- Email: [email protected]
Magnetic susceptibility anomalies and inverse magnetic transitions in iron-enriched garnet films
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Magnetic susceptibility anomalies and inverse magnetic transitions in ironenriched garnet films
T
N.I. Mezin , Yu.I. Nepochatykh, N.Yu. Starostyuk, S.V. Yampolskii ⁎
A.A. Galkin Donetsk Institute for Physics and Engineering, R. Luxemburg Str. 72, 83114 Donetsk, Ukraine
ARTICLE INFO
ABSTRACT
Keywords: Yttrium-iron garnet films Cluster solid solution Dynamic susceptibility Spontaneous magnetization Magnetic hysteresis
Anomalous properties both of the dynamic magnetic susceptibility and the spontaneous magnetization of Y3 x Fe5 + x O12 garnet films have been experimentally observed. The most significant anomalies are the following: (a) an orientational magnetic transition at room temperature in the range of the applied magnetic field of 300–700 Oe; (b) a spontaneous magnetization vector reversal in the temperature range of 110–275 °C and the corresponding jump of the dynamic susceptibility at zero magnetic field; (c) oscillations of the magnetization in the paramagnetic state of the sample and the corresponding jumps of the dynamic susceptibility at the planar magnetic field H = 200 Oe. It has been established that all reported anomalies exhibit an inverse behavior, namely, with decrease of the applied magnetic field (or temperature) a reverse hysteresis of the field (or temperature) dependences both of the dynamic magnetic susceptibility and the spontaneous magnetization is observed. Possible reasons for such a behavior of the measured dependences are also discussed.
1. Introduction Epitaxial films of yttrium iron garnet (YIG) Y3Fe5O12 are widely used in such areas as spin-wave electronics, spintronics, sensors of weak magnetic fields, and recently have attracted more attention in view of their possible application to create communication systems based on chaotic signals [1–6]. Despite the fact that properties of YIG films have been studied in detail both theoretically and experimentally (see, e.g., [7] and references cited therein), specific effects may be observed in these objects in practice because of the technological features of their preparation. Recently, a new ferrite material has been obtained on the YIG basis, which differs from the conventional YIG in an increased iron content and has the general chemical formula Y3 x Fe5 + x O12 , where 0 x 1.5 [8]. The films of this material were grown on Gd3 Ga5O12 (111) substrates by liquid-phase epitaxy from a solution-melt containing hereditary clusters both of YIG and yttrium orthoferrite YFeO3. The obtained novel ferrite films revealed both values, the saturation magnetization and magnetic anisotropy, larger than those for the conventional YIG, while having the similar characteristics of the ferromagnetic resonance (FMR) spectrum. From the features of the crystallization kinetics and the specific physical properties of the obtained films, it was concluded that the Y3 x Fe5 + x O12 compound can be interpreted as a special kind of solid solutions, namely as a cluster solid
⁎
Corresponding author. E-mail address: [email protected] (N.I. Mezin).
https://doi.org/10.1016/j.jmmm.2018.12.099 Received 26 November 2018; Accepted 28 December 2018 Available online 28 December 2018 0304-8853/ © 2018 Elsevier B.V. All rights reserved.
solution. Its difference from the conventional solid solution consists in the fact that not individual atoms or ions but entire unit cell fragments of another crystal structure are embedded into the crystalline structure of the initial substance. In other words, the novel Y3 x Fe5 + x O12 compound is a solid solution of yttrium orthoferrite in YIG. It was also assumed that the obtained novel films have an additional metastable magnetic subsystem. In the present paper, we report the results of further studies of the magnetic properties of Y3 x Fe5 + x O12 films. In particular, the magnetic field and temperature dependences of the dynamic magnetic susceptibility are investigated, as well as the temperature dependence of the spontaneous magnetization. The observed anomalies of these dependences indicate an unusual nature of the magnetic structure of the material under study and confirm further the possible existence of an additional magnetic subsystem therein. The paper is organized as follows. In Section 2.1, a brief description of the investigated samples and the specifics of the measurement procedures are presented. Then, we study the magnetic and temperature response characteristics of the iron-enriched and conventional garnet films. First, we analyze the dependences of the dynamic magnetic susceptibility of Y2.6Fe5.4 O12 and Y3Fe5O12 films both on the applied magnetic field (Section 2.2) and on temperature (Section 2.3). The temperature dependence of the spontaneous magnetization of the Y2.6Fe5.4 O12 ferrite film is discussed in Section 2.4. Finally, in Section 3, a phenomenological explanation for
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
the observed features of the field and temperature dependences is proposed as well as all the conclusions are summarized. 2. Experiment 2.1. Investigated samples and experimental procedure A single crystal film of Y2.6Fe5.4 O12 composition in the form of a disk with diameter of about 5 mm and with the thickness of 17 µ m was chosen as a sample for studying the high-frequency magnetic susceptibility. Also, a film sample of conventional YIG, having the same shape and thickness, was used for comparative measurements. The field and temperature dependences of the dynamic magnetic susceptibility, (H ) and (T ) , were measured using the autodyne modulation method. The frequency of the autodyne generator was 5 MHz, and the amplitude of the generated high-frequency field on the sample was about 0.01 Oe. The modulation frequency of the carrier was 330 Hz. The amplitude of the modulating field was chosen in the range of 0.1–2 Oe. The samples were placed in the remote inductor of the autodyne, which was located in the working gap of the electromagnet and/or in the cell with a controlled temperature. The modulation field was produced by additional windings of the electromagnet or by Helmholtz rings. The modulating magnetic field changes the magnetic susceptibility of the sample, leading to modulation of the inductance of the external coil and, accordingly, of the autodyne’s oscillation amplitude, with the frequency of the modulating field. The amplitude A of modulation of the autodyne oscillation frequency f is proportional to the magnetic susceptibility of the material under study at the modulation frequency. Therefore, the trend of the curve A = f (T ) , recorded after its detection, is equivalent to that of the temperature dependence (T ) as well as the trend of the curve A = f (H ) is equivalent to that of the field dependence (H ) . The measured dependences were recorded with a uniform change in one of the parameters, H or T, remaining constant the second parameter. To study the temperature dependence of the spontaneous magnetization, a Y2.6Fe5.4 O12 film sample, having the thickness of 17 µ m and the dimensions of 10 × 20 mm, was magnetized and then placed in a miniature furnace made of nonmagnetic materials. A bifilar platinum wire winding was used as a heating element. The strength of the magnetic field, produced by the film’s remanent magnetization upon its heating and cooling, was measured. The typical strength value of this field on the film surface was about 1.5 Oe at room temperature (T = 23 °C). The magnetization was measured by a vector magnetometer, which fixed the magnetic field component lying in the film plane and had a sensitivity threshold of 10 3 Oe. To reduce the effect of magnetic noise, the furnace with the sample in it and the magnetometer were magnetically shielded. The zero setting of the switched-on magnetometer was achieved by the orientation of the magnetic sensor axis perpendicular to the Earth’s magnetic field line. After zeroing the magnetometer, the furnace with the sample approached the sensor of the magnetometer at a distance of 3 cm, and then the heating was turned on.
Fig. 1. Dependence of the dynamic susceptibility of the Y2.6Fe5.4 O12 film on the magnetic field H, applied perpendicular to the film plane. The red curve 1 was measured with increasing field, the black curve 2 – with decreasing field.
Fig. 2. The same as in Fig. 1, but for the conventional YIG film.
and the high-frequency field h was parallel to H . As can be seen from the figures, these dependences are significantly different. At first, let us consider the range of weak fields from 0 to 200 Oe. With increasing field H, two peaks are observed in this range in Fig. 1, while only one peak exists in Fig. 2. It has been shown in Ref. [9] that a magnetic domain structure (DS) plays an important role in producing of the response of a magnetic material to an external magnetic field. Therefore, it should be expected that the observed peaks arise as a result of the DS reconfiguration under the magnetic field H . This is confirmed by direct DS observations in the Y2.6Fe5.4 O12 film by means of the Faraday effect. With increasing the field H from 0 to 50 Oe, the labyrinth DS is transformed into a parquet-like one, this corresponds to the first peak of the red curve 1 in Fig. 1. With further increase in the field H, the latter structure changes in a strip DS whose period increases with increasing field, this causes the appearance of the second peak on the same curve. During the reverse course of the (H ) dependence (the black curve 2 in Fig. 1), the second peak is not observed, since, with decreasing field H, the parquet-like DS appears in the sample immediately from the singledomain state. In the conventional YIG film (Fig. 2), the parquet-like DS is not observed. It should be noted that the DS in the Y2.6Fe5.4 O12 film has both quality and visibility better than in the YIG one. This is apparently caused by the fact that the field of uniaxial anisotropy in the Y2.6Fe5.4 O12 film is approximately three times larger than in the YIG [8].
2.2. Field dependences of the dynamic susceptibility A study of the dynamic magnetic susceptibility provides valuable information not only about the behaviour of the magnetic system, but also about the structure of the material. It is well known that orientational and spontaneous magnetic phase transitions relate unambiguously to anomalies of the sample’s magnetic susceptibility [9]. The magnetic susceptibility of iron garnets has been studied earlier in sufficient detail, both theoretically and experimentally [9–12]. Therefore, a comparative study of the dynamic susceptibilities of the novel iron-enriched and conventional YIG films seems quite reasonable. Figs. 1 and 2 show the field dependences of the dynamic magnetic susceptibility of Y2.6Fe5.4 O12 and Y3Fe5O12 films, respectively. The external magnetic field H was applied perpendicular to the film plane, 448
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
Next, the pronounced (H ) peak in the field range of 300–700 Oe, which is observed in the Y2.6Fe5.4 O12 film and absent in the YIG one, is of the greatest interest. When observing the DS with increasing field H, it was established that approximately at the field H = 500 Oe the DS in the Y2.6Fe5.4 O12 film disappeared, i.e. transition to the single-domain state has occurred in the whole sample. The small jump in the susceptibility at the field H = 500 Oe, located on the ascending side of the large peak in Fig. 1, is apparently caused by this transition. This is confirmed by the appearance of both the strip DS and the clear susceptibility peak during the reverse course of the (H ) dependence at the same H value. It is surprising that, with a further increase in the applied field, the susceptibility increases sharply after the DS disappearance. It has been shown in Ref. [9] that, together with the DS contribution, a homogeneous component of the magnetization also substantially contributes the susceptibility value. Therefore, it is logical to assume that, in the field range of 300–700 Oe, the spin subsystem rotates as a whole by a certain angle, i.e. a field-induced orientational phase transition occurs in the sample. Notice, that the orientational phase transitions in crystals and films of rare-earth iron garnets were not previously observed at room temperatures. The phase transitions of this kind were experimentally confirmed in these materials only at low temperatures [12]. And last but not least, the main observed feature of this transition is its inverse behavior. It means that the transition exhibits a reverse hysteresis, i.e., as can be seen from Fig. 1, the susceptibility peak arises in the reverse course of the (H ) dependence (the curve 2) earlier than in its direct course (the curve 1). It should be noted that the reverse magnetic hysteresis is extremely rare in homogeneous systems. In the literature known to us, there is no information about magnetic transitions exhibiting such a type of hysteresis. Finally, let us consider the high-field region. The peaks in the (H ) dependences, located in the range of H = 1700 Oe, are present for both films studied. However, for the Y2.6Fe5.4 O12 film this peak is narrower than for the conventional YIG one, which can indicate a more perfect magnetic structure in the former film. In the literature on the magnetic susceptibility of YIG, there is no unambiguous interpretation of the nature of the high-field peaks. For example, in Ref. [11], the high-field peak is treated as a jump in the magnetic susceptibility caused by the second-order orientational phase transition. The authors of Ref. [12] give a number of counter-arguments against this treatment and guess that this anomaly of the high-frequency susceptibility is of a dual nature, arising simultaneously due to a jump-like collapse of a strip DS, whose magnetic moments are parallel to the film plane, and to a FMR which occurs under these conditions. In this paper, we will not go into this problem. When studying the field dependence of the dynamic susceptibility in the geometry of the field H being parallel to the film plane, no specific differences were observed in the magnetic susceptibilities of Y2.6Fe5.4 O12 and conventional YIG films. In general, the susceptibilities of these films depend strongly on the field H orientation with respect to the crystallographic axes in the film plane. The angular dependence ( ) , where is the angle between one of the easy magnetization axes and the field H , is characterized by regular periodicity, in accordance with the direction of the axes of easy and hard magnetization. The ( ) dependence for YIG films has been studied in detail in Refs. [13,14]. 2.3. Temperature dependences of the dynamic susceptibility Fig. 3. Temperature dependence of the dynamic susceptibility of the Y2.6Fe5.4 O12 film at the different values of the magnetic field H, applied parallel to the film plane: (a) H = 0 , (b) H = 20 Oe, (c) H = 200 Oe. The red curves 1 were measured under heating of the sample, the black curves 2 – when the sample was cooled.
Figs. 3a–c demonstrate the temperature dependences of the dynamic magnetic susceptibility, (T ) , of the Y2.6Fe5.4 O12 film at the different values of the field H applied parallel to the easy magnetization axis in the film plane. As it is seen from the figures, these dependences are extremely unusual. At zero field (Fig. 3a), under heating of the sample, an anomaly is observed in the form of an abrupt decrease in the susceptibility in the region of T = 130 °C. With a further temperature increase up to the Curie temperature TC = 287 °C, the susceptibility increases with the appearance of a series of small peaks. In the vicinity of TC , a sharp jump in the susceptibility arises, followed by a drop in its
value to almost zero. Under cooling of the sample, the (T ) dependence as a whole exhibits an inverse behavior, namely, the main peaks on the curve 2 are shifted to the higher temperatures by about 10 °C with respect to the corresponding heating peaks on the curve 1. 449
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
When the field H = 20 Oe was applied in the film plane (Fig. 3b), the susceptibility curve changed qualitatively as compared with the case of zero field. However, in the region of temperature T = 130 °C, an anomaly remained in the form of a sharp peak of the susceptibility. In general, the (T ) dependence in Fig. 3b exhibits the inverse behavior, similarly to the dependence in Fig. 3a. Also, when the temperature TC is reached, the value of susceptibility in Fig. 3,b drops to rather small values, like the case of zero field (Fig. 3a). At the field H = 200 Oe (Fig. 3c), all anomalies of the (T ) dependence, which were present in Figs. 3a and 3b in the range from room temperature to TC , disappeared. Under heating of the sample, the susceptibility curve 1 has the form of an ideal wide step that drops abruptly near TC . However, when temperature exceeds TC , three strong susceptibility peaks appear in the temperature range of 287–350 °C. Probably, the first of these peaks can be attributed to the Hopkinson peak effect [15]. The other two peaks at higher temperatures are surprising, since in this temperature range the film is in the paramagnetic state. According to traditional concepts, there should be no magnetic transformations in this state. Moreover, it should be noted that in all (T ) dependences in Fig. 3a–c, the susceptibility of the Y2.6Fe5.4 O12 film, reaching a minimum at the Curie temperature TC , tends to increase monotonically with a further increase in temperature. Such a behavior contradicts the classical concepts of the susceptibility of magnetic materials in the paramagnetic state [16]. After cooling of the sample from the maximum to room temperature, the susceptibility retains the same value that it had in the paramagnetic state. However, after 24 h, remaining at the field H = 200 Oe, the susceptibility recovered spontaneously to its original value (as depicted in Fig. 3c by the vertical dashed line). The last feature as well as the increase in susceptibility and its peaks under heating of the sample at T > TC , described above, indicate that in the paramagnetic state of the sample under the applied magnetic field some new metastable magnetic phase is formed, which after a certain time turns into an original magnetic state.
Fig. 5. Temperature dependence of the planar component of spontaneous magnetization, M0, , of the Y2.6Fe5.4 O12 film. The red curve 1 was measured under heating of the sample, the black curve 2 – when the sample was cooled.
2.4. Temperature dependence of the spontaneous magnetization To interpret the anomalies of the magnetic susceptibility, information on the field and temperature dependences of the sample magnetization, M (H ) and M (T ) , is useful. Comparative studies of the field dependences of the magnetization, M (H ) , in the Y2.6Fe5.4 O12 and conventional YIG films did not reveal any significant differences. These dependences virtually do not differ from those given in textbooks (see, for example, Ref. [16]). The temperature dependence of magnetization, M (T ) , is well known for the conventional YIG films. At temperatures T TC , it is approximately described by the Brillouin function and equals zero at higher temperatures [17]. Thus, we believe that it is not necessary to reproduce this dependence in the present paper. The temperature dependence of the spontaneous magnetization, M0, (T ) , of the Y2.6Fe5.4 O12 film under heating and cooling of the sample is shown in Fig. 5. One can see that it has an extremely unusual form and, in contrast to the conventional YIG, reveals a number of features. Under heating of the sample, the planar component of the spontaneous magnetization changed sign in the temperature range of 110–275 °C, and then, in the temperature range of 275–360 °C, made small amplitude oscillations with a change in sign, when the sample is in the paramagnetic state. The inverse behavior of the M0, (T ) dependence is also clearly seen in the figure, exhibiting a reverse hysteresis. Namely, under cooling of the sample, the broad peak of the negative magnetization is shifted to higher temperatures by about 70 °C with respect to the heating curve 1. By observing the DS, it was established that, during heating of the sample in the temperature range of 20–110 °C, the labyrinth and parquet-like DSs were transformed into the strip one, which then disappeared completely at T = 140 °C. During the cooling process, the strip DS appeared at T = 150 °C. It was characterized by a large period and a low contrast. Then, at T = 140 °C, this structure was transformed into the labyrinth DS, whose period decreased and the contrast increased considerably. With a further cooling of the film to room temperature, the labyrinth DS remained virtually unchanged. Finally, it should be also noted that the M0, (T ) dependences in Fig. 5 possessed satisfactory reproducibility.
Fig. 4. Temperature dependence of the dynamic susceptibility of the conventional YIG film at the field H = 20 Oe, applied parallel to the film plane. The red curve 1 was measured under heating of the sample, the black curve 2 – when the sample was cooled.
The (T ) dependence for the YIG film, corresponding to the same conditions as in Fig. 3b, was measured for comparison and is shown in Fig. 4. As it is seen, this dependence demonstrates the absence of any anomalies and, accordingly, of any peculiarities in the magnetic structure of the conventional YIG, in contrast to the iron-enriched garnet film. This fact can also be considered as additional evidence of the existence of a metastable magnetic phase in the latter object.
3. Discussion and conclusion Based on the results obtained previously [8], one could be concluded that the Y3 x Fe5 + x O12 compound represents a conventional YIG, which has higher values of magnetization and anisotropy field. Really, the crystal lattice of the Y3 x Fe5 + x O12 compound does not differ from 450
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
the YIG one, except the unit cell size, which is approximately 0.2 nm smaller than that of the YIG. However, the anomalous dependences of the dynamic magnetic susceptibility, (H ) and (T ) , as well as of the spontaneous magnetization, M0, (T ) , obtained in the present study, do not fit such an interpretation. Thus, if based on the YIG structure, there are no physical reasons for the appearance of a strong additional peak in the (H ) dependence (Fig. 1) in the range of field H = 300 700 Oe. Indeed, at the field of maximum of this peak, the DS in the sample is absent. Moreover, any magnetization anomalies are not observed in the considered range of applied field H for all combinations of the uniaxial and cubic anisotropy constants, Ku , K1 and K2 , possible in the conventional YIG structure [18]. The temperature anomalies of the susceptibility, (T ) , also can not be explained only by the YIG structure. They are uniquely related to the temperature anomaly of the spontaneous magnetization M0, (T ) , which changes sign in the same temperature range where the susceptibility anomalies are observed in Figs. 3a and b. It is clear that the strong susceptibility peaks in the paramagnetic state (Fig. 3c) are also associated with the magnetization oscillations in this state. However, the M0, (T ) dependence itself remains incomprehensible. Really, based on the YIG crystal structure, it is impossible to imagine the spontaneous reorientation of the magnetic moment by 180 °, as is the case in Fig. 5. The transition of the magnetic system to the metastable state in the paramagnetic phase, when exposed to the magnetic field, also requires separate interpretation. Taking into account the available data, it is possible to propose the following qualitative model, which could partially explain the anomalies obtained. Since there are excess ions of iron in the Y2.6Fe5.4 O12 film, which are located in the dodecahedral positions of the garnet structure (see Ref. [8]), it is logical to assume that, in addition to the two magnetic sublattices a and d containing Fe3 + cations, the third magnetic sublattice c, containing such cations, exists in the structure. By analogy with the magnetic structure of the Gd3 Fe5 O12 garnet, where the Gd3 + cations possess a magnetic moment, it can be assumed that, in Y3 x Fe5 + x O12 compounds, there is a ‘weak’ magnetic sublattice resulted from the unidirectional magnetic anisotropy [19]. In the Gd3 Fe5 O12 compound, the magnetic ordering in the ‘weak’ sublattice is caused only by the negative effective exchange field produced by the ‘strong’ sublattice ad. The magnetic moment of the ‘weak’ sublattice is antiparallel to the total magnetic moment of the ‘strong’ sublattice ad. At the same time, in the Y3 x Fe5 + x O12 compound, the magnetic moment of the ‘weak’ sublattice is parallel to the moment of the sublattice ad. This is evidenced by higher values of the saturation magnetization in Y3 x Fe5 + x O12 films, as compared to the YIG ones [8]. The ‘intrinsic’ exchange interaction between the Fe3 + cations in the c-sublattice is apparently not as weak as that between the Gd3 + ones. It is commensurate with the positive effective exchange field produced by the ‘strong’ ad-sublattice. Therefore, the magnetic ordering in the c-sublattice is caused by both the above interactions. If the magnetizations of the ‘strong’ and ‘weak’ sublattices have different temperature and field dependences, the resulting magnetic moment will have an increased sensitivity to temperature and/or an external magnetic field, exhibiting various anomalies. It can be deduced from the anomaly of the M0, (T ) dependence (the red curve 1 in Fig. 5) that, as a result of the competition between the exchange interactions of the ‘strong’ and ‘weak’ sublattices, a 180-degree reorientation of the easy magnetization axis occurs in the film plane with increasing temperature in the range of 110–275 °C. Apparently, the appearance of spontaneous magnetization oscillations and susceptibility peaks in the paramagnetic state in the Y2.6Fe5.4 O12 film (Figs. 3c and 5) can also be associated with the competitive interaction between the ‘weak’ and ‘strong’ magnetic sublattices. However, a monotonic increase in the magnetic susceptibility in the paramagnetic state with increasing temperature can hardly be attributed to the interaction of the magnetic sublattices. To make any assumption about this phenomenon, it is necessary to follow the changes of both magnetization and dynamic
susceptibility at higher temperatures. The inverse behavior of the anomalies of both magnetic susceptibility and magnetization is of particular interest. As was already noted above, in the known literature, there is no information about magnetic transformations possessing a reverse hysteresis. The results obtained in this paper are not enough to offer, at least, a phenomenological model that could explain adequately this phenomenon. However, at the present stage of research, one can come closer to understanding its nature by allowing an analogy between reverse magnetic hysteresis, observed in the Y3 x Fe5 + x O12 compound, and inverted hysteresis loops known in heterogeneous structures [20–23]. The peculiarity of the latter is that a negative remanent magnetization is observed, when the positive magnetic field is turned off. This effect is observed exclusively in heterogeneous (non-single phase) magnetic systems. These systems have a non-uniform layered or granular structure with clearly defined interfaces between the phases. The magnetostatic or exchange interaction between these phases causes the appearance of inverted hysteresis loops. Thus, by allowing an analogy between inverted hysteresis loops and inverse magnetic transitions in our material, we can make some assumptions about the nature of the observed anomalies. It is obvious that in this case it is necessary to abandon the concept of a single-phase material. However, the single-phase structure of Y3 x Fe5 + x O12 compound is not in doubt, because this is evidenced by X-ray data as well as by perfect dynamic characteristics (for example, the FMR line width in Y3 x Fe5 + x O12 films is the same as in the best YIG samples [8]). As a result, a paradoxical situation arises. On the one hand, we have a singlephase, homogeneous system. On the other hand, the observed anomalies force us to make an assumption about the existence of another phase in this system, ensuring the heterogeneity of the system’s magnetic structure. We believe that the resolution of this contradiction is possible by considering the structure of a cluster solid solution, to which type also the Y3 x Fe5 + x O12 compound belongs. Namely, the existence of magnetic heterogeneity in the ideal (in the first approximation) homogeneous crystal structure is, probably, the main distinctive feature of a cluster solid solution. In our case, the role of the second phase is played by the clusters of yttrium orthoferrite YFeO3 . Being embedded into the YIG structure, they form an additional metastable magnetic subsystem (i.e., a ‘weak’ sublattice), which manifests itself in the measured dependences as detected anomalies related to induced and spontaneous magnetic transitions. The phenomenological model of the formation of a unit cell fragment from the clusters of orthoferrite and garnet is presented in Ref. [8]. Apparently, the reverse magnetic hysteresis is also associated with the orthoferrite clusters. In this connection, and also taking into account the anomalies in the magnetic susceptibility and magnetization observed in the paramagnetic state, it should be noted that induced and spontaneous spin-reorientation transitions are commonplace in orthoferrites, and the Curie temperature for the YFeO3 compound is almost 180 °C higher than for the YIG [10]. In conclusion, anomalies of dynamic magnetic susceptibility and spontaneous magnetization of the iron-enriched garnet film Y2.6Fe5.4 O12 have been experimentally found. The most significant of them are the following: (a) the existence of an additional peak in the magnetic field dependence of the dynamic susceptibility, (H ) , at relatively small applied fields; (b) a sharp jump in the temperature dependence of the dynamic susceptibility, (T ) , at temperatures T < TC and at zero magnetic field; (c) the presence of strong susceptibility peaks at T > TC as well as a tendency to increase the susceptibility value in the paramagnetic state of the sample; (d) a change in the direction of the spontaneous magnetization vector, M0, (T ) , at T < TC and its oscillation with a change of sign in the paramagnetic state of the sample; 451
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
(e) the inverse hysteresis behavior of all observed magnetic anomalies.
[7] V. Cherepanov, I. Kolokolov, V. L’vov, Phys. Rep.-Rev. Sec. Phys. Lett. 229 (1993) 81. [8] N.I. Mezin, N.Yu. Starostyuk, S.V. Yampolskii, J. Magn. Magn. Mater. 442 (2017) 189. [9] I.E. Dikstein, F.V. Lisovskii, E.G. Mansvetova, E.S. Chizhik, Zh. Eksp. Teor. Fiz. 90 (1986) 614 [Sov. Phys. JETP 63 (1986) 357]. [10] K.P. Belov, A.K. Zvezdin, A.M. Kadomtseva, R.Z. Levitin, Orientational Transitions in Rare-Earth Magnets, Nauka, Moscow, 1979 (in Russian). [11] V.D. Buchel’nikov, N.K. Dan’shin, A.I. Linnik, L.T. Tsymbal, V.G. Shavrov, Zh. Eksp. Teor. Fiz. 122 (2002) 122 [JETP 95 (2002) 106]. [12] V.F. Shkar’, E.I. Nikolaev, V.N. Sayapin, V.D. Poimanov, Fiz. Tverd. Tela 46 (2004) 1043 [Phys. Solid State 46 (2004) 1073]. [13] B.A. Belyaev, S.N. Kulinich, V.V. Tyurnev, Investigation of Quasistatic Magnetization Reversal and High-Frequency Susceptibility of Yttrium Iron Garnet Films, Preprint No. 556F, Institute of Physics, Siberian Division, USSR Academy of Sciences, Krasnoyarsk, 1989 (in Russian). [14] I.I. Syvorotka, I.M. Syvorotka, V.G. Shavrov, V.A. Skidanov, P.M. Vetoshko, Inplane transverse susceptibility of (111)-oriented iron garnet films, 10th European Conference on Magnetic Sensors and Actuators July 6–9, EMSA-2014, Vienna, Austria, 2014, p. 153. [15] J. Hopkinson, Phil. Trans. R. Soc. Lond. A 180 (1889) 443, https://doi.org/10. 1098/rsta.1889.0014. [16] S. Chikazumi, Physics of Magnetism, Wiley, New York, 1964. [17] E.E. Anderson, Phys. Rev. 134 (1964) A1581. [18] S.B. Ubizskii, J. Magn. Magn. Mater. 219 (2000) 127. [19] K.P. Belov, Uspekhi Fiz. Nauk 169 (1999) 797 [Phys. Usp. 42 (1999) 711]. [20] A.S. Arrott, Origin of Hysteresis in Ultra Thin Films, in: A. Hernando (Ed.), Nanomagnetism, NATO ASI Series, Kluwer Academic Publisher, Dordrecht, 1993, p. 73. [21] M.J. Oshea, A.L. Al-Sharif, J. Appl. Phys. 75 (1994) 6673. [22] P.W. Haycock, M.F. Chioncel, J. Shal, J. Magn. Magn. Mater. 242–245 (2002) 1057. [23] K. Takanashi, H. Kurokawa, H. Fujimori, Appl. Phys. Lett. 63 (1993) 1585.
These anomalies can not be explained exclusively on the basis of the crystal structure of a conventional YIG. Therefore, it was assumed that an additional metastable magnetic subsystem of the ‘weak’ sublattice type exists in the Y2.6Fe5.4 O12 film, causing all the anomalies noted above. The existence of such a subsystem is possible in the structure of a cluster solid solution, the type of which also includes the Y2.6Fe5.4 O12 compound. To confirm these assumptions, additional studies of the magnetic structure of films by neutron diffraction, as well as X-ray diffraction studies of samples during their heating and cooling in an applied magnetic field, are necessary. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] Y.F. Chen, K.T. Wu, T.D. Yao, C.H. Peng, K.L. You, W.S. Tse, Microelectron. Eng. 81 (2005) 329. [2] A.A. Serga, A.V. Chumak, B. Hillebrands, J. Phys. D: Appl. Phys. 43 (2010) 264002 . [3] O. Kamada, H. Minemoto, S. Ishizuka, J. Appl. Phys. 61 (1987) 3268. [4] O. d’Allivy Kelly, A. Anane, R. Bernard, J. Ben Youssef, C. Hahn, A.H. Molpeceres, C. Carrétéro, E. Jaue, C. Deranlot, P. Bortolotti, R. Lebourgeois, J.C. Mage, G. de Loubens, O. Klein, V. Cros, A. Fert, Appl. Phys. Lett. 103 (2013) 082408 . [5] M. Wu, B.A. Kalinikos, C.E. Patton, Phys. Rev. Lett. 95 (2005) 237202. [6] N.I. Mezin, A.A. Glushchenko, Yu.E. Kuzovlev, Pis’ma Zh. Tekh. Fiz. 38 (2012) 14 [Tech. Phys. Lett. 38 (2012) 876].
452
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Magnetic susceptibility anomalies and inverse magnetic transitions in ironenriched garnet films
T
N.I. Mezin , Yu.I. Nepochatykh, N.Yu. Starostyuk, S.V. Yampolskii ⁎
A.A. Galkin Donetsk Institute for Physics and Engineering, R. Luxemburg Str. 72, 83114 Donetsk, Ukraine
ARTICLE INFO
ABSTRACT
Keywords: Yttrium-iron garnet films Cluster solid solution Dynamic susceptibility Spontaneous magnetization Magnetic hysteresis
Anomalous properties both of the dynamic magnetic susceptibility and the spontaneous magnetization of Y3 x Fe5 + x O12 garnet films have been experimentally observed. The most significant anomalies are the following: (a) an orientational magnetic transition at room temperature in the range of the applied magnetic field of 300–700 Oe; (b) a spontaneous magnetization vector reversal in the temperature range of 110–275 °C and the corresponding jump of the dynamic susceptibility at zero magnetic field; (c) oscillations of the magnetization in the paramagnetic state of the sample and the corresponding jumps of the dynamic susceptibility at the planar magnetic field H = 200 Oe. It has been established that all reported anomalies exhibit an inverse behavior, namely, with decrease of the applied magnetic field (or temperature) a reverse hysteresis of the field (or temperature) dependences both of the dynamic magnetic susceptibility and the spontaneous magnetization is observed. Possible reasons for such a behavior of the measured dependences are also discussed.
1. Introduction Epitaxial films of yttrium iron garnet (YIG) Y3Fe5O12 are widely used in such areas as spin-wave electronics, spintronics, sensors of weak magnetic fields, and recently have attracted more attention in view of their possible application to create communication systems based on chaotic signals [1–6]. Despite the fact that properties of YIG films have been studied in detail both theoretically and experimentally (see, e.g., [7] and references cited therein), specific effects may be observed in these objects in practice because of the technological features of their preparation. Recently, a new ferrite material has been obtained on the YIG basis, which differs from the conventional YIG in an increased iron content and has the general chemical formula Y3 x Fe5 + x O12 , where 0 x 1.5 [8]. The films of this material were grown on Gd3 Ga5O12 (111) substrates by liquid-phase epitaxy from a solution-melt containing hereditary clusters both of YIG and yttrium orthoferrite YFeO3. The obtained novel ferrite films revealed both values, the saturation magnetization and magnetic anisotropy, larger than those for the conventional YIG, while having the similar characteristics of the ferromagnetic resonance (FMR) spectrum. From the features of the crystallization kinetics and the specific physical properties of the obtained films, it was concluded that the Y3 x Fe5 + x O12 compound can be interpreted as a special kind of solid solutions, namely as a cluster solid
⁎
Corresponding author. E-mail address: [email protected] (N.I. Mezin).
https://doi.org/10.1016/j.jmmm.2018.12.099 Received 26 November 2018; Accepted 28 December 2018 Available online 28 December 2018 0304-8853/ © 2018 Elsevier B.V. All rights reserved.
solution. Its difference from the conventional solid solution consists in the fact that not individual atoms or ions but entire unit cell fragments of another crystal structure are embedded into the crystalline structure of the initial substance. In other words, the novel Y3 x Fe5 + x O12 compound is a solid solution of yttrium orthoferrite in YIG. It was also assumed that the obtained novel films have an additional metastable magnetic subsystem. In the present paper, we report the results of further studies of the magnetic properties of Y3 x Fe5 + x O12 films. In particular, the magnetic field and temperature dependences of the dynamic magnetic susceptibility are investigated, as well as the temperature dependence of the spontaneous magnetization. The observed anomalies of these dependences indicate an unusual nature of the magnetic structure of the material under study and confirm further the possible existence of an additional magnetic subsystem therein. The paper is organized as follows. In Section 2.1, a brief description of the investigated samples and the specifics of the measurement procedures are presented. Then, we study the magnetic and temperature response characteristics of the iron-enriched and conventional garnet films. First, we analyze the dependences of the dynamic magnetic susceptibility of Y2.6Fe5.4 O12 and Y3Fe5O12 films both on the applied magnetic field (Section 2.2) and on temperature (Section 2.3). The temperature dependence of the spontaneous magnetization of the Y2.6Fe5.4 O12 ferrite film is discussed in Section 2.4. Finally, in Section 3, a phenomenological explanation for
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
the observed features of the field and temperature dependences is proposed as well as all the conclusions are summarized. 2. Experiment 2.1. Investigated samples and experimental procedure A single crystal film of Y2.6Fe5.4 O12 composition in the form of a disk with diameter of about 5 mm and with the thickness of 17 µ m was chosen as a sample for studying the high-frequency magnetic susceptibility. Also, a film sample of conventional YIG, having the same shape and thickness, was used for comparative measurements. The field and temperature dependences of the dynamic magnetic susceptibility, (H ) and (T ) , were measured using the autodyne modulation method. The frequency of the autodyne generator was 5 MHz, and the amplitude of the generated high-frequency field on the sample was about 0.01 Oe. The modulation frequency of the carrier was 330 Hz. The amplitude of the modulating field was chosen in the range of 0.1–2 Oe. The samples were placed in the remote inductor of the autodyne, which was located in the working gap of the electromagnet and/or in the cell with a controlled temperature. The modulation field was produced by additional windings of the electromagnet or by Helmholtz rings. The modulating magnetic field changes the magnetic susceptibility of the sample, leading to modulation of the inductance of the external coil and, accordingly, of the autodyne’s oscillation amplitude, with the frequency of the modulating field. The amplitude A of modulation of the autodyne oscillation frequency f is proportional to the magnetic susceptibility of the material under study at the modulation frequency. Therefore, the trend of the curve A = f (T ) , recorded after its detection, is equivalent to that of the temperature dependence (T ) as well as the trend of the curve A = f (H ) is equivalent to that of the field dependence (H ) . The measured dependences were recorded with a uniform change in one of the parameters, H or T, remaining constant the second parameter. To study the temperature dependence of the spontaneous magnetization, a Y2.6Fe5.4 O12 film sample, having the thickness of 17 µ m and the dimensions of 10 × 20 mm, was magnetized and then placed in a miniature furnace made of nonmagnetic materials. A bifilar platinum wire winding was used as a heating element. The strength of the magnetic field, produced by the film’s remanent magnetization upon its heating and cooling, was measured. The typical strength value of this field on the film surface was about 1.5 Oe at room temperature (T = 23 °C). The magnetization was measured by a vector magnetometer, which fixed the magnetic field component lying in the film plane and had a sensitivity threshold of 10 3 Oe. To reduce the effect of magnetic noise, the furnace with the sample in it and the magnetometer were magnetically shielded. The zero setting of the switched-on magnetometer was achieved by the orientation of the magnetic sensor axis perpendicular to the Earth’s magnetic field line. After zeroing the magnetometer, the furnace with the sample approached the sensor of the magnetometer at a distance of 3 cm, and then the heating was turned on.
Fig. 1. Dependence of the dynamic susceptibility of the Y2.6Fe5.4 O12 film on the magnetic field H, applied perpendicular to the film plane. The red curve 1 was measured with increasing field, the black curve 2 – with decreasing field.
Fig. 2. The same as in Fig. 1, but for the conventional YIG film.
and the high-frequency field h was parallel to H . As can be seen from the figures, these dependences are significantly different. At first, let us consider the range of weak fields from 0 to 200 Oe. With increasing field H, two peaks are observed in this range in Fig. 1, while only one peak exists in Fig. 2. It has been shown in Ref. [9] that a magnetic domain structure (DS) plays an important role in producing of the response of a magnetic material to an external magnetic field. Therefore, it should be expected that the observed peaks arise as a result of the DS reconfiguration under the magnetic field H . This is confirmed by direct DS observations in the Y2.6Fe5.4 O12 film by means of the Faraday effect. With increasing the field H from 0 to 50 Oe, the labyrinth DS is transformed into a parquet-like one, this corresponds to the first peak of the red curve 1 in Fig. 1. With further increase in the field H, the latter structure changes in a strip DS whose period increases with increasing field, this causes the appearance of the second peak on the same curve. During the reverse course of the (H ) dependence (the black curve 2 in Fig. 1), the second peak is not observed, since, with decreasing field H, the parquet-like DS appears in the sample immediately from the singledomain state. In the conventional YIG film (Fig. 2), the parquet-like DS is not observed. It should be noted that the DS in the Y2.6Fe5.4 O12 film has both quality and visibility better than in the YIG one. This is apparently caused by the fact that the field of uniaxial anisotropy in the Y2.6Fe5.4 O12 film is approximately three times larger than in the YIG [8].
2.2. Field dependences of the dynamic susceptibility A study of the dynamic magnetic susceptibility provides valuable information not only about the behaviour of the magnetic system, but also about the structure of the material. It is well known that orientational and spontaneous magnetic phase transitions relate unambiguously to anomalies of the sample’s magnetic susceptibility [9]. The magnetic susceptibility of iron garnets has been studied earlier in sufficient detail, both theoretically and experimentally [9–12]. Therefore, a comparative study of the dynamic susceptibilities of the novel iron-enriched and conventional YIG films seems quite reasonable. Figs. 1 and 2 show the field dependences of the dynamic magnetic susceptibility of Y2.6Fe5.4 O12 and Y3Fe5O12 films, respectively. The external magnetic field H was applied perpendicular to the film plane, 448
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
Next, the pronounced (H ) peak in the field range of 300–700 Oe, which is observed in the Y2.6Fe5.4 O12 film and absent in the YIG one, is of the greatest interest. When observing the DS with increasing field H, it was established that approximately at the field H = 500 Oe the DS in the Y2.6Fe5.4 O12 film disappeared, i.e. transition to the single-domain state has occurred in the whole sample. The small jump in the susceptibility at the field H = 500 Oe, located on the ascending side of the large peak in Fig. 1, is apparently caused by this transition. This is confirmed by the appearance of both the strip DS and the clear susceptibility peak during the reverse course of the (H ) dependence at the same H value. It is surprising that, with a further increase in the applied field, the susceptibility increases sharply after the DS disappearance. It has been shown in Ref. [9] that, together with the DS contribution, a homogeneous component of the magnetization also substantially contributes the susceptibility value. Therefore, it is logical to assume that, in the field range of 300–700 Oe, the spin subsystem rotates as a whole by a certain angle, i.e. a field-induced orientational phase transition occurs in the sample. Notice, that the orientational phase transitions in crystals and films of rare-earth iron garnets were not previously observed at room temperatures. The phase transitions of this kind were experimentally confirmed in these materials only at low temperatures [12]. And last but not least, the main observed feature of this transition is its inverse behavior. It means that the transition exhibits a reverse hysteresis, i.e., as can be seen from Fig. 1, the susceptibility peak arises in the reverse course of the (H ) dependence (the curve 2) earlier than in its direct course (the curve 1). It should be noted that the reverse magnetic hysteresis is extremely rare in homogeneous systems. In the literature known to us, there is no information about magnetic transitions exhibiting such a type of hysteresis. Finally, let us consider the high-field region. The peaks in the (H ) dependences, located in the range of H = 1700 Oe, are present for both films studied. However, for the Y2.6Fe5.4 O12 film this peak is narrower than for the conventional YIG one, which can indicate a more perfect magnetic structure in the former film. In the literature on the magnetic susceptibility of YIG, there is no unambiguous interpretation of the nature of the high-field peaks. For example, in Ref. [11], the high-field peak is treated as a jump in the magnetic susceptibility caused by the second-order orientational phase transition. The authors of Ref. [12] give a number of counter-arguments against this treatment and guess that this anomaly of the high-frequency susceptibility is of a dual nature, arising simultaneously due to a jump-like collapse of a strip DS, whose magnetic moments are parallel to the film plane, and to a FMR which occurs under these conditions. In this paper, we will not go into this problem. When studying the field dependence of the dynamic susceptibility in the geometry of the field H being parallel to the film plane, no specific differences were observed in the magnetic susceptibilities of Y2.6Fe5.4 O12 and conventional YIG films. In general, the susceptibilities of these films depend strongly on the field H orientation with respect to the crystallographic axes in the film plane. The angular dependence ( ) , where is the angle between one of the easy magnetization axes and the field H , is characterized by regular periodicity, in accordance with the direction of the axes of easy and hard magnetization. The ( ) dependence for YIG films has been studied in detail in Refs. [13,14]. 2.3. Temperature dependences of the dynamic susceptibility Fig. 3. Temperature dependence of the dynamic susceptibility of the Y2.6Fe5.4 O12 film at the different values of the magnetic field H, applied parallel to the film plane: (a) H = 0 , (b) H = 20 Oe, (c) H = 200 Oe. The red curves 1 were measured under heating of the sample, the black curves 2 – when the sample was cooled.
Figs. 3a–c demonstrate the temperature dependences of the dynamic magnetic susceptibility, (T ) , of the Y2.6Fe5.4 O12 film at the different values of the field H applied parallel to the easy magnetization axis in the film plane. As it is seen from the figures, these dependences are extremely unusual. At zero field (Fig. 3a), under heating of the sample, an anomaly is observed in the form of an abrupt decrease in the susceptibility in the region of T = 130 °C. With a further temperature increase up to the Curie temperature TC = 287 °C, the susceptibility increases with the appearance of a series of small peaks. In the vicinity of TC , a sharp jump in the susceptibility arises, followed by a drop in its
value to almost zero. Under cooling of the sample, the (T ) dependence as a whole exhibits an inverse behavior, namely, the main peaks on the curve 2 are shifted to the higher temperatures by about 10 °C with respect to the corresponding heating peaks on the curve 1. 449
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
When the field H = 20 Oe was applied in the film plane (Fig. 3b), the susceptibility curve changed qualitatively as compared with the case of zero field. However, in the region of temperature T = 130 °C, an anomaly remained in the form of a sharp peak of the susceptibility. In general, the (T ) dependence in Fig. 3b exhibits the inverse behavior, similarly to the dependence in Fig. 3a. Also, when the temperature TC is reached, the value of susceptibility in Fig. 3,b drops to rather small values, like the case of zero field (Fig. 3a). At the field H = 200 Oe (Fig. 3c), all anomalies of the (T ) dependence, which were present in Figs. 3a and 3b in the range from room temperature to TC , disappeared. Under heating of the sample, the susceptibility curve 1 has the form of an ideal wide step that drops abruptly near TC . However, when temperature exceeds TC , three strong susceptibility peaks appear in the temperature range of 287–350 °C. Probably, the first of these peaks can be attributed to the Hopkinson peak effect [15]. The other two peaks at higher temperatures are surprising, since in this temperature range the film is in the paramagnetic state. According to traditional concepts, there should be no magnetic transformations in this state. Moreover, it should be noted that in all (T ) dependences in Fig. 3a–c, the susceptibility of the Y2.6Fe5.4 O12 film, reaching a minimum at the Curie temperature TC , tends to increase monotonically with a further increase in temperature. Such a behavior contradicts the classical concepts of the susceptibility of magnetic materials in the paramagnetic state [16]. After cooling of the sample from the maximum to room temperature, the susceptibility retains the same value that it had in the paramagnetic state. However, after 24 h, remaining at the field H = 200 Oe, the susceptibility recovered spontaneously to its original value (as depicted in Fig. 3c by the vertical dashed line). The last feature as well as the increase in susceptibility and its peaks under heating of the sample at T > TC , described above, indicate that in the paramagnetic state of the sample under the applied magnetic field some new metastable magnetic phase is formed, which after a certain time turns into an original magnetic state.
Fig. 5. Temperature dependence of the planar component of spontaneous magnetization, M0, , of the Y2.6Fe5.4 O12 film. The red curve 1 was measured under heating of the sample, the black curve 2 – when the sample was cooled.
2.4. Temperature dependence of the spontaneous magnetization To interpret the anomalies of the magnetic susceptibility, information on the field and temperature dependences of the sample magnetization, M (H ) and M (T ) , is useful. Comparative studies of the field dependences of the magnetization, M (H ) , in the Y2.6Fe5.4 O12 and conventional YIG films did not reveal any significant differences. These dependences virtually do not differ from those given in textbooks (see, for example, Ref. [16]). The temperature dependence of magnetization, M (T ) , is well known for the conventional YIG films. At temperatures T TC , it is approximately described by the Brillouin function and equals zero at higher temperatures [17]. Thus, we believe that it is not necessary to reproduce this dependence in the present paper. The temperature dependence of the spontaneous magnetization, M0, (T ) , of the Y2.6Fe5.4 O12 film under heating and cooling of the sample is shown in Fig. 5. One can see that it has an extremely unusual form and, in contrast to the conventional YIG, reveals a number of features. Under heating of the sample, the planar component of the spontaneous magnetization changed sign in the temperature range of 110–275 °C, and then, in the temperature range of 275–360 °C, made small amplitude oscillations with a change in sign, when the sample is in the paramagnetic state. The inverse behavior of the M0, (T ) dependence is also clearly seen in the figure, exhibiting a reverse hysteresis. Namely, under cooling of the sample, the broad peak of the negative magnetization is shifted to higher temperatures by about 70 °C with respect to the heating curve 1. By observing the DS, it was established that, during heating of the sample in the temperature range of 20–110 °C, the labyrinth and parquet-like DSs were transformed into the strip one, which then disappeared completely at T = 140 °C. During the cooling process, the strip DS appeared at T = 150 °C. It was characterized by a large period and a low contrast. Then, at T = 140 °C, this structure was transformed into the labyrinth DS, whose period decreased and the contrast increased considerably. With a further cooling of the film to room temperature, the labyrinth DS remained virtually unchanged. Finally, it should be also noted that the M0, (T ) dependences in Fig. 5 possessed satisfactory reproducibility.
Fig. 4. Temperature dependence of the dynamic susceptibility of the conventional YIG film at the field H = 20 Oe, applied parallel to the film plane. The red curve 1 was measured under heating of the sample, the black curve 2 – when the sample was cooled.
The (T ) dependence for the YIG film, corresponding to the same conditions as in Fig. 3b, was measured for comparison and is shown in Fig. 4. As it is seen, this dependence demonstrates the absence of any anomalies and, accordingly, of any peculiarities in the magnetic structure of the conventional YIG, in contrast to the iron-enriched garnet film. This fact can also be considered as additional evidence of the existence of a metastable magnetic phase in the latter object.
3. Discussion and conclusion Based on the results obtained previously [8], one could be concluded that the Y3 x Fe5 + x O12 compound represents a conventional YIG, which has higher values of magnetization and anisotropy field. Really, the crystal lattice of the Y3 x Fe5 + x O12 compound does not differ from 450
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
the YIG one, except the unit cell size, which is approximately 0.2 nm smaller than that of the YIG. However, the anomalous dependences of the dynamic magnetic susceptibility, (H ) and (T ) , as well as of the spontaneous magnetization, M0, (T ) , obtained in the present study, do not fit such an interpretation. Thus, if based on the YIG structure, there are no physical reasons for the appearance of a strong additional peak in the (H ) dependence (Fig. 1) in the range of field H = 300 700 Oe. Indeed, at the field of maximum of this peak, the DS in the sample is absent. Moreover, any magnetization anomalies are not observed in the considered range of applied field H for all combinations of the uniaxial and cubic anisotropy constants, Ku , K1 and K2 , possible in the conventional YIG structure [18]. The temperature anomalies of the susceptibility, (T ) , also can not be explained only by the YIG structure. They are uniquely related to the temperature anomaly of the spontaneous magnetization M0, (T ) , which changes sign in the same temperature range where the susceptibility anomalies are observed in Figs. 3a and b. It is clear that the strong susceptibility peaks in the paramagnetic state (Fig. 3c) are also associated with the magnetization oscillations in this state. However, the M0, (T ) dependence itself remains incomprehensible. Really, based on the YIG crystal structure, it is impossible to imagine the spontaneous reorientation of the magnetic moment by 180 °, as is the case in Fig. 5. The transition of the magnetic system to the metastable state in the paramagnetic phase, when exposed to the magnetic field, also requires separate interpretation. Taking into account the available data, it is possible to propose the following qualitative model, which could partially explain the anomalies obtained. Since there are excess ions of iron in the Y2.6Fe5.4 O12 film, which are located in the dodecahedral positions of the garnet structure (see Ref. [8]), it is logical to assume that, in addition to the two magnetic sublattices a and d containing Fe3 + cations, the third magnetic sublattice c, containing such cations, exists in the structure. By analogy with the magnetic structure of the Gd3 Fe5 O12 garnet, where the Gd3 + cations possess a magnetic moment, it can be assumed that, in Y3 x Fe5 + x O12 compounds, there is a ‘weak’ magnetic sublattice resulted from the unidirectional magnetic anisotropy [19]. In the Gd3 Fe5 O12 compound, the magnetic ordering in the ‘weak’ sublattice is caused only by the negative effective exchange field produced by the ‘strong’ sublattice ad. The magnetic moment of the ‘weak’ sublattice is antiparallel to the total magnetic moment of the ‘strong’ sublattice ad. At the same time, in the Y3 x Fe5 + x O12 compound, the magnetic moment of the ‘weak’ sublattice is parallel to the moment of the sublattice ad. This is evidenced by higher values of the saturation magnetization in Y3 x Fe5 + x O12 films, as compared to the YIG ones [8]. The ‘intrinsic’ exchange interaction between the Fe3 + cations in the c-sublattice is apparently not as weak as that between the Gd3 + ones. It is commensurate with the positive effective exchange field produced by the ‘strong’ ad-sublattice. Therefore, the magnetic ordering in the c-sublattice is caused by both the above interactions. If the magnetizations of the ‘strong’ and ‘weak’ sublattices have different temperature and field dependences, the resulting magnetic moment will have an increased sensitivity to temperature and/or an external magnetic field, exhibiting various anomalies. It can be deduced from the anomaly of the M0, (T ) dependence (the red curve 1 in Fig. 5) that, as a result of the competition between the exchange interactions of the ‘strong’ and ‘weak’ sublattices, a 180-degree reorientation of the easy magnetization axis occurs in the film plane with increasing temperature in the range of 110–275 °C. Apparently, the appearance of spontaneous magnetization oscillations and susceptibility peaks in the paramagnetic state in the Y2.6Fe5.4 O12 film (Figs. 3c and 5) can also be associated with the competitive interaction between the ‘weak’ and ‘strong’ magnetic sublattices. However, a monotonic increase in the magnetic susceptibility in the paramagnetic state with increasing temperature can hardly be attributed to the interaction of the magnetic sublattices. To make any assumption about this phenomenon, it is necessary to follow the changes of both magnetization and dynamic
susceptibility at higher temperatures. The inverse behavior of the anomalies of both magnetic susceptibility and magnetization is of particular interest. As was already noted above, in the known literature, there is no information about magnetic transformations possessing a reverse hysteresis. The results obtained in this paper are not enough to offer, at least, a phenomenological model that could explain adequately this phenomenon. However, at the present stage of research, one can come closer to understanding its nature by allowing an analogy between reverse magnetic hysteresis, observed in the Y3 x Fe5 + x O12 compound, and inverted hysteresis loops known in heterogeneous structures [20–23]. The peculiarity of the latter is that a negative remanent magnetization is observed, when the positive magnetic field is turned off. This effect is observed exclusively in heterogeneous (non-single phase) magnetic systems. These systems have a non-uniform layered or granular structure with clearly defined interfaces between the phases. The magnetostatic or exchange interaction between these phases causes the appearance of inverted hysteresis loops. Thus, by allowing an analogy between inverted hysteresis loops and inverse magnetic transitions in our material, we can make some assumptions about the nature of the observed anomalies. It is obvious that in this case it is necessary to abandon the concept of a single-phase material. However, the single-phase structure of Y3 x Fe5 + x O12 compound is not in doubt, because this is evidenced by X-ray data as well as by perfect dynamic characteristics (for example, the FMR line width in Y3 x Fe5 + x O12 films is the same as in the best YIG samples [8]). As a result, a paradoxical situation arises. On the one hand, we have a singlephase, homogeneous system. On the other hand, the observed anomalies force us to make an assumption about the existence of another phase in this system, ensuring the heterogeneity of the system’s magnetic structure. We believe that the resolution of this contradiction is possible by considering the structure of a cluster solid solution, to which type also the Y3 x Fe5 + x O12 compound belongs. Namely, the existence of magnetic heterogeneity in the ideal (in the first approximation) homogeneous crystal structure is, probably, the main distinctive feature of a cluster solid solution. In our case, the role of the second phase is played by the clusters of yttrium orthoferrite YFeO3 . Being embedded into the YIG structure, they form an additional metastable magnetic subsystem (i.e., a ‘weak’ sublattice), which manifests itself in the measured dependences as detected anomalies related to induced and spontaneous magnetic transitions. The phenomenological model of the formation of a unit cell fragment from the clusters of orthoferrite and garnet is presented in Ref. [8]. Apparently, the reverse magnetic hysteresis is also associated with the orthoferrite clusters. In this connection, and also taking into account the anomalies in the magnetic susceptibility and magnetization observed in the paramagnetic state, it should be noted that induced and spontaneous spin-reorientation transitions are commonplace in orthoferrites, and the Curie temperature for the YFeO3 compound is almost 180 °C higher than for the YIG [10]. In conclusion, anomalies of dynamic magnetic susceptibility and spontaneous magnetization of the iron-enriched garnet film Y2.6Fe5.4 O12 have been experimentally found. The most significant of them are the following: (a) the existence of an additional peak in the magnetic field dependence of the dynamic susceptibility, (H ) , at relatively small applied fields; (b) a sharp jump in the temperature dependence of the dynamic susceptibility, (T ) , at temperatures T < TC and at zero magnetic field; (c) the presence of strong susceptibility peaks at T > TC as well as a tendency to increase the susceptibility value in the paramagnetic state of the sample; (d) a change in the direction of the spontaneous magnetization vector, M0, (T ) , at T < TC and its oscillation with a change of sign in the paramagnetic state of the sample; 451
Journal of Magnetism and Magnetic Materials 476 (2019) 447–452
N.I. Mezin et al.
(e) the inverse hysteresis behavior of all observed magnetic anomalies.
[7] V. Cherepanov, I. Kolokolov, V. L’vov, Phys. Rep.-Rev. Sec. Phys. Lett. 229 (1993) 81. [8] N.I. Mezin, N.Yu. Starostyuk, S.V. Yampolskii, J. Magn. Magn. Mater. 442 (2017) 189. [9] I.E. Dikstein, F.V. Lisovskii, E.G. Mansvetova, E.S. Chizhik, Zh. Eksp. Teor. Fiz. 90 (1986) 614 [Sov. Phys. JETP 63 (1986) 357]. [10] K.P. Belov, A.K. Zvezdin, A.M. Kadomtseva, R.Z. Levitin, Orientational Transitions in Rare-Earth Magnets, Nauka, Moscow, 1979 (in Russian). [11] V.D. Buchel’nikov, N.K. Dan’shin, A.I. Linnik, L.T. Tsymbal, V.G. Shavrov, Zh. Eksp. Teor. Fiz. 122 (2002) 122 [JETP 95 (2002) 106]. [12] V.F. Shkar’, E.I. Nikolaev, V.N. Sayapin, V.D. Poimanov, Fiz. Tverd. Tela 46 (2004) 1043 [Phys. Solid State 46 (2004) 1073]. [13] B.A. Belyaev, S.N. Kulinich, V.V. Tyurnev, Investigation of Quasistatic Magnetization Reversal and High-Frequency Susceptibility of Yttrium Iron Garnet Films, Preprint No. 556F, Institute of Physics, Siberian Division, USSR Academy of Sciences, Krasnoyarsk, 1989 (in Russian). [14] I.I. Syvorotka, I.M. Syvorotka, V.G. Shavrov, V.A. Skidanov, P.M. Vetoshko, Inplane transverse susceptibility of (111)-oriented iron garnet films, 10th European Conference on Magnetic Sensors and Actuators July 6–9, EMSA-2014, Vienna, Austria, 2014, p. 153. [15] J. Hopkinson, Phil. Trans. R. Soc. Lond. A 180 (1889) 443, https://doi.org/10. 1098/rsta.1889.0014. [16] S. Chikazumi, Physics of Magnetism, Wiley, New York, 1964. [17] E.E. Anderson, Phys. Rev. 134 (1964) A1581. [18] S.B. Ubizskii, J. Magn. Magn. Mater. 219 (2000) 127. [19] K.P. Belov, Uspekhi Fiz. Nauk 169 (1999) 797 [Phys. Usp. 42 (1999) 711]. [20] A.S. Arrott, Origin of Hysteresis in Ultra Thin Films, in: A. Hernando (Ed.), Nanomagnetism, NATO ASI Series, Kluwer Academic Publisher, Dordrecht, 1993, p. 73. [21] M.J. Oshea, A.L. Al-Sharif, J. Appl. Phys. 75 (1994) 6673. [22] P.W. Haycock, M.F. Chioncel, J. Shal, J. Magn. Magn. Mater. 242–245 (2002) 1057. [23] K. Takanashi, H. Kurokawa, H. Fujimori, Appl. Phys. Lett. 63 (1993) 1585.
These anomalies can not be explained exclusively on the basis of the crystal structure of a conventional YIG. Therefore, it was assumed that an additional metastable magnetic subsystem of the ‘weak’ sublattice type exists in the Y2.6Fe5.4 O12 film, causing all the anomalies noted above. The existence of such a subsystem is possible in the structure of a cluster solid solution, the type of which also includes the Y2.6Fe5.4 O12 compound. To confirm these assumptions, additional studies of the magnetic structure of films by neutron diffraction, as well as X-ray diffraction studies of samples during their heating and cooling in an applied magnetic field, are necessary. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] Y.F. Chen, K.T. Wu, T.D. Yao, C.H. Peng, K.L. You, W.S. Tse, Microelectron. Eng. 81 (2005) 329. [2] A.A. Serga, A.V. Chumak, B. Hillebrands, J. Phys. D: Appl. Phys. 43 (2010) 264002 . [3] O. Kamada, H. Minemoto, S. Ishizuka, J. Appl. Phys. 61 (1987) 3268. [4] O. d’Allivy Kelly, A. Anane, R. Bernard, J. Ben Youssef, C. Hahn, A.H. Molpeceres, C. Carrétéro, E. Jaue, C. Deranlot, P. Bortolotti, R. Lebourgeois, J.C. Mage, G. de Loubens, O. Klein, V. Cros, A. Fert, Appl. Phys. Lett. 103 (2013) 082408 . [5] M. Wu, B.A. Kalinikos, C.E. Patton, Phys. Rev. Lett. 95 (2005) 237202. [6] N.I. Mezin, A.A. Glushchenko, Yu.E. Kuzovlev, Pis’ma Zh. Tekh. Fiz. 38 (2012) 14 [Tech. Phys. Lett. 38 (2012) 876].
452