Coexisting ferro-and antiferromagnetism in Ni 2 MnAl Heusler alloys

The structural and magnetic properties of stoichiometric Ni 2MnAl are studied to clarify the conditions for ferromagnetic and antiferromagnetic ordering claimed to occur in this compound. X-ray and magnetization measurements show that although a single phase B2 tructure can be stabilized at room temperature, a single L21 phase is not readily stabilized, but rather a mixed L211B2 state occurs. The mixed state incorporates ferromagnetic and antiferromagnetic parts for which close-lying Curie and a Ne ́el temperatures can be identified from magnetization measurements. ©2002 American Institute of Physics. @DOI: 10.1063/1.1504498 #


I. INTRODUCTION
2][3] Ni 2 MnGa is ferromagnetic in both the parent L2 1 and the product martensitic phase, 4 and it has been demonstrated that in the martensitic phase, strains on the order of 10% can be induced in single crystals by applying an external magnetic field of about 1 T leading to the magnetic shape memory effect. 5[8][9][10][11] Stoichiometric Ni 2 MnAl is structurally stable down to the lowest temperatures, but martensitic transformations occur in the slightly off-stoichiometric compounds, and their mechanical properties are more favorable than those of the relatively brittle Ni 2 MnGa.It is, therefore, thought that Ni 2 MnAl could be provided as an alternative material if its magnetic shape memory properties are as favorable as those of Ni 2 MnGa.However, the magnetic state of Ni 2 MnAl has been an issue that has not been adequately clarified, and whether a single L2 1 parent phase that is not mixed with the B2 phase can be stabilized is still controversial.The pure B2 phase in Ni 2 MnAl can be retained by annealing at 950 K and subsequently quenching to room temperature.On the other hand, it appears that it is difficult to produce a single L2 1 phase, since the B2 -L2 1 transformation in this compound requires long term annealing at about 650 K where the diffusion kinetics are relatively slow as compared to the faster kinetics at 1000 K where Ni 2 MnGa can be annealed to readily stabilize the L2 1 phase.
The magnetic ordering in the retained metastable B2 phase of Ni 2 MnAl is conical antiferromagnetic. 12In the L2 1 phase, there is some indirect evidence based on calorimetric measurements that the magnetic ordering is ferromagnetic. 13lthough no direct evidence has been reported on either the ferromagnetic nature of the L2 1 parent phase or the martensitic product phase of off-stoichiometric Ni 2 MnAl, it has been possible to induce considerable strain on a single crystal specimen which has, however, not exceeded about 0.2%. 14This appears to be a problem of not having a single L2 1 parent phase in the sample.If it were possible to increase the amount of L2 1 in an L2 1 ϩB2 mixed phase, the strain in the martensitic state would also increase.This is a point that certainly requires further investigation.However, to be able to give a thorough account on the properties of structural phase transitions and magnetic shape memory effects in off-stoichiometric Ni 2 MnAl alloys, it is necessary, first, to understand the magnetic properties of the relatively simpler stoichiometric Ni 2 MnAl compound in the B2 and L2 1 phases. 15This makes up the theme of the present article, in which we investigate the structural and magnetic properties by x-ray diffraction, magnetization, magnetic susceptibility, and specific heat measurements.

II. EXPERIMENT
The sample with stoichiometric composition was prepared by induction melting in a water cooled Cu crucible.The concentration of the sample was determined by energy dispersive x ray analysis to be 50.4at.% Ni, 24.7 at.% Mn, and 24.9 at.% Al.To stabilize the B2 phase, the sample was annealed at T a ϭ923 K for 30 days and subsequently quenched in water to room temperature.The L2 1 phase was prepared by annealing a separate sample at T a ϭ653 K for 30 days cut from the same ingot.The structure was examined by x-ray diffraction on the polycrystalline samples.Susceptibility measurements were carried out in a field-cooled ͑FC͒ and zero-FC ͑ZFC͒ sequence using a superconducting quantum interference device magnetometer in the temperature range 4 KрTр400 K and using a vibrating sample magnetometer in the temperature range 300 KрTр600 K. M versus B mea-a͒ Author to whom correspondence should be addressed; electronic mail: acet@ttphysik.uni-duisberg.desurements were carried out in fields up to 5 T. The specific heat was measured in the interval 200 KрTр500 K in a modulated differential scanning calorimeter with a temperature modulation of 0.5 K with a period of 80 s and a heating and cooling rate of 2 K/min.

A. X-ray measurements
For both samples, the results of the x-ray measurements in the interval 30°р2р60°and 60°р2р90°are shown in Figs.1͑a͒ and 1͑b͒, respectively.The locations of the expected reflection peaks are indicated by the arrows.Because of texturing in the polycrystalline specimen, the relative intensities are not in proportion, and some reflections are absent such as the ͑111͒ reflection for the sample with T a ϭ923 K.The broad character of the peaks for T a ϭ653 K indicates that this temperature is not sufficient to remove the strains.The strains are relaxed when annealed at T a ϭ923 K as seen by the relatively narrower line shapes in the data for this annealing temperature.
For T a ϭ923 K, only peaks associated with the B2 phase are found, whereas for T a ϭ653 K, the ͑331͒ peak related to the L2 1 phase emerges as seen in Fig. 1͑b͒.Less obvious is the emergence of a peak at the position of the ͑311͒ reflection in Fig. 1͑a͒.The L2 1 phase is certainly present, but it cannot be concluded from these data whether the phase is single phase or mixed with B2.The lattice constant of the B2 phase is estimated to be aϭ0.2909nm, half that of the L2 1 phase with aϭ0.5818 nm, which is in agreement with earlier reported values. 12

B. The magnetization and susceptibility
The magnetic field dependence of the magnetization M (B) and the temperature dependence of the magnetic susceptibility (T) of the two samples are shown in Figs.2-5.
(T) was measured first in the ZFC state followed by the measurement in the FC state.Prior to each M (B) measurement, the samples were prepared in the ZFC state by bringing them above 350 K.In the following, the samples are referred to by their annealing temperatures.

Magnetization and susceptibility of the T a Ä923 K sample
For the sample prepared in the B2 phase, the M versus B curves up to 5 T in Fig. 2 have no substantial curvature, indicating that ferromagnetic coupling is not present or very weak in the case where there are traces of ferromagnetic inhomogeneities.
(T) in FC and ZFC states shown in Fig. 3 exhibits a peak at about 313 K.This temperature coincides with the Ne ´el temperature T N given as the onset of conical antiferromagnetic ordering previously reported for this system. 12herefore, referring back to Fig. 2, it becomes clear that the nearly linear behavior of the M versus B curves is due to the antiferromagnetism.Below T N , the susceptibility decreases with decreasing temperature and increases again below about 130 K in both modes of measurement.Since the magnetization curves at 5 and 150 K in Fig. 2 appear not to be much different from one another, the rise in (T) below 130 K cannot be associated with some partial ferromagnetic ordering.It is not possible to give a detailed account for this behavior from the susceptibility data alone, but this property could be related to a reorientation of the conical structure which is frequently encountered in compounds incorporating Mn.
Another dominant feature in Fig. 3 is the splitting between the FC and the ZFC data below T N .Such a splitting that occurs just below a magnetic transition temperature is usually an indication of different configurational ''pinning'' FIG. 1.The x-ray spectrum of Ni 2 MnAl: ͑a͒ for 30°р2р60°and ͑b͒ for 60°р2р90°under both annealing conditions.͑331͒ peak in part ͑b͒ is the indication for the presence of the L2 1 phase.The ͑311͒ position in part ͑a͒, which would also be associated with the L2 1 phase, is also indicated.
of residual or intrinsic ferromagnetic parts by the antiferromagnetic environment depending on whether the sample is brought into a FC or a ZFC state. 16This property is discussed in more detail in Sec.IV.

Magnetization and susceptibility of the T a Ä653 K sample
As seen in Fig. 4, the M versus B curves of this sample have substantial curvature between 5 and 340 K as compared to the curves in Fig. 2, but they do not saturate even at the highest fields.M versus B becomes linear first above 400 K where the sample is paramagnetic ͑the maximum field in the vibrating sample magnetometer is 1 T͒.These data indicate FIG. 2. The magnetic field dependence of the magnetization for the sample with T a ϭ923 K.There is no appreciable curvature at any of the temperatures.that annealing at T a ϭ653 K generates ferromagnetism and, evidently, the ferromagnetic entity is then the L2 1 phase.However, the fact that M versus B does not saturate implies that a nonferromagnetic entity is also present.According to x-ray data, this entity can only be the antiferromagnetism of the B2 phase.Therefore, even after 30 days of annealing at 653 K, the sample cannot be brought into a single L2 1 phase.
The mixed nature of this state can be further evidenced from (T) in Fig. 5 when the features are compared to those of (T) in Fig. 3.The features of the two curves appear similar at first.In Fig. 5, a peak in (T) is present at 293 K, which is somewhat lower than the temperature corresponding to the peak in Fig. 3.A splitting is present below the temperature corresponding to this peak, and (T) runs through a minimum at lower temperatures.However, the value of in Fig. 5 is about an order of magnitude greater and, furthermore, the approach from high temperatures to the maximum in (T) shows a ferromagnetic-like behavior.The Curie temperature T C is estimated to be about 375 K from this figure, which is close to the temperature where an anomaly was observed in previous differential scanning calorimetry measurements on an off-stoichiometric compound. 13owever, the fact that (T) decreases below 293 K indicates that antiferromagnetism is simultaneously present in this state of the sample.The feature in the curve close to T N is somewhat rounded out and is not as sharp as in Fig. 3 due to the close neighboring of T N and the temperature of about 300 K at which the magnetization of the ferromagnetic contribution begins to level out as the temperature decreases.
Also, in Fig. 5, a splitting between the FC and ZFC susceptibilities occurs as the temperature decreases as in the data of Fig. 3.The magnitude of the splitting is larger than that in Fig. 3, because of the larger number of ferromagnetic parts in the sample in the L2 1 ϩB2 phase as compared to that in the sample in the B2 state.(T) increases with decreasing temperature below 90 K in the FC case and below 75 K in the ZFC case.The cause is expected to be related to the same effect giving rise to the minimum in (T) of the B2 phase sample.

C. Specific heat
The specific heat c p (T) of the samples with the two different heat treatments is shown in Fig. 6. c p (T) of Ni 2 MnGa measured in the same calorimeter is also shown for comparison. 10c p (T) of Ni 2 MnAl in the B2 state reaches a peak value at about T max ϭ305 K, which is somewhat lower than T N ϭ313 K determined from (T).The structure of the curve around the maximum is not as sharp as the peak at T C ϭ390 K of the ferromagnetic compound Ni 2 MnGa.c p (T) of the sample in the L2 1 ϩB2 state has a broad shoulder centered around T max ϭ350 K, and the narrower feature seen in the peak in the data of the B2 sample is lost.The Curie temperature of the L2 1 phase determined from the (T) data lies closer to the minimum observed at 380 K.The mixed nature of the state produced by annealing at T a ϭ653 K is reflected in c p (T) as well, whereby the closelying T N and T C of the L2 1 ϩB2 phase leads to an overlap of the features in the data of both magnetic states that causes any sharp details at the transitions to be smeared out.

IV. DISCUSSION
With the present magnetization measurements, we give evidence that the L2 1 phase of Ni 2 MnAl is ferromagnetic.T C determined from (T) data is found to be nearly the same as that of Ni 2 MnGa.This is understandable, since the valence electron concentration e/a of both compounds is the same, and it is known that for Ni 2 MnGa T C varies systematically and very slowly with e/a. 4 T C of the L2 1 phase of Ni 2 MnAl also agrees well with the temperature corresponding to the anomaly occurring in calorimetric studies on an off-stoichiometric compound. 13The nature of the magnetic coupling in Ni 2 MnAl appears to be governed essentially by the Mn-Mn distance as in many other ordered compounds incorporating a sufficiently high concentration of Mn.At large separations the compounds are ferromagnetic and at small separations they tend to be antiferromagnetic.This is a tendency that is also found in the results of band calculations on Heusler alloys. 6,17The shortest distance between Mn atoms in the L2 1 phase of Ni 2 MnAl is 0.411 nm.The B2 phase occurs when Mn and Al atoms are arranged randomly, and the shortest Mn-Mn distance can then become 0.291 nm.
The B2 to L2 1 transformation in Ni 2 MnAl occurs at a temperature where diffusion kinetics in a solid are slow.This enables the high temperature B2 phase to be readily retained at room temperature as a metastable state rather than the thermodynamically more favorable L2 1 phase.The development of the L2 1 phase on annealing just below the temperatures of the transformation boundary does not produce a single L2 1 phase in Ni 2 MnAl in a period of 30 days, because either this time is too short or a metastable equilibrium be- tween the B2 and the L2 1 phase is reached.The amount of L2 1 can certainly depend on the metallurgical state of the sample.However, this must be checked by examining the field dependence of the magnetization on samples prepared with different grain sizes and internal strain.For Ni 2 MnAl, the field dependence of the magnetization can give strong evidence as to whether the sample is a single phase B2 or L2 1 , or mixed.
In magnetically heterogeneous systems where ferromagnetism and antiferromagnetism coexist in the form of granular precipitates or in the form of independent long range ordered entities, a divergence of the FC and ZFC susceptibilities is encountered at the lower magnetic transition temperature be it T C or T N . 16The only condition is that the external field should be sufficiently small, otherwise the effect can be lost or the point of divergence will shift to low temperatures.When a sample is cooled from T N ϾTϾT C to below T C , or from T C ϾTϾT N to below T N in finite or zero magnetic field, the spins become pinned in different configurations by the antiferromagnetic anisotropy.Therefore, the FC-ZFC mode of measurement in small fields becomes useful when it comes to deciding whether different forms of long range magnetic structures coexist.If Ni 2 MnAl in the B2 phase were a collinear antiferromagnet, no splitting between the FC and ZFC modes would be observed.Therefore, in this sample, there is either some residual L2 1 phase, which provides the ferromagnetic exchange, or the conical antiferromagnetic structure of the B2 phase has a ferromagnetic component.Both can give rise to pinning.
Despite the metallurgical problems of obtaining a single L2 1 phase, off-stoichiometric Ni 2 MnAl remains as a potential candidate for a magnetic shape memory material if this problem can be overcome.A further problem is to be able to give a clear picture on the magnetism of the martensitic phase of the alloys.Although there have been some useful attempts to provide an understanding of the magnetic states in such alloys, 18 the details of the magnetic interactions remain to be clarified.

FIG. 3 .
FIG. 3. The temperature dependence of the FC and ZFC magnetic susceptibility of Ni 2 MnAl for T a ϭ923 K.The peak at 313 K corresponds to T N .

FIG. 6 .
FIG. 6.The temperature dependence of the specific heat of Ni 2 MnAl under both annealing conditions.That of Ni 2 MnGa is shown for comparison.