Altering the magnetic ordering of Fe₃Ga₄ via thermal annealing and hydrostatic pressure

Bulk samples of Fe₃Ga₄ were synthesized via arc-melting of elements in corresponding stoichiometric ratios using an Edmund Buehler MAM-1 under ultra-high purity Ar atmosphere. The arc-melted ingots were loaded into quartz tubes and sealed under moderate vacuum ($<10^{-2}$ Torr). The samples were then annealed at various temperatures of 550, 700, 800, 900, 925, 950, 975, and 1000 ^∘C for 48 hours allowed to cool to room temperature naturally.

High resolution synchrotron X-ray diffraction was performed on powders of ground as-recovered ingots at Beamline 11-BM at the Advanced Photon Source at Argonne National Lab. Ground powders were packed in 0.4 mm Kapton capillary tubes and sealed with clay under atmospheric conditions. Diffraction data was collected between 0.5 and 46 degrees with a step size of 0.0001^∘ using a constant wavelength of 0.457921 Å at 300 K. Rietveld refinements and data analysis was performed using the GSAS software suite. GSAS EDS spectra were collected on a LEO SEM/EDAX system at a beam energy of 20kV. The tabulated compositions were obtained as an averages of 5 different sites collected from a cleaved edge surface of each specimen.

A Quantum Design Dynacool Physical Property Measurement System (PPMS) was used to measure the magnetization of the Fe₃Ga₄ samples in magnetic fields up to 5 T and in the temperature interval of 300-800 K. Magnetic measurements under applied hydrostatic pressure (P) was performed in a commercial CuBe cylindrical pressure cell (Quantum Design). Daphne 7373 oil was used as the pressure transmitting medium. The applied pressure value was calibrated by measuring the shift of the superconducting transition temperature of Pb, which was used as a reference manometer. Errors due to differential thermal contraction between the pressure cell components and the pressure transmitting the medium was minimized by setting a 1 K/min temperature sweep-rate. Ambient pressure thermomagnetic characterization was carried out on all annealed samples using a Quantum Design SQUID MPMS system. Samples were first saturated in a field of 1500 Oe, then the field was removed and the sample was cooled to 5 K. A field of 100 Oe was then applied and the magnetic moment was measured while heating to 400 K to obtain the zero-field-cooled (ZFC) curve. The sample was then cooled back to 5 K and the magnetic moment was then measured again in a 100 Oe field while heating to 400 K to obtained the field-cooled curve (FC).

Fe₃Ga₄ crystallizes in the monoclinic C2/m space group with a complex network of four unique Fe atoms within the unit cell. These unique Fe atoms are shown in Figure 1 with a representative XRD powder pattern and refinement for the 1000 ^∘C annealed Fe₃Ga₄ sample. The XRD and refinement show that no unknown phases are present. Previous reports have stated that crystallographic changes caused by annealing, vacancy defects, or anti-site defects can cause changes in the magnetic order of this system as these changes alter the Fe atom network within the unit cell, but a systematic study has not been reported. Mendez We have synthesized polycrystalline ingots of Fe₃Ga₄ through arc-melting of stoichiometric elements and subsequently annealed under vaccuum conditions at various temperature for 48 hours. High-resolution synchrotron x-ray diffraction (XRD) was employed in order to understand the crystallographic changes induced by annealing temperature and relate those to changes in the magnetic ordering of the system. Table 1 shows the results of Rietveld refinement on all annealed Fe₃Ga₄ samples. From this data, we can observe that the secondary impurity phase FeGa₃ appears at all annealing temperature but the phase fraction is significantly decreased with annealing temperatures above 900 ^∘C, but is always present. This is expected as Fe₃Ga₄ does not have a congruent melting point within the Fe-Ga phase diagram. This is important to note as the synthesis method performed for this work is in line with previous polycrystalline work and this quantitative phase analysis of impurity FeGa₃ has not been performed in previous work.Al1995 ; Samatham ; Kawamiya The phase fraction of Fe₃Ga₄ begins to significantly increase above 900 ^∘C due to the melting point of FeGa₃ and Fe₃Ga₄ occurring at 824 and 906 ^∘C respectively. Additionally for stoichiometric mixture of Fe:Ga in 3:4 ratio, the liquidus line is accessible at temperatures above $\sim 950^{\circ}$C and this decreases with higher Ga ratio in the system. FeGa₃ is well-reported as a non-magnetic semiconductorGippius ; Hadano ; Haeussermann and thus its phase fraction should have no direct impact on the magnetic signal for these ingots.

It would also appear that the phase fraction of FeGa₃ does not have a systematic impact on the stoichiometry of the Fe₃Ga₄ phase. This is determined from XRD refinement which is an average structure analysis - microstructure analysis could be important to understand how intergrown FeGa₃ grains affect the magnetic properties of Fe₃Ga₄ polycrystalline material. The refinement process allowed for Fe atom vacancies, Ga atom vacancies, and anti-site mixing after all structural and instrumental parameters have been refined to their optimum values. This process showed that forced Fe vacancies and anti-site mixing always negatively impacted the fit statistics and fit profile; however, Ga vacancies on the order of < 3 % on some sites improved the refinement statistics. This makes sense as the starting material was stoichiometric and any non-zero amount of FeGa₃ impurity should affect the Ga stoichiometry of the Fe₃Ga₄ phase. The only other structural parameter which shows change across these annealing temperature is the unit cell volume which changes on the order of 0.1% between these samples. However, the driving force for unit cell changes cannot be determined as its volume does not systematically trend with Ga vacancies or annealing temperature. Attempts to refine other crystallographic factors such as crystallite strain for example were not useful with the current data due to the multiphase nature of the samples. Future work on single phase Fe₃Ga₄ which has been post-annealed at various temperatures could offer insight into the affects of crystallite strain on the magnetic properties of the system. Lastly, the four unique Fe atoms in the monoclinic unit cell host a large number of nearest and next-nearest-neighbor interactions which all may play a critical role in the manifestation of magnetic order in this system. Rietveld analysis allows Fe-Fe bond distances to be determined and they are reported in Supplementary Information; however, they show no direct trends with annealing temperature.

We have measured the temperature and field-dependent magnetization for all annealed samples and the data can be found in Supplementary Information with summarized transition temperatures in Table 1. For the remainder of this manuscript, we focus on the two most important samples which catalogue the magnetic properties of Fe₃Ga₄ at two different annealing temperature, 900 and 1000 ^∘C. These samples show significant differences in magnetic behavior. Figure 2 shows the temperature-dependent magnetization at 100 Oe applied external field from 400 K to base temperature in the 900 and 1000 ^∘C annealed samples. The differences in the magnetic response of the two samples are clear - both samples have the same general behavior with a ferromagnetic (FM) ground state transitioning to an intermediate ISDW phase before returning to a re-entrant FM phase at high temperature. However, the ordering temperatures of the two are much different. The 1000 ^∘C sample shows expected behavior with a FM to ISDW transition around 68 K and an ISDW to FM transition in the range of previous work. Mendez ; Al1995 The 900 ^∘C shows similar behavior for the FM-ISDW transition with a transition temperature of about 68 K, but the ISDW-FM transition is suppressed down to about 299 K and this is accompanied by a much sharper increase in magnetization upon heating through this range compared to the 1000 ^∘C sample.

The change in ISDW-FM transition temperature between the 900 and 1000 ^∘C samples points toward a significant change in the energy of the ISDW phase relative to the FM phase. Figure 2 shows the field-dependent magnetization at various temperatures for the 900 and 1000 ^∘C samples which further illustrates the differences between the two samples especially in the ISDW-FM transition temperature range. Previous work has shown that within the ISDW phase, a metamagnetic transition is observed with applied field and the required field to induce this metamagentic transition increases with temperature. Samatham ; Mendez Our data supports this observation for both samples. The key difference between the two samples is the response to field prior to the metamagnetic transition. At all temperatures within the ISDW phase prior to the metamagnetic transition, the change in magnetization with respect to applied field is much sharper for the 900 ^∘C sample compared to the 1000 ^∘C sample and at similar temperatures the required metamagnetic field is smaller for the 900 ^∘C sample. This can be seen at the 150 K isotherm in which the 900 ^∘C sample displays a metamagnetic transition at 1 T whereas the 1000 ^∘C displays the same transition at 1.5 T applied field. Similar phenomena was observed in single crystals oriented with the external field applied in different crystallographic directions - where field applied perpendicular to the $c$-axis induced the metamagnetic transition with smaller applied field than with field parallel to the $c$-axis. Mendez Crystallographic anisotropy is unlikely to be the cause of this deviation from normal behavior seen in the 900 ^∘C sample since these samples are not single crystals. Therefore, when considering the decrease in ISDW-FM transition temperature as well as changes in the magnetic field response within the ISDW phase for the 900 ^∘C sample, there must be some external factor driving these observed changes in magnetism within this system.

From Table 1, both samples contain a small amount of FeGa₃ and are Ga deficient on the order of less than 2%, which is similar for the other annealed samples. The magnetic behavior of the other annealed samples is shown in Supplementary Information and from these, it is clear there is no direct trend between annealing temperature, phase fraction of FeGa₃ impurity and the ISDW-FM and FM-ISDW magnetic transition temperatures. However, from the Rietveld refinements of the annealed samples we can observe that there is a direct trend between the volume of the Fe₃Ga₄ unit cell and the ISDW-FM transition; we have shown this trend in Supplementary Information (all transition temperatures were determined by the inflection point of the derivative of magnetization with respect to temperature in the transition temperature range). This is important as it shows that this transition temperature can be altered to room temperature to allow for the possibility of this ISDW-FM phase transition to be incorporated for use in devices. Importantly, previous work showed that volumetric changes in Fe₃Ga₄ from above 400 K to 2 K is less than 0.5% and the change from across the ISDW-FM transition is less than 0.1% such that the observed change in unit cell volume cannot be solely attributed to structural changes between the ISDW and FM states and no structural transition accompanies the ISDW-FM magnetic transition.DuijnThesis ; Benavides Future work is necessary to determine the factors which drive these measured changes in the unit cell volume caused by annealing or changes in the synthesis method in this system. So, although we cannot currently tune unit cell volume from a growth perspective through annealing or defects/occupancy, we can simulate unit cell volume changes through external pressure and determine the changes in magnetic order of the system, especially within the ISDW phase.

In order to reliably probe the affect of unit cell volume changes on the magnetic order of the system, we have measured the magnetic properties of the 1000 ^∘C sample under high pressure. Figure 3 shows the magnetization as a function of temperature at various applied external pressure. We observe that external pressure tunes both the low temperature FM-ISDW transition as well as the high temperature ISDW-FM transition and these trends are summarized in Fig 3b for both transitions. In particular, the ISDW-FM transition is suppressed from around 320 K at ambient pressure down to below 295 K with 10 kbar of applied pressure which brings the transition temperature in line with the observed transition for the 900 ^∘C sample. Concurrently, the low temperature FM-ISDW transition temperature is increased meaning that the temperature regime for the stability of the ISDW phase is growing smaller with applied pressure. Combined, these two factors show that unit cell volume, which is directly being changed through external pressure and was inherently smaller in the 900 ^∘C sample, can be used to tune the intermediate ISDW phase in this system. This points toward a significant impact of crystallographic parameters on the stability of the ISDW phase with regard to its mechanism of formation and stabilization. Previous neutron work has suggested that the high temperature FM phase and low temperature FM phase are identical and the intermediate ISDW phase arises from an Fermi surface instability. Wu This work showed that itinerant magnetism is co-existing with rather large localized magnetic moments of the Fe sites in the Fe₃Ga₄ lattice and thus a coupling mechanism between itinerant spins and the localized moments must play a role in stabilizing this magnetic order in this system. In previous systems, the spin density wave formation is driven by Fermi surface nesting by which different portions of the Fermi surface are coupled by the interaction of itinerant spins and local moments via the RKKY interaction. Feng ; Overhauser ; Overhauser2 If this type of mechanism holds for Fe₃Ga₄ then the effects of pressure and unit cell volume changes should affect the stability of the intermediate ISDW phase through electronic structure and/or magnetic interaction changes. Further work would be necessary to uncover the crystallographic changes caused by external high pressure to relate those changes to the changes in ISDW ordering temperature and stability.

We have shown that the intermediate ISDW phase is sensitive to applied external pressure or internal pressure due to crystallographic factors and previous work has shown that this phase can be affected by applied field as well, but only below 400 K has been reported. Mendez ; Samatham ; Al1995 Figure 4a shows the temperature-dependent magnetization at various applied fields below 400 K. At 0.1 T applied field, the aforementioned low temperature FM-ISDW transition and high temperature ISDW-FM transition are clear and match well with previous reports. As the applied field is increased, the FM-ISDW transition temperature is increased in temperature with applied field and the ISDW-FM transition is broadened greatly with applied field. At high enough field, > 2 T, which is the maximum metamagnetic field required in the ISDW phase, the ISDW phase is seemingly fully suppressed so that the entire magnetization signal below 400 K is ferromagnetic owning from the FM-PM transition at 420 K above the measured range. From this, it appears that the intermediate ISDW can be fully suppressed to stabilize the ferromagnetic ground state across the entire temperature regime below the initial FM-PM transition with high applied field. Furthermore, we have measured the same properties in the range from 400 - 700 K in order to understand the effects of applied field for the FM-PM transition. Figure 4b shows the temperature-dependent magnetization at various applied fields from 300 - 700 K. At low fields (0.1 T), the ISDW-FM transition is clear as well as the FM-PM transition which occurs at 420 K, matching previous reports. Mendez As expected, higher applied fields suppresses the ISDW-FM transition until it is no longer observable. Curiously, the FM-PM transition temperature increases with applied field as shown by Figure 4b inset. It is unclear what is driving this change but similar behavior has been noted in other systems and discussed as the observation of itinerant metamagnetism in the region of the ferromagnetic to paramagnetic transition. CoS1 ; CoS2 ; CoS3 ; levitin ; Goto ; Yoshimura For this reason, this anomalous behavior in the region of the FM-PM transition requires further investigation to understand the field-dependence especially above the proposed ferromagnetic transition.