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Magnetic properties of amorphous Mn–Y alloys
Journal of Magnetism and Magnetic Materials 202 (1999) 505}513
Magnetic properties of amorphous Mn}Y alloys Y. Obi *, S. Murayama, A. Azuma, H. Fujimori , K.V. Rao Institute for Materials Research, Tohoku University, Sendai 980, Japan Muroran Institute of Technology, Muroran 050, Japan The Royal Institute of Technology, S-100 44 Stockholm, Sweden Received 1 September 1998
Abstract Magnetic properties of amorphous Mn Y alloys have been investigated by means of the measurement of V \V magnetization and low "eld AC-susceptibility at temperature range from 4.2 K to room temperature. All the samples investigated show spin glass properties at low-temperature region. The spin glass transition temperature ¹ increases linearly with increasing Mn content. This spin glass characteristic results from the frustration in the spin system which is caused by the competition of positive and negative interactions between the randomly distributed Mn atoms. 1999 Elsevier Science B.V. All rights reserved. PACS: 75.50.Kj; 75.50.Lk; 81.15.Cd Keywords: Amorphous alloys; Magnetic properties; AC-susceptibility; Spin glasses
1. Introduction Magnetic properties of Mn-based binary amorphous alloys have not been so much investigated in comparison with those of other 3d magnetic element-based amorphous alloys such as Fe-, Co- and Ni-X (where X denotes 3d, 4d or 5d metal element). Several investigations, however, have been reported, for example, Mn}Sn [1}3], Mn}Zr [4,5], Mn}Nb [5], Mn}La [6], Mn}Al [7], Mn-X (X"3d, 4d, 5d elements) [8], etc. Much discussion has focused into the magnetic nature of Mn atoms located in randomly distributed con"g-
* Corresponding author. Tel.: #81-22-215-2097; fax: #8122-215-2096. E-mail address: [email protected] (Y. Obi)
urations in the amorphous network, so far. Usually magnetic behavior of Mn atoms is much in#uenced by its environment. In crystalline Mn-based binary alloys or intermetallic compounds the de"nite con"guration of Mn atoms gives the de"nite spin structure such as ferromagnetic or antiferromagnetic depending on a sign of overall exchange interactions. For example, Mn Pt is ferromagnetic [9], while MnPt is antiferromagnetic [10]. On the other hand, in crystalline dilute Mn alloys such as CuMn [11,12] and AgMn [13,14], spin glass characteristics often appear. The reason is that each Mn atom locates randomly, and the direct exchange interaction between Mn}Mn pairs is negligible but instead the indirect long-range RKKY interactions through conduction electrons play an important role. These interactions oscillate between positive and negative sign depending on Mn}Mn atomic
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separations [15,16], and as a result frustrations occur in the spin system, giving rise to randomly freezing of spins at low temperatures. In the amorphous alloys, even though the alloys contain high concentration of Mn atoms, the spin glass like behavior appears occasionally for both the Mn}metalloid and Mn}metal alloy systems, such as Mn}B [17}19], Mn}C [20], Mn}Si [20}22], Mn}Ge [20], Mn}Sn [3], Mn}Al [7], and Mn}La [6]. In these amorphous alloys, Mn atoms do not take a de"nite ferromagnetic or antiferromagnetic ordering due to the structure disorder and random distribution of Mn atoms, but instead the spin system causes the frustration due to the random distribution of the exchange interactions between Mn}Mn pairs. Mn and Y have almost no solubility with each other [23,24]. They form several intermetallic compounds such as Mn Y, Mn Y and Mn Y. Mn Y takes the Laves phase structure and below about 100 K it becomes to an itinerant electron antiferromagnetic state [25}27]. Mn Y is also an itinerant electron antiferromagnet having ¹ &120 K [28]. While Mn Y is ferrimagnetic , having ¹ &500 K [29,30]. Shimizu and Inoue [31] calculated the density of state for these compounds on the basis of the band model. Shiga reported [32] that Mn Y is very favorable to the band magnetism and has large spin #uctuations. Usually, Mn-based intermetallic compounds have much variety of magnetism related to its structure and/or its local environment of Mn atoms. Since Mn and Y are not soluble with each other, the magnetic properties of overall composition regions of the crystalline Mn}Y alloy are never known while amorphous (a-) Mn}Y alloy is able to be synthesized for wide range of Mn content. Accordingly, the magnetic properties of this alloy, especially the magnetic behavior of Mn atoms, is possible to be an object of a study. Thus, it is interesting and desirable to investigate in detail the magnetic properties of a-Mn}Y alloys for wide range of Mn content and compare them to the crystalline compounds. Our preliminary report have revealed [6,33] that a-Mn}Y alloys have a spin glass phase for wide region of Mn content by means of the measurement of AC-susceptibility. In the present study, we have
investigated the magnetic properties of aMn Y alloys in detail, and especially the V \V nature of the spin glass characteristics in a wide range of Mn content. Recently, Kakehashi and Yu (KY) [34,35] have investigated theoretically the magnetism of a-TMY (TM denotes 3d-element) alloys using the "nitetemperature theory based on the itinerant electron magnetism. According to their theory, Fe-based amorphous alloys such as Fe}Y, La, Ce, etc. exhibit the itinerant electron spin glass characteristics which are caused by the competition of the ferromagnetic and antiferromagnetic interactions due to the structure disorder. They also analyzed [36,37] the spin glass behavior of a-Mn}Y alloy on the basis of their theory. We will attempt to interpret our experimental data from the standpoint of their theory.
2. Experimental Amorphous Mn Y alloys were prepared by V \V a DC high rate sputtering method onto watercooled Cu substrates. Target materials of Mn}Y were made by arc melting of Mn (99.9% in purity) and Y (99.9% in purity) to desirable compositions. Thicknesses of sputtered samples are about 400}800 lm. The amorphous structure was con"rmed by an X-ray di!raction analysis (XRD). Mn concentrations were changed from x"20 to 80 nominally. All the samples having the nominal Mn concentrations of x"20 to 80 were con"rmed to amorphous structure by XRD. The compositions of these amorphous samples were analyzed chemically and the results are listed in Table 1. Near the composition of Mn Y which nearly corresponds to the crystalline Laves phase compound (Mn Y), it was very hard to make a target material because of its brittleness. The above composition of thus made amorphous alloy is fairly shifted as shown in Table 1. Isothermal magnetizations around the liquid He temperature and the temperature dependence of magnetization have been measured by a pendulum-type magnetometer (PTM), VSM and SQUID magnetometer under the temperature range from 4.2 K to room temperature applying the magnetic
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Table 1 Several physical parameters for the present a-Mn Y alloy V \V Concentration
Notation
Mn Y (Nominal)
Mn (Analyzed)
Y
20 30 40 50 55 60 60 70 70 80
18.4 27.6 37.0 48.3 52.3 54.1 56.6 56.8 53.2 75.8
81.6 72.4 63.0 51.7 47.7 45.9 43.4 43.2 46.8 24.2
80 70 60 50 45 40 40 30 30 20
Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y
p
¹
s
(emu/g)
(K)
2.75 2.66 2.38 1.90 1.53 } 1.41 } 1.46 0.784
12.1 17.5 26.0 34.0 37.2 } } 39.4 } 53.0
h
C
p [Mn]
p [Mn,Y]
(10\ emu/g) (K)
(10\ emu deg/g)
(k )
(k )
0.34 9 0.430 0.537 0.664 } } } 0.708 0.670 0.800
164.5 210.0 204.7 186.5 } } } 159.8 165.1 93.56
2.46 2.18 1.84 1.50 } } } 1.25 1.33 0.788
1.04 1.15 1.12 1.04 } } } 0.943 0.967 0.687
!3.2 !5.2 !6.9 !8.2 } } } !11.2 !9.2 !13.6
Values are taken at 48 kOe and at 4.5 K.
"eld up to about 18 kOe for PTM and VSM, and up to 50 kOe for SQUID. Low "eld AC-susceptibility was measured by an AC-bridge mutual inductance method at a constant AC "eld of 4 Oe operated by a constant frequency of 400 Hz.
3. Results and discussion Fig. 1 shows magnetization curves of the present a-Mn}Y alloys at 4.5 K under the applied magnetic "eld up to 50 kOe. Curves of Y-rich region (x(40) behave as convex upward but do not saturate up to 50 kOe and those having x'40 are slightly concave upward in low and medium "eld regions. In addition, all the curves exhibit a large hysteresis phenomenon and "eld-cooled samples from about 100 K under a constant magnetic "eld of 50 kOe show unsymmetrical hysteresis loop (not shown here), suggesting that present alloys are not simply paramagnetic and that there exist certain exchange couplings between magnetic spins. In this "gure, the value of the magnetization at a "xed magnetic "eld (for instance, at H"48 kOe) decreases with increasing Mn content. This result is clearly seen in Fig. 2 which also includes peak values of ACsusceptibility versus temperature s as shown later (Fig. 4). Decreases of p and s with increas ing Mn content predict the increase of the strength
Fig. 1. Magnetization curves of a-Mn Y alloys at 4.5 K as V \V a function of applied magnetic "eld.
of Mn}Mn negative exchange interactions. KY [37] calculated the exchange pair energies for a-Mn with changing the local environment (l) and deduced that the pair energy increases negatively as l increases (Fig. 6a in Ref. [37]). The temperature dependence of magnetization under the constant magnetic "eld of H"9.5 kOe is shown in Fig. 3. All the curves have a broad peak at low-temperature regions, showing that a certain ordering occurs there. Below those peaks, p}¹ curves accompany a large thermal hysteresis depending on the direction of measurements. A typical
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Fig. 2. Magnetic moment p at H"48 kOe and AC-susceptibility peak s as a function of Mn content x of Mn Y . V \V
Fig. 4. Real part of AC-susceptibility s under a low AC "eld of 4 Oe as a function of temperature for Mn Y . V \V
Fig. 3. Temperature dependence of the magnetization p under a constant magnetic "eld of H"9.5 kOe for Mn Y . Inset V \V shows the thermal hysteresis of magnetization of Mn Y as a typical example. Arrows show the direction of measurement.
Fig. 5. The spin glass transition temperature ¹ as a function of Mn content x for Mn Y . A full line is a result of the V \V least-squares "t.
example is shown in the inset of this "gure for Mn Y . Arrows indicate the direction of decreas ing temperatures, or of increasing temperature, respectively, under the constant "eld. This phenomenon is characteristic to the randomly quenched spin ordering such as a spin glass state. The real part of AC-susceptibility as a function of temperature is shown in Fig. 4. All the curves have a cusp at low-temperature region, showing an evidence of the spin glass transition for all the samples investigated. With decreasing Mn content the cusp becomes sharper and shifts to low-temperature
side. In Mn Y the measurement of thermal-hys teresis of AC-susceptibility has revealed the existence of a spin glass phase but not an antiferromagnetic phase below the peak though the transition is not so sharp and not so clear. Mn concentration x dependence of the spin glass transition temperature ¹ is shown in Fig. 5. ¹ changes linearly on the whole as a function of the Mn content, suggesting that ¹ is closely re lated to the number of Mn}Mn pairs as mentioned below. Since Mn and Y atoms distribute statistically, the number of nearest-neighbor (nn) Mn
Y. Obi et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 505}513
atoms (coordination number) z depends on the + Mn content (x) and is nearly proportional to it, and the number of Mn}Mn pairs increase roughly proportional to x. Sherrington and Kirkpatrick (SK) [38,39] have calculated theoretically the spin glass transition temperature of dilute magnetic alloys based on the molecular "eld formalism. Krusin-Elbaum et al. have extended [40] their theory for the amorphous Heusler alloys Cu MnZ (Z"Al, In or Sn), which include long-range indirect ferromagnetic and antiferromagnetic exchange interactions and direct antiferromagnetic exchange interactions of Mn atoms. The result is that ¹ "( /3(3)S(S#1)( Z J#Z J) . G G G
(1)
The summation represents a sum over the i nearG est neighbors. Here S is the spin quantum number, and Z is the number of interacting pairs at radius G r around a given Mn atom, and J is the exchange G G integral between atom i and the given atom. Z is the number of nearest neighbors which interact via the antiferromagnetic direct exchange J . In conformity with this formula, ¹ depends directly on Z (here, Z includes both Z and Z ). Since G Z depends on the Mn content, the increase of ¹ with respect to Mn concentration for the present amorphous alloys might be roughly interpreted as the increase of Z . SK-model followed by several models [41,42], however, are based on the Ising spin system where each spin has S "$. While in 8 our amorphous system the spin values of each Mn atom cannot be estimated suitably, and they probably distribute statistically depending on the local environment of the Mn atom and an average nn Mn}Mn distance. Strictly, this model is not always applicable in the present case, because the di!erence in S and also its distribution must in#uence the value of ¹ . In such a case Eq. (1) must be modi"ed. Nevertheless, it is plausible that ¹ is closely related to the number of Mn}Mn pairs. With increasing Mn content, Mn gradually loses the magnetic moment. This is attributed to the fact that net antiferromagnetic interaction becomes larger with an increasing Mn content. Therefore, s
509
is suppressed by degrees and the cusp is smeared out inspite of an increase in ¹ . KY have calculated the spin glass transition temperature ¹ as a func tion of the Y content for a-Mn}Y (Fig. 10 in Ref. [37]). Their result has the same tendency to our experimental results but the absolute values are 2.5}3 times larger. They ascribed this discrepancy to (i) the theoretically adopted molecular "eld approximation and the neglect of the transverse spin #uctuations, and (ii) existing of the atomic short range order in the present amorphous samples. Temperature dependence of the magnetic susceptibility (p/H) shown in Fig. 3 can be "tted by the so-called Curie}Weiss (CW) law including a constant term of susceptibility s . In both (a) the local magnetic moment limit and (b) the weakly ferromagnetic limit (for instance, ZrZn and Ni Al, etc. are corresponded), susceptibility versus temperature curves often obey the ¹\ rule (CW-law) s"s #C/(¹!h),
(2)
where s is the constant term of susceptibility, C the e!ective Curie constant and h the asymptotic Curie temperature. Using the above equation we can calculate the e!ective values of h, s and C. Results are listed in Table 1, and s and h are also shown in Figs. 6 and 7, respectively. As mentioned later the e!ective paramagnetic moment p can be deduced
Fig. 6. The constant term of susceptibility s as a function of x for Mn Y (closed circles). The spin susceptibility of pure V \V Mn and Y metals [44] is also shown (open circles). A dotted line is a guide to the eye.
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Fig. 7. The asymptotic Curie temperature (h) as a function of Mn content x for Mn Y . V \V
Fig. 8. The e!ective paramagnetic moment (p ) as a function of Mn content x for Mn Y . Dotted and broken lines are V \V a guide to the eye.
from the Curie constant C for (a) the local moment limit. In (b) the weakly ferromagnetic limit, however, C does not give correctly the e!ective paramagnetic moment. According to SCR theory [43] the CW law originates from the linear increase of S(¹), where S(¹) is the average squared ampli* * tude of the local spin #uctuation, and C is proportional to ¹\ which is the longitudinal sti!ness constant for the spin #uctuation. In this paragraph we discuss provisionally on the basis of (a) the localized magnetic scheme. The constant term s as seen in Fig. 6 describes a tem perature-independent susceptibility. s usually comes from a non-localized origin. In this "gure the spin susceptibility of pure Mn and Y metals [44] are also shown. Present data of s smoothly con nect with those of Mn and Y locating on each end of abscissa. h versus x curve shown in Fig. 7 indicates that overall Mn}Mn interactions are negative regardless of the Mn content. This negative interaction becomes greater with increasing the Mn content. The reason can be considered that the nn Mn}Mn negative interaction becomes more intensive with increasing Mn content due to the increase of z , whereas the sum of the long-range interac+ tions through conduction electrons (RKKY-type) is probably not dependent on Mn content because they compete as a whole due to their oscillating nature. Though present argument stands on the hypothesis of the localized model, the result has
the same tendency with the theoretical one for the exchange pair energies of a-Mn by KY (Fig. 6a in Ref. [37]). The e!ective paramagnetic moment p is calculated as p "C(3k /Nk)(A/a),
(3)
where N is the Avogadro's number, k the Bohr magneton, A the atomic weight and a the atomic fraction of magnetic atoms. The parameter p is listed in Table 1 and shown in Fig. 8 as a function of Mn content. In this "gure, we exhibit two di!erent values of p [Mn] where only Mn bears the mag netic moment and p [Mn,Y] where both Mn and Y have the magnetic moment. p [Mn] linearly decreases with increasing Mn content. This is the same tendency to the magnetization at 48 kOe as seen in Fig. 2. But p [Mn, Y] does not change so steeply compared to p [Mn] but it takes a broad maximum around x&30. As a matter of course, the value of p has certain ambiguity depending on the choice of s even though the estimation of Curie constant C has been done by the leastsquares "t. KY shows theoretically that the calculated results of s\}¹ curve with upwards convexities below 1000 K for Mn Y is originated from the amplitude #uctuation of local moments. Actually as shown in Fig. 9, all the present s\}¹ curves have upward convexities. Two basic mechanisms can be considered for these upward convexities:
Y. Obi et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 505}513
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Fig. 9. Inverse susceptibility as a function of temperature for Mn Y . V \V
Fig. 10. Values of AC-susceptibility at 80 K, and DC-susceptibility at 80 and 300 K as a function of Mn content. Lines are a guide to the eye.
one is the existence of nearly temperature-independent paramagnetic moment and another is the linear temperature variation of amplitude #uctuation as argued by CW. But these two mechanisms are di$cult to be separated well. At the present time, it is well known that the magnetism of Mn-based metallic alloys obeys (b) the itinerant electron magnetism. Therefore, it is rather essential to discuss the magnetic properties of the present alloys on the basis of the itinerant electron magnetism. To do so, it is necessary to accumulate experimental data giving the informations about the itinerant electronic behaviors such as the spin #uctuation. Our recent study [45] of thermal expansion measurements has revealed the existence of appreciable spin #uctuations in aMn Y , which anticipates the itinerant electronic behavior in this alloy. KY have calculated the spin susceptibility of a-Mn}Y (Fig. 16 in Ref. [37]). They have explained in the "gure that the calculated susceptibility peak is characterized as a crossover from the itinerant behavior to the local moment behavior. In Fig. 10, AC-susceptibility at 80 K and DC-susceptibilities at 80 and 300 K are shown. Both susceptibilities at 80 K have a peak around x&35. Susceptibility at 300 K also have a peak around x&50. These results may indicate the crossover between itinerant behavior and local moment behavior. More detailed experimental studies for the basic magnetic properties based on the
itinerant electron magnetism is necessary to the better understandings of the present amorphous alloys. Here we consider about a criterion for the appearance of the spin glass phase in the present amorphous alloys. For the appearance of the spin glass phase in condensed random alloy systems the following conditions might be necessary: (i) certain frustration exists in the spin system due to lattice disorders or frustrated spin arrangements and (ii) the system has basically the negative magnetic interactions. Amorphous Mn}Y alloys satisfy the above conditions su$ciently. Therefore, the spin glass characteristic is anticipated to be easily realized. As reported already [5,8], several Mn-based amorphous binary alloys such as Mn}Ti, Zr, Nb and Ta, however, do not show the spin glass characteristics down to 4.2 K despite probably satisfying the above conditions. The reason is not clear now. One possibility that the spin glass ordering occurs at very low temperature (below 4.5 K) for these alloys is still left unsolved. We now attempt to analyze the magnetic behavior of present a-Mn}Y alloys comprehensively as follows: (i) a given Mn atom roughly has about 12 coordination number (z &12) like crystalline +>7 FCC or HCP structure. The magnetic moment of each Mn atom is subjected to the Mn-coordination number z . When z is small (that is, in Y-rich + + side) Mn atom has rather large moment, while
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when z is large (that is, in Mn-rich side) it has + a rather small moment, (ii) the nearest neighbor Mn}Mn interaction which is determined by nn Mn}Mn distance r is antiferromagnetic. The net magnetic interaction may be dominated by the nn Mn}Mn interaction, since the long-range Mn}Mn interactions may oscillate between positive and negative and they are totally leveled o! towards nearly zero. Thus, the net negative magnetic interaction becomes greater when z is large and + (iii) Mn}Mn antiferromagnetic exchange interactions cause the spin glass freezing at low temperature. Besides, the spin glass transition temperature ¹ strongly depends on the Mn concentration.
4. Summary We have investigated the magnetic properties of a-Mn Y alloys and obtained the following V \V results. (1) The magnetization versus applied magnetic "eld at 4.5 K does not saturate up to about 50 kOe and shows a large hysteresis. (2) The values of magnetization at H"48 kOe and at 4.5 K decrease almost linearly with increasing the Mn content, suggesting that the net antiferromagnetic interactions becomes larger. (3) The spin glass nature appears for all the Mn concentration range investigated. The spin glass transition temperature ¹ increases al most linearly with increasing the Mn content, whereas AC-susceptibility peak is gradually suppressed owing to the increase of the net antiferromagnetic couplings. (4) The present results are qualitatively explained by Kakehashi and Yu's "nite-temperature theory based on the itinerant electron magnetism.
Acknowledgements This work was supported by a Grant-in-Aid for Scienti"c Research on Priority Areas (No. 03240102) from the Ministry of Education, Science, Sports and Culture, Japan.
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Magnetic properties of amorphous Mn}Y alloys Y. Obi *, S. Murayama, A. Azuma, H. Fujimori , K.V. Rao Institute for Materials Research, Tohoku University, Sendai 980, Japan Muroran Institute of Technology, Muroran 050, Japan The Royal Institute of Technology, S-100 44 Stockholm, Sweden Received 1 September 1998
Abstract Magnetic properties of amorphous Mn Y alloys have been investigated by means of the measurement of V \V magnetization and low "eld AC-susceptibility at temperature range from 4.2 K to room temperature. All the samples investigated show spin glass properties at low-temperature region. The spin glass transition temperature ¹ increases linearly with increasing Mn content. This spin glass characteristic results from the frustration in the spin system which is caused by the competition of positive and negative interactions between the randomly distributed Mn atoms. 1999 Elsevier Science B.V. All rights reserved. PACS: 75.50.Kj; 75.50.Lk; 81.15.Cd Keywords: Amorphous alloys; Magnetic properties; AC-susceptibility; Spin glasses
1. Introduction Magnetic properties of Mn-based binary amorphous alloys have not been so much investigated in comparison with those of other 3d magnetic element-based amorphous alloys such as Fe-, Co- and Ni-X (where X denotes 3d, 4d or 5d metal element). Several investigations, however, have been reported, for example, Mn}Sn [1}3], Mn}Zr [4,5], Mn}Nb [5], Mn}La [6], Mn}Al [7], Mn-X (X"3d, 4d, 5d elements) [8], etc. Much discussion has focused into the magnetic nature of Mn atoms located in randomly distributed con"g-
* Corresponding author. Tel.: #81-22-215-2097; fax: #8122-215-2096. E-mail address: [email protected] (Y. Obi)
urations in the amorphous network, so far. Usually magnetic behavior of Mn atoms is much in#uenced by its environment. In crystalline Mn-based binary alloys or intermetallic compounds the de"nite con"guration of Mn atoms gives the de"nite spin structure such as ferromagnetic or antiferromagnetic depending on a sign of overall exchange interactions. For example, Mn Pt is ferromagnetic [9], while MnPt is antiferromagnetic [10]. On the other hand, in crystalline dilute Mn alloys such as CuMn [11,12] and AgMn [13,14], spin glass characteristics often appear. The reason is that each Mn atom locates randomly, and the direct exchange interaction between Mn}Mn pairs is negligible but instead the indirect long-range RKKY interactions through conduction electrons play an important role. These interactions oscillate between positive and negative sign depending on Mn}Mn atomic
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separations [15,16], and as a result frustrations occur in the spin system, giving rise to randomly freezing of spins at low temperatures. In the amorphous alloys, even though the alloys contain high concentration of Mn atoms, the spin glass like behavior appears occasionally for both the Mn}metalloid and Mn}metal alloy systems, such as Mn}B [17}19], Mn}C [20], Mn}Si [20}22], Mn}Ge [20], Mn}Sn [3], Mn}Al [7], and Mn}La [6]. In these amorphous alloys, Mn atoms do not take a de"nite ferromagnetic or antiferromagnetic ordering due to the structure disorder and random distribution of Mn atoms, but instead the spin system causes the frustration due to the random distribution of the exchange interactions between Mn}Mn pairs. Mn and Y have almost no solubility with each other [23,24]. They form several intermetallic compounds such as Mn Y, Mn Y and Mn Y. Mn Y takes the Laves phase structure and below about 100 K it becomes to an itinerant electron antiferromagnetic state [25}27]. Mn Y is also an itinerant electron antiferromagnet having ¹ &120 K [28]. While Mn Y is ferrimagnetic , having ¹ &500 K [29,30]. Shimizu and Inoue [31] calculated the density of state for these compounds on the basis of the band model. Shiga reported [32] that Mn Y is very favorable to the band magnetism and has large spin #uctuations. Usually, Mn-based intermetallic compounds have much variety of magnetism related to its structure and/or its local environment of Mn atoms. Since Mn and Y are not soluble with each other, the magnetic properties of overall composition regions of the crystalline Mn}Y alloy are never known while amorphous (a-) Mn}Y alloy is able to be synthesized for wide range of Mn content. Accordingly, the magnetic properties of this alloy, especially the magnetic behavior of Mn atoms, is possible to be an object of a study. Thus, it is interesting and desirable to investigate in detail the magnetic properties of a-Mn}Y alloys for wide range of Mn content and compare them to the crystalline compounds. Our preliminary report have revealed [6,33] that a-Mn}Y alloys have a spin glass phase for wide region of Mn content by means of the measurement of AC-susceptibility. In the present study, we have
investigated the magnetic properties of aMn Y alloys in detail, and especially the V \V nature of the spin glass characteristics in a wide range of Mn content. Recently, Kakehashi and Yu (KY) [34,35] have investigated theoretically the magnetism of a-TMY (TM denotes 3d-element) alloys using the "nitetemperature theory based on the itinerant electron magnetism. According to their theory, Fe-based amorphous alloys such as Fe}Y, La, Ce, etc. exhibit the itinerant electron spin glass characteristics which are caused by the competition of the ferromagnetic and antiferromagnetic interactions due to the structure disorder. They also analyzed [36,37] the spin glass behavior of a-Mn}Y alloy on the basis of their theory. We will attempt to interpret our experimental data from the standpoint of their theory.
2. Experimental Amorphous Mn Y alloys were prepared by V \V a DC high rate sputtering method onto watercooled Cu substrates. Target materials of Mn}Y were made by arc melting of Mn (99.9% in purity) and Y (99.9% in purity) to desirable compositions. Thicknesses of sputtered samples are about 400}800 lm. The amorphous structure was con"rmed by an X-ray di!raction analysis (XRD). Mn concentrations were changed from x"20 to 80 nominally. All the samples having the nominal Mn concentrations of x"20 to 80 were con"rmed to amorphous structure by XRD. The compositions of these amorphous samples were analyzed chemically and the results are listed in Table 1. Near the composition of Mn Y which nearly corresponds to the crystalline Laves phase compound (Mn Y), it was very hard to make a target material because of its brittleness. The above composition of thus made amorphous alloy is fairly shifted as shown in Table 1. Isothermal magnetizations around the liquid He temperature and the temperature dependence of magnetization have been measured by a pendulum-type magnetometer (PTM), VSM and SQUID magnetometer under the temperature range from 4.2 K to room temperature applying the magnetic
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507
Table 1 Several physical parameters for the present a-Mn Y alloy V \V Concentration
Notation
Mn Y (Nominal)
Mn (Analyzed)
Y
20 30 40 50 55 60 60 70 70 80
18.4 27.6 37.0 48.3 52.3 54.1 56.6 56.8 53.2 75.8
81.6 72.4 63.0 51.7 47.7 45.9 43.4 43.2 46.8 24.2
80 70 60 50 45 40 40 30 30 20
Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y Mn Y
p
¹
s
(emu/g)
(K)
2.75 2.66 2.38 1.90 1.53 } 1.41 } 1.46 0.784
12.1 17.5 26.0 34.0 37.2 } } 39.4 } 53.0
h
C
p [Mn]
p [Mn,Y]
(10\ emu/g) (K)
(10\ emu deg/g)
(k )
(k )
0.34 9 0.430 0.537 0.664 } } } 0.708 0.670 0.800
164.5 210.0 204.7 186.5 } } } 159.8 165.1 93.56
2.46 2.18 1.84 1.50 } } } 1.25 1.33 0.788
1.04 1.15 1.12 1.04 } } } 0.943 0.967 0.687
!3.2 !5.2 !6.9 !8.2 } } } !11.2 !9.2 !13.6
Values are taken at 48 kOe and at 4.5 K.
"eld up to about 18 kOe for PTM and VSM, and up to 50 kOe for SQUID. Low "eld AC-susceptibility was measured by an AC-bridge mutual inductance method at a constant AC "eld of 4 Oe operated by a constant frequency of 400 Hz.
3. Results and discussion Fig. 1 shows magnetization curves of the present a-Mn}Y alloys at 4.5 K under the applied magnetic "eld up to 50 kOe. Curves of Y-rich region (x(40) behave as convex upward but do not saturate up to 50 kOe and those having x'40 are slightly concave upward in low and medium "eld regions. In addition, all the curves exhibit a large hysteresis phenomenon and "eld-cooled samples from about 100 K under a constant magnetic "eld of 50 kOe show unsymmetrical hysteresis loop (not shown here), suggesting that present alloys are not simply paramagnetic and that there exist certain exchange couplings between magnetic spins. In this "gure, the value of the magnetization at a "xed magnetic "eld (for instance, at H"48 kOe) decreases with increasing Mn content. This result is clearly seen in Fig. 2 which also includes peak values of ACsusceptibility versus temperature s as shown later (Fig. 4). Decreases of p and s with increas ing Mn content predict the increase of the strength
Fig. 1. Magnetization curves of a-Mn Y alloys at 4.5 K as V \V a function of applied magnetic "eld.
of Mn}Mn negative exchange interactions. KY [37] calculated the exchange pair energies for a-Mn with changing the local environment (l) and deduced that the pair energy increases negatively as l increases (Fig. 6a in Ref. [37]). The temperature dependence of magnetization under the constant magnetic "eld of H"9.5 kOe is shown in Fig. 3. All the curves have a broad peak at low-temperature regions, showing that a certain ordering occurs there. Below those peaks, p}¹ curves accompany a large thermal hysteresis depending on the direction of measurements. A typical
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Fig. 2. Magnetic moment p at H"48 kOe and AC-susceptibility peak s as a function of Mn content x of Mn Y . V \V
Fig. 4. Real part of AC-susceptibility s under a low AC "eld of 4 Oe as a function of temperature for Mn Y . V \V
Fig. 3. Temperature dependence of the magnetization p under a constant magnetic "eld of H"9.5 kOe for Mn Y . Inset V \V shows the thermal hysteresis of magnetization of Mn Y as a typical example. Arrows show the direction of measurement.
Fig. 5. The spin glass transition temperature ¹ as a function of Mn content x for Mn Y . A full line is a result of the V \V least-squares "t.
example is shown in the inset of this "gure for Mn Y . Arrows indicate the direction of decreas ing temperatures, or of increasing temperature, respectively, under the constant "eld. This phenomenon is characteristic to the randomly quenched spin ordering such as a spin glass state. The real part of AC-susceptibility as a function of temperature is shown in Fig. 4. All the curves have a cusp at low-temperature region, showing an evidence of the spin glass transition for all the samples investigated. With decreasing Mn content the cusp becomes sharper and shifts to low-temperature
side. In Mn Y the measurement of thermal-hys teresis of AC-susceptibility has revealed the existence of a spin glass phase but not an antiferromagnetic phase below the peak though the transition is not so sharp and not so clear. Mn concentration x dependence of the spin glass transition temperature ¹ is shown in Fig. 5. ¹ changes linearly on the whole as a function of the Mn content, suggesting that ¹ is closely re lated to the number of Mn}Mn pairs as mentioned below. Since Mn and Y atoms distribute statistically, the number of nearest-neighbor (nn) Mn
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atoms (coordination number) z depends on the + Mn content (x) and is nearly proportional to it, and the number of Mn}Mn pairs increase roughly proportional to x. Sherrington and Kirkpatrick (SK) [38,39] have calculated theoretically the spin glass transition temperature of dilute magnetic alloys based on the molecular "eld formalism. Krusin-Elbaum et al. have extended [40] their theory for the amorphous Heusler alloys Cu MnZ (Z"Al, In or Sn), which include long-range indirect ferromagnetic and antiferromagnetic exchange interactions and direct antiferromagnetic exchange interactions of Mn atoms. The result is that ¹ "( /3(3)S(S#1)( Z J#Z J) . G G G
(1)
The summation represents a sum over the i nearG est neighbors. Here S is the spin quantum number, and Z is the number of interacting pairs at radius G r around a given Mn atom, and J is the exchange G G integral between atom i and the given atom. Z is the number of nearest neighbors which interact via the antiferromagnetic direct exchange J . In conformity with this formula, ¹ depends directly on Z (here, Z includes both Z and Z ). Since G Z depends on the Mn content, the increase of ¹ with respect to Mn concentration for the present amorphous alloys might be roughly interpreted as the increase of Z . SK-model followed by several models [41,42], however, are based on the Ising spin system where each spin has S "$. While in 8 our amorphous system the spin values of each Mn atom cannot be estimated suitably, and they probably distribute statistically depending on the local environment of the Mn atom and an average nn Mn}Mn distance. Strictly, this model is not always applicable in the present case, because the di!erence in S and also its distribution must in#uence the value of ¹ . In such a case Eq. (1) must be modi"ed. Nevertheless, it is plausible that ¹ is closely related to the number of Mn}Mn pairs. With increasing Mn content, Mn gradually loses the magnetic moment. This is attributed to the fact that net antiferromagnetic interaction becomes larger with an increasing Mn content. Therefore, s
509
is suppressed by degrees and the cusp is smeared out inspite of an increase in ¹ . KY have calculated the spin glass transition temperature ¹ as a func tion of the Y content for a-Mn}Y (Fig. 10 in Ref. [37]). Their result has the same tendency to our experimental results but the absolute values are 2.5}3 times larger. They ascribed this discrepancy to (i) the theoretically adopted molecular "eld approximation and the neglect of the transverse spin #uctuations, and (ii) existing of the atomic short range order in the present amorphous samples. Temperature dependence of the magnetic susceptibility (p/H) shown in Fig. 3 can be "tted by the so-called Curie}Weiss (CW) law including a constant term of susceptibility s . In both (a) the local magnetic moment limit and (b) the weakly ferromagnetic limit (for instance, ZrZn and Ni Al, etc. are corresponded), susceptibility versus temperature curves often obey the ¹\ rule (CW-law) s"s #C/(¹!h),
(2)
where s is the constant term of susceptibility, C the e!ective Curie constant and h the asymptotic Curie temperature. Using the above equation we can calculate the e!ective values of h, s and C. Results are listed in Table 1, and s and h are also shown in Figs. 6 and 7, respectively. As mentioned later the e!ective paramagnetic moment p can be deduced
Fig. 6. The constant term of susceptibility s as a function of x for Mn Y (closed circles). The spin susceptibility of pure V \V Mn and Y metals [44] is also shown (open circles). A dotted line is a guide to the eye.
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Fig. 7. The asymptotic Curie temperature (h) as a function of Mn content x for Mn Y . V \V
Fig. 8. The e!ective paramagnetic moment (p ) as a function of Mn content x for Mn Y . Dotted and broken lines are V \V a guide to the eye.
from the Curie constant C for (a) the local moment limit. In (b) the weakly ferromagnetic limit, however, C does not give correctly the e!ective paramagnetic moment. According to SCR theory [43] the CW law originates from the linear increase of S(¹), where S(¹) is the average squared ampli* * tude of the local spin #uctuation, and C is proportional to ¹\ which is the longitudinal sti!ness constant for the spin #uctuation. In this paragraph we discuss provisionally on the basis of (a) the localized magnetic scheme. The constant term s as seen in Fig. 6 describes a tem perature-independent susceptibility. s usually comes from a non-localized origin. In this "gure the spin susceptibility of pure Mn and Y metals [44] are also shown. Present data of s smoothly con nect with those of Mn and Y locating on each end of abscissa. h versus x curve shown in Fig. 7 indicates that overall Mn}Mn interactions are negative regardless of the Mn content. This negative interaction becomes greater with increasing the Mn content. The reason can be considered that the nn Mn}Mn negative interaction becomes more intensive with increasing Mn content due to the increase of z , whereas the sum of the long-range interac+ tions through conduction electrons (RKKY-type) is probably not dependent on Mn content because they compete as a whole due to their oscillating nature. Though present argument stands on the hypothesis of the localized model, the result has
the same tendency with the theoretical one for the exchange pair energies of a-Mn by KY (Fig. 6a in Ref. [37]). The e!ective paramagnetic moment p is calculated as p "C(3k /Nk)(A/a),
(3)
where N is the Avogadro's number, k the Bohr magneton, A the atomic weight and a the atomic fraction of magnetic atoms. The parameter p is listed in Table 1 and shown in Fig. 8 as a function of Mn content. In this "gure, we exhibit two di!erent values of p [Mn] where only Mn bears the mag netic moment and p [Mn,Y] where both Mn and Y have the magnetic moment. p [Mn] linearly decreases with increasing Mn content. This is the same tendency to the magnetization at 48 kOe as seen in Fig. 2. But p [Mn, Y] does not change so steeply compared to p [Mn] but it takes a broad maximum around x&30. As a matter of course, the value of p has certain ambiguity depending on the choice of s even though the estimation of Curie constant C has been done by the leastsquares "t. KY shows theoretically that the calculated results of s\}¹ curve with upwards convexities below 1000 K for Mn Y is originated from the amplitude #uctuation of local moments. Actually as shown in Fig. 9, all the present s\}¹ curves have upward convexities. Two basic mechanisms can be considered for these upward convexities:
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511
Fig. 9. Inverse susceptibility as a function of temperature for Mn Y . V \V
Fig. 10. Values of AC-susceptibility at 80 K, and DC-susceptibility at 80 and 300 K as a function of Mn content. Lines are a guide to the eye.
one is the existence of nearly temperature-independent paramagnetic moment and another is the linear temperature variation of amplitude #uctuation as argued by CW. But these two mechanisms are di$cult to be separated well. At the present time, it is well known that the magnetism of Mn-based metallic alloys obeys (b) the itinerant electron magnetism. Therefore, it is rather essential to discuss the magnetic properties of the present alloys on the basis of the itinerant electron magnetism. To do so, it is necessary to accumulate experimental data giving the informations about the itinerant electronic behaviors such as the spin #uctuation. Our recent study [45] of thermal expansion measurements has revealed the existence of appreciable spin #uctuations in aMn Y , which anticipates the itinerant electronic behavior in this alloy. KY have calculated the spin susceptibility of a-Mn}Y (Fig. 16 in Ref. [37]). They have explained in the "gure that the calculated susceptibility peak is characterized as a crossover from the itinerant behavior to the local moment behavior. In Fig. 10, AC-susceptibility at 80 K and DC-susceptibilities at 80 and 300 K are shown. Both susceptibilities at 80 K have a peak around x&35. Susceptibility at 300 K also have a peak around x&50. These results may indicate the crossover between itinerant behavior and local moment behavior. More detailed experimental studies for the basic magnetic properties based on the
itinerant electron magnetism is necessary to the better understandings of the present amorphous alloys. Here we consider about a criterion for the appearance of the spin glass phase in the present amorphous alloys. For the appearance of the spin glass phase in condensed random alloy systems the following conditions might be necessary: (i) certain frustration exists in the spin system due to lattice disorders or frustrated spin arrangements and (ii) the system has basically the negative magnetic interactions. Amorphous Mn}Y alloys satisfy the above conditions su$ciently. Therefore, the spin glass characteristic is anticipated to be easily realized. As reported already [5,8], several Mn-based amorphous binary alloys such as Mn}Ti, Zr, Nb and Ta, however, do not show the spin glass characteristics down to 4.2 K despite probably satisfying the above conditions. The reason is not clear now. One possibility that the spin glass ordering occurs at very low temperature (below 4.5 K) for these alloys is still left unsolved. We now attempt to analyze the magnetic behavior of present a-Mn}Y alloys comprehensively as follows: (i) a given Mn atom roughly has about 12 coordination number (z &12) like crystalline +>7 FCC or HCP structure. The magnetic moment of each Mn atom is subjected to the Mn-coordination number z . When z is small (that is, in Y-rich + + side) Mn atom has rather large moment, while
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when z is large (that is, in Mn-rich side) it has + a rather small moment, (ii) the nearest neighbor Mn}Mn interaction which is determined by nn Mn}Mn distance r is antiferromagnetic. The net magnetic interaction may be dominated by the nn Mn}Mn interaction, since the long-range Mn}Mn interactions may oscillate between positive and negative and they are totally leveled o! towards nearly zero. Thus, the net negative magnetic interaction becomes greater when z is large and + (iii) Mn}Mn antiferromagnetic exchange interactions cause the spin glass freezing at low temperature. Besides, the spin glass transition temperature ¹ strongly depends on the Mn concentration.
4. Summary We have investigated the magnetic properties of a-Mn Y alloys and obtained the following V \V results. (1) The magnetization versus applied magnetic "eld at 4.5 K does not saturate up to about 50 kOe and shows a large hysteresis. (2) The values of magnetization at H"48 kOe and at 4.5 K decrease almost linearly with increasing the Mn content, suggesting that the net antiferromagnetic interactions becomes larger. (3) The spin glass nature appears for all the Mn concentration range investigated. The spin glass transition temperature ¹ increases al most linearly with increasing the Mn content, whereas AC-susceptibility peak is gradually suppressed owing to the increase of the net antiferromagnetic couplings. (4) The present results are qualitatively explained by Kakehashi and Yu's "nite-temperature theory based on the itinerant electron magnetism.
Acknowledgements This work was supported by a Grant-in-Aid for Scienti"c Research on Priority Areas (No. 03240102) from the Ministry of Education, Science, Sports and Culture, Japan.
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