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Antiferromagnetic long-range order caused by nonmagnetic impurities; magnetization of single-crystal Cu1−xZnxGeO3
Illllgl Physica B 215 (1995) 164-170
ELSEVIER
Antiferromagnetic long-range order caused by nonmagnetic impurities; magnetization of single-crystal Cul_xZnxGeO3 M a s a s h i H a s e a'*, N a o k i K o i d e a, K e n z o u M a n a b e a, Y o s h i t a k a S a s a g o a, K u n i m i t s u U c h i n o k u r a a, A k i h i t o S a w a h Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan b Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba-shi, lbarald 305, Japan
Received4 January 1995
Abstract
The magnetization was obtained as a function of temperature and magnetic field of a C u 1 xZn~GeO3 single-crystal with x ~ 0.04. The temperature dependence of the magnetic susceptibility in 0.1 T parallel to the c axis shows a clear cusp around 4.5 K and decreases rapidly below 4.5 K. There is no hysteresis between the data measured in zero-field-cooling and field-cooling processes. The field dependence of the magnetization parallel to the c axis at 2.0 K exhibits an apparent increase around 1.0T, which corresponds to a spin-flop transition. The temperature and field dependences, the anisotropy, and the absence of the hysteresis undoubtedly prove the occurrence of an antiferromagnetic long-range order below 4.5 K instead of the spin-glass-like transition reported previously. Spins below the transition temperature are ordered almost parallel to the c axis. This is the first report of magnetic long-range order caused by nonmagnetic impurities.
A quasi-one-dimensional (quasi-lD) antiferromagnetic (AF) spin system CuGeO3 exhibits the spin-Peierls (SP) transition [1] and has attracted much attention. In this cuprate, there are some advantages to investigations of the SP transition, which organic SP materials do not have. One of the advantages is that the influence of impurities in AF chains on the SP transition can be studied. In our previous work [2], we measured the magnetic susceptibility [3] of polycrystalline CUl_xZnxGeO3 and observed a rapid decrease of the SP-transition temperature upon Zn doping and a disappearance of the SP transition for x >/0.030. In addition, an occurrence of another phase transition was discovered in the samples with 0.020 ~< x ~< 0.080 below 5 K. We thought that this new transition was
*Corresponding author.
a spin-glass-like (SG-like) transition on the basis of two experimental results. There is a hysteresis between susceptibilities measured in zero-field-cooling (ZFC) and field-cooling (FC) processes below the transition temperature. With increasing magnetic field (H), the susceptibility reduces, and the hysteresis and the transition become unclear. However, the susceptibility in Cul-xZnxGeO3 shows two queer behaviors in comparison with an ordinary SG material. The magnitude of the hysteresis (the difference between ZFC and FC susceptibilities) is very small. Below the transition temperature, the ZFC susceptibility of Cul xZnxGeO3 exhibits a weak temperature (T) dependence, while that of a typical SG compound reduces drastically with decreasing T. In order to study in detail the transition below 5 K in CUl -xZnxGeO3, we have grown single crystals and measured T and H dependences of the
0921-4526/95/$09.50 © 1995 ElsevierScienceB.V. All rights reserved SSDI 092 1-4526(95)00405-X
165
M. Hase et al./Physica B 215 (1995) 164-170
magnetization. Most unexpectedly, the present results prove that an AF long-range order (AF-LRO) appears at low T instead of the SG phase. Single crystals of Cul -~ Zn~GeO3 were grown by a floating-zone method. The magnetization was measured by a superconducting quantum interference device (SQUID) magnetometer. The data were obtained for several crystals, although we show only the data of one single crystal (9.3 mg) in this paper. We show the temperature dependence of the susceptibility in 0.1 T below 15 K in Fig. l(a).
1.5
i
Circles, squares, and diamonds represent the susceptibilities measured in H parallel to the a [zo(H, T)], b [gb(a, T)], and c [zJH, T)] axes, respectively. Below 8.0 K, the susceptibility was obtained in both the ZFC and FC processes. Closed and open marks denote the ZFC and FC susceptibilities, respectively. As is clearly seen in zJH, T), a phase transition characterized by a cusp occurs around 4.5 K. The magnitude of zJH, T) decreases drastically below the transition temperature. Considering the orbital
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Fig. 1. The temperature dependence of the magnetic susceptibility of single-crystal Cut _xZnxGeO3. We measured the data at intervals of 0.1, 0.5, 2.0, and 4.0 K at 2-5, 5-20, 20-80, and 80-300 K, respectively. In the data expressed by solid curves, many experimental points have been suppressed in order to improve the clarity of the figure. Closed and open marks represent the data obtained in the ZFC and FC processes, respectively. The value of x is estimated to be about 0.04 (see text). (a) The susceptibility in 0.1 T below 15 K. Circles, squares, and diamonds denote z=(H, T), zb(H, T), and xc(H, T), respectively. (b) Z,ve(H, T) in 0.1 T below 15 K. (c) zc(H, T) in 0.1 (diamonds), 2.0 (circles), and 5.5 (squares)T below 10 K. (d) The susceptibility in 0.1 T below 300 K. Circles, squares, and diamonds denote za(H, T), zb(H, T), and x((H, T), respectively.
166
M. Hase et al./Physica B 215 (1995) 164 170
susceptibility ( ~ 8 x 10 -7 emu/g [-1]), the spin susceptibility seems to be 0 at 0 K. It should be emphasized that no hysteresis was observed between the ZFC and FC z~(H, T)'s, which is expected to appear in a SG transition. On the other hand, the cusp around 4.5 K is less evident in both z,(H, T) and zb(H, T). As T reduces, z,(H, T ) and )~b(H,T) increase gradually except for around 4.5 K. There is also no hysteresis in z,(H, T ) and
zb(H, r ). Fig. l(b) shows an average among z , ( H , T ) ,
Zb(H,T), and z¢(H,T) in the ZFC process [Zave(H, T)]. Since Zave(H, T ) is similar to the susceptibility of polycrystalline Cul _ xZnxGeO3 with x --~ 0.04 [2], the transition seen in the single crystal is identical with the transition below 5 K in the polycrystalline samples with 0.020 ~< x ~< 0.080. Considering that the transition temperature is 4.5 K, the value of x is about 0.04 in this single crystal. The SP transition was not detected, which agrees with the absence of the SP transition in polycrystalline Cul _xZnxGeO3 with x ~ 0.04. The anisotropy and the absence of the hysteresis in the susceptibility strongly indicate an occurrence of a transition to an AF-LRO (an AF transition) with the transition temperature (TN) of 4.5 K, although it was reported that this is a SG-like transition [2]. Since zc(H, T ) reduces rapidly below TN, spins are ordered nearly parallel to the c axis, In order to investigate the H dependence of the transition, we measured z~(H, T) in various H's. Fig. l(c) shows the ZFC z~(H, T ) in 0.1 (diamond), 2.0 (circle), and 5.5 (square)T below 10 K. Above 2.0 T, zc(H, T) increases monotonically with decreasing T. The H dependence of z~(H, T ) was seen below 8 K. In Fig. l(d), we show the ZFC susceptibility in 0.1 T below 300 K. Closed circles, squares, and diamonds denote z,(H, T), zb(H, T), and z~(H, T), respectively. T h e T dependences of all the susceptibilities are similar to one another above TN. The anisotropy is due to that of the g value. The spin susceptibilities z~(H,T) ( i = a , b, and c) were roughly eStimated by the subtraction of the orbital part ( ~ 8 x 10 7emu/g [,1]) from the measured data. The values of z~(H,T)/z~(H,T) and z~(H, T)/z~(H, T) are about 1.05 and 1.19. These values are consistent with (g~/g~)2 (~1.06) and
1.15), respectively [g{s (i = a,b, and c) are the 9 values parallel to the a,b, and c axes, respectively], which were obtained in the electronspin-resonance (ESR) measurement of single-crystal CuGeO3 [4]. As T is lowered, the susceptibility increases gradually and exhibits a broad maximum around 55 K and increases once again below 17 K. The broad maximum is a characteristic behavior observed in low-dimensional AF spin systems. On the contrary, the increase below 17 K is possibly due to finite chains with an odd number of spins (odd chains) parallel to the c axis generated by Zn doping. The susceptibility of odd chains usually diverges as T - 1 [5]. However, the measured susceptibility between 4.5 and 17 K does not obey a simple Curie Weiss law, but is proportional to T-'¢ (0 < y < 1), which was also observed in the polycrystalline samples [-2]. In the previous work, we reported that the above-mentioned T dependence may be caused by nonuniformity of the AF exchange interaction in chains due to local lattice distortion associated with the SP transition and/or disorder. In addition, the T ;' behavior probably comes from interchain exchange interactions, because it exists just above the transition temperature to the three-dimensional long-range order. Assuming that the AF transition occurs at 4.5 K, we expect that a spin-flop transition would appear below 4.5 K. Thus we measured the H dependence of the magnetization. Fig. 2(a) shows the magnetization in H parallel to the c axis [M~(H, T ) ] below 5.5 T. Circles, squares, and diamonds represent the data at 2.0, 5.0 (just above TN), and 10.0 K, respectively. The magnetization at 2.0 K was measured in both increasing (closed circles) and decreasing (open circles) fields. The vertical positions of Me(H, T) are shifted as indicated on the left-hand side of the figure. At 2.0 K, M,,(H, T ) changes rapidly around 1 T, which means a phase transition. Although Mc(H, T) increases with increasing H in all the fields, Me(H, T ) has a larger slope in high H than in low H. No hysteresis was seen between Me(H, T)'s measured in both increasing and decreasing H. On the other hand, the transition was not observed in MAH, T ) measured in increasing H at 5.0 K. This transition is strongly related to the AF transition (gb/gc) 2 ( ~
167
M. Hase et el./Physica B 215 (1995) 164-170
seen in z~(H,T) in 0.1 T, because the former transition disappears above TN. Since the transition in M~(H, T) occurs around 1 T, the AF transition was not observed in z~(H, T ) above 2.0 T [Fig. l(c)]. As is indicated by a dashed (linear) line, M~(H, T ) below 2.0 T is proportional to H at 5.0 K. On the contrary, M~(H, T) above 3.0 T deviates downward from the dashed line and shows a convex-up behavior. As will be described below, the convex-up behavior is also seen in the magnetization parallel to the a and b axes below 5.0 K. This convex-up behavior may be produced by finite odd
i
chains, because the magnetization of nearly isolated spins also shows both a divergent term in the T dependence and the H dependence as a convexup behavior expressed as a Brillouin function. On the other hand, M,(H, T) at 10.0 K increases linearly up to 5.5 T as is represented by a dotted line. We show the magnetization measured in increasing H parallel to the a [M,(H,T)] and b [M~(H, T)] axes below 5.5 T in Figs. 2(b) and (c), respectively. As is mentioned below, all the six experimental data in these figures are proportional to H below 1.0 T. We obtained each linear line so as
,
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Fig. 2. The magnetic-field dependences of the magnetization and the magnetic susceptibility of single-crystal Cu1_~ZnxGeO3 below 5.5 T. Closed and open marks represent the data obtained in increasing and decreasing fields, respectively. Circles, squares, and diamonds denote the data at 2.0, 5.0, and 10.0 K, respectively. Solid, dashed, and dotted linear lines were obtained to fit them to corresponding data below 1.0 T. (a) Me(H, T) versus H. At 2.0 K, we measured the data at intervals of 0.1 T. Many points have been suppressed to improve the clarity of the figure. (b) M~(H,T) versus H. (c) Mb(H,T) versus H. (d) %,re(H, T) versus H. The data below 0.6 T are omitted because of the scatter of the data.
168
M. Hase et al./Physica B 215 (1995) 164 170
to fit it to the corresponding data. In contrast to M~(H, T ) at 2.0 K, a phase transition was observed in neither Mo(H, T) nor Mb(H, T). At 2.0 K, M,,(H, T) and Mb(H, T) below 1.0 T are proportional to H, while those above 2.0 T deviate downward from the solid lines and show convex-up behaviors. The magnetizations at both 2.0 and 5.0 K are similar to each other. The deviations were seen above 2.5 T in both M , ( H , T ) and Mb(H,T) at 5.0 K. On the contrary, the magnetizations at 10.0 K are linear functions of H. In both M,(H, T ) and Mb(H, T ), the magnetizations reduce with increasing T. Although we do not show the data of other single crystals here, the above-mentioned magnetic properties are reproducible. The phase transition observed in the magnetization in a spin-flop transition, because it was observed only in Mc(H, T) below TN. As a result, the T and H dependences of the magnetization prove the appearance of the AF-LRO in Cul xZn~GeO3. It is noted that the present result is very significant and interesting, because nonmagnetic impurities cause the magnetic long-range order. To our best knowledge, this is the first report of the AF-LRO induced by nonmagnetic impurities. Of course, some diluted systems have an AF-LRO [6]. However, in these systems, end materials have magnetic long-range orders. On the other hand, in CHl_xZnxGeO 3, end materials CuGeO3 and ZnGeO3 have no magnetic long-range order
[73. Let us now discuss the mechanism of the appearance of the AF-LRO in Cul xZn~GeO3. If the SP transition does not exist in CuGeO3, the AF-LRO possibly occurs, because this cuprate has, as a 1D magnetic system [8], relatively large interchain exchange interactions especially along the b direction. As was reported in the previous work [2] impurities in AF chains destroy significantly the SP order, which leads to development of 1D AF correlation in each chain. Therefore the 1D AF correlation and the interchain exchange interaction cause the AF-LRO. We emphasize the following two points. First of all, the AF-LRO is preserved in ordinary antiferromagnets even if a small amount of impurities are added. Thus it is not strange that the AF-LRO exists in CUl-~Zn~GeO3. Secondly, the SP system is purely I D in the magnetic net-
work, while an antiferromagnet with an AF-LRO is not 1D. Therefore, impurities affect the SP order more drastically than the AF-LRO. In the following paragraphs, we reconsider the results of polycrystalline Cu~ xZnxGeO3. We must discuss the three points; the x dependence of the transition temperature, the reason why the hysteresis exists in the polycrystalline samples, and the H dependence of the magnetization. The x dependence of TN can be explained. The following explanation is basically identical with that of the x dependence of a SG-like transition temperature described in Ref. [2]. The energy of the 3D magnetic correlation and TN are probably proportional to [~liJinter[ where ~l and Ji,ter are the 1D AF correlation length in the chain and the interchain exchange interaction, respectively. The value of ~, is generally proportional to T-1 [9], whereas Jinter is nearly independent of T. Thus a phase transition appears when the magnetic energy, which increases with decreasing temperature, coincides with the thermal energy. The Zn substitution hardly changes the value of Jinter, while it does ~. In low x, ~, increases with Zn doping because of the destruction of the SP order and the corresponding development of the 1D AF correlation. As a result, TN increases. On the contrary, in high x, the increase of ~, is prevented by an average distance between two neighboring Zn ions in chains, because the two Cu spins located on opposite sides of Zn within a chain interact weaklier than the two neighboring Cu spins within a chain. Since the average distance between two neighboring Zn ions in chains decreases upon doping, ~, and TN reduce. Since the polycrystalline sample consists of many fine crystals, the small hysteresis may be due to changes of directions of fine crystals during the measurement. It is noted that the hysteresis is related to the AF transition, because the hysteresis starts to appear near TN. Spins below 7~ are ordered according to fine crystals which the spins belong to. However, in addition, these spins prefer to align perpendicular to the magnetic field, because the perpendicular susceptibility is larger than the parallel one. Therefore, if a gain of a magnetic energy produced by aligning spins perpendicular to H overcomes an energy to alter the directions of the fine crystals, the directions of some of the fine
M. Hase et al./Physica B 215 (1995) 164-170
crystals may change. The possibility of the direction change increases with increasing T because of a thermal energy to redistribute the directions. In the FC process in low H, when spins are ordered at TN, the magnetic field has been already applied. Since the thermal energy is not small, it could be easy to change the directions of the fine crystals. On the other hand, in the ZFC process, the magnetic field is applied after the spins are ordered. Since the thermal energy is small for example at 2.0K, it is hard to change the directions of the fine crystals. Thus the susceptibility can have a slightly larger value in the FC process than in the ZFC one, since in the former process there are more perpendicular components. On the contrary, in high H, the perpendicular components can be increased by the field in both ZFC and FC processes. Therefore, the hysteresis reduces relatively and cannot be detected. It is emphasized that the susceptibilities in 1.0 and 5.5 T of the polycrystalline samples (Fig. 2 in Ref. [2]) are similar to the perpendicular susceptibility such as za(H,T) and )b(H, T ). In this paragraph, we compare the H dependence of the susceptibility of the single crystal with that of the polycrystalline sample with x = 0.040. Roughly speaking, both of the H dependences are similar to each other. In the polycrystalline sample, the susceptibility reduces with increasing H below 7.8 K. The AF transition becomes unclear above 1.0 T. On the other hand, Fig. 2(d) shows the H dependence of Zave(H, T ) of the single crystal. The susceptibility of the single crystal also decreases as H increases except for the data at 2.0 K below 1.5 T. Considering zc(H, T) in various H's in Fig. l(c), we may conclude that the disappearance of the AF transition above 1.0T in the polycrystalline sample is due to the spin-flop transition. We cannot at present determine the reason of the discrepancy between H dependences of the susceptibilities of both samples at 2.0K below 1.5 T. It is probably caused by changes of directions of fine crystals in the polycrystalline sample. The results in this work undoubtedly prove that the AF-LRO appears at low T in Cul _xZn~GeO3. As for another work on Cu~ _xZnxGeO3, the existence of a SG-like transition was reported in the
169
~tSR measurement [10], which should be reconsidered. Since the exchange interactions in the c and b directions are AF [8], it is expected that spins are ordered antiferromagnetically in both the c and b directions below TN. The magnetic lattice should be determined completely by the neutron diffraction. In summary, we measured the temperature and the magnetic-field dependences of the magnetization of single-crysal CUl_xZnxGeO3 with x ~ 0.04. The magnetic susceptibility in 0.1 T parallel to the c axis exhibits a clear cusp around 4.5 K, and reduces drastically below 4.5 K. No hysteresis was observed between the data measured in zerofield-cooling and field cooling processes. On the other hand, the susceptibilities parallel to the a and b axes increase gradually with decreasing temperature below 17 K except for small cusps around 4.5 K. The anisotropy and the absence of the hysteresis mean an appearance of an antiferromagnetic long-range order below the transition temperature of 4.5 K instead of a spin-glass-like transition reported in the previous work. Spins in the ordered state are nearly parallel to the c axis. The magneticfield dependence of the magnetization parallel to the c axis at 2.0 K shows a rapid change around 1.0T. The rapid change disappears above the transition temperature, and is not also seen in the magnetizations parallel to the a and b axes. The results of the magnetization prove that the spin-flop transition in the antiferromagnetic longrange order occurs around 1.0T parallel to the c axis. We have discovered the magnetic long-range order caused by nonmagnetic impurities for the first time.
We would like to thank H. Kojima, I. Tanaka, and Y. Shibuya of Yamanashi University for advice on the growth of single crystals. This work is partially supported by a Grant-in-Aid from the Japan Society for the Promotion of Science.
References [-1] M. Hase, I. Terasaki and K. Uchinokura, Phys. Rev. Lett. 70 0993) 3651.
170
M. Hase et al. /Physica B 215 (1995) 164-170
[2] M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura and H. Obara, Phys. Rev. Lett. 71 (1993) 4059. [3] In this paper, the susceptibility is defined as the magnetization divided by H. [4] N. Adachi, T. Hamamoto, G. Kido, M. Hase, Y. Sasago, K. Uchinokura, S. Noro and T. Yamadaya, Physica B 201 (1994) 174. We used the g values of CuGeO3. Since the g value mainly depends on the spin-orbit interaction of d electrons, it is probably independent of x. [5] J.C. Bonner and M.E. Fisher, Phys. Rev. 135 (1964) A640.
[6] For example, the result of Fe~ xCoxCl2, P. Wong, P.M. Horn, R.J. Birgeneau, C.R. Safinya and G. Shirane, Phys. Rev. Lett. 45 (1980) 1974. [7] Although the compound ZnGeO3 exists, CuGeO3 and ZnGeO3 are not isostructural. [8] M. Nishi, O. Fujita and J. Akimitsu, Phys. Rev. B 50 (1994) 6508. [9] A. Luther and I. Peschel, Phys. Rev. B 12 (1975) 3908. [10] O. Tchernyshyov, A.S. Blaer, K. Keren, K. Kojima, G.M. Luke, W.D. Wu, Y.J. Uemura, M. Hase, K. Uchinokura and Y. Ajiro, J. Magn. Magn. Mater. 140-144 (1995) 1687.
ELSEVIER
Antiferromagnetic long-range order caused by nonmagnetic impurities; magnetization of single-crystal Cul_xZnxGeO3 M a s a s h i H a s e a'*, N a o k i K o i d e a, K e n z o u M a n a b e a, Y o s h i t a k a S a s a g o a, K u n i m i t s u U c h i n o k u r a a, A k i h i t o S a w a h Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan b Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba-shi, lbarald 305, Japan
Received4 January 1995
Abstract
The magnetization was obtained as a function of temperature and magnetic field of a C u 1 xZn~GeO3 single-crystal with x ~ 0.04. The temperature dependence of the magnetic susceptibility in 0.1 T parallel to the c axis shows a clear cusp around 4.5 K and decreases rapidly below 4.5 K. There is no hysteresis between the data measured in zero-field-cooling and field-cooling processes. The field dependence of the magnetization parallel to the c axis at 2.0 K exhibits an apparent increase around 1.0T, which corresponds to a spin-flop transition. The temperature and field dependences, the anisotropy, and the absence of the hysteresis undoubtedly prove the occurrence of an antiferromagnetic long-range order below 4.5 K instead of the spin-glass-like transition reported previously. Spins below the transition temperature are ordered almost parallel to the c axis. This is the first report of magnetic long-range order caused by nonmagnetic impurities.
A quasi-one-dimensional (quasi-lD) antiferromagnetic (AF) spin system CuGeO3 exhibits the spin-Peierls (SP) transition [1] and has attracted much attention. In this cuprate, there are some advantages to investigations of the SP transition, which organic SP materials do not have. One of the advantages is that the influence of impurities in AF chains on the SP transition can be studied. In our previous work [2], we measured the magnetic susceptibility [3] of polycrystalline CUl_xZnxGeO3 and observed a rapid decrease of the SP-transition temperature upon Zn doping and a disappearance of the SP transition for x >/0.030. In addition, an occurrence of another phase transition was discovered in the samples with 0.020 ~< x ~< 0.080 below 5 K. We thought that this new transition was
*Corresponding author.
a spin-glass-like (SG-like) transition on the basis of two experimental results. There is a hysteresis between susceptibilities measured in zero-field-cooling (ZFC) and field-cooling (FC) processes below the transition temperature. With increasing magnetic field (H), the susceptibility reduces, and the hysteresis and the transition become unclear. However, the susceptibility in Cul-xZnxGeO3 shows two queer behaviors in comparison with an ordinary SG material. The magnitude of the hysteresis (the difference between ZFC and FC susceptibilities) is very small. Below the transition temperature, the ZFC susceptibility of Cul xZnxGeO3 exhibits a weak temperature (T) dependence, while that of a typical SG compound reduces drastically with decreasing T. In order to study in detail the transition below 5 K in CUl -xZnxGeO3, we have grown single crystals and measured T and H dependences of the
0921-4526/95/$09.50 © 1995 ElsevierScienceB.V. All rights reserved SSDI 092 1-4526(95)00405-X
165
M. Hase et al./Physica B 215 (1995) 164-170
magnetization. Most unexpectedly, the present results prove that an AF long-range order (AF-LRO) appears at low T instead of the SG phase. Single crystals of Cul -~ Zn~GeO3 were grown by a floating-zone method. The magnetization was measured by a superconducting quantum interference device (SQUID) magnetometer. The data were obtained for several crystals, although we show only the data of one single crystal (9.3 mg) in this paper. We show the temperature dependence of the susceptibility in 0.1 T below 15 K in Fig. l(a).
1.5
i
Circles, squares, and diamonds represent the susceptibilities measured in H parallel to the a [zo(H, T)], b [gb(a, T)], and c [zJH, T)] axes, respectively. Below 8.0 K, the susceptibility was obtained in both the ZFC and FC processes. Closed and open marks denote the ZFC and FC susceptibilities, respectively. As is clearly seen in zJH, T), a phase transition characterized by a cusp occurs around 4.5 K. The magnitude of zJH, T) decreases drastically below the transition temperature. Considering the orbital
1.2
i
single crystal CUl_xZnxGeO3
~, 1.(3 Q
,
,
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.
.
.
.
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~
~0.5
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Temperature i
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1.5
i
i
•
(c)
~ .... 10
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single crystal CUl_xZnxGeO3
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Temperature (K)
single crystal CUl _×ZnxGeO3
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,
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Temperature
I00
(K)
Fig. 1. The temperature dependence of the magnetic susceptibility of single-crystal Cut _xZnxGeO3. We measured the data at intervals of 0.1, 0.5, 2.0, and 4.0 K at 2-5, 5-20, 20-80, and 80-300 K, respectively. In the data expressed by solid curves, many experimental points have been suppressed in order to improve the clarity of the figure. Closed and open marks represent the data obtained in the ZFC and FC processes, respectively. The value of x is estimated to be about 0.04 (see text). (a) The susceptibility in 0.1 T below 15 K. Circles, squares, and diamonds denote z=(H, T), zb(H, T), and xc(H, T), respectively. (b) Z,ve(H, T) in 0.1 T below 15 K. (c) zc(H, T) in 0.1 (diamonds), 2.0 (circles), and 5.5 (squares)T below 10 K. (d) The susceptibility in 0.1 T below 300 K. Circles, squares, and diamonds denote za(H, T), zb(H, T), and x((H, T), respectively.
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M. Hase et al./Physica B 215 (1995) 164 170
susceptibility ( ~ 8 x 10 -7 emu/g [-1]), the spin susceptibility seems to be 0 at 0 K. It should be emphasized that no hysteresis was observed between the ZFC and FC z~(H, T)'s, which is expected to appear in a SG transition. On the other hand, the cusp around 4.5 K is less evident in both z,(H, T) and zb(H, T). As T reduces, z,(H, T ) and )~b(H,T) increase gradually except for around 4.5 K. There is also no hysteresis in z,(H, T ) and
zb(H, r ). Fig. l(b) shows an average among z , ( H , T ) ,
Zb(H,T), and z¢(H,T) in the ZFC process [Zave(H, T)]. Since Zave(H, T ) is similar to the susceptibility of polycrystalline Cul _ xZnxGeO3 with x --~ 0.04 [2], the transition seen in the single crystal is identical with the transition below 5 K in the polycrystalline samples with 0.020 ~< x ~< 0.080. Considering that the transition temperature is 4.5 K, the value of x is about 0.04 in this single crystal. The SP transition was not detected, which agrees with the absence of the SP transition in polycrystalline Cul _xZnxGeO3 with x ~ 0.04. The anisotropy and the absence of the hysteresis in the susceptibility strongly indicate an occurrence of a transition to an AF-LRO (an AF transition) with the transition temperature (TN) of 4.5 K, although it was reported that this is a SG-like transition [2]. Since zc(H, T ) reduces rapidly below TN, spins are ordered nearly parallel to the c axis, In order to investigate the H dependence of the transition, we measured z~(H, T) in various H's. Fig. l(c) shows the ZFC z~(H, T ) in 0.1 (diamond), 2.0 (circle), and 5.5 (square)T below 10 K. Above 2.0 T, zc(H, T) increases monotonically with decreasing T. The H dependence of z~(H, T ) was seen below 8 K. In Fig. l(d), we show the ZFC susceptibility in 0.1 T below 300 K. Closed circles, squares, and diamonds denote z,(H, T), zb(H, T), and z~(H, T), respectively. T h e T dependences of all the susceptibilities are similar to one another above TN. The anisotropy is due to that of the g value. The spin susceptibilities z~(H,T) ( i = a , b, and c) were roughly eStimated by the subtraction of the orbital part ( ~ 8 x 10 7emu/g [,1]) from the measured data. The values of z~(H,T)/z~(H,T) and z~(H, T)/z~(H, T) are about 1.05 and 1.19. These values are consistent with (g~/g~)2 (~1.06) and
1.15), respectively [g{s (i = a,b, and c) are the 9 values parallel to the a,b, and c axes, respectively], which were obtained in the electronspin-resonance (ESR) measurement of single-crystal CuGeO3 [4]. As T is lowered, the susceptibility increases gradually and exhibits a broad maximum around 55 K and increases once again below 17 K. The broad maximum is a characteristic behavior observed in low-dimensional AF spin systems. On the contrary, the increase below 17 K is possibly due to finite chains with an odd number of spins (odd chains) parallel to the c axis generated by Zn doping. The susceptibility of odd chains usually diverges as T - 1 [5]. However, the measured susceptibility between 4.5 and 17 K does not obey a simple Curie Weiss law, but is proportional to T-'¢ (0 < y < 1), which was also observed in the polycrystalline samples [-2]. In the previous work, we reported that the above-mentioned T dependence may be caused by nonuniformity of the AF exchange interaction in chains due to local lattice distortion associated with the SP transition and/or disorder. In addition, the T ;' behavior probably comes from interchain exchange interactions, because it exists just above the transition temperature to the three-dimensional long-range order. Assuming that the AF transition occurs at 4.5 K, we expect that a spin-flop transition would appear below 4.5 K. Thus we measured the H dependence of the magnetization. Fig. 2(a) shows the magnetization in H parallel to the c axis [M~(H, T ) ] below 5.5 T. Circles, squares, and diamonds represent the data at 2.0, 5.0 (just above TN), and 10.0 K, respectively. The magnetization at 2.0 K was measured in both increasing (closed circles) and decreasing (open circles) fields. The vertical positions of Me(H, T) are shifted as indicated on the left-hand side of the figure. At 2.0 K, M,,(H, T ) changes rapidly around 1 T, which means a phase transition. Although Mc(H, T) increases with increasing H in all the fields, Me(H, T ) has a larger slope in high H than in low H. No hysteresis was seen between Me(H, T)'s measured in both increasing and decreasing H. On the other hand, the transition was not observed in MAH, T ) measured in increasing H at 5.0 K. This transition is strongly related to the AF transition (gb/gc) 2 ( ~
167
M. Hase et el./Physica B 215 (1995) 164-170
seen in z~(H,T) in 0.1 T, because the former transition disappears above TN. Since the transition in M~(H, T) occurs around 1 T, the AF transition was not observed in z~(H, T ) above 2.0 T [Fig. l(c)]. As is indicated by a dashed (linear) line, M~(H, T ) below 2.0 T is proportional to H at 5.0 K. On the contrary, M~(H, T) above 3.0 T deviates downward from the dashed line and shows a convex-up behavior. As will be described below, the convex-up behavior is also seen in the magnetization parallel to the a and b axes below 5.0 K. This convex-up behavior may be produced by finite odd
i
chains, because the magnetization of nearly isolated spins also shows both a divergent term in the T dependence and the H dependence as a convexup behavior expressed as a Brillouin function. On the other hand, M,(H, T) at 10.0 K increases linearly up to 5.5 T as is represented by a dotted line. We show the magnetization measured in increasing H parallel to the a [M,(H,T)] and b [M~(H, T)] axes below 5.5 T in Figs. 2(b) and (c), respectively. As is mentioned below, all the six experimental data in these figures are proportional to H below 1.0 T. We obtained each linear line so as
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Fig. 2. The magnetic-field dependences of the magnetization and the magnetic susceptibility of single-crystal Cu1_~ZnxGeO3 below 5.5 T. Closed and open marks represent the data obtained in increasing and decreasing fields, respectively. Circles, squares, and diamonds denote the data at 2.0, 5.0, and 10.0 K, respectively. Solid, dashed, and dotted linear lines were obtained to fit them to corresponding data below 1.0 T. (a) Me(H, T) versus H. At 2.0 K, we measured the data at intervals of 0.1 T. Many points have been suppressed to improve the clarity of the figure. (b) M~(H,T) versus H. (c) Mb(H,T) versus H. (d) %,re(H, T) versus H. The data below 0.6 T are omitted because of the scatter of the data.
168
M. Hase et al./Physica B 215 (1995) 164 170
to fit it to the corresponding data. In contrast to M~(H, T ) at 2.0 K, a phase transition was observed in neither Mo(H, T) nor Mb(H, T). At 2.0 K, M,,(H, T) and Mb(H, T) below 1.0 T are proportional to H, while those above 2.0 T deviate downward from the solid lines and show convex-up behaviors. The magnetizations at both 2.0 and 5.0 K are similar to each other. The deviations were seen above 2.5 T in both M , ( H , T ) and Mb(H,T) at 5.0 K. On the contrary, the magnetizations at 10.0 K are linear functions of H. In both M,(H, T ) and Mb(H, T ), the magnetizations reduce with increasing T. Although we do not show the data of other single crystals here, the above-mentioned magnetic properties are reproducible. The phase transition observed in the magnetization in a spin-flop transition, because it was observed only in Mc(H, T) below TN. As a result, the T and H dependences of the magnetization prove the appearance of the AF-LRO in Cul xZn~GeO3. It is noted that the present result is very significant and interesting, because nonmagnetic impurities cause the magnetic long-range order. To our best knowledge, this is the first report of the AF-LRO induced by nonmagnetic impurities. Of course, some diluted systems have an AF-LRO [6]. However, in these systems, end materials have magnetic long-range orders. On the other hand, in CHl_xZnxGeO 3, end materials CuGeO3 and ZnGeO3 have no magnetic long-range order
[73. Let us now discuss the mechanism of the appearance of the AF-LRO in Cul xZn~GeO3. If the SP transition does not exist in CuGeO3, the AF-LRO possibly occurs, because this cuprate has, as a 1D magnetic system [8], relatively large interchain exchange interactions especially along the b direction. As was reported in the previous work [2] impurities in AF chains destroy significantly the SP order, which leads to development of 1D AF correlation in each chain. Therefore the 1D AF correlation and the interchain exchange interaction cause the AF-LRO. We emphasize the following two points. First of all, the AF-LRO is preserved in ordinary antiferromagnets even if a small amount of impurities are added. Thus it is not strange that the AF-LRO exists in CUl-~Zn~GeO3. Secondly, the SP system is purely I D in the magnetic net-
work, while an antiferromagnet with an AF-LRO is not 1D. Therefore, impurities affect the SP order more drastically than the AF-LRO. In the following paragraphs, we reconsider the results of polycrystalline Cu~ xZnxGeO3. We must discuss the three points; the x dependence of the transition temperature, the reason why the hysteresis exists in the polycrystalline samples, and the H dependence of the magnetization. The x dependence of TN can be explained. The following explanation is basically identical with that of the x dependence of a SG-like transition temperature described in Ref. [2]. The energy of the 3D magnetic correlation and TN are probably proportional to [~liJinter[ where ~l and Ji,ter are the 1D AF correlation length in the chain and the interchain exchange interaction, respectively. The value of ~, is generally proportional to T-1 [9], whereas Jinter is nearly independent of T. Thus a phase transition appears when the magnetic energy, which increases with decreasing temperature, coincides with the thermal energy. The Zn substitution hardly changes the value of Jinter, while it does ~. In low x, ~, increases with Zn doping because of the destruction of the SP order and the corresponding development of the 1D AF correlation. As a result, TN increases. On the contrary, in high x, the increase of ~, is prevented by an average distance between two neighboring Zn ions in chains, because the two Cu spins located on opposite sides of Zn within a chain interact weaklier than the two neighboring Cu spins within a chain. Since the average distance between two neighboring Zn ions in chains decreases upon doping, ~, and TN reduce. Since the polycrystalline sample consists of many fine crystals, the small hysteresis may be due to changes of directions of fine crystals during the measurement. It is noted that the hysteresis is related to the AF transition, because the hysteresis starts to appear near TN. Spins below 7~ are ordered according to fine crystals which the spins belong to. However, in addition, these spins prefer to align perpendicular to the magnetic field, because the perpendicular susceptibility is larger than the parallel one. Therefore, if a gain of a magnetic energy produced by aligning spins perpendicular to H overcomes an energy to alter the directions of the fine crystals, the directions of some of the fine
M. Hase et al./Physica B 215 (1995) 164-170
crystals may change. The possibility of the direction change increases with increasing T because of a thermal energy to redistribute the directions. In the FC process in low H, when spins are ordered at TN, the magnetic field has been already applied. Since the thermal energy is not small, it could be easy to change the directions of the fine crystals. On the other hand, in the ZFC process, the magnetic field is applied after the spins are ordered. Since the thermal energy is small for example at 2.0K, it is hard to change the directions of the fine crystals. Thus the susceptibility can have a slightly larger value in the FC process than in the ZFC one, since in the former process there are more perpendicular components. On the contrary, in high H, the perpendicular components can be increased by the field in both ZFC and FC processes. Therefore, the hysteresis reduces relatively and cannot be detected. It is emphasized that the susceptibilities in 1.0 and 5.5 T of the polycrystalline samples (Fig. 2 in Ref. [2]) are similar to the perpendicular susceptibility such as za(H,T) and )b(H, T ). In this paragraph, we compare the H dependence of the susceptibility of the single crystal with that of the polycrystalline sample with x = 0.040. Roughly speaking, both of the H dependences are similar to each other. In the polycrystalline sample, the susceptibility reduces with increasing H below 7.8 K. The AF transition becomes unclear above 1.0 T. On the other hand, Fig. 2(d) shows the H dependence of Zave(H, T ) of the single crystal. The susceptibility of the single crystal also decreases as H increases except for the data at 2.0 K below 1.5 T. Considering zc(H, T) in various H's in Fig. l(c), we may conclude that the disappearance of the AF transition above 1.0T in the polycrystalline sample is due to the spin-flop transition. We cannot at present determine the reason of the discrepancy between H dependences of the susceptibilities of both samples at 2.0K below 1.5 T. It is probably caused by changes of directions of fine crystals in the polycrystalline sample. The results in this work undoubtedly prove that the AF-LRO appears at low T in Cul _xZn~GeO3. As for another work on Cu~ _xZnxGeO3, the existence of a SG-like transition was reported in the
169
~tSR measurement [10], which should be reconsidered. Since the exchange interactions in the c and b directions are AF [8], it is expected that spins are ordered antiferromagnetically in both the c and b directions below TN. The magnetic lattice should be determined completely by the neutron diffraction. In summary, we measured the temperature and the magnetic-field dependences of the magnetization of single-crysal CUl_xZnxGeO3 with x ~ 0.04. The magnetic susceptibility in 0.1 T parallel to the c axis exhibits a clear cusp around 4.5 K, and reduces drastically below 4.5 K. No hysteresis was observed between the data measured in zerofield-cooling and field cooling processes. On the other hand, the susceptibilities parallel to the a and b axes increase gradually with decreasing temperature below 17 K except for small cusps around 4.5 K. The anisotropy and the absence of the hysteresis mean an appearance of an antiferromagnetic long-range order below the transition temperature of 4.5 K instead of a spin-glass-like transition reported in the previous work. Spins in the ordered state are nearly parallel to the c axis. The magneticfield dependence of the magnetization parallel to the c axis at 2.0 K shows a rapid change around 1.0T. The rapid change disappears above the transition temperature, and is not also seen in the magnetizations parallel to the a and b axes. The results of the magnetization prove that the spin-flop transition in the antiferromagnetic longrange order occurs around 1.0T parallel to the c axis. We have discovered the magnetic long-range order caused by nonmagnetic impurities for the first time.
We would like to thank H. Kojima, I. Tanaka, and Y. Shibuya of Yamanashi University for advice on the growth of single crystals. This work is partially supported by a Grant-in-Aid from the Japan Society for the Promotion of Science.
References [-1] M. Hase, I. Terasaki and K. Uchinokura, Phys. Rev. Lett. 70 0993) 3651.
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M. Hase et al. /Physica B 215 (1995) 164-170
[2] M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura and H. Obara, Phys. Rev. Lett. 71 (1993) 4059. [3] In this paper, the susceptibility is defined as the magnetization divided by H. [4] N. Adachi, T. Hamamoto, G. Kido, M. Hase, Y. Sasago, K. Uchinokura, S. Noro and T. Yamadaya, Physica B 201 (1994) 174. We used the g values of CuGeO3. Since the g value mainly depends on the spin-orbit interaction of d electrons, it is probably independent of x. [5] J.C. Bonner and M.E. Fisher, Phys. Rev. 135 (1964) A640.
[6] For example, the result of Fe~ xCoxCl2, P. Wong, P.M. Horn, R.J. Birgeneau, C.R. Safinya and G. Shirane, Phys. Rev. Lett. 45 (1980) 1974. [7] Although the compound ZnGeO3 exists, CuGeO3 and ZnGeO3 are not isostructural. [8] M. Nishi, O. Fujita and J. Akimitsu, Phys. Rev. B 50 (1994) 6508. [9] A. Luther and I. Peschel, Phys. Rev. B 12 (1975) 3908. [10] O. Tchernyshyov, A.S. Blaer, K. Keren, K. Kojima, G.M. Luke, W.D. Wu, Y.J. Uemura, M. Hase, K. Uchinokura and Y. Ajiro, J. Magn. Magn. Mater. 140-144 (1995) 1687.