Spin reorientation in premartensite and austenite Ni2MnGa

doi:10.21203/rs.3.rs-2841879/v1

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Spin reorientation in premartensite and austenite Ni2MnGa

https://doi.org/10.21203/rs.3.rs-2841879/v1

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Symmetry breaking in the pre-martensite state, sometimes called the martensite precursor state, has been hotly debated for decades. Incompletely softened phonon modes and the diffuse scattering suggest dynamical effects without a static symmetry breaking. Here we use careful measurement of magnetization curves of magnetically closed samples to evidence local symmetry breaking, at and above the pre-martensite transition in off-stoichiometry Ni-Mn-Ga Heusler alloy. During the heating cycle after the martensite transformation the differential susceptibility curve slowly transforms from a typical one-peak corresponding to the magnetization along the easy axis to two-peaks typical for magnetization along the harder magnetic axis. It is explained by change of the macroscopic magnetic easy axis from [100] to [110]. Above the premartensite transformation temperature the magnetic easy axis slowly changes back to [100]. Reorientation of the easy axis with temperature can be explained by the phonon domains model.

Physical sciences/Physics/Condensed-matter physics/Ferroelectrics and multiferroics

Physical sciences/Materials science/Condensed-matter physics/Ferromagnetism

Ni-Mn-Ga magnetic shape memory alloys (MSMA) have been extensively investigated in the past decades due to their magnetic shape memory properties ^1–21. They exhibit a large magnetic field induced strain MFIS, up to 10% ²².

MSMA undergo several phase transformations with temperature increase – from non-modulated martensite to 7M modulated, then to 5M and finally to the austenite. The transformation temperature from martensite to austenite is called the martensite transformation temperature, T_M. If it is below 260K, the additional 3M modulated phase is usually observed around 250-260K called the premartensite.

The magnetic properties of Ni-Mn-Ga and their temperature dependence are crucial for understanding the material performance. These properties should be accurately measured in all details as a function of temperature, stress and composition to provide very key and unique evidence in the debate about the symmetry breaking in the pre-martensite state. Despite of several decades of intensive investigation of the MSMA, till now there are no accurate measured MH-loops of Ni-Mn-Ga cubic (austenite), not speaking about their derivative – the differential susceptibility curves. The reason is extreme magnetic softness of the cubic phase, very small magnetic anisotropy and very high magnetostriction.

In most works on MSMA only certain points of the MH-loop are given - the saturation magnetization M_S and ac or dc susceptibility as a function of temperature. These parameters can give only values of the phase transition temperatures without any details about magnetic properties evolution. The ac or dc susceptibility on short magnetically open samples gives only qualitative information, not quantitative and are usually given in arbitrary units. Even the magnetic easy axis is not known for austenite and premartensite phases because of very small magnetic anisotropy.

Despite the fact that permeameters were the first devices for magnetization curves of high-permeability samples in the shape of a bar or thin sheets since the end of 19 century²³ and became magnetic measurement standards, in the MSMA community they have never been used. Conventionally, MSMA samples are measured in vibrating sample magnetometers (VSM) or PPMS.

The internal magnetic field in a typical small sample for VSM or PPMS is at least 10–100 times smaller than the applied one and is given by the sample geometry and the magnetization curve of the material. The magnetization curve as a function of the applied field is given mostly by demagnetizing fields ignoring the MH-curve of the material. The apparent susceptibility of a short magnetically soft sample in VSM is nearly constant if the sample is not saturated. As a result, the intrinsic properties of magnetically open samples with large demagnetizing fields can’t be obtained and measurements of samples with different geometries are incomparable.

Here we use a single-yoke setup with the driving coil on the yoke, which is commonly used nowadays in nondestructive measurement of steel bars and sheets^24,25. In this setup the demagnetizing fields are minimized and typically several orders of magnitude smaller than conventional measurements of samples that are magnetically open. Using this technique, the demagnetization effects are given by air gaps between the yoke and the sample and can be minimized further by polishing both the sample and the yoke legs. This measurement configuration gives extremely accurate MH-loops of a material and its derivative – the differential susceptibility curve. We will show that it is extremely sensitive to the temperature evolution of Ni-Mn-Ga and is a unique method to reveal the nature of the magnetic anomalies and local symmetry breaking in the premartensitic state.

In this work we measured a slightly off-stoichiometric Ni_50.5Mn₂₃Ga_26.5 60x4x1.45 mm³ single crystal cut with all faces approximately along [100] in the temperature range from 200K to 372K (the heating cycle) with 1K/min rate. The sample was magnetized by the yoke.

In Fig. 1 the evolution of the maximum differential susceptibility (DS), χ^MAX(T) and the zero-field DS, χ₀(T) are given together with the saturation magnetization, M_S and the coercive field, H_C. Also, the ascending branches of the MH-loop are shown at different temperatures.

From the χ(T) curves we see that the martensitic transformation temperature, T_M is around 222K and the Curie temperature, T_C = 361K. From other side, surprisingly, the saturation magnetization, M_S gives another values for T_C = 371K and T_M = 218K. M_S has no hysteresis at T_C that corresponds to the second-order phase transition, while the χ(T) shows the hysteresis of about 5K. The T_M by M_S at the cooling cycle is 14K lower – about 206K. The coercive field, H_C gives T_M = 218K - the same value as by M_S. H_C slowly decreases from 60 A/m at 225K to zero at the T_C together with M_S.

There are anomalies around the premartensitic transformation temperature T_PM = 253K – χ^MAX(T) has a very narrow maximum, while χ₀(T) has a minimum. H_C has a 12% peak at T_PM while the M_S – hardly noticeable 1.5% valley. The MH-curve at 225K, immediately after the martensitic transformation, has the usual sigmoidal shape corresponding to magnetization along the magnetic easy axis (EA). With temperature increase the curve becomes constricted and three segments are clearly seen. With field increase starting from the negative saturation at the first critical field the magnetization suddenly jumps to nearly zero, then it increases with a small constant slope and at the second critical field the magnetization jumps again to the positive saturation. The critical fields quickly increase with temperature and reach maximum values at T_PM = 253K. Above T_PM the process reverses and at 315K the MH-curve become again a typical sigmoidal shape similar to that at 225K. We see that the loops around T_PM are not only constricted but also reentrant – the magnetic field at the critical fields for a short period returns to smaller values. As a result, the derivative diverges. So, in Fig. 1a the scale for χ^MAX(T) is the magnetization rate divided by an average field rate 5000 Am^− 1s^− 1. For values below 5000 this corresponds to the DS.

In Fig. 2 the DS curves, χ_DIFF(H) – derivatives of MH-curves (see Fig. 1c-d) are shown for different temperatures. At 228K the curve has one-shape peak typical for magnetization along EA. With temperature increase two additional peaks appear, while the central peak gradually disappears. Above 245K the DS curve becomes two-peaks that corresponds to a constricted MH-loop. With further temperature increase the peaks move from each other and become very high and narrow. For temperature between 250K and 255K due to self-inductance the field rate changes its sign at critical fields so the magnetization rates, dM/dt normalized to the average field rate are shown instead of DS. Above 270K (see Fig. 2d) we see the same evolution as in Fig. 2a but in the opposite order and much slower. At 355K the DS curve is similar to that at 228K.

In Fig. 3 the evolution of the critical fields of a constricted MH-loop is shown. H_CR2 has a very sharp maximum of 1200 A/m at 253K and decreases with temperature change in both directions, first quickly to 400 A/m with temperature change by 2K and then much slower.

In Fig. 4 change of the magnetostrain along [100] (the field direction) with temperature is shown. The maximum magnetostrain, λ^MAX has a very sharp peak of -550ppm at 253K and decreases with temperature change in both direction from 253K in a similar way as the critical fields and the susceptibility. All the measured DS curves, MH-loops and magnetostrain curves can be found in the Supplementary video 2.

The behavior of zero-field DS, χ₀(T) is typical for Ni-Mn-Ga alloys with T_M < 260K and has been reported in many works in the form of ac or dc susceptibilities sometimes wrongly labelled as “magnetization” ^{8,12,14,18, 26–29}. Below T_M the sample is in the martensitic state and thus is divided into domains of self-accommodated twin variants, each with different easy magnetization axes, c. In the pseudo-tetragonal 10M martensite structure the compressed c-axis is the easy magnetization axis and from the cubic austenite structure the resulting variants that are nucleated can have their c-axis pointing along one of the original cubic < 100 > directions. Only one of these possible directions is parallel to the field, and the two others are perpendicular to it. So, 2/3 of the sample are twin domains with c axis perpendicular to the field. Since the magnetic anisotropy in the martensite is by several orders higher than in the austenite, the sample can’t be magnetized to saturation by the yoke. During the heating cycle at T_M= 220K the sample transforms into the cubic 3M modulated phase called the premartensite ^{3,6, 9–12,14,16,21,27, 29–35}. At T_PM= 253K the premartensite transforms to the non-modulated austenite. With further temperature increase the DS constantly grows up to the Curie transformation, after-which it drops to zero. Such a shape of χ₀(T) is typical for different compositions of Ni-Mn-Ga and even in alloys with different doping elements – Pt, Al, In, Cr etc. ^{3, 28–29,36}. The nature of this susceptibility drop at T_PM has never been explained and has remained an enigma for the last three decades.

The maximum DS, χ^MAX(T) up to the Curie point has never reported before, due to the issues of demagnetization effects when using magnetically-open sample measurement techniques. We also could not find any work on the temperature dependence of the coercive field up to T_C, not only for MSMAs but even for nickel, iron, and any other ferromagnetic alloys.

The measured MH-loops are most intriguing. For a wide temperature range, they are constricted – DS curves have two peaks. There are several situations that can lead to the observation of “constricted” or “wasp-wasted” MH-loops, and we must discuss each to clarify the mechanism:

1) A macroscopically homogeneous sample magnetized along a single easy axis magnetic anisotropy, which is disfavored by stress or sample geometry;

2) A magnetically distinct layer on a magnetically closed sample, with no interaction between these inhomogeneous components;

3) Distinct microwires, ribbons or sheets interacting magnetically through the stray fields at the ends or on the surface (known as Néel “orange-peel” coupling);

4) Exchange-spring interaction in multilayer films;

5) A single crystal in which a single lattice splits into two interacting or non-interacting ferromagnetic sublattices;

6) Magnetically field induced reorientation (MFIR) in MSMA under elastic stress.

The MH-loops in all the cases look similar and sometimes the constricted loops due to specific sample geometry have been mistakenly clamed as evidence of MFIR^37–38 .

In the case of two non-interacting magnetic phases (2), the critical fields of both components have to be positive, corresponding to distinct coercivities of each phase. In our case one critical field is negative, ruling out this scenario. In the case of two magnetic systems with negative magnetostatic interaction two susceptibility peaks move from each other and as we showed previously that amount of this motion (the positions of the peaks) strongly depends on the applied field amplitude^39–41. We performed measurements of minor loops at T_PM and found that the critical fields do not change with the magnetic field amplitude.

So, we excluded all variants except for the domain reorientation caused by the magnetic anisotropy. We have investigated in all details such constricted loops on steels including magnetic domains observations^42–46. Typicaly one of the three equivalent magnetic easy axes was favored by local stress or demagnetizing fields (sample geometry, gross texture of Fe-3%Si steel). The MH-loops were measured along the harder (disfavoured) magnetic easy axis, which was at 45 or 90 degrees to the preferred EA. All MH-curves always crossed at the same point close the coercive field and amounts of the magnetization jumps at each critical field were equal. From Fig. 1 and Fig. 3 we see that the behavior in our previously investigated steels is exactly the same behavior of MH-loops in our investigated MSMA sample in the premartensite state. The only difference is in the positions of critical fields. In steels with stress- or orientation-induced anisotropy the critical fields are always symmetrical with respect to the coercive field. In Ni-Mn-Ga for temperatures around T_PM from 247K to 256K the first critical field is substantially smaller (see Fig. 2b,c). Outside this temperature region the critical fields become more symmetric with respect to H_C (see Fig. 2a,d and Fig. 3). Close to T_PM at the first critical field the magnetic polarization drops to -0.05T and at the second critical field it jumps from 0.13T to nearly saturation.

Our results show that macroscopically the [100] EA close to the premartensitic transition becomes harder comparing to another axes, [110] or [111]. To confirm this hypothesis, we have cut a φ6x0.15mm disk perpendicular to the long side of our sample at the end of it and placed it into a constant field of 50mT. On the heating cycle, immediately after martensitic transformation the disk [100] axis was parallel to the field. Close to the premartensitic transformation the disk rotated by 45, with the field parallel to the [110] direction. With further heating, close to the room temperature it rotated back to [100] (see Supplementary video 3).

So, approaching the T_PM from both sides either from the premartensite or from high-temperature austenite the macroscopic EA appears to change from [100] to [110] and at T_PM the anisotropy, given by critical fields, has a sharp maximum. It is difficult to say why the EA in Ni-Mn-Ga austenite changes with temperature. One may think that the magnetization is facilitated along [110] by the premartensite 3M structural modulation since the anisotropy has a sharp maximum at T_PM. Conversely, the modulation not only does not disappear going further down to the martensitic transformation, but just the opposite – the modulation amplitude increases several times⁴⁷ that surprisingly leads to rapid decrease of the anisotropy and change of the EA back to [100]. As a result, the magnetization loops and DS curves in the premartensite at the maximum amplitude modulation and that close to the Curie temperature are very similar. The magnetic anisotropy is symmetric around T_PM = 253K and decreases in both temperature directions.

Evidently, it cannot be the modulation of the premartensite responsible for the EA change from [100] to [110] direction. Looking at DS starting from Tc with temperature decrease (see Fig. 1a) we see that the EA starts to change long before T_M – already just below the room temperature.

Spin-reorientation transitions (change of the EA) with temperature are observed in many materials: orthoferrites, a series of uniaxial rare-earth ferro- and ferrimagnets, Gadolinium etc.⁴⁸. It was first shown by Bozorth that the easy magnetization direction in a cubic crystal is defined by the signs and magnitudes of the first and second magnetic anisotropy constants²³. A change of the anisotropy constants with temperature can lead to a change of the EA.

Belov considered spin reorientation transitions in crystals with different symmetry from a thermodynamical point of view⁴⁸. He concluded that in cubic crystals spin-reorientation transitions from < 100 > to < 110 > is an anhysteretic phase transition of the first order⁴⁸. It was discovered that the spin-reorientation transition is accompanied by anomalies of the elastic properties. For Ni-Mn-Ga change of the anisotropy in favor of < 110 > correlates with the phonon softening along [110] with a minimum at T_PM. The observed softening corresponds to the DS and magnetostrain peaks. Such changes of elastically properties together with spin reorientation transitions are typical for many materials ⁴⁸.

First-principle calculations can help guide us towards the physical reason of change of anisotropy constants with temperature leading to the spin reorientation. Ni-Mn-Ga has two different magnetic ions – Mn and Ni. Mn is responsible for 90% of the magnetization but surprisingly it is Ni that defines the magnetic anisotropy⁴⁹. In most published ab initio theoretical investigations the magnetic anisotropy is calculated for zero temperature only. There only a few efforts to calculate the temperature dependence of the anisotropy constants using specific models and approximations⁵⁰.

Recently a statistical mechanics-based Grüneisen-type phonon theory is developed which predicts the existence of phonon domains in austenite and premartensite states, confirmed experimentally³⁴. Phonon-strain coupling leads to domains with locally broken cubic symmetry– one [100] axis becomes the shortest and subsequently a unique easy magnetization axis. In this case in the absence of the magnetic field all {100} directions are equivalent since the amount of the phonon domains in each three direction is the same – 1/3. It was shown that even the stress of 20 MPa could not change this ratio (reference 34). Certainly, very low fields of 100–1000 A/m also can’t significantly shift the ratio of domains. Then, the only possible scenario of the magnetization jump at critical fields is a sudden reorientation of the magnetic domains in the hard phonon domains from easy {100} directions perpendicular to the field into the one parallel to it (hard axes). In Fig. 5 we see that under tensile stress of 4MPa (ε = 0.00016) at room temperature the critical fields are 1000 A/m – the same as at T_PM without external stress. From other side, the magnetization jump is very small, the magnetization reversal is realized mostly through the magnetization rotation from {100} axes perpendicular to the field to one parallel to it. The reason is a very small magnetic anisotropy at room temperature – up to two orders smaller comparing to that at T_PM and up to five order smaller to that of the martensite. Then, there is a question how the existence of phonon domains can lead to the overall macroscopic magnetic easy axis along [110]. Imagining that a flat thin sample with two {100} axes in the plane (a thin disk, for example). Then there will be two preferable by geometry phonon domains with the EA along {100} directions. The magnetization in the {100} direction perpendicular to the plane will be disfavored by much larger demagnetizing fields in that direction. The vector sum of magnetization along equally populated [100] and [010] domain easy axes will give a net magnetization along [110]. If one applies the field in the plane and allow the disk to rotate freely, the lowest energy will be with the sample oriented along [110] – both easy axes of two phonon domains will be at the same 45⁰ angle to the field leading to zero torque. In the case of a spherical sample that can freely rotate in all directions, the sample would orient along [111] – the direction symmetrical to all three {100} easy axes of phonon domains. Then, the material softening when approaching T_PM would lead to higher distortion of the cubic lattice in each phonon domain – larger strain. The critical fields are proportional to that strain. From the value of critical fields at T_PM and that of the same order as of the stressed sample (1000 A/m) (see Fig. 5) one can estimate maximum strain in the phonon domains at T_PM of about several hundred microstrains since the strain of the stressed sample is ~ 160 ppm.

The situation is similar to twin variants in the martensite. There are two variants/twins with the easy axes in the plane. The EA in one variant is perpendicular to that of another variant. This results in the stair-case magnetic domain structure – the magnetization in each variant follows its own EA. On the larger scale these domains form quasidomains with the average magnetization direction at a certain angle between easy axes of variants. This angle is defined by the ratio of variants’ volumes. For equal population (a 1:1 ratio) this angle is 45⁰ - exactly like in our case. The difference is that the ratio of the different phonon domains is fixed and can’t be changed by a magnetic field – all of them occupy the same volume ³⁴. Also, there is the third phonon domain with the EA perpendicular to both the field and the sample plane. Both in-plane {100} axes for that domain are hard axes.

We see that there are two possibilities: 1) EA changes from [100] to [110] homogeneously in the whole crystal on both the microscopic and macroscopic levels, due to change of the sign and values of the anisotropy constants; 2) the crystal becomes inhomogeneous divided into phonon domains, in each domain the cubic cell is tetragonally deformed with EA parallel to the chosen shortest {100}. The ratio of three variants is fixed – 1/3, 1/3 and 1/3. The answer whether or not this conclusions based on the phonon domains model are correct can be given by high-resolution magnetic domains observations at different temperatures by Kerr microscopy as we have already done in the case of martensite Ni-Mn-Ga⁵¹.

In the first case of a homogeneous switch of EA from [100] to [100] the sample cut and measured along [110] would be expected to show a normal magnetization curve at T_PM with a single-peak DS with no jumps at the critical fields. We cut the 1.4x1.1x6mm³ sample from our ingot along [110] and measured the magnetization curves from 220K to 372K. At T_PM we again observed magnetization jumps at critical fields. The same results were obtained on a thin φ6x0.15mm disc measured along [110] and [011] direction. This speaks in favor of the phonon domains model – there are always the third phonon domains with EA perpendicular to the sample plane. At critical fields the magnetic domains in these phonon domains will suddenly reorient into the in-plane {100} axis (-es).

Let us finally explain what happens in our sample showing the constricted MH-loops. At negative saturation the magnetic domains are along [100] parallel to the field (see Fig. 6). At H_CR1 the magnetic domains are suddenly reorganized with the average magnetic moment along [110], at H_CR2 – back to [100]. The magnetic domain sketch for zero field in Fig. 6 is just illustrative, the real domain structure can be much more complex. In the phonon domains model the stripe domains at H = 0 are macroscopic quasidomains, on the microscopic level there should be stair-case magnetic domains with the magnetization in each phonon domain following its own EA.

We have got not only the constricted but also the so-called reentrant loops at T_PM. After reaching the critical field the magnetization changes at high speed around 200 T/s in 0.004 seconds with dM/dt nearly independent on the magnetization frequency in the range from 0.01 to 0.2 Hz. We assume that a single 180⁰ domain wall nucleates along the sample and then propagates with a high speed that can be estimated from the dM/dt peak duration and the sample width as 1m/s. This one-domain wall state can be obtained only in high-quality single crystals. Any local stress, for example by a strain gauge (see Fig. 5), can prevent the nucleation of a single domain wall. Also, we could obtain the reentrant but not constricted MH-loop on our sample at room temperature by application of 10 MPa external compressive stress.

To summarize, in Fig. 7 the evolution of EA together with DS curves is shown. From T_M = 220K to 240K EA is [100]. Actually, that continuous drop of DS that starts immediately after T_M is due to the split of one peak into two peaks. Since it is a continuous process, it is difficult to tell just from DS at which temperature the anisotropy reaches zero but 240K is just a rough estimation. In the range from 240 to 300K the average macroscopic EA is [110], approximately at 300K the anisotropy reaches zero again – no difference in magnetic energy between [100] and [110]. Close to Tc, the magnetic EA is [100]. At room temperature the DS curve at the heating cycle still has three peaks that completely disappear only at 353K, at which the DS curve is identical to that for 225K if scaled by saturation magnetization and the coercivity (see Fig. 8).

We leave open the question of DS hysteresis at Tc since we do not know if it is normal for all ferromagnetic materials or if it is unique to our alloy. We could not find detailed measurements of MH-loops, DS and H_C around T_C for any material. Some authors claim that this susceptibility hysteresis that they call “magnetization hysteresis” is the evidence of the premartensite up to T_C and higher temperatures¹².

We have measured magnetization MH-loops and differential susceptibility curves in the temperature range from 200 to 372K on Ni2MnGa sample in a single-yoke permeameter. From these curves it is seen that in the temperature range from 240 to 300K the average microscopic easy magnetic axis of the sample changes from [100] to [110] with the maximum anisotropy at the premartensitic transition temperature T_PM = 253K. In this temperature range the MH-loops are constricted and the DS curve has two peaks that correspond to the magnetization jumps at the critical fields due to magnetic domain reorientation into [100] direction parallel to the applied field.

The change of average magnetic EA from [100] to [110] can be explained by the phonon domains model³⁴, where phonon-strain coupling of an incompletely softened phonon mode leads to local symmetry breaking and domain formation. The magnetization in each domain in absence of an external field is parallel to the shortest {100} axis of that locally distorted domain. For a flat sample all in-plane {100} axis are equally occupied by magnetic domains, resulting in a net (macroscopically observed) magnetization along the [110] axis. At high enough fields the magnetization in all three phonon domains reorients along the in-plane [100] axis - the applied field direction. High-resolution magnetic domains observations are necessary to check these conclusions that are based on the phonon domains model by Jin et al.³⁴. The results of our work suggest that possibly in the austenitic Ni-Mn-Ga the structure similar to twins (variants) of martensite can exist even at room temperature but with two orders of magnitude smaller tetragonality ratio. Additional experiments are necessary to check that hypothesis.

Sample preparation.

Prior to crystal growth, a mixture according to the intended stoichiometry of Ni₅₀Mn_21.5Ga_28.5 was prepared by pre-alloying the elements. The elemental Ni (99.995 ≡ 4N5) and Ga (6N) were used at purchased from Alfa Aesar. The Mn (3N8), also from Alfa Aesar, showed surface oxidation that was first cleaned by washing in dilute nitric acid followed by distilled water and ethanol prior to use. Pre-alloying was accomplished in a home-built induction furnace, under inert Argon atmosphere. The elements were initially alloyed in a ceramic crucible before decanting and quench-casting into a copper mold with suitable dimensions for crystal growth (6mm diameter rods, up to 80 mm in length).

Single crystal growth was performed in a Crystal Systems Corp. floating zone furnace (FZ-T-4000-VI-VPM-PC). The pre-alloyed rod was placed inside a (7mm diameter) sapphire cylindrical crucible above an oriented seed crystal (growth axis along [100]), and evacuated to < 1×10^− 5 mbar before backfilling with high purity Argon (6N) to an overpressure of 2.5 bar to minimize evaporation during growth. The furnace was centered on the bottom of the pre-alloyed ingot and slowly heated to the melt (~ 42% power). Once a stable molten zone was created inside the sapphire crucible, partially melting the top of the seed crystal, the crucible and alloy rod were translated through the hot zone at a speed of 2 mm/hr, growing from the interface between the seed crystal and the melt. After the hot zone had been passed through the length of the ingot, the furnace was ramped back to zero power over 1 hour.

Longitudinal composition analysis of the crystallized ingot was performed by X-ray fluorescence spectroscopy using an Edax Ametek Orbis-PC spectrometer with a Rh-anode tube (50 µA, 200 kV) and Apollo XRF ML-50 EDS detector, using polycapillary focusing optics (~ 184 × 69 µm² spot size). The single crystal samples were cut from a section of long homogeneous composition at the center of the ingot.

The 1.45x4x60 mm³ sample was cut from the initial ingot, 6 mm in diameter and 100 mm long (see Supplementary Fig. 2) using the electrical discharge machine. Then the sample was mechanically polished.

Magnetic measurements.

Made-in-house magnetic measurement setup was constructed. The 1.45x4x60 mm³ sample was magnetized by the yoke with the driving coil on it (see Supplementary Figs. 3–4). The triangular voltage was generated by the PCIe-6351 National Instruments card and amplified by the made-in-house power amplifier based on APEX MP39CL integrated scheme. The flux density rate dB/dt was measured by pickup coils at different places and the current was given by the voltage on the 0.33 Ohms shunt. All the signals were digitalized by the same PCIe-6351 card at 50kS/sec and then downsampled to 1 kS/sec thus reducing the signal noise.

We sample-yoke system was put into a thermally insulating box (see Supplementary Fig. 5) and the entire yoke setup and sample was cooled by liquid nitrogen 80K. Then the yoke and the sample were heated up at a rate of 1K/min, using a resistive heating under the yoke to continue to heat above room temperature up to ~ 274K. After that the heating was switched off and the yoke and the sample slowly naturally cooled down to the room temperature. The temperature was measured by the T-type thermocouple attached directly to the sample and digitalized by the National Instruments NI-9211 cars four times per second. The maximum field amplitude was 5000 Am^− 1 and the field rate was 5000Am^− 1 s^− 1. The pick-up coil signals were amplified by Analog Devices 5B40 modules, the strain gauge signal – by the 5B38-04 half bridge module.

Custom made software was created in Labview for simultaneous measurements of MH-loops and temperature, as well as software for automatic post processing of data.

Acknowledgements.

This work was supported by the Czech OP VVV project SOLID21-CZ.02.1.01/0.0/0.0/16_019/0000760.

The work of RHC was supported by the Czech Science Foundation (project no. 22-22063S). The sample preparation was performed in MGML (http://mgml.eu/), which was also supported within the program of Czech Research Infrastructures (project no. LM2023065),

Author contributions

A. Perevertov. Task formulation. Building the magnetic measurement setup for temperatures from 80K to 380K. Creating measurement and evaluation software in LabView. Cutting and polishing the samples. All experiments. Data evaluation, analysis and conclusions. Writing the manuscript text.

Ross H. Colman. Single crystal ingot preparation, orientation and chemical composition analysis. Results discussion. Revising and finalizing the manuscript.

Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

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Spin reorientation in premartensite and austenite Ni2MnGa

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