Magnetic Field-Induced Reverse Martensitic Transformation and Thermal Transformation Arrest Phenomenon of Ni 41 Co 9 Mn 39 Sb 11 Alloy

In order to investigate behavior of magnetic field-induced reverse martensitic transformation for Ni-Co-Mn-Sb, magnetization experiments up to a static magnetic field of 18 T and a pulsed magnetic field of 40 T were carried out. In the thermomagnetization curves for Ni41Co9Mn39Sb11 alloy, the equilibrium transformation temperature T0 was observed to decrease with increasing applied magnetic field, μ0H, at a rate of dT0/dμ0H = 4.6 K/T. The estimated value of entropy change evaluated from the Clausius-Clapeyron relation was about OPEN ACCESS


Introduction
Since a new type of magnetic shape memory alloy was reported for off-stoichiometric NiMn-based Heusler alloys in 2004 [1], related studies have been intensively carried out.This shape memory alloy is different from the conventional one of Ni-Mn-Ga, in which a large magnetostriction occurs due to a re-arrangement of the martensitic variant [2,3].In off-stoichiometric Ni-Mn-Z (Z = In, Sn and Sb) alloys, a drastic change of magnetization is obtained during the martensitic transformation because the parent phase orders ferromagnetically and the martensite phase shows weak magnetism.Application of a magnetic field decreases the martensitic transformation temperature because of the gain of the Zeeman energy, and thus magnetic field-induced transformation from the martensite phase to the parent phase occurs.This behavior is called the metamagnetic shape memory effect from the experimental fact that almost complete shape recovery was observed during the magnetic field-induced transformation in a Ni-Co-Mn-In specimen in which the strain had been previously introduced [4].At the same time, as the martensitic transformation, various physical properties also drastically change, such as huge magnetoresistance [5][6][7], magnetic superelasticity [8], a large inverse magnetocaloric effect [9][10][11][12] and large change of the thermal transport properties [13][14][15].Therefore, NiMn-based Heusler alloys have attracted interest in both scientific and applicative aspects.
Recently, it has been reported that a thermal transformation arrest phenomenon is observed in Ni-Mn-In [16,17], Ni-Co-Mn-In [5,18], Ni-Co-Mn-Sn [19], Ni-Co-Mn-Ga [20] and Ni-Co-Mn-Al [21][22][23] alloys, thermally induced martensitic transformation being interrupted below a certain temperature during the magnetic field cooling process, and the parent phase remaining even at the low temperature.The characteristic temperature is called the thermal transformation arrest temperature and is defined as the point where the transformation is interrupted and does not proceed with further cooling.In systematic studies on this phenomenon, it has been found that the equilibrium magnetic field for the martensitic transformation increases with decreasing temperature, and reaches a constant value at lower temperature.This means that the entropy change of the martensitic transformation becomes smaller and smaller with decreasing temperature, and finally becoming zero.That is, it results in a lack of thermal driving force of the martensitic transformation.On the other hand, transformation hysteresis in the magnetic field becomes larger at lower temperature.These behaviors are common to the above NiMn-based shape memory alloys showing the thermal transformation arrest phenomenon, and the temperature dependence of the magnetic field hysteresis has been examined by dividing it into two parts, i.e., a thermally activated term and an athermal term [17,18,22,23].It has been considered that the components of these terms are different in different alloy systems, such as between Ni-Co-Mn-In and Ni-Co-Mn-Al and that the difference would originate in the different energy barriers related to the thermal activations [22,23].
Stoichiometric Ni2MnSb with the L21-type ordered structure is ferromagnetic having a magnetic moment of 4.2 μB/f.u. and the Curie temperature of 334 K [24,25].In addition, positive pressure dependence of the Curie temperature has been reported by Kaneko et al. [26] and Kanomata et al. [25].Since the reports of the occurrence of the martensitic transformation in the off-stoichiometric composition [1], a large number of investigations have been performed and many interesting physical properties have been reported in Ni-Mn-Sb and Co-substituted Ni-Co-Mn-Sb alloys, such as large magnetoresistance [27,28], a negative magnetocaloric effect [29,30], a metamagnetic shape memory effect [31] and exchange biasing behavior [32,33], similar to properties of other NiMn-based alloys.In order to investigate metamagnetic behavior and magnetic moment of the field-induced parent phase of Ni-Co-Mn-Sb alloy, magnetization experiments up to a static magnetic field of 18 T and a pulsed magnetic field of 40 T were performed.

Metamagnetic Behavior of Ni41Co9Mn39Sb11
X-ray powder diffraction pattern measured at room temperature for Ni41Co9Mn39Sb11 alloy annealed and quenched from 1173 K is shown in Figure 1, together with that for a simulated pattern.The alloy is in the parent phase state at room temperature, and the pattern can be indexed as the L21-type ordered phase.The lattice parameter is refined to be a = 0.5962 nm. Figure 2a indicates DSC heating and cooling curves measured at a rate of 10 K/min for Ni41Co9Mn39Sb11 alloy.TMs, TMf, TAs and TAf in the figure are martensitic transformation starting temperature, finishing temperature, and reverse martensitic transformation starting temperature and finishing temperature, respectively.TC means the Curie temperature and is 368 K. From the DSC measurements, entropy change between the martensite phase and parent phase is obtained to be 15.2 J/(K• kg).Thermomagnetization curves measured under applied magnetic fields of 0.05, 1, 3 and 5 T for Ni41Co9Mn39Sb11 alloy are shown in Figure 2b.It was confirmed that the martensitic transformation temperature decreases with increasing applied magnetic field, and actually decreases by 23 K when the magnetic field is 5 T. According to the Clausius-Clapeyron relation between magnetism and temperature, the rate of the martensitic transformation temperature change by the magnetic field is given as where T0 is the equilibrium transformation temperature, which is assumed to be T0 = (TMs + TAf)/2.ΔM is magnetization change between the parent phase and the martensite phase, and ΔS is the entropy change during the martensitic transformation.From Equation ( 1), ΔS is deduced to be 14.1 J/(K• kg).This is in good agreement with the value of 15.2 J/(K• kg), which is obtained from the DSC measurement in Figure 2a.Magnetization curves measured at various temperatures are shown in Figure 3. Here, (a) is that in a static magnetic field up to 18 T applied by a superconducting magnet; and (b) and (c) are those in a magnetic field up to 40 T applied by a pulsed magnet.As shown in these figures, metamagnetic behavior attributed to the field-induced reverse martensitic transformation is observed.Here, μ0HAf and μ0HMs are the critical magnetic fields of the reverse transformation finishing magnetic field and the martensitic transformation starting magnetic field, respectively.It is shown that the critical magnetic fields increase with decreasing measurement temperature and that magnetic field hysteresis becomes enlarged.
Figure 4 is the plot of μ0HAf, μ0HMs and the equilibrium martensitic transformation field, μ0H0 (≡ (μ0HAf + μ0HMs)/2), as a function of temperature, together with the reverse martensitic transformation finishing temperature, TAf, martensitic transformation starting temperature, TMs, and the equilibrium martensitic transformation temperature, T0 (≡ (TAf + TMs)/2), obtained by the DSC and thermomagnetization experiments.μ0H0 and T0 are considered to be the equilibrium magnetic field and the equilibrium temperature, respectively, where the Gibbs free energy in the parent phase and that in the martensite phase are equal under the condition that a small amount of martensite phase exists in the matrix of the parent phase [34].Although μ0H0 increases with decreasing temperature while keeping the same rate, it tends to be saturated under a temperature of about 50 K.The gradient of μ0H0 to temperature is linear to ΔS as expressed in Equation (1) if ΔM does not so change.Thus, the approach of dμ0H0/dT to zero means that ΔS becomes zero.Similar behavior has been observed in Ni-Co-Mn-In [5], Ni-Mn-In [16,17], Ni-Co-Mn-Sn [19], Ni-Co-Mn-Ga [20] and Ni-Co-Mn-Al [21][22][23].The temperature at which dμ0H0/dT approaches zero was previously termed kinetically arrest temperature.This is now, however, called "thermal transformation arrest temperature".Basically, the driving force of the thermal transformation, ΔG, can be expressed by ΔG ≈ ΔS• ΔT, where ΔT means supercooling.Therefore, the cessation of the transformation when ΔS = 0 is caused by the thermodynamic origin and the phenomenon should be named "thermodynamic arrest" [23,35].The thermal transformation arrest temperature differs for different compositions and/or alloy systems, such as 150 K in Ni45Co5Mn36.7In13.3[5], 40 K in Ni45Co5Mn30Al20 [21], 160 K in Ni45Co15Mn32.5Al17.5 [23] and 50 K in the present Ni41Co9Mn39Sb11 alloy.It seems that material having a higher Curie temperature tends to show a higher thermal transformation arrest temperature, however, the specific interrelation between them has not been clarified.
Recently, temperature dependence of the magnetic field hysteresis has been studied for Ni-Mn-In, Ni-Co-Mn-In and Ni-Co-Mn-Al, and a certain level of quantitatively analyses has been successful [17,22,23].The model is based on the theory of temperature dependence of critical resolved shear stress (CRSS) proposed by Seeger and Kocks et al. [36][37][38].Here, the energy of the movement of a dislocation introduced by shear stress is thought to be divided into a thermally activated term and an athermal term.The magnitude of the athermal term is independent of temperature, while the thermally activated term indicates a certain value at 0 K and decreases with increasing temperature, finally approaching zero at high temperature.Ghosh et al. have found that similar treatment of CRSS is available for the behavior of the martensitic transformation from fcc to bcc as in the concept for temperature dependence of nucleation energy because the diffusionless nature of the martensitic transformation is analogous to plastic deformation [39].In addition, temperature dependence of stress hysteresis accompanied by stress-induced martensitic transformation for Ti-Ni [40] and Ni-Co-Mn-In [18] has been analyzed by the same model.In the case of Ni-Co-Mn-In, where the transformation can be induced by both magnetic field and stress, temperature dependences of the magnetic field hysteresis and stress hysteresis are similar.Furthermore, dissipation energy, which is required to introduce the stress-induced transformation and magnetic field-induced transformation, has been approximately evaluated and showed same temperature dependences in each other.Therefore, it has been concluded that the effects of the energy applied by the magnetic field and by the stress on the martensitic transformation are equivalent [18], suggesting that the application for the model to the phenomenon in the magnetic field-induced martensitic transformation is available.Here, the first and second terms mean the athermal and thermally activated terms, respectively.μ0HTA(0) is the value of μ0HTA(T) at 0 K. Q0K is the activation energy necessary to overcome the kinetic barrier without thermal assist and kB is the Boltzmann constant.p and q are the shape parameters related to the activation barrier.In this phenomenological description, the combination of the p and q is related to the shape of the dislocation-obstacle interaction profile and governs the shape of the μ0Hhys-T profile.In the case of the magnetic field-induced martensitic transformation, they have been obtained to be p = 1/2, q = 3/2 [17,22,23].m is the kinetic coefficient, and it is written as in the case of the model CRSS by the critical dislocation: where τ  is the rate of the loading speed, dτ/dt, and 0  is a characteristic constant for the material.
Because the magnetic field-induced martensitic transformation is analogous to stress-induced deformation, Equation (3) can be rewritten as follows: The change of the sweeping rate of the applying magnetic field induces a change of the coefficient of m.Xu et al. demonstrated the systematic changes of the curvature of the temperature dependence of the magnetic field hysteresis by purposely changing the sweeping rate from 0.001 to 10,000 T/s for Ni-Co-Mn-In [41].In the present investigation, the sweeping rate of the magnetic field applied by the superconducting magnet and that applied by the pulsed magnet are about 0.005 and 5000 T/s, respectively.Temperature dependence of the magnetic field hysteresis, μ0Hhys (≡ μ0HAf − μ0HMs), is shown in Figure 5, together with that for NiCoMnIn [5] and NiCoMnAl [22].Based on Equation ( 2 energy more quantitatively.Because the sweeping rate of the applied magnetic field is completely different between that by the superconducting magnet and that by the pulsed magnet, the closed circles and open circles are well fitted individually by the factor of mkB/Q0K = 0.00198 and 0.00310, respectively.From these fitting factors and Equations ( 2) and ( 4), 0 lnH  and Q0K can be roughly estimated to be 33.0 and 1.06 eV, respectively.Q0K for Ni-Co-Mn-In has been reported to be around 0.7 eV by the same method, which is fitting by the temperature dependence of μ0Hhys based on the CRSS model [41].Activation energy of Ni-Mn-Ga for the temperature dependence of the critical stress for twin boundary motion has been reported to be about 0.006-0.04eV [42,43].On the other hand, the values of 0.6-0.8eV have also been reported [43,44].This discrepancy would be due to the different structures in the martensite phase or different algorithms used to express the temperature dependence of the characteristic properties [44].Although further investigations are needed to clarify the mechanism, the present results reflect the difference of the sweeping rate of the applied magnetic field, and the obtained value of the activation energy seems to be reasonable.

Magnetic Moment and Magnetic Structure of Ni41Co9Mn39Sb11
Here, mNi, mMn and mSb are magnetic moments of Ni, Mn and Sb atoms, respectively, and theoretical values of 0.14, 3.70, and 0.14 μB for the Ni2MnSb stoichiometric alloy are used in the present study [47].These equations indicate that the slope of the magnetic moment as a function of composition depends on the magnetic configuration of the Mn atoms.That is, line of the cal.( 1) is the situation in where the magnetic moment of Mn at the ordinary (4a) site and at the Sb (4b) site couples ferromagnetically; on the other hand, the line of the cal.(2) means it couples antiferromagnetically.Here, it is assumed that the magnetic moment of Mn at the Sb site is same as that at the ordinary site and that it only changes the direction of the magnetic moment.Total magnetic moments obtained theoretically for Ni2MnIn, Ni2MnSn and Ni2MnSb are 4.21, 4.08 and 3.95 μB/f.u., respectively.These values are comparable, and thus the slopes are not thought to be so different in the two systems.Actually, composition dependence of Is for the Ni-Mn-In system well follows the line of cal.(1) in spite of the magnetic moment of Ni2MnSb being used here.This means that the assumption would follow the experimental fact for the Ni-Mn-In system.In addition, for the Ni-Mn-Sb ternary alloy system, behavior of the concentration dependence of Is also well follows the line of cal.(2) indicating antiferromagnetic coupling between the Mn atoms.For Ni-Mn-Sn, the upturn behavior would be due to the change of the magnitude of the magnetic moment and/or the change of the direction of the magnetic moment at the Sn site.Co substituted alloy for the Ni-Mn-Sn, Is becomes to follow the line of cal.(1), and the change of the magnetic configuration is directly observed by the neutron diffraction experiments [48].The present result for the Ni-Co-Mn-Sb also indicates evidence of the change of the magnetic configuration, that is, Is of the present alloy of Ni41Co9Mn39Sb11 becomes larger than that of the total magnetic moment of the stoichiometric composition of Ni2MnSb.This obtained result is the first evidence of the change of the magnetic configuration for the Ni(Co)-Mn-Sb system as well as the Ni(Co)-Mn-Sn system although the value of Is for the present alloy does not completely reach the straight line of cal.(1) in Figure 6b.

Experimental Procedure
A polycrystalline specimen of Ni41Co9Mn39Sb11 was prepared by induction melting under an argon atmosphere.The obtained ingot was annealed at 1173 K for 1 day in a vacuum for homogenization, and subsequently quenched into water.An X-ray powder diffraction experiment was conducted for structural identification.Transformation temperatures and entropy change between the martensite phase and parent phase were examined with differential scanning calorimetric (DSC) measurement (Seiko Instruments Inc., Chiba, Japan).Magnetic measurements were performed using the SQUID magnetometer (Quantum Design Japan, Inc., Tokyo, Japan) up to 5 T, by an extraction method up to 18 T static magnetic fields, and also by an induction method up to 40 T pulsed magnetic fields.The 18 T superconducting magnet at the Institute for Materials Research, Tohoku University was employed and a sweeping rate of the applying magnetic field was fixed at 0.005 T/s.A pulsed magnetic field was obtained with a condenser bank-powered magnet at the Institute for Solid State Physics, The University of Tokyo, its sweeping rate being around 5000 T/s in the present experiments.

Conclusions
In order to study the behavior of the magnetic field-induced reverse transformation of Ni41Co9Mn39Sb11 alloy, magnetic measurements up to a static magnetic field of 18 T and a pulsed magnetic field of 40 T were performed.of the sweeping rate of the applied magnetic field is reflected in the experimental results and activation energy of around 1.06 eV for Ni41Co9Mn39Sb11 was obtained.4. Spontaneous magnetization at 4.2 K for the magnetically induced parent phase of Ni41Co9Mn39Sb11 is 5.4 μB/f.u.This value deviates from the extrapolation from the concentration dependence of the magnetic moment of Ni-Mn-Sb ternary alloy system.The experimental fact suggests a change of the magnetic configuration between Mn atoms at the 4a site and Mn at the 4b site by Co substitution.

Figure 1 .
Figure 1.X-ray powder diffraction patterns for Ni41Co9Mn39Sb11 alloy annealed and quenched from 1173 K.

Figure 2 .
Figure 2. (a) DSC heating and cooling curves measured at a rate of 10 K/min for Ni41Co9Mn39Sb11 alloy.TMs, TMf, TAs and TAf are martensitic transformation starting temperature, finishing temperature, and reverse martensitic transformation starting temperature and finishing temperature, respectively.TC means the Curie temperature; (b) Thermomagnetization curves were measured under applied magnetic fields of 0.05, 1, 3 and 5 T for Ni41Co9Mn39Sb11 alloy.

Figure 3 .
Figure 3. Magnetization curves measured at various temperatures for Ni41Co9Mn39Sb11 alloy.(a) is measured under static magnetic fields up to 18 T, and (b) and (c) are under pulsed magnetic fields up to 40 T.
), fitting of the experimental data was attempted.In the figure, the solid line and dashed line are the fitting curves obtained by Equation (2).The dot-dashed horizontal line stands for the athermal component.Best fitting was obtained when μBHμ = 3.0 (T) and μBHTA(0) = 15.3 (T).Comparing these values with those for Ni-Co-Mn-In and Ni-Co-Mn-Al, it is seen that the value of μBHμ is between Ni-Co-Mn-In and Ni-Co-Mn-Al; however, μBHTA(0) is comparatively larger than those, indicating that the activation energy of the present Ni-Co-Mn-Sb is larger than the others.Let us consider activation

Figure 6a indicates temperatureFigure 6 .
Figure 6a indicates temperature dependence of the spontaneous magnetization, Is, of the present alloy of Ni41Co9Mn39Sb11.Here, Is is obtained from the Arrott plot (μ0H/M-M 2 plot) at each measured temperature, as shown in the inset.The curve corresponds to the thermomagnetization curve of the ferromagnetic parent phase.The value of Is at 4.2 K is 117.2A• m 2 /kg, corresponding to the total magnetic moment of 5.4 μB/f.u.Concentration dependence of Is measured at 4.2 or 5 K for various Ni-based metamagnetic shape memory alloys of Ni(Co)MnIn, Ni(Co)MnSn and Ni(Co)MnSb alloys are shown in Figure 6b [45,46].In the figure, open symbols are Is for the ternary alloy systems of Ni50Mn50−xInx (○), Ni50Mn50−xSnx (□) and Ni50Mn50−xSbx (∆), and closed symbols are those for their Co substituted systems.In the case of the Ni-Mn-In system, Is increases linearly with a decrease of In content.On the other hand, Is for Ni-Mn-Sn

1 .
The equilibrium magnetic field, μ0H0, linearly increases with decreasing temperature just below the martensitic transformation temperature.The value of dμ0H0/dT is about 0.22 T/K and gives the value of the entropy change during the martensitic transformation ΔS = 14.1 J/(K• kg) from the Clausius-Clapeyron relation.The obtained value is in good agreement with the result given by the DSC measurement of 15.2 J/(K• kg). 2. The equilibrium magnetic field, μ0H0, tends to become flat in the low temperature region, showing arresting behavior of the martensitic transformation, analogous with what occurs in the Ni(Co)-Mn-Z (Z = In, Sn, Ga, Al) alloys.The thermal transformation arrest temperature of the preset alloy is about 50 K. 3. The temperature dependence of the magnetic field hysteresis, μ0Hhys, well follows the fitting curves based on the model for the plastic deformation introduced by the dislocations.The difference