M1 2b vs. H1 2 (g 1b ) for a La0.7Ca0.3MnO3 single crystal, using g 0.81 and b 0.14.
380
H.S. Shin et al. / Solid State Communications 118 (2001) 377±380
Table 1 Experimental values of the critical exponents for manganite oxides and theoretical values of the critical exponents for various models Materials
TC (K)
b
g
La0.7Sr0.3MnO3 [6] La0.67Ba0.33MnO3 [14] La0.7Ca0.3MnO3 [this work] CrO2 [15] Ni [10] MF theory [11] 3d Ising theory [11] 3d Heisenberg theory [11]
354 338.1 222.2 ^ 0.2 386.5 635.5
0.37 ^ 0.04 0.464 ^ 0.003 0.14 ^ 0.02 0.95 ^ 0.04 0.395 ^ 0.01 0.5 0.325 ^ 0.002 0.365 ^ 0.003
1.22 ^ 0.03 1.29 ^ 0.02 0.81 ^ 0.03 1.63 ^ 0.02 1.345 ^ 0.001 1 1.241 ^ 0.002 1.336 ^ 0.004
of Figs. 2 and 3, the scaled data were plotted in Fig. 4. We can see that the data points for T , TC 2 0.02TC merge into a single line as do those for TC 1 0.01TC , T. Contrastingly, for TC 2 0.02TC , T , TC, the data points are below the f2, and, for TC , T , TC 1 0.01TC, the data points are below the f1. Thus, the scaling hypothesis for La0.7Ca0.3MnO3 is not valid for TC 2 0.02TC , T , TC 1 0.01TC. The critical exponents b and g of some manganite oxides and those of various models are summarized in Table 1. We can see that the b values for manganite oxides with high-TC, such as La0.67Sr0.33MnO3 (TC 354 K) and La0.67Ba0.33MnO3 (TC 338.1 K), are close to those of conventional ferromagnets such as Ni and the Heisenberg model, while the experimental g values are not close to any values of those theoretical models listed in Table 1. In the case of La0.7Ca0.3MnO3, the b and g values are close neither to those of higher TC manganite oxides nor to those of any theoretical model in Table 1. In addition, the value of b is less than any value in the theoretical model based on second-order transitions. Therefore, the nature of the magnetic transition of La0.7Ca0.3MnO3 is completely different from that of high-TC manganite oxides and conventional ferromagnets. The nature of the magnetic transition has been found to be strongly dependent on TC even in manganite oxides having the same perovskite structure. The small value of b and the failure of the scaling hypothesis in the immediate vicinity of TC for La0.7Ca0.3MnO3 suggest that the magnetic transition for La0.7Ca0.3MnO3 may not in fact be second-order.
4. Conclusion In conclusion, we have studied the critical phenomena of the low-TC manganese oxide La0.7Ca0.3MnO3 using isothermal magnetization. Assuming a continuous (i.e. second-order) phase transition, we have determined the Curie temperature TC 222 ^ 0.2 K and the critical exponents b 0.14 ^ 0.02, g 0.81 ^ 0.03, and d 1.22 ^ 0.02 for these compounds. The values of b , g , and d are signi®cantly different from those arrived at using various previous models, and even from those yielded by
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