# Fileset

[10.3390-cryst13050760.pdf](https://mdr.nims.go.jp/filesets/1dab88ec-b752-43f4-9925-fc74cfd97d67/download)

## Creator

[Naoki Kikugawa](https://orcid.org/0000-0003-3975-4478), [Takashi Kato](https://orcid.org/0000-0002-3317-7481), Momoko Hayashi, [Hitoshi Yamaguchi](https://orcid.org/0000-0002-4878-4073)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Single-Crystal Growth of a Cubic Laves-Phase Ferromagnet HoAl2 by a Laser Floating-Zone Method](https://mdr.nims.go.jp/datasets/854e24ab-9632-40be-bb95-fb693fbc0c72)

## Fulltext

Single-Crystal Growth of a Cubic Laves-Phase Ferromagnet HoAl2 by a Laser Floating-Zone MethodCitation: Kikugawa, N.; Kato, T.;Hayashi, M.; Yamaguchi, H.Single-Crystal Growth of a CubicLaves-Phase Ferromagnet HoAl2 by aLaser Floating-Zone Method. Crystals2023, 13, 760. https://doi.org/10.3390/cryst13050760Academic Editor: Nikolia LaliotiReceived: 12 April 2023Revised: 25 April 2023Accepted: 1 May 2023Published: 3 May 2023Copyright: © 2023 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).crystalsArticleSingle-Crystal Growth of a Cubic Laves-Phase FerromagnetHoAl2 by a Laser Floating-Zone MethodNaoki Kikugawa 1,*, Takashi Kato 2,3, Momoko Hayashi 2 and Hitoshi Yamaguchi 21 National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan2 National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan; katou@fukushima-nct.ac.jp (T.K.);hayashi.momoko@nims.go.jp (M.H.); yamaguchi.hitoshi@nims.go.jp (H.Y.)3 National Institute of Technology, Fukushima College, Iwaki, Fukushima 970-8034, Japan* Correspondence: kikugawa.naoki@nims.go.jpAbstract: The successful growth of single crystals of a cubic Laves-phase material HoAl2 with thespace group Fd-3m is reported in this study. The crystals were grown by a floating-zone methodwith five laser diodes as a heat source. Al-rich feed rods were prepared as compensation for heavyevaporation during the growth. The nominal ratio for the feed rods was optimized as Ho:Al = 1:2.5.Single crystals of HoAl2 with a length of 50 mm were first grown in this technique. Obtaining the large-sized crystal by the floating-zone method enabled us to systematically explore the physical propertiesusing the same batch crystal. The crystal possessed a second-ordered ferromagnetic transition at 29 Kand a first-ordered spin-reorientation transition at 20 K. The bulk physical properties, such as specificheat, magnetic susceptibility, isothermal magnetization, and thermal expansion measurements, weremeasured. Additionally, a magnetocaloric effect was evaluated by the magnetic entropy change.We demonstrate that anisotropic physical properties along the principal axes ([100], [110], and[111]) emerged below the magnetically ordered states, in contrast to the isotropic behavior in theparamagnetic state.Keywords: HoAl2; crystal growth; laser floating-zone technique; bulk physical properties;magnetocaloric effect1. IntroductionThe magnetocaloric effect is a thermodynamic phenomenon of temperature change ona magnetic material controlled by an external magnetic field in adiabatic conditions [1,2].Magnetic refrigeration is a promising application based on the magnetocaloric effect be-cause of its potential for being environmentally friendly and highly efficient [3]. Thematerial design exhibiting an efficient magnetocaloric effect has been a central key tothe practical use of magnetic refrigeration. One of the efficiencies of the magnetocaloriceffect can be assessed by the magnetic entropy change in the material, defined as thedifference in entropy between the magnetized and demagnetized process. Ferromagneticmaterials have usually been targeted because these materials should generally gain largermagnetic entropy change between the demagnetized (higher entropy) and magnetized(lower entropy) process near the transition temperature [4]. As the transition temperaturewidely varies from material to material, we can focus on the design of the material bydemonstrating the excellent magnetocaloric effect at the focused temperature. Amongthe target temperature ranging from room temperature for air conditioners to extremelylow temperatures, one of the focused temperatures is approximately 20 K which liquefieshydrogen as a next-generation clean-energy source [5,6].Very recently, an active magnetic regenerative refrigerator combined with a super-conducting magnet has been developed and succeeded in liquefying hydrogen [7]. Thisopens a new window to hydrogen liquefaction through the novel magnetic refrigerationtechnique in addition to the conventional gas compression/expansion technique. Here,Crystals 2023, 13, 760. https://doi.org/10.3390/cryst13050760 https://www.mdpi.com/journal/crystalshttps://doi.org/10.3390/cryst13050760https://doi.org/10.3390/cryst13050760https://creativecommons.org/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/crystalshttps://www.mdpi.comhttps://doi.org/10.3390/cryst13050760https://www.mdpi.com/journal/crystalshttps://www.mdpi.com/article/10.3390/cryst13050760?type=check_update&version=1Crystals 2023, 13, 760 2 of 13HoAl2 was selected as a magnetic refrigerant among the materials because this materialhas a large magnetic entropy change around the temperature for hydrogen liquefaction.HoAl2 has the cubic Laves-phase structure with the space group Fd-3m (No. 227) [8].The crystal structure is illustrated in Figure 1. HoAl2 exhibits a ferromagnetic transitionaround 30 K as well as another spin-reorientation transition at 20 K [9]. For the above mag-netic refrigeration, the HoAl2 polycrystalline material with a total weight of 250 g was filledinside the refrigerator as stamped particles with a diameter of 300–500 µm [7]. Additionally,a gas-atomization process was applied to make spherical polycrystalline particles with adiameter of 200–400 µm [10]. Producing many particles with homogeneous quality is oneof the important factors for efficient liquefaction. Since the quality of the produced particlesis directly linked to the liquefaction efficiency, it is useful to assess the variation in qualitybased on a “standard dataset” obtained from the reference material, preferably high-qualitysingle crystals of HoAl2. In addition, the materials are exposed to both the cryogeniccycle and the application/removal of the magnetic fields during the liquefaction [7,11].Since the crystalline material generally has anisotropic physical properties such as thermalcontraction/expansion and magnetostriction, these may affect the sample durability underthese extreme circumstances. Acquiring the anisotropic physical properties is an importanttask, and the investigation using a single crystal is in high demand.Crystals 2023, 13, x FOR PEER REVIEW 3 of 14    Figure 1. Crystal structure of a cubic Laves-phase material HoAl2 with the space group Fd-3m (No. 227). 2. Materials and Methods 2.1. Growth by the Floating-Zone Technique We employed a floating-zone technique using a laser diode as the heat source (L-FZ 2000, Quantum Design Japan, Tokyo, Japan) with five 400 W GaAs-based 940 nm laser heads for the growth of HoAl2 single crystals. Since the laser emission can be sharply fo-cused, a steep temperature gradient can be created between the laser-heated narrower molten zone and the grown crystal. That provides a stable molten zone during crystal growth. Additionally, we optimized the distribution profile of the vertical irradiation in-tensity along the length of the rod, improving from a “flat” to a “bell-shaped” form, while the original flat temperature profile was kept along the radial direction of the rod (see Figure 2 of [19]). Such a modified profile reduces thermal stress inside the grown crystals. HoAl2 single crystals were grown using a laser-diode floating-zone furnace where five laser diodes provide the mentioned vertically bell-shaped distribution of temperature at the focal point. 2.2. Feed and Seed Rods Preparation When we first attempted the crystal growth of HoAl2 using the feed rod with the nominal stoichiometric ratio Ho:Al = 1:2, the molten zone was stable during the growth process. However, we found high volatility from the feed rods, and the evaporated pow-der was deposited inside the quartz tube. The grown bulk crystal finally collapsed into powder when it was left in the air overnight. The collapsed powder was composed of Ho2O3, and HoN after probably absorbing the air, together with HoAl2 as the main phase by the X-ray diffraction measurements. Additionally, the evaporated powder was identi-fied as aluminum. To grow the stoichiometric crystals, we made the Al-rich feed rods. The nominal ratio was finally optimized as Ho:Al = 1:2.5 to compensate for the Al evaporation Figure 1. Crystal structure of a cubic Laves-phase material HoAl2 with the space group Fd-3m (No. 227).Physical properties of the single-crystalline HoAl2 grown by the Czochralski andBridgman methods have been presented both experimentally and theoretically [9,12–16].However, to our knowledge, crystal growth with a floating-zone technique has not beenreported. An advantage of the floating-zone method is minimized contamination levelduring the growth procedure due to the absence of the crucible, as well as the possibility toobtain large and homogeneous crystals [17]. These enable us to perform characterizationby several experimental techniques using the same batch of grown crystals. In this paper,we first present the successful growth of HoAl2 crystals by the floating-zone techniquewith five laser diodes as the heat source [18,19]. Although we found that the procedure forthe growth process of another intermetallic system NdAlGe [20] was partly applicable tothe growth of HoAl2, we mention improved steps, such as the fabrication of Al-rich feedCrystals 2023, 13, 760 3 of 13rods to compensate for the heavy evaporation during the growth of HoAl2. We show thethermodynamic physical properties such as specific heat, magnetic susceptibility, magneti-zation, and thermal expansion of the grown crystals. Throughout the measurements, theanisotropic physical properties are revealed in the ferromagnetic ordered state along theprincipal axes, in sharp contrast to the isotropic behavior in the paramagnetic state.2. Materials and Methods2.1. Growth by the Floating-Zone TechniqueWe employed a floating-zone technique using a laser diode as the heat source (L-FZ2000, Quantum Design Japan, Tokyo, Japan) with five 400 W GaAs-based 940 nm laserheads for the growth of HoAl2 single crystals. Since the laser emission can be sharplyfocused, a steep temperature gradient can be created between the laser-heated narrowermolten zone and the grown crystal. That provides a stable molten zone during crystalgrowth. Additionally, we optimized the distribution profile of the vertical irradiationintensity along the length of the rod, improving from a “flat” to a “bell-shaped” form, whilethe original flat temperature profile was kept along the radial direction of the rod (seeFigure 2 of [19]). Such a modified profile reduces thermal stress inside the grown crystals.HoAl2 single crystals were grown using a laser-diode floating-zone furnace where fivelaser diodes provide the mentioned vertically bell-shaped distribution of temperature atthe focal point.2.2. Feed and Seed Rods PreparationWhen we first attempted the crystal growth of HoAl2 using the feed rod with thenominal stoichiometric ratio Ho:Al = 1:2, the molten zone was stable during the growthprocess. However, we found high volatility from the feed rods, and the evaporated powderwas deposited inside the quartz tube. The grown bulk crystal finally collapsed into powderwhen it was left in the air overnight. The collapsed powder was composed of Ho2O3,and HoN after probably absorbing the air, together with HoAl2 as the main phase by theX-ray diffraction measurements. Additionally, the evaporated powder was identified asaluminum. To grow the stoichiometric crystals, we made the Al-rich feed rods. The nominalratio was finally optimized as Ho:Al = 1:2.5 to compensate for the Al evaporation during thegrowth. We denote the feed rod as HoAl2.5 hereafter. For making a feed rod, polycrystallineingots of HoAl2.5 were first prepared using an arc-melting furnace under an Ar atmosphere(Techno Search Corp., Model SE-11399, Tokyo, Japan) with Ho (3N) and Al (5N) as startingmaterials. The ingot with a button shape was inverted and melted several times to ensurehomogeneity. No weight loss by evaporation was detected at this stage. Next, the ingotswith a typical weight of 15 g were powdered using an agate mortar and pestle. We shapedthe powder into a cylindrical rod in a tubular rubber balloon and then applied hydrostaticpressure of 40 MPa for 5 min. The uniformly shaped rods removed from the balloon weresintered for 24 h at 1123 K in a tube furnace under flowing Ar gas at 3 L/min. Here, the Argas was circulated by using a yttria-stabilized zirconia-based oxygen pump heated at 873 K.The oxygen pump produced an extremely low oxygen partial pressure below 10−28 atm(Canon Machinery Inc., Model ULOCE-530, Shiga, Japan) [21]. Finally, the sintered rodwith typically 5.5 mm diameter was cut into two unequal parts. The longer (shorter) parts95 mm (30 mm) in length were designated as the feed (seed) rods. Based on the experienceof working in ruthenates [22], great care was taken in all the preparation steps to preventcontamination risk.2.3. Crystal GrowthThe sintered feed rod (HoAl2.5) was attached to a platinum hock in the upper shaftwith a molybdenum wire, and the seed rod was mounted on an alumina holder in thelower shaft. As the growth space was isolated from the outside environment by a quartztube, the desired gas atmosphere and pressure were selected throughout the crystal growth.For the HoAl2 growth, a gas mixture of Ar (96%) and H2 (4%) was used for reduction.Crystals 2023, 13, 760 4 of 13An additional thinner quartz tube of smaller diameter was installed inside the main tubeto prevent damage to the outer tube by evaporating Al. The melting started from thebottom edge of the feed rod with increasing laser power. Then, the molten feed rod wasattached to the upper end of the seed rod. The growth began with necking twice to ensurehigh crystallinity as a polycrystalline seed rod was used. The molten zone was stabilizedat both feed and growth speeds of 5 mm/h after the second necking. The growth wasperformed at 0.3 MPa under a flow rate of 1 L/min to suppress the evaporation. To growunder homogenized molten liquid and temperature distribution, the feed and seed wererotated at 10 rpm in opposite directions. A stable molten zone was formed during thegrowth process until the end without cracks in the sintered feed rods prepared using thegiven procedure. After growth, the crystal was carefully removed from the furnace. Thecrystal grown using the HoAl2.5 rod was kept in bulk without collapsing to powder afterthe crystal was left in the air. We observed successful growth using a feed rod with thenominal ratio of Ho:Al = 1:2.2, and the crystal did not collapse under air. However, thegrown crystal from the HoAl2.2 rod was still off-stoichiometry, suggesting Al deficiency, asdescribed later.2.4. CharacterizationTo check the phase purity, the ground single crystals were measured with powderX-ray diffraction using Cu Kα radiation at room temperature (MiniFlex600, Rigaku, Tokyo,Japan). The grown crystals were cut along the principle crystallographic axes ([100],[110], and [111] directions) by determining their orientations using a back-scattered X-rayLaue diffraction technique (SA-HF3S, Rigaku Co., Ltd., Tokyo, Japan, and s-Laue, PulstecIndustrial Co., Ltd., Shizuoka, Japan). The chemical composition of the grown crystals wasanalyzed using inductively coupled plasma optical emission spectrometry (ICP-OES).Thermodynamically bulk physical properties of the grown crystals were measureddown to 2 K using a Physical Property Measurement System (Dynacool, Quantum Design).The specific heat (CP) as a function of temperature (T) was performed by a relaxationmethod. The magnetic susceptibility between 2 and 300 K was measured in a magnetic field(H) of 0.01 T under both zero-field-cooled (ZFC) and field-cooled (FC) conditions. Here, theZFC and FC refer to cooling conditions before and after applying a static magnetic fieldto the sample, respectively. The isothermal magnetization (M) at various temperatureswas measured up to 9 T. The thermal expansion was performed by a capacitive-basedmethod [23] with decreasing temperature at the control of 0.1 K/min. The magnetic entropychange (∆SM) along the magnetic field directions of [100], [110], and [111] was deducedfrom the thermodynamic Maxwell relation, ∆SM =∫ H0∂M∂T dH [4], which was obtainedfrom the magnetization (M) measurement as a function of temperature measured up to 5 Tunder the FC process.3. Results and Discussion3.1. Growth of HoAl2 CrystalsA photograph of the HoAl2 crystal with a length of 50 mm grown under stableconditions is demonstrated in Figure 2a. The evaporated Al powder from the rod wasdeposited on the internal surface of the quartz tube and the shafts. No sign of the moltenliquid dropping during the growth was spotted on the crystal surface, indicating stabletemperature control. Figure 3 presents the powder X-ray diffraction profile of a partiallycrushed crystal. For comparison, an X-ray diffraction profile of HoAl2 from a database(PDF-2 03-065-7339 (ICDD, 2021)) [24] is added with red color. All peaks were sharp andwell indexed to the Fd-3m space group without detecting impurity phases. The latticeparameters were deduced to be a = 0.7838 nm, which was consistent with the previousreport [25]. The back-scattered Laue photos of the crystal along the axes [100], [110], and[111] after polishing are presented in Figure 2b–d, respectively, with sharp and clear spotsfrom the bulk crystal. We can clearly see the four-, two-, and three-fold symmetry in thephotos of [100], [110], and [111], respectively, reflecting the crystal symmetry of the cubicCrystals 2023, 13, 760 5 of 13structure (Fd-3m). ICP-OES suggests the molar ratios of Ho:Al = 1.00:1.97, and 1.00:2.00in the grown crystals for the HoAl2.2 and HoAl2.5 nominal compositions of the feed rods,respectively. Each ratio was identical to the different positions of the grown crystal withinthe experimental error, indicating the homogeneity of the grown crystal. This certifiesthat the stoichiometric crystal was grown from the HoAl2.5 feed rod where excess Alcompensated for the evaporation, whereas the crystal grown from the HoAl2.2 feed rodstill had Al deficiency. The possibility of Al embedding into the grown crystals when usingoff-stoichiometric (Al-rich) feed rods had to be verified following our experience in growingRu-embedded Sr2RuO4 [26]. Any signals of quantum oscillatory effects originating fromaluminum were not detected within the experimental resolution when the measured ACsusceptibility of the grown material was at 30 mK. Since the AC susceptibility measurementusing a field modulation technique [27] is a powerful tool that can detect the micrometer-size metal inclusions inside the bulk material, our results strongly suggest that there isno effect of Al embedding on the bulk physical properties of HoAl2. Hereafter, we showthe bulk physical properties of the stoichiometric crystal HoAl2 (grown from the feedrod of HoAl2.5). Here, the thermodynamic physical properties in bulk were measuredwith dimensions of 2.0 mm and a weight of 47 mg after cutting and polishing along theprincipal axes ([100], [110], and [111]), as shown in Figure 2e. Appendix A shows thesample dependence between HoAl2 and HoAl1.97 found in the specific heat measurements.Crystals 2023, 13, x FOR PEER REVIEW 6 of 14    Figure 2. (a) A photograph of the grown HoAl2 crystal after the floating-zone method using five laser diodes as the heat source. The crystal was obtained after necking twice at the beginning of the growth. (b–d) Back-scattered Laue photos along the principal axes [100], [110], and [111], respec-tively. (e) A photograph of the HoAl2 crystal after cutting and polishing along the principal axes for the measurements of the thermodynamic physical properties used in this study.  Figure 3. Powder X-ray diffraction pattern with indices of the partially crushed HoAl2 crystal using Cu Kα radiation at room temperature. For comparison, an X-ray diffraction profile of HoAl2 from a database (PDF-2 03-065-7339 (ICDD, 2021)) [24] is added with red color. 3.2. Bulk Thermodynamic Properties of the Grown Crystal In Figure 4, the temperature dependence of the specific heat (CP) for the stoichio-metric HoAl2 without field represents a clear lambda-type anomaly with a second-ordered transition temperature at 29 K defined by the midpoint of the jump. The transition corre-sponds well to the onset of the ferromagnetic transition at TC from the paramagnetic state. Another sharp transition was seen at 20 K (TSR), defined at the peak, which corresponds Figure 2. (a) A photograph of the grown HoAl2 crystal after the floating-zone method using fivelaser diodes as the heat source. The crystal was obtained after necking twice at the beginning of thegrowth. (b–d) Back-scattered Laue photos along the principal axes [100], [110], and [111], respectively.(e) A photograph of the HoAl2 crystal after cutting and polishing along the principal axes for themeasurements of the thermodynamic physical properties used in this study.Crystals 2023, 13, 760 6 of 13Crystals 2023, 13, x FOR PEER REVIEW 6 of 14    Figure 2. (a) A photograph of the grown HoAl2 crystal after the floating-zone method using five laser diodes as the heat source. The crystal was obtained after necking twice at the beginning of the growth. (b–d) Back-scattered Laue photos along the principal axes [100], [110], and [111], respec-tively. (e) A photograph of the HoAl2 crystal after cutting and polishing along the principal axes for the measurements of the thermodynamic physical properties used in this study.  Figure 3. Powder X-ray diffraction pattern with indices of the partially crushed HoAl2 crystal using Cu Kα radiation at room temperature. For comparison, an X-ray diffraction profile of HoAl2 from a database (PDF-2 03-065-7339 (ICDD, 2021)) [24] is added with red color. 3.2. Bulk Thermodynamic Properties of the Grown Crystal In Figure 4, the temperature dependence of the specific heat (CP) for the stoichio-metric HoAl2 without field represents a clear lambda-type anomaly with a second-ordered transition temperature at 29 K defined by the midpoint of the jump. The transition corre-sponds well to the onset of the ferromagnetic transition at TC from the paramagnetic state. Another sharp transition was seen at 20 K (TSR), defined at the peak, which corresponds Figure 3. Powder X-ray diffraction pattern with indices of the partially crushed HoAl2 crystal usingCu Kα radiation at room temperature. For comparison, an X-ray diffraction profile of HoAl2 from adatabase (PDF-2 03-065-7339 (ICDD, 2021)) [24] is added with red color.3.2. Bulk Thermodynamic Properties of the Grown CrystalIn Figure 4, the temperature dependence of the specific heat (CP) for the stoichiomet-ric HoAl2 without field represents a clear lambda-type anomaly with a second-orderedtransition temperature at 29 K defined by the midpoint of the jump. The transition corre-sponds well to the onset of the ferromagnetic transition at TC from the paramagnetic state.Another sharp transition was seen at 20 K (TSR), defined at the peak, which corresponds toa first-ordered spin-reorientation transition [9]. The results certify that the observed phasetransitions occur in bulk. No other transitions from impurity phases were detected in ourexperimental resolution down to 2 K except for these two sharp ones. For comparison,the CP of Al-deficient HoAl1.97 crystal is shown in Appendix A (Figure A1). We can seethat the TC of HoAl1.97 is lower than that of the stoichiometric HoAl2. On the other hand,TSR seems almost identical. It should be noted that we were careful about evaluating thespecific heat value for the first-ordered transition when the relaxation method is applied.Crystals 2023, 13, x FOR PEER REVIEW 7 of 14   to a first-ordered spin-reorientation transition [9]. The results certify that the observed phase transitions occur in bulk. No other transitions from impurity phases were detected in our experimental resolution down to 2 K except for these two sharp ones. For compar-ison, the CP of Al-deficient HoAl1.97 crystal is shown in Appendix A (Figure A1). We can see that the TC of HoAl1.97 is lower than that of the stoichiometric HoAl2. On the other hand, TSR seems almost identical. It should be noted that we were careful about evaluating the specific heat value for the first-ordered transition when the relaxation method is applied.  Figure 4. Temperature dependence of specific heat (CP) of HoAl2 crystal under zero field. Clear tran-sitions with a second-ordered and a first-ordered feature are seen at TC = 29 K and TSR = 20 K, respec-tively. In Figures 5a–c, temperature dependences of the magnetic susceptibility (M/H) were presented under the applied magnetic field of 0.01 T under H//[100], [110], and [111], re-spectively. A clear ferromagnetic transition (TC) at 29 K as well as the spin-reorientation transition at 20 K (TSR) was seen in all field directions. Both TC and TSR correspond to the transitions seen at the specific heat in Figure 4. The hysteresis between ZFC and FC pro-cess is clearly observed below TSR as demonstrated in the inset of Figure 5b. The inverse magnetic susceptibility (M/H)−1 as a function of temperature along the field directions [100], [110], and [111] in Figure 5d–f, respectively, involves the black lines, which repre-sent the fits to the Curie–Weiss law, 𝑀𝐻=𝑁A𝜇eff2 𝜇B23𝑘B(𝑇− 𝜃P)+ 𝜒0. Here, kB, NA, and μB are the Boltz-mann constant, Avogadro’s number, and the Bohr magneton, respectively. The effective magnetic moments (μeff) determined from the fits between 110 and 300 K were μeff = 11.1 μB, 11.0 μB, and 11.2 μB under H//[100], [110], and [111], respectively. These values match with the theoretical value of the free Ho3+ with a total angular momentum of J = 8, which corresponds to μeff = 10.6 μB. This suggests that the nature of the 4f electrons is well local-ized. The χ0 is a small temperature-independent term and typically represents Larmor Figure 4. Temperature dependence of specific heat (CP) of HoAl2 crystal under zero field. Clear transitionswith a second-ordered and a first-ordered feature are seen at TC = 29 K and TSR = 20 K, respectively.Crystals 2023, 13, 760 7 of 13In Figure 5a–c, temperature dependences of the magnetic susceptibility (M/H) werepresented under the applied magnetic field of 0.01 T under H//[100], [110], and [111],respectively. A clear ferromagnetic transition (TC) at 29 K as well as the spin-reorientationtransition at 20 K (TSR) was seen in all field directions. Both TC and TSR correspond tothe transitions seen at the specific heat in Figure 4. The hysteresis between ZFC and FCprocess is clearly observed below TSR as demonstrated in the inset of Figure 5b. Theinverse magnetic susceptibility (M/H)−1 as a function of temperature along the field di-rections [100], [110], and [111] in Figure 5d–f, respectively, involves the black lines, whichrepresent the fits to the Curie–Weiss law, MH =NAµ2effµ2B3kB(T−θP)+ χ0. Here, kB, NA, and µB arethe Boltzmann constant, Avogadro’s number, and the Bohr magneton, respectively. Theeffective magnetic moments (µeff) determined from the fits between 110 and 300 K wereµeff = 11.1 µB, 11.0 µB, and 11.2 µB under H//[100], [110], and [111], respectively. Thesevalues match with the theoretical value of the free Ho3+ with a total angular momentum ofJ = 8, which corresponds to µeff = 10.6 µB. This suggests that the nature of the 4f electronsis well localized. The χ0 is a small temperature-independent term and typically representsLarmor diamagnetic and Pauli paramagnetic contributions. The values from the fits were+7.65 × 10−4, +6.20 × 10−4, and +5.87 × 10−4 emu/mol for H//[100], [110], and [111],respectively. The Weiss temperatures under H//[100], [110], and [111] were obtainedas θP = +34.6 K, +33.4 K, and +36.1 K, respectively. The positive values of θP indicate aferromagnetic coupling. Thus, the magnetic susceptibility measurements reveal almostisotropic behavior in the paramagnetic region, as found in the previous result that reportsonly under H//[100] and [110] [15].Crystals 2023, 13, x FOR PEER REVIEW 8 of 14   diamagnetic and Pauli paramagnetic contributions. The values from the fits were +7.65 × 10−4, +6.20 × 10−4, and +5.87 × 10−4 emu/mol for H//[100], [110], and [111], respectively. The Weiss temperatures under H//[100], [110], and [111] were obtained as θP = +34.6 K, +33.4 K, and +36.1 K, respectively. The positive values of θP indicate a ferromagnetic coupling. Thus, the magnetic susceptibility measurements reveal almost isotropic behavior in the paramagnetic region, as found in the previous result that reports only under H//[100] and [110] [15].  Figure 5. Temperature dependencies of the magnetic susceptibility (M/H) of HoAl2 under the ap-plied field along (a) H//[100], (b) H//[110], and (c) H//[111]. Measurements were performed at 0.01 T under zero-field-cooled (open circles) and field-cooled (closed circles) processes. The inset shows the hysteresis between ZFC and FC processes. Inverse magnetic susceptibility, (M/H)−1, as a function of temperature under (d) H//[100], (e) H//[110], and (f) H//[111]. Solid black lines represent fits to the Curie–Weiss law between 110 and 300 K. The isothermal magnetization of HoAl2 under H//[100], [110], and [111] at several temperatures between 2 and 50 K in Figures 6a–c, respectively, was taken after the field cooling process. The rapid increase at lower fields was gradually suppressed under any field directions as the temperature increased. Under H//[100], the upward behavior around 2 T observed at low temperatures was suppressed with increasing temperature. At a high field, the magnetization is saturated toward the full moment (10 μB), which Figure 5. Temperature dependencies of the magnetic susceptibility (M/H) of HoAl2 under the appliedfield along (a) H//[100], (b) H//[110], and (c) H//[111]. Measurements were performed at 0.01 T underCrystals 2023, 13, 760 8 of 13zero-field-cooled (open circles) and field-cooled (closed circles) processes. The inset shows thehysteresis between ZFC and FC processes. Inverse magnetic susceptibility, (M/H)−1, as a function oftemperature under (d) H//[100], (e) H//[110], and (f) H//[111]. Solid black lines represent fits tothe Curie–Weiss law between 110 and 300 K.The isothermal magnetization of HoAl2 under H//[100], [110], and [111] at severaltemperatures between 2 and 50 K in Figure 6a–c, respectively, was taken after the fieldcooling process. The rapid increase at lower fields was gradually suppressed under anyfield directions as the temperature increased. Under H//[100], the upward behavior around2 T observed at low temperatures was suppressed with increasing temperature. At a highfield, the magnetization is saturated toward the full moment (10 µB), which correspondsto a free Ho3+ (J = 8) with the g-factor gJ = 5/4, irrespective of the field directions. Theremnant magnetization that was seen under all the field directions disappears at TC.Crystals 2023, 13, x FOR PEER REVIEW 9 of 14   corresponds to a free Ho3+ (J = 8) with the g-factor gJ = 5/4, irrespective of the field direc-tions. The remnant magnetization that was seen under all the field directions disappears at TC.  Figure 6. Isothermal magnetization (M) of HoAl2 under (a) H//[100], (b) H//[110], and (c) H//[111] up to 9 T at several temperatures across the magnetic phase transitions (TC and TSR). The data were taken under the field-cooled processes at 2, 10, 15, 20, 24, 26, 29, 32, 37 and 50 K. In Figure 7, the linear thermal expansions ∆𝐿𝑖𝐿𝑖=𝐿𝑖(𝑇)−𝐿𝑖(300 K)𝐿𝑖(300 K) as a function of temper-ature, where the index i refers to the principal crystallographic axes (100), (110), and (111), represent a clear kink at TC = 29 K for all ∆𝐿𝑖𝐿𝑖, corresponding to the second-ordered ferro-magnetic transition. In addition, a jump is seen at TSR = 20 K, indicating the first-ordered transition associated with the spin reorientation. As shown in the inset of Figure 7, the ∆𝐿𝑖𝐿𝑖 is almost isotropic at the paramagnetic region. In contrast, we can see the anisotropic be-havior below TC: on cooling, the ∆𝐿𝑖𝐿𝑖 decreases along all the directions with the largest re-sponse to the (110) direction. Additionally, the ∆𝐿𝑖𝐿𝑖 along the (100) and (111) directions decrease suddenly at TSR, whereas the ∆𝐿𝑖𝐿𝑖 along the (110) direction increases. This result Figure 6. Isothermal magnetization (M) of HoAl2 under (a) H//[100], (b) H//[110], and (c) H//[111]up to 9 T at several temperatures across the magnetic phase transitions (TC and TSR). The data weretaken under the field-cooled processes at 2, 10, 15, 20, 24, 26, 29, 32, 37 and 50 K.Crystals 2023, 13, 760 9 of 13In Figure 7, the linear thermal expansions ∆LiLi= Li(T)−Li(300 K)Li(300 K)as a function of temper-ature, where the index i refers to the principal crystallographic axes (100), (110), and (111),represent a clear kink at TC = 29 K for all ∆LiLi, corresponding to the second-ordered ferro-magnetic transition. In addition, a jump is seen at TSR = 20 K, indicating the first-orderedtransition associated with the spin reorientation. As shown in the inset of Figure 7, the∆LiLiis almost isotropic at the paramagnetic region. In contrast, we can see the anisotropicbehavior below TC: on cooling, the ∆LiLidecreases along all the directions with the largestresponse to the (110) direction. Additionally, the ∆LiLialong the (100) and (111) directionsdecrease suddenly at TSR, whereas the ∆LiLialong the (110) direction increases. This resultmay be related to the spin-reorientation transition toward the (110) direction. Thus, thethermal expansion experiments offer directionally bulk information along the indepen-dent crystallographic axes throughout the magneto-volume coupling in the magneticallyordered phase.Crystals 2023, 13, x FOR PEER REVIEW 10 of 14   may be related to the spin-reorientation transition toward the (110) direction. Thus, the thermal expansion experiments offer directionally bulk information along the independ-ent crystallographic axes throughout the magneto-volume coupling in the magnetically ordered phase.  Figure 7. Temperature dependences of thermal expansion ∆𝐿𝑖𝐿𝑖=𝐿𝑖(𝑇)−𝐿𝑖(300 K)𝐿𝑖(300 K). Here, the index i re-fers to the principal crystallographic axes [100], [110], and [111], respectively. To evaluate the magnetic entropy change ΔSM of single-crystalline HoAl2, the tem-perature dependences of the magnetization (M vs. T) of HoAl2 under H//[100], [110], and [111] under various static magnetic fields up to 5 T were plotted in Figures. 8(a), (b), and (c), respectively. These were measured under the FC process. The Maxwell relation as mentioned above was applied to evaluate the magnetic entropy change ΔSM. The ΔSM as the functions of temperature under H//[100], [110], and [111] are shown in Figs. 8(d), (e), and (f), respectively, for various applied fields up to 5 T. The ΔSM has a minimum near TC for all the field directions. The minimum values obtained for a field change between 0 and 5 T are −5.9, −5.8, and −4.9 J/K mol under H//[100], [110], and [111], respectively. These negative ΔSM with relatively large values around 30 K indicates the entropy release (gain) under magnetization (demagnetization) independent of the magnetic field directions. This result of being nearly field-independent might be advantageous as a magnetic refrig-erant where polycrystalline particles are used [7,10]. Additionally, under H//[110] and [111], a convex (concave) upward behavior was seen around 20 K, although overall ΔSM behavior became negative. The ΔSM under H//[100] showed a positive peak at low tem-peratures as well as a negative peak around 30 K. Similar sign change can be seen in the previous report [15]. The anisotropic behavior around 20 K might be associated with the spin-reorientation transition. These results indicate that the main contribution in ΔSM orig-inates from the paramagnetic to the ferromagnetic transition at TC irrespective of the field directions, and the spin orientation transition induces the anisotropic behavior in ΔSM. Figure 7. Temperature dependences of thermal expansion ∆LiLi=Li(T)−Li(300 K)Li(300 K). Here, the index irefers to the principal crystallographic axes [100], [110], and [111], respectively.To evaluate the magnetic entropy change ∆SM of single-crystalline HoAl2, the temper-ature dependences of the magnetization (M vs. T) of HoAl2 under H//[100], [110], and[111] under various static magnetic fields up to 5 T were plotted in Figure 8a–c, respectively.These were measured under the FC process. The Maxwell relation as mentioned abovewas applied to evaluate the magnetic entropy change ∆SM. The ∆SM as the functionsof temperature under H//[100], [110], and [111] are shown in Figure 8d–f, respectively,for various applied fields up to 5 T. The ∆SM has a minimum near TC for all the fielddirections. The minimum values obtained for a field change between 0 and 5 T are −5.9,−5.8, and −4.9 J/K mol under H//[100], [110], and [111], respectively. These negative∆SM with relatively large values around 30 K indicates the entropy release (gain) undermagnetization (demagnetization) independent of the magnetic field directions. This resultCrystals 2023, 13, 760 10 of 13of being nearly field-independent might be advantageous as a magnetic refrigerant wherepolycrystalline particles are used [7,10]. Additionally, under H//[110] and [111], a convex(concave) upward behavior was seen around 20 K, although overall ∆SM behavior becamenegative. The ∆SM under H//[100] showed a positive peak at low temperatures as well asa negative peak around 30 K. Similar sign change can be seen in the previous report [15].The anisotropic behavior around 20 K might be associated with the spin-reorientationtransition. These results indicate that the main contribution in ∆SM originates from theparamagnetic to the ferromagnetic transition at TC irrespective of the field directions, andthe spin orientation transition induces the anisotropic behavior in ∆SM.Crystals 2023, 13, x FOR PEER REVIEW 11 of 14    Figure 8. Temperature dependence of magnetization of HoAl2 under (a) H//[100], (b) H//[110], and (c) H//[111]. The applied magnetic fields are 0.01, 0.1, 0.3, 0.5, 0.7, 1, 2, 3, 4, and 5 T. The data were taken under field-cooled processes. The magnetic entropy change ΔSM as a function of temperature under (d) H//[100], (e) H//[110], and (f) H//[111]. 4. Summary Single crystals of a cubic Laves-phase ferromagnet HoAl2 were successfully grown by the laser diode-based floating-zone method. Here, the laser diodes as the heat source provided the vertically bell-shaped distribution of temperature at the focal point. Since Al evaporation was inevitable during the growth, we prepared Al-rich feed rods to compen-sate for the evaporation. The nominal ratio was optimized as Ho:Al = 1:2.5 to grow the stoichiometric crystals. Finally, a large-size crystal with a 50 mm length was obtained un-der stable conditions. The crystal exhibited a second-ordered ferromagnetic transition at TC = 29 K and a first-ordered spin-reorientation transition at TSR = 20 K. These transitions occurred in bulk. The isothermal magnetization showed a typical ferromagnetic behavior along the field directions [110] and [111]. For the magnetization under H//[100], the upward behavior around 2 T observed at low temperatures was suppressed with increasing temperature. The magnetic entropy changes under the applied field along the principal axes had a rel-atively similar minimum value around TC, and the anisotropy became obvious at lower temperatures. In particular, the magnetic entropy change under H//[100] showed a posi-tive peak at lower temperatures. The linear thermal expansion measurements to detect the Figure 8. Temperature dependence of magnetization of HoAl2 under (a) H//[100], (b) H//[110], and(c) H//[111]. The applied magnetic fields are 0.01, 0.1, 0.3, 0.5, 0.7, 1, 2, 3, 4, and 5 T. The data weretaken under field-cooled processes. The magnetic entropy change ∆SM as a function of temperatureunder (d) H//[100], (e) H//[110], and (f) H//[111].Crystals 2023, 13, 760 11 of 134. SummarySingle crystals of a cubic Laves-phase ferromagnet HoAl2 were successfully grownby the laser diode-based floating-zone method. Here, the laser diodes as the heat sourceprovided the vertically bell-shaped distribution of temperature at the focal point. SinceAl evaporation was inevitable during the growth, we prepared Al-rich feed rods to com-pensate for the evaporation. The nominal ratio was optimized as Ho:Al = 1:2.5 to growthe stoichiometric crystals. Finally, a large-size crystal with a 50 mm length was obtainedunder stable conditions.The crystal exhibited a second-ordered ferromagnetic transition at TC = 29 K and afirst-ordered spin-reorientation transition at TSR = 20 K. These transitions occurred in bulk.The isothermal magnetization showed a typical ferromagnetic behavior along the fielddirections [110] and [111]. For the magnetization under H//[100], the upward behavioraround 2 T observed at low temperatures was suppressed with increasing temperature.The magnetic entropy changes under the applied field along the principal axes had arelatively similar minimum value around TC, and the anisotropy became obvious at lowertemperatures. In particular, the magnetic entropy change under H//[100] showed apositive peak at lower temperatures. The linear thermal expansion measurements to detectthe directional information also revealed an anisotropic behavior below TC. The anisotropicbehavior in the ordered state is in sharp contrast to the almost isotropic behavior shownin the paramagnetic region beyond TC. We emphasize that the floating-zone techniqueis useful for the crystal growth of intermetallic alloys because this method enables us tosystematically investigate the fundamental properties of materials throughout a varietyof experimental probes using the same batch with large crystals. We believe that these“standard dataset” should contribute to bridging the future application as a properlyestablishing the magnetic refrigerant.Author Contributions: N.K. planned the project. N.K. grew and characterized the bulk crystals. T.K.,M.H. and H.Y. analyzed the ICP-OES. N.K. wrote the manuscript with input from all co-authors. Allauthors have read and agreed to the published version of the manuscript.Funding: This work has been supported by the KAKENHI Grants-in-Aid for Scientific Research (GrantNos. 18K0475, 21H01033, and 22K19093), and the Core-to-Core Program (No. JPJSCCA20170002)from the Japan Society for the Promotion of Science (JSPS), and the JST-Mirai Program (Grant No.JPMJMI18A3).Data Availability Statement: The data supporting the findings of this study are available from thecorresponding authors upon reasonable request.Acknowledgments: We acknowledge Yoshio Kaneko for the fruitful advice about the laser floating-zone furnace, and Taichi Terashima, Ayumi Kawaguchi, Takanobu Hiroto, Takeshi Shimada, AkiraKamimura, John McArthur, Noritaka Kimura, Naohiro Kaga, Yuta Maegawa, Tohru Nagasawa, andNobuyuki Ochiai for their technical support.Conflicts of Interest: The authors declare no conflict of interest.Appendix AIn Figure A1, we present the specific heat as a function of the temperature of thestoichiometric HoAl2 and Al-deficiency HoAl1.97 crystals. The sample dependence showsthat the aluminum deficiency suppresses the ferromagnetic transition temperature at TC,whereas it has little effect on the spin reorientation temperature at TSR. Additionally, wecan see that the peak height is suppressed, and the peak width becomes broadened atTSR for the Al deficiency sample, although we need to be careful to evaluate the specificheat with the first-ordered phase transition when the relaxation method is applied forthe measurements.Crystals 2023, 13, 760 12 of 13Crystals 2023, 13, x FOR PEER REVIEW 13 of 14    Figure A1. Temperature dependence of specific heat (CP) of the stoichiometric HoAl2 and Al-defi-ciency HoAl1.97 crystals. References 1. Tishin, A.M. Magnetocaloric Effect: From Theory to Practice. In Encyclopedia of Materials: Science and Technology; Buschow, K.H.J., Cahn, R.W., Flemings, M.C., Ilschner, B., Kramer, E.J., Mahajan, S., Veyssière, P., Eds.; Elsevier: Oxford, UK, 2001; pp. 5035–5041. https://doi.org/10.1016/B0-08-043152-6/00874-3. 2. Pecharsky, V.K.; Gschneidner, K.A. Magnetocaloric Effect from Indirect Measurements: Magnetization and Heat Capacity. J. Appl. Phys. 1999, 86, 565. https://doi.org/10.1063/1.370767. 3. Gschneidner, K.A. The Magnetocaloric Effect, Magnetic Refrigeration and Ductile Intermetallic Compounds. Acta Mater. 2009, 57, 18. https://doi.org/10.1016/j.actamat.2008.08.048. 4. Gschneidner, K.A.; Pecharsky, V.K. Magnetocaloric Materials. Annu. Rev. Mater. Sci. 2000, 30, 387. https://doi.org/10.1146/annurev.matsci.30.1.387. 5. Zhu, Y.; Asamoto, K.; Nishimura, Y.; Kouen, T.; Abe, S.; Matsumoto, K.; Numazawa, T. Magnetocaloric Effect of (ErxR1−x)Co2 (R = Ho, Dy) for Magnetic Refrigeration between 20 and 80K. Cryogenics 2011, 51, 494. https://doi.org/10.1016/j.cryogenics.2011.06.004. 6. Zhang, H.; Gimaev, R.; Kovalev, B.; Kamilov, K.; Zverev, V.; Tishin, A. Review on the Materials and Devices for Magnetic Refrigeration in the Temperature Range of Nitrogen and Hydrogen Liquefaction. Phys. B Condens. Matter 2019, 558, 65. https://doi.org/10.1016/j.physb.2019.01.035. 7. Kamiya, K.; Matsumoto, K.; Numazawa, T.; Masuyama, S.; Takeya, H.; Saito, A.T.; Kumazawa, N.; Futatsuka, K.; Matsunaga, K.; Shirai, T.; et al. Active Magnetic Regenerative Refrigeration Using Superconducting Solenoid for Hydrogen Liquefaction. Appl. Phys. Express 2022, 15, 053001. https://doi.org/10.35848/1882-0786/ac5723. 8. Oesterreicher, H. Structural, Magnetic and Neutron Diffraction Studies on TbFe2-TbAl2, TbCo2-TbAl2 and HoCo2-HoAl2. J. Phys. Chem. Solids 1973, 34, 1267. https://doi.org/10.1016/S0022-3697(73)80216-1. 9. Williams, C.M.; Koon, N.C.; Das, B.N. Spin Reorientations in Single Crystal HoAl2. J. Appl. Phys. 1979, 50, 1669. https://doi.org/10.1063/1.327232. 10. Yamamoto, T.D.; Takeya, H.; Saito, A.T.; Terashima, K.; Numazawa, T.; Takano, Y. Magnetocaloric Particles of the Laves Phase Compound HoAl2 Prepared by Electrode Induction Melting Gas Atomization. J. Magn. Magn. Mater. 2022, 547, 168906. https://doi.org/10.1016/j.jmmm.2021.168906. 11. Numazawa, T.; Kamiya, K.; Utaki, T.; Matsumoto, K. Magnetic Refrigerator for Hydrogen Liquefaction. Cryogenics 2014, 62, 185. https://doi.org/10.1016/j.cryogenics.2014.03.016. Figure A1. Temperature dependence of specific heat (CP) of the stoichiometric HoAl2 and Al-deficiency HoAl1.97 crystals.References1. Tishin, A.M. Magnetocaloric Effect: From Theory to Practice. In Encyclopedia of Materials: Science and Technology; Buschow, K.H.J.,Cahn, R.W., Flemings, M.C., Ilschner, B., Kramer, E.J., Mahajan, S., Veyssière, P., Eds.; Elsevier: Oxford, UK, 2001; pp. 5035–5041.[CrossRef]2. Pecharsky, V.K.; Gschneidner, K.A. Magnetocaloric Effect from Indirect Measurements: Magnetization and Heat Capacity. J. Appl.Phys. 1999, 86, 565. [CrossRef]3. Gschneidner, K.A. The Magnetocaloric Effect, Magnetic Refrigeration and Ductile Intermetallic Compounds. Acta Mater. 2009,57, 18. [CrossRef]4. Gschneidner, K.A.; Pecharsky, V.K. Magnetocaloric Materials. Annu. Rev. Mater. Sci. 2000, 30, 387. [CrossRef]5. Zhu, Y.; Asamoto, K.; Nishimura, Y.; Kouen, T.; Abe, S.; Matsumoto, K.; Numazawa, T. Magnetocaloric Effect of (ErxR1−x)Co2 (R= Ho, Dy) for Magnetic Refrigeration between 20 and 80K. Cryogenics 2011, 51, 494. [CrossRef]6. Zhang, H.; Gimaev, R.; Kovalev, B.; Kamilov, K.; Zverev, V.; Tishin, A. Review on the Materials and Devices for MagneticRefrigeration in the Temperature Range of Nitrogen and Hydrogen Liquefaction. Phys. B Condens. Matter 2019, 558, 65. [CrossRef]7. Kamiya, K.; Matsumoto, K.; Numazawa, T.; Masuyama, S.; Takeya, H.; Saito, A.T.; Kumazawa, N.; Futatsuka, K.; Matsunaga, K.;Shirai, T.; et al. Active Magnetic Regenerative Refrigeration Using Superconducting Solenoid for Hydrogen Liquefaction. Appl.Phys. Express 2022, 15, 053001. [CrossRef]8. Oesterreicher, H. Structural, Magnetic and Neutron Diffraction Studies on TbFe2-TbAl2, TbCo2-TbAl2 and HoCo2-HoAl2. J. Phys.Chem. Solids 1973, 34, 1267. [CrossRef]9. Williams, C.M.; Koon, N.C.; Das, B.N. Spin Reorientations in Single Crystal HoAl2. J. Appl. Phys. 1979, 50, 1669. [CrossRef]10. Yamamoto, T.D.; Takeya, H.; Saito, A.T.; Terashima, K.; Numazawa, T.; Takano, Y. Magnetocaloric Particles of the Laves PhaseCompound HoAl2 Prepared by Electrode Induction Melting Gas Atomization. J. Magn. Magn. Mater. 2022, 547, 168906. [CrossRef]11. Numazawa, T.; Kamiya, K.; Utaki, T.; Matsumoto, K. Magnetic Refrigerator for Hydrogen Liquefaction. Cryogenics 2014, 62, 185.[CrossRef]12. Barbara, B.; Rossignol, M.F.; Boucherle, J.X. Magnetic Behavior of HoAl2 Single Crystal. Phys. Lett. A 1975, 55, 321. [CrossRef]13. Ibarra, M.R.; Lee, E.W.; del Moral, A.; Moze, O. Magnetic Anisotropy and Spin-Reorientation in HoAl2. Solid State Commun. 1985,53, 183. [CrossRef]14. Ibarra, M.R.; Moze, O.; Algarabel, P.A.; Arnaudas, J.I.; Abell, J.S.; del Moral, A. Magnetoelastic Behaviour and the Spin-Reorientation Transition in HoAl2. J. Phys. C Solid State Phys. 1988, 21, 2735. [CrossRef]https://doi.org/10.1016/B0-08-043152-6/00874-3https://doi.org/10.1063/1.370767https://doi.org/10.1016/j.actamat.2008.08.048https://doi.org/10.1146/annurev.matsci.30.1.387https://doi.org/10.1016/j.cryogenics.2011.06.004https://doi.org/10.1016/j.physb.2019.01.035https://doi.org/10.35848/1882-0786/ac5723https://doi.org/10.1016/S0022-3697(73)80216-1https://doi.org/10.1063/1.327232https://doi.org/10.1016/j.jmmm.2021.168906https://doi.org/10.1016/j.cryogenics.2014.03.016https://doi.org/10.1016/0375-9601(75)90489-2https://doi.org/10.1016/0038-1098(85)90122-Xhttps://doi.org/10.1088/0022-3719/21/14/013Crystals 2023, 13, 760 13 of 1315. Patra, M.; Majumdar, S.; Giri, S.; Xiao, Y.; Chatterji, T. Magnetic, Magnetocaloric and Magnetoresistive Properties of Cubic LavesPhase HoAl2 Single Crystal. J. Phys. Condens. Matter 2014, 26, 046004. [CrossRef] [PubMed]16. Gil, L.A.; Campoy, J.C.P.; Plaza, E.J.R.; de Souza, M.V. Conventional and Anisotropic Magnetic Entropy Change in HoAl2Ferromagnetic Compound. J. Magn. Magn. Mater. 2016, 409, 45. [CrossRef]17. Pistawala, N.; Rout, D.; Saurabh, K.; Bag, R.; Karmakar, K.; Harnagea, L.; Singh, S. Crystal Growth of Quantum Materials: AReview of Selective Materials and Techniques. Bull. Mater. Sci. 2021, 45, 10. [CrossRef]18. Ito, T.; Ushiyama, T.; Yanagisawa, Y.; Tomioka, Y.; Shindo, I.; Yanase, A. Laser-Diode-Heated Floating Zone (LDFZ) MethodAppropriate to Crystal Growth of Incongruently Melting Materials. J. Cryst. Growth 2013, 363, 264. [CrossRef]19. Kaneko, Y.; Tokura, Y. Floating Zone Furnace Equipped with a High Power Laser of 1 KW Composed of Five Smart Beams.J. Cryst. Growth 2020, 533, 125435. [CrossRef]20. Kikugawa, N.; Terashima, T.; Kato, T.; Hayashi, M.; Yamaguchi, H.; Uji, S. Bulk Physical Properties of a Magnetic Weyl SemimetalCandidate NdAlGe Grown by a Laser Floating-Zone Method. Inorganics 2023, 11, 20. [CrossRef]21. Nagai, I.; Shirakawa, N.; Ikeda, S.-I.; Iwasaki, R.; Nishimura, H.; Kosaka, M. Highest Conductivity Oxide SrMoO3 Grown by aFloating-Zone Method under Ultralow Oxygen Partial Pressure. Appl. Phys. Lett. 2005, 87, 024105. [CrossRef]22. Bobowski, J.S.; Kikugawa, N.; Miyoshi, T.; Suwa, H.; Xu, H.-S.; Yonezawa, S.; Sokolov, D.A.; Mackenzie, A.P.; Maeno, Y. ImprovedSingle-Crystal Growth of Sr2RuO4. Condens. Matter 2019, 4, 6. [CrossRef]23. Martien, D.; Williamsen, M.; Spagna, S.; Black, R.; DaPron, T.; Hogan, T.; Snow, D. An Ultrasensitive Differential CapacitiveDilatometer. IEEE Trans. Magn. 2019, 55, 1. [CrossRef]24. Pourarian, F. Exchange-Striction of Rare Earth-Al2 Laves Phase Compounds. J. Phys. Chem. Solids 1980, 41, 123. [CrossRef]25. Baran, S.; Duraj, R.; Szytuła, A. Magnetocaloric Effect and Transition Order in HoAl2. Acta Phys. Pol. A 2015, 127, 815. [CrossRef]26. Maeno, Y.; Ando, T.; Mori, Y.; Ohmichi, E.; Ikeda, S.; NishiZaki, S.; Nakatsuji, S. Enhancement of Superconductivity of Sr2RuO4 to3 K by Embedded Metallic Microdomains. Phys. Rev. Lett. 1998, 81, 3765. [CrossRef]27. Shoenberg, D. Magnetic Oscillations in Metals; Cambridge University Press: Cambridge, UK, 2009; ISBN 9781316583173.Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.https://doi.org/10.1088/0953-8984/26/4/046004https://www.ncbi.nlm.nih.gov/pubmed/24592489https://doi.org/10.1016/j.jmmm.2016.02.085https://doi.org/10.1007/s12034-021-02612-1https://doi.org/10.1016/j.jcrysgro.2012.10.059https://doi.org/10.1016/j.jcrysgro.2019.125435https://doi.org/10.3390/inorganics11010020https://doi.org/10.1063/1.1992671https://doi.org/10.3390/condmat4010006https://doi.org/10.1109/TMAG.2018.2866831https://doi.org/10.1016/0022-3697(80)90042-6https://doi.org/10.12693/APhysPolA.127.815https://doi.org/10.1103/PhysRevLett.81.3765 Introduction  Materials and Methods  Growth by the Floating-Zone Technique  Feed and Seed Rods Preparation  Crystal Growth  Characterization  Results and Discussion  Growth of HoAl2 Crystals  Bulk Thermodynamic Properties of the Grown Crystal  Summary  Appendix A References