The inﬂuence of magnetic dilution in the Zn 1− x Mn x Ga 2 Se 4 series with 0.5 < x Ï 1

The Zn 1− x Mn x Ga 2 Se 4 system with 0.5 (cid:1) x (cid:1) 1, which represents a magnetic dilution of the tetragonal MnGa 2 Se 4 , retains the defective chalcopyrite structure of the parent compound. Neutron powder diffraction experiments and temperature dependent magnetic susceptibility measurements show that such dilution has a signiﬁcant inﬂuence on the magnetic properties of the system. The distance between the closest magnetic atoms decreases from a to a / (cid:3) 2 Å (cid:1) where a is the lattice parameter and a (cid:4) 5.6 Å (cid:2) , making the Curie-Weiss temperature greater than the expected value. The magnetic dilution also decreases the internal distortion, so that the structure becomes closer to that of the ideal zinc-blende arrangement. Although MnGa 2 Se 4 behaves as an antiferromagnet below T C =6.4±0.1 K, the magnetic properties of Zn 1− x Mn x Ga 2 Se 4 with 0.5 (cid:1) x (cid:1) 1 suggest a glassy type behavior at low temperatures. This magnetic behavior is found to be compatible with the distribution of the Mn ions within the lattice and can be tuned by tailoring the concentration of magnetic ions. Surprisingly, the magnetically undiluted system corresponding to the Zn 1− x Mn x Ga 2 Se 4 0.5 (cid:1) x (cid:1) 1 series is not MnGa 2 Se 4 , a magnetic lattice with a body centered cubic symmetry, but a structure possessing a greater number of sites available to the magnetic


I. INTRODUCTION
Unique results can be often obtained from the combination of two or more seemingly independent fields of research. Diluted magnetic semiconductors ͑DMSs͒, sometimes also referred to as "semimagnetic" semiconductors, constitute a beautiful example. Any known semiconductor with a fraction of its ions replaced by some magnetic cations is a potential member of this group, and these materials are of interest owing to the interplay between their semiconducting and magnetic properties. A unique and important feature of DMSs is the interaction which exists between the conduction and/or valence band electrons and the localized magnetic moments of the magnetic ions. Thus, these materials are interesting subjects for scientific research and potential device applications due to the combination of electronic, optical, and magnetic properties. [1][2][3][4] A detailed knowledge of the arrangement of the cations in the crystal lattice of DMSs is of particular significance since the physical properties ͑optical, electronic, magnetic, etc.͒ of the material are crucially influenced by the degree of atomic ordering. [5][6][7][8] In most DMSs, the distribution of the cations is random, 9 so that many variables follow a linear dependence with the content of the magnetic ions. This is the case with the Curie-Weiss temperature ͑͒. 10 However, the calculation of reliable values is difficult in DMSs since most of them exhibit comparatively high Weiss temperatures. 11 As the values increase, the temperatures required to perform its accurate calculation also increase and such temperatures are difficult to access experimentally.
To achieve specific requirements, various solid solutions of DMSs with different desired properties can be synthesized by varying the chemical composition. 12,13 However, if the crystal structures of the nonmagnetic and magnetic materials are not sufficiently compatible, some problems can be encountered. 14 In fact, it is found experimentally that it is generally difficult to achieve a high substitution of diamagnetic ions by magnetic ones in the host semiconductor matrix. 9 Most of the experimental results concerning DMSs have been obtained in the range of low magnetic concentration. In this paper we analyze the magnetic and structural behaviors of a magnetic dilution of MnGa 2 Se 4 in the high Mn concentration regime. Mn 2+ is a magnetic ion with spin S =5/2. The diamagnetic Zn 2+ cation has been used for generating the Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x Ͻ 1͒ series. Both MnGa 2 Se 4 and ZnGa 2 Se 4 are semiconductors with direct gaps of around 2.5 and 2.3 eV, respectively. 15,16 Although the manganese ions exhibit a completely ordered distribution within MnGa 2 Se 4 , the Zn cations are completely disordered in ZnGa 2 Se 4 . 17,18 This is an additional point of interest of the series under study due to the competition between the order and disorder tendencies. In addition, both crystal structures are rather compatible, with the tetragonal defective chalcopyrite structure adopted by MnGa 2 Se 4 and the tetragonal defective stannite structure adopted by ZnGa 2 Se 4 . The Weiss temperature for MnGa 2 Se 4 is 23 K, 19 a value low enough that the temperatures required to calculate accurate values for Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x Ͻ 1͒ are ac-cessible experimentally. Moreover, in order to increase the magnitudes of the magneto-optical effects in DMSs, it is interesting to search for materials in which the antiferromagnetic interaction between the magnetic cations is weaker, as in the case of MnGa 2 Se 4 . 19 We have performed neutron powder diffraction experiments to determine the degree of atomic ordering as a function of Zn/ Mn dilution x in the Zn 1−x Mn x Ga 2 Se 4 system with 0.5Ͻ x ഛ 1, complemented by dc and ac magnetic susceptibility measurements, with superconducting quantum interference device ͑SQUID͒ detection, to analyze the magnetic behavior. The magnetic properties of MnGa 2 Se 4 are analyzed in this paper together with the influence of the magnetic dilution. A detailed knowledge of the structural arrangement of the atoms in the lattice is essential in order to understand the magnetic behavior of this DMS series.

II. EXPERIMENT
Orange single crystals of Zn 1−x Mn x Ga 2 Se 4 with x = 0.63͑1͒, 0.77͑1͒, 0.900͑7͒, and 1 were obtained using the chemical vapor transport method with iodine as transport agent. 20,21 The manganese content of each sample was determined by both magnetic and neutron powder diffraction experiments ͑see Sec. III below for additional information͒. The results obtained by these two independent methods agree within experimental error and are also in excellent agreement with the nominal value calculated from the quantity of Mn used for the chemical synthesis.
Room temperature time-of-flight neutron diffraction experiments were performed on the Polaris powder diffractometer 22 at the ISIS source, UK. Thin-walled vanadium cans were used as sample containers. Diffraction data were collected in all available detector banks over a d-spacing range of 0.5Ͻ d͑Å͒ Ͻ 12.0. Neutron diffraction experiments are judged more suitable than x-ray technique to determine the distribution of magnetic ions in the series under study because the negative coherent nuclear scattering length of Mn makes it more clearly distinguishable from the other elements. The GENIE software 23 was employed for the normalization of the data and correction for sample absorption. The Rietveld analysis of the diffraction patterns was performed with the program TF14LS, based on the Cambridge Crystallographic Subroutine Library. 24 Refinements of the crystal structure were carried out using data in the range of 0.8Ͻ d͑Å͒ Ͻ 3.2, with an essentially constant resolution of ⌬d / d Ϸ 5 ϫ 10 −3 , obtained using the highest-resolution backscattering detectors.
ac and dc magnetic susceptibility data were collected on polycrystalline samples in the range of 1.8-300 K using a magnetometer, manufactured by Quantum Design, with SQUID detection. The ac experiments were performed under an oscillating magnetic field of 1 Oe and at frequency of 10 Hz, while the dc measurements were taken using an external magnetic field of 1 T.

A. Structural arrangement
In order to determine the distribution of the magnetic ions within Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1, the crystal structures of the end members of the series have been taken into account. Thus, MnGa 2 Se 4 crystallizes in the tetragonal space group I4 with a = 5.677͑1͒ Å and c = 10.761͑2͒ Å, showing a defective chalcopyrite structure. 17 The structural arrangement of this material is shown in Fig. 1. The structure is defective in the sense that there are vacancies which are ordered and situated at the 2b ͑0,0,1/2͒ lattice site. The cations are tetrahedrally coordinated by four Se atoms located at a general position 8g ͑x , y , z͒. Half of the Ga cations occupy the 2a ͑0, 0, 0͒ site, while the rest are located at the 2c ͑0,1/2,1/4͒ crystallographic position. The Mn cations are placed at the 2d ͑0,1/2,3/4͒ lattice site. Thus, the crystal structure exhibits a complete ordering of the magnetic ions.
The crystal structure of the other end member of the series, ZnGa 2 Se 4 , is rather similar to that reported for MnGa 2 Se 4 ͑see Fig. 1͒. The structural arrangement of the atoms exhibits a tetragonal defective stannite structure, with a = 5.5117͑3͒ Å, and c = 10.9643͑6͒ Å and space group I42m. 18 As shown in Fig. 1, one significant difference between the crystal structure of the Zn and Mn analogs is the presence of cation disorder in ZnGa 2 Se 4 . Thus, half of the Ga cations share the 4d ͑0,1/2,1/4;0,1/2,3/4͒ position with the Zn atoms, while the remaining trivalent ions occupy the 2a ͑0, 0, 0͒ lattice site. This disorder results in the anions moving into a special position ͑8i͒ with x = y, while in the case of total order, that is MnGa 2 Se 4 , the x and y coordinates of the Se atoms are different ͑see above͒. As in the case of the Mn derivative, the coordination of the cations ZnGa 2 Se 4 is tetrahedral and the vacancies are located at the 2b ͑0,0,1/2͒ lattice site.
A major motivation of this work is to study the effects of substituting a fraction of the magnetic atoms ͑Mn͒ by diamagnetic ones ͑Zn͒. The crystal structure of Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x ഛ 1 has been refined using the Rietveld method applied to the neutron powder diffraction data. The results of this analysis are shown in Table I Table I. As shown in this table, only the the 2d and 2c lattice sites are available to the Mn ions. Therefore, the magnetic ions are partially disordered between two different lattice sites in such a way that the transference of the Mn cations from the 2d to the 2c lattice site increases as the magnetic dilution progresses. As discussed in the next section, this lack of complete order significantly influences the magnetic properties of the system. Moreover, the values of the tetragonal parameters a and c are depicted in Table I as a function of x. While a increases with the Mn content, c decreases. This is in contrast with the nearly constant value of c detected in Zn 1−x Mn x Ga 2 Se 4 with 0 ഛ x Ͻ 0.5, which exhibit a completely random distribution of the Zn cations. 25 The increase of c / a with decreasing x suggests a tendency to an increase in cation ordering as the concentration of Mn progresses. 26 This conclusion also agrees with the distribution of the magnetic ions determined for Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x ഛ 1 ͑see Table I͒.
The partial substitution of Zn by Mn does not change the population of the 2a lattice site and, as expected, the bond distance Ga͑2a͒ -Se in Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1 is not significantly affected by the substitution process ͑see Table II͒. Its value is in agreement with that reported for ZnGa 2 Se 4 ͓2.4204͑10͒ Å͔ ͑Ref. 18͒ and MnGa 2 Se 4 ͓2.42͑2͒ Å͔. 17 By contrast, the distance Mn, Zn, Ga͑2d͒ -Se increases with x. This is to be expected, since the Mn-Se bond distance in this type of materials is larger than the Ga-Se and ͑Zn,Ga͒-Se distances. The bond distances Mn-Se and ͑Zn,Ga͒-Se have been reported to be 2.55͑2͒ and 2.4365͑5͒ Å, respectively, in MnGa 2 Se 4 ͑Ref. 17͒ and ZnGa 2 Se 4 . 18 More interestingly, the Mn, Zn, Ga͑2c͒ -Se distance increases smoothly when x is decreased, in good agreement with an increase of the Mn content in the 2c crystallographic site as x decreases.
A detailed knowledge of the atomic structure of such defective compounds is of interest due to the sensitivity of the electronic properties to the internal distortion, 27 represented by the displacement of the anion from its position  I. Mn content ͑x diff ͒, lattice parameters, atomic coordinates for Se ͓Se at general position 8g; Mn, Zn, and Ga͑1͒ at special positions 2d and 2c; Ga͑2͒ at special position 2a͔, internal distortion parameter ͑␦ = ͓͑1/4−x Se ͒ 2 + ͑1/4− y Se ͒ 2 + ͑1/8−z Se ͒ 2 ͔ 1/2 ͒, occupancy factor of Mn ͑2d and 2c sites͒, isotropic temperature factors ͓ITF͑2d͒ =ITF͑2c͔͒, and conventional goodness-of-fit factors from Rietveld refinement of the neutron diffraction data obtained at 300 K for Zn 1  within an ideal zinc-blende structure. The tetragonal defective stannite and chalcopyrite structural arrangements can both be derived from the cubic zinc-blende structure by doubling the unit cell parameter c, considering two different cations rather than one and introducing vacancies into the lattice. As a consequence of the lowering of symmetry, the anions are forced to relax with respect to ͑1/4,1/4,1/8͒, the ideal position of the anion in the zinc-blende structure. The coordinates of the Se atoms ͑x Se , y Se , z Se ͒ are shown in Table  I for Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x ഛ 1. The dependence of the internal distortion parameter, defined as ␦ = ͓͑1/4−x Se ͒ 2 + ͑1/4− y Se ͒ 2 + ͑1/8−z Se ͒ 2 ͔ 1/2 , has been calculated for this series as a function of the manganese content and is shown in Table I. The decrease of ␦ with x indicates that the displacement of the anion from its position in the ideal zinc-blende structure decreases as the proportion of magnetic ions diminishes. The same tendency occurs for Zn 1−x Mn x Ga 2 Se 4 with 0 ഛ x Ͻ 0.5 when the Zn cations are progressively substituted by Mn ions. 25 These results indicate that when starting the dilution from either ZnGa 2 Se 4 or MnGa 2 Se 4 , the crystal structure of Zn 1−x Mn x Ga 2 Se 4 with 0 Ͻ x Ͻ 1 series tends to minimize the internal distortion, becoming closer to that of the ideal zinc-blende arrangement ͑see

B. Magnetic behavior
The magnetic properties of the Zn 1−x Mn x Ga 2 Se 4 series are determined by the presence of the magnetic manganese ion. MnGa 2 Se 4 has been reported to order as an antiferromagnet below T c = 6.4± 0.1 K, with =−23±2 K. 19 Superexchange has been proposed as the main mechanism to explain the magnetic interaction between Mn cations in Mn-based DMSs. 28,29 The members of the Zn 1−x Mn x Ga 2 Se 4 series with 0.5Ͻ x ഛ 1 behave as paramagnets in the high temperature region, as shown by the dc magnetic susceptibility data depicted as a function of temperature in Fig. 5. In order to calculate the Curie constant C and the temperature correction , the magnetic data have been fitted to a Curie-Weiss law = C / ͑T − ͒ over the temperature range of 130-250 K. A nonzero value of indicates the presence of magnetic interactions within the paramagnetic phase. The mathematical expression for the Curie constant is C = xNg 2 B 2 S͑S +1͒ /3k B , where x represents the fraction of magnetic ions, N is Avogadro's constant, g is the Landé factor, B the Bohr magneton, S the spin of the magnetic ion ͑5 / 2 for Mn 2+ ͒, and k B is Boltzmann's constant. 30 The g factor can be calculated from the experimental Curie constant C x=1 of MnGa 2 Se 4 , since this compound has x = 1 and the only unknown in the above expression for the Curie constant is the Landé factor g. The content of Mn in each sample can be obtained from this magnetic data since C is a function of x ͓the estimated accuracy of the method is ϳ ±5% ͑Ref. 31͔͒. The Mn content of the members of the Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1 series calculated from the magnetic data, x mag , are in good agreement with those obtained from analysis of the neutron powder diffraction, x diff . Both values are shown in Table II for  comparison. Depending on the temperature range used for fitting the experimental susceptibility data to the inverse of a Curie-Weiss law, the values can be very different for a given TABLE II. Main bond distances obtained from Rietveld refinement of the neutron diffraction data taken at 300 K for Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x ഛ 1͒. Space group: tetragonal I4. The experimental Curie-Weiss constant exp and the manganese content x mag have been calculated from magnetic susceptibility data ͑see text͒. excess is defined as excess = exp − x x=1 , while T f is the temperature associated with the low temperature magnetic anomaly ͑Neel temperature for MnGa 2 Se 4 ͒.  series of DMSs. Following that law, 1 / =− / C + T / C, the agreement between the slope 1 / C calculated from both diffraction and magnetic data has been used as a criterion to support the choice of temperature range used for the fitting of the magnetic data and, as a consequence, the reliability of the resultant values. 25 The Curie constant C can be calculated from the diffraction data using the Mn content obtained from such data, x diff , and the mathematical expression of C, which is a function of x ͑see above͒. The results for are shown in Table II. The negative values are indicative of predominant antiferromagnetic interactions in Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1.
In the bibliography related to DMSs, Curie-Weiss temperatures are typically reported over a limited range of composition, frequently in the low concentration regime of magnetic ions. These temperatures show a ͑usually linear͒ reduction with the concentration of magnetic ions, that is ͑x͒ = x x=1 where x=1 represents the Curie-Weiss temperature for the undiluted compound. 10 This decrease does not occur in the case of Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x ഛ 1 ͑see Table II͒. An excess over the value expected for can be calculated following the expression excess ͑x͒ = experimental ͑x͒ − x x=1 . The results of these calculations are shown in Table  II for the series under study. It is clear that excess increases as x decreases, in accord with the increase in the number of magnetic ions promoted from the 2d to the 2c crystallographic sites as x is decreased ͑see Table I͒. The presence of magnetic ions in both the 2d and 2c lattice sites gives rise to Mn ͑2d͒ -Se-Mn ͑2c͒ superexchange pathways, which are shorter than those Mn ͑2d͒ -Se¯Se-Mn ͑2d͒ ones present in MnGa 2 Se 4 . In fact, the magnetic constant corresponding to Mn ͑2d͒ -Mn ͑2d͒ contacts has been estimated as 0.1-0.5 K for MnGa 2 Se 4 , 19 while that associated with the Mn ͑2d͒ -Mn ͑2c͒ contacts has been calculated as 12.2 K for the magnetic system Zn 1−x Mn x Se. 32 The low temperature magnetic behavior of Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x ഛ 1͒ is illustrated in Fig. 6. MnGa 2 Se 4 exhibits a broad peak centered at 7.9± 0.5 K. The out-of-phase component of the ac magnetic susceptibility Љ is three orders of magnitude smaller than Ј and shows no anomaly for this compound. The temperature dependence of both Ј and Љ indicates that antiferromagnetic ordering occurs in MnGa 2 Se 4 below T C = ͑d / dT͒ max = 6.4± 0.1 K, in ex-cellent agreement with a transition temperature of 6.4± 0.1 K calculated from specific heat measurements. 19 Interestingly, the specific heat data collected on MnGa 2 Se 4 show that approximately 30% of the magnetic entropy is gained above the Neel temperature, indicating that short-range order persists at temperatures much higher than the ordering temperature.
In order to understand this experimental result, it is necessary to analyze the main magnetic superexchange pathways acting in MnGa 2 Se 4 . The associated magnetic constants are J 2 , along ͓100͔ and ͓010͔, J 3 , along ͓1/2,1/2,1/2͔, and J 4 , along ͓110͔. For simplicity we have used the convention of placing the reference magnetic atom at the ͑0,0,0͒ crystallographic position. The exchange constants J 2 and J 4 involve magnetic interactions within the xy plane. Thus, the magnetic constant J 2 relates Mn atoms located at the corners of the unit cell along the x or y axis, while J 4 links Mn atoms situated along the diagonal of the xy plane. Therefore, the only way of propagating the magnetic interaction in the third dimension, the z axis, is the magnetic pathway associated with J 3 . This relates the reference Mn atom situated in one corner of the unit cell to another Mn located at the body center position. The distance between Mn atoms linked by J 2 is shorter than those linked by J 3 ͑see Fig. 7͒. Only the order of magnitude of the superexchange constants is known for MnGa 2 Se 4 ͑0.1-0.5 K͒. 19 The exchange constants for Zn 1−x Mn x Se, with a similar crystal structure, have been reported as J 2 / k B = −0.2 K, J 4 / k B = −0.4 K, and J 3 / k B = −0.1 K. 32 Therefore, the magnitude of the exchange interactions is expected to be higher within the xy plane than along the z axis. This spatial anisotropy is consistent with the presence of short-range order, as detected by the heat capacity measurements at temperatures much higher than the ordering temperature ͑see above͒. Moreover, some degree of magnetic frustration is present in MnGa 2 Se 4 . An antiferromagnetic ordering between nearest neighbors without frus- tration is possible within the xy plane. The difficulty arises when attempting to propagate the antiferromagnetic ordering along the third dimension, the z axis, through the magnetic ion situated at the body center position. A collinear antiferromagnetic three dimensional ordering without frustration is not possible due to the spatial arrangement of the Mn atoms.
We now consider how the partial substitution of the Mn atoms by diamagnetic ones affects the magnetic configuration of the parent compound. To address this issue we have performed ac magnetic susceptibility experiments on the Zn 1−x Mn x Ga 2 Se 4 series with 0.5Ͻ x Ͻ 1. The evolution of the in-phase component of the ac magnetic susceptibility data, Ј, also shows a maximum as a function of the temperature in all the members of the series ͑see Fig. 6͒. The magnetic dilution creates additional superexchange pathways due to the migration of magnetic ions from the 2d to the 2c lattice positions ͑see Table I͒. The additional exchange constants are J 1 along ͓1/2,1/2,0͔ associated with Mn-Se-Mn interactions; J 2 Ј , along ͓0,0,1/2͔ and J 4 Ј , along ͓1,0,1/2͔ and ͓0,1,1/2͔. Again, for simplicity, we place the reference magnetic atom at the ͑0,0,0͒ crystallographic position. The distances between Mn atoms along the main magnetic superexchange pathways have been calculated as a function of the Mn content for Zn 1−x Mn x Ga 2 Se 4 ͑see Fig. 7͒. The Mn-Mn distances associated with J 1 , J 2 , J 4 , and J 4 Ј decrease with x, predicting an increase in these magnetic constants as the concentration of the magnetic atoms decreases. By contrast, as the Mn-Mn distance corresponding to J 2 Ј and J 3 increases when the internal variable x is reduced, a decrease of these superexchange constants with the Mn content would be expected. Both J 2 Ј and J 3 are associated with the propagation of the magnetic interaction along the z axis. The evolution of Ј͑T͒ for Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x Ͻ 1͒ shows a decrease of T f ͑the temperature associated with the magnetic anomaly͒ with x and a loss of the broad nature of the maximum shown in MnGa 2 Se 4 ͑see Fig. 6͒. On the other hand, it is interesting to note that, due to the promotion of Mn ions from 2d to 2c lattice sites, the magnetic archetype of Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x Ͻ 1͒ is not that corresponding to MnGa 2 Se 4 , a magnetic lattice with a body centered cubic symmetry, but rather a structure with more lattice sites available to the manganese cations ͑see dark circles in ZnGa 2 Se 4 , Fig. 1͒.
At this point, it is significant to remark the existence, in all the members of the series except MnGa 2 Se 4 , of a nonnegligable out-of-phase component of the ac magnetic susceptibility Љ ͑see Fig. 6͒. This magnitude exhibits a sharp increase with decreasing temperature near T f . Although MnGa 2 Se 4 behaves as an antiferromagnet, the thermal dependence of both Ј and Љ for Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x Ͻ 1͒ is consistent with the presence of a spin-glass-like magnetic state at low temperatures. 9,33 The interactions between magnetic moments in spin glasses are frequently in conflict with each other due to some form of frozen-in disorder, so that they exhibit a "freezing transition" to a state in which the spins are aligned in random directions. In order to determine the spin-freezing temperature T f in a consistent manner, straight lines were fitted on either side of the transition through the data points. The transition temperature was taken to be the point of intersection of these two lines. 34 The values of T f determined in this way are shown in Table II and demonstrate a decrease of T f as x is decreased. For a large number of II-VI compounds, the spin-freezing temperature T f can be fitted to a power law of the type T f ϳ x n/3 , which is a function of the concentration of magnetic ions. 35 In this expression the exponent n relates the dependence of the superexchange interaction J with the distance between magnetic atoms. 35 In the case of Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1, the exponent is determined to be n ϳ 5.6. The value of n is found to lie in the range from 5 to 6.8 for II 1−x Mn x -VI compounds. 35 Therefore, the result obtained for Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1 illustrates the applicability of this approach for a nonrandom distribution of magnetic ions and validates its use outside the limit of the dilute regime to which it is usually restricted. 35 Further studies are in progress to obtain a deeper understanding of the magnetic behavior exhibited by Zn 1−x Mn x Ga 2 Se 4 with 0.5Ͻ x Ͻ 1 at low temperatures, including the variation of the magnetic susceptibility with the frequency of the ac field, the thermal evolution of the magnetization in the presence or absence of a magnetic field, and the variation of the heat capacity with the temperature.

IV. CONCLUSIONS
The end member of the Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x ഛ 1͒ series, MnGa 2 Se 4 , exhibits a completely ordered distribution of the magnetic ions on the 2d lattice site of the tetragonal space group I4. However, the partial substitution of Mn by Zn produces a partially, rather than totally, disordered distribution of the magnetic ions on the 2d and 2c lattice sites of the defective chalcopyrite structure. The increase of the unit cell parameter c / a as the Mn content decreases is consistent with the increased degree of cation disorder as the magnetic dilution progresses. The magnetic dilution also decreases the internal distortion, the structure becoming closer to that of the ideal zinc-blende structure. Another consequence of the partial substitution of Mn by Zn is that the minimum distance between magnetic atoms decreases from a to a / ͱ 2 Å, increasing the strength of the magnetic constant between nearest neighbors. This fact, together with the increase in the population of magnetic ions at the 2c lattice site, causes excess , the excess over the value expected for the Curie-Weiss temperature, to increase with the magnetic dilution.
The low dimensional magnetic behavior of MnGa 2 Se 4 detected at temperatures higher than that of the antiferromagnetic ordering has been explained in terms of the spatial anisotropy of the magnetic interactions within and perpendicular to the xy plane. Although MnGa 2 Se 4 orders as an antiferromagnet below T C = 6.4± 0.1 K, the presence of a cusplike anomaly in the evolution of both the in-phase, Ј, and the out-of-phase, Љ, components of the magnetic susceptibility suggests a glassy type magnetic behavior of Zn 1−x Mn x Ga 2 Se 4 ͑0.5Ͻ x Ͻ 1͒ at low temperatures. This magnetic behavior is consistent with the distribution of the Mn ions in the lattice. Interestingly, although the Curie-Weiss temperature increases as x decreases, the spin-freezing temperature T f decreases as x decreases. The magnetic archetype of the series under study is not MnGa 2 Se 4 , where the manganese cations are distributed on a body centered cubic lattice, but a system possessing a greater number of sites available for the magnetic ions.