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[Naoki Kikugawa](https://orcid.org/0000-0003-3975-4478), [Taichi Terashima](https://orcid.org/0000-0001-9239-0621), [Takashi Kato](https://orcid.org/0000-0002-3317-7481), Momoko Hayashi, [Hitoshi Yamaguchi](https://orcid.org/0000-0002-4878-4073), [Shinya Uji](https://orcid.org/0000-0001-9351-6388)

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[Bulk Physical Properties of a Magnetic Weyl Semimetal Candidate NdAlGe Grown by a Laser Floating-Zone Method](https://mdr.nims.go.jp/datasets/ced39fb6-22a4-4271-9c6c-e095ea933a91)

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Bulk Physical Properties of a Magnetic Weyl Semimetal Candidate NdAlGe Grown by a Laser Floating-Zone MethodCitation: Kikugawa, N.; Terashima,T.; Kato, T.; Hayashi, M.; Yamaguchi,H.; Uji, S. Bulk Physical Properties ofa Magnetic Weyl Semimetal CandidateNdAlGe Grown by a LaserFloating-Zone Method. Inorganics2023, 11, 20. https://doi.org/10.3390/inorganics11010020Academic Editor: W. Adam PhelanReceived: 1 December 2022Revised: 21 December 2022Accepted: 25 December 2022Published: 1 January 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/).inorganicsArticleBulk Physical Properties of a Magnetic Weyl Semimetal CandidateNdAlGe Grown by a Laser Floating-Zone MethodNaoki Kikugawa 1,*, Taichi Terashima 1, Takashi Kato 2,3, Momoko Hayashi 2, Hitoshi Yamaguchi 2 and Shinya Uji 11 National Institute for Materials Science, Ibaraki 305-0003, Japan2 National Institute for Materials Science, Ibaraki 305-0047, Japan3 National Institute of Technology, Fukushima College, Fukushima 970-8034, Japan* Correspondence: kikugawa.naoki@nims.go.jpAbstract: In this study, we report the successful growth of single crystals of a magnetic Weylsemimetal candidate NdAlGe with the space group I41md. The crystals were grown using a floating-zone technique, which used five laser diodes, with a total power of 2 kW, as the heat source. Toensure that the molten zone was stably formed during the growth, we employed a bell-shapeddistribution profile of the vertical irradiation intensity. After the nominal powder, crushed from anarc-melted ingot, was shaped under hydrostatic pressure, we sintered the feed and seed rods in anAr atmosphere under ultra-low oxygen partial pressure (<10−26 atm) generated by an oxygen pumpmade of yttria-stabilized zirconia heated at 873 K. Single crystals of NdAlGe were successfully grownto a length of 50 mm. The grown crystals showed magnetic order in bulk at 13.5 K. The fundamentalphysical properties were characterized by magnetic susceptibility, magnetization, specific heat, ther-mal expansion, and electrical resistivity measurements. This study demonstrates that the magneticorder induces anisotropic magnetoelasticity, magneto-entropy, and charge transport in NdAlGe.Keywords: NdAlGe; magnetic Weyl semimetal; crystal growth; laser floating-zone technique; bulkphysical properties1. IntroductionWeyl semimetals have been rapidly advanced as a topologically nontrivial phase ofmatter. As the low-energy, excited quasiparticles are characterized by relativistic fermions,the electronic structures yield exotic physical phenomena such as Fermi arcs and chiralanomaly [1–5]. The topological Weyl semimetals can be realized when either the spatialinversion or time-reversal symmetry is broken. As well as these semimetals, magnetictopological materials have attracted much attention because the interplay between theirmagnetic correlations and topological electronic structures can provide rich physical prop-erties. Novel magnetoresistance, anomalous Hall and Nernst effects, axion insulator, andchiral domain walls have been experimentally revealed in several materials [6–9]. Es-tablishing a fundamental framework of magnetic Weyl semimetals is a demand for thenext generation of spintronics applications, such as high-density and high-speed memorydevices, and quantum information technology, because development of these technologiesis based on the intrinsic physical properties of the Weyl semimetals [10].The RAlT family (R: lanthanides, T: Si, Ge) with the space group I41md (No. 109) hasbeen considered to be a candidate material in a new class of magnetic topological semimet-als, because the system breaks both the spatial inversion and time-reversal symmetries [11].The crystal structure of RAlT is shown in Figure 1. As theoretically predicted [12], thereports of topological magnetic order [13,14], topological Hall effect [15], anomalous Halland Nernst effects [16–18], unusual quantum oscillatory effect [14,19,20], possible axialgauge fields [17], domain wall chirality [21], and Fermi arcs [22] have revealed that RAlTInorganics 2023, 11, 20. https://doi.org/10.3390/inorganics11010020 https://www.mdpi.com/journal/inorganicshttps://doi.org/10.3390/inorganics11010020https://doi.org/10.3390/inorganics11010020https://creativecommons.org/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/inorganicshttps://www.mdpi.comhttps://orcid.org/0000-0001-9351-6388https://doi.org/10.3390/inorganics11010020https://www.mdpi.com/journal/inorganicshttps://www.mdpi.com/article/10.3390/inorganics11010020?type=check_update&version=2Inorganics 2023, 11, 20 2 of 15can offer rich electromagnetic properties. Since these properties can be tuned by exchang-ing the rare-earth elements (R) and T [17], this motivates us to systematically explore therelationship between the topology and magnetism in the RAlT family.Inorganics 2022, 10, x FOR PEER REVIEW 2 of 17   predicted [12], the reports of topological magnetic order [13,14], topological Hall effect [15], anomalous Hall and Nernst effects [16–18], unusual quantum oscillatory effect [14,19,20], possible axial gauge fields [17], domain wall chirality [21], and Fermi arcs [22] have revealed that RAlT can offer rich electromagnetic properties. Since these properties can be tuned by exchanging the rare-earth elements (R) and T [17], this motivates us to systematically explore the relationship between the topology and magnetism in the RAlT family.  Figure 1. Crystal structure of a magnetic Weyl semimetal candidate RAlT (R: rare earth element, T: Si, Ge), with the space group I41md (No. 109). Thus far, a series of flux-grown crystals of RAl(Si,Ge) with R = Ce, Pr, Nd, and Sm, has been investigated [11,14,16–19,21–23], whereas floating-zone crystals have been examined only in CeAlGe and PrAlGe [11,15,17]. The floating-zone method offers two main advantages: (1) it minimizes the contamination level during the growth process, (2) it can obtain large crystals in cm size [24–26]. This enables us to deepen our knowledge of the materials through several experimental probes of the same batch of crystals. In this paper, we present the successful growth of NdAlGe crystals with the length of 50 mm by the floating-zone method, adopting laser diodes as the heat source. We demonstrate the fundamental physical properties of NdAlGe, focusing on its anisotropic response with magnetic order at 13.5 K.   Figure 1. Crystal structure of a magnetic Weyl semimetal candidate RAlT (R: rare earth element, T:Si, Ge), with the space group I41md (No. 109).Thus far, a series of flux-grown crystals of RAl(Si,Ge) with R = Ce, Pr, Nd, andSm, has been investigated [11,14,16–19,21–23], whereas floating-zone crystals have beenexamined only in CeAlGe and PrAlGe [11,15,17]. The floating-zone method offers two mainadvantages: (1) it minimizes the contamination level during the growth process, (2) it canobtain large crystals in cm size [24–26]. This enables us to deepen our knowledge ofthe materials through several experimental probes of the same batch of crystals. In thispaper, we present the successful growth of NdAlGe crystals with the length of 50 mm bythe floating-zone method, adopting laser diodes as the heat source. We demonstrate thefundamental physical properties of NdAlGe, focusing on its anisotropic response withmagnetic order at 13.5 K.2. Materials and Methods2.1. Crystal Growth by the Floating-Zone MethodCrystal growth by using the floating-zone method is mainly composed of a polycrys-talline feed-rod, molten zone, and a seed/grown crystal. As these components never touchany other part of the apparatus (including the quartz tube) throughout the growth, thegrowing crystal is protected from accidental contamination of any kind of impurity [24–26].However, as the molten zone is fragilely supported only at the edges of the feed and seedrods, it is easily destabilized. Maintaining a stable molten zone requires great care andthe optimizing of many parameters, such as the heat power required to melt the rods, thefeed/seed speed, the gas atmosphere, and the applied pressure. In this study, the NdAlGegrowth was kept stable by employing a laser diode as the heat source, and preparing aInorganics 2023, 11, 20 3 of 15feed/seed rod: the latter has been successfully applied to oxides in previous studies [27].These two stabilization techniques are described in detail below.2.2. Laser Floating-Zone TechniqueThe recently developed laser-based floating-zone technique has opened a new windowfor crystal growth, because the laser diode enables the growth of materials that have notbeen obtained under optical halogen/xenon lamps connected to an infrared image furnace,which is used as the conventional heat source [28]. The laser emission can sharply define thefocal point of melting, forming a narrower molten zone than can be achieved by radiationfrom lamps reflected at the elliptical mirrors of an image furnace [29]. Consequently, thelaser-heated molten zone is homogeneous and tolerates a steeper temperature gradient atthe boundary between the molten zone and the grown crystal. Most recently, the distribu-tion profile of the vertical irradiation intensity along the length of the rod has progressedfrom flat to bell-shaped, where the original flat horizontal profile was maintained alongthe radical direction of the rod (see Figure 2 of [30]). The new bell-shaped distribution is asignificant advance because it relaxes the thermal stress in the grown crystals. The modi-fied temperature gradient imposed by the bell-shaped distribution prevents the as-growncrystals from cracking. Crystals grown under the original flat laser profile are frequentlycracked by the too-sharp temperature gradient developed at the boundary [30]. Thus,modern laser technology has dramatically advanced the crystal growth field in recentyears [29–31]. We grew single-crystalline NdAlGe using a laser diode floating-zone furnace,in which five laser diodes produce a vertical bell-shaped distribution around the focal point.Inorganics 2022, 10, x FOR PEER REVIEW 4 of 17    Figure 2. (a) Picture of crystal growth of NdAlGe using a laser diode heated floating-zone furnace. Dotted white lines outline the rod and grown crystal for clarity. (b) Photograph of the grown NdAlGe crystal showing the necking formed at the beginning of the growth; (c) and (d) back-scattered Laue photographs along the [100] and [001] axes, respectively. 2.3. Preparation of Feed and Seed Rods The floating-zone technique has grown intermetallic compounds, as well as oxides and chalcogenides [28–35]. Feed rod preparation is an important procedure for the entire growth process because the quality of the feed rods strongly affects the stability of the molten zone. In particular, the feed rods must be well-shaped, and mechanically robust with uniform density and composition [36]. The rods for intermetallic alloys have been conventionally shaped by melting the starting materials in an arc furnace or a radio-frequency induction-heating furnace. However, these methods may introduce cracks inside the resultant rods, and the cracks prevent a stable form of the molten zone during the crystal growth. An alternative advanced method has been reported, consisting of designing a modified radio-frequency induction-heating furnace [36]. We prepared a polycrystalline feed rod of NdAlGe by the following process. First, we prepared polycrystalline ingots of NdAlGe with a nominal composition via arc-melting under an Ar atmosphere (Techno Search Corp., SE-11399). The button-shaped ingot was turned over and melted several times to ensure homogeneity. The arc-melted ingots were subsequently powdered using an agate mortar and pestle. The powder with a typical weight of 18 g was packed into a tubular rubber balloon for shaping into a cylindrical rod. The powder-filled balloon was pressed under hydrostatic pressure at 40 MPa for 5 min. Here, to avoid the contamination from the as-purchased balloon of which surfaces were coated with a fine powder, we carefully cleaned both the inner and outer surfaces of the balloon before filling the NdAlGe powder, as experienced from the growth of ruthenates [27]. After their removal from the balloon, the uniform-shaped rods were sintered at 1123 K for 24 h in a tube furnace under an Ar gas flowing at 3 L/min. The Ar gas was regenerated using an oxygen pump made of yttria-stabilized zirconia heated at 873 K and circulated under an ultra-low oxygen partial pressure of less than 10−26 atm (Canon Machinery Inc., ULOCE-530) [37]. Finally, the sintered rod with a typical diameter of 6 mm was cut into two unequal parts. The longer part, with a length of 80 mm, was designated as the feed rod and the shorter part, with a length of 30 mm, was used as the seed. High-quality ruthenates were previously grown by a similar procedure [27,38–43]. This process obtained homogeneous rods with a minimal contamination risk; consequently, a series of ruthenate crystals was successfully grown under stable Figure 2. (a) Picture of crystal growth of NdAlGe using a laser diode heated floating-zone furnace.Dotted white lines outline the rod and grown crystal for clarity. (b) Photograph of the grown NdAlGecrystal showing the necking formed at the beginning of the growth; (c) and (d) back-scattered Lauephotographs along the [100] and [001] axes, respectively.2.3. Preparation of Feed and Seed RodsThe floating-zone technique has grown intermetallic compounds, as well as oxidesand chalcogenides [28–35]. Feed rod preparation is an important procedure for the entiregrowth process because the quality of the feed rods strongly affects the stability of themolten zone. In particular, the feed rods must be well-shaped, and mechanically robustwith uniform density and composition [36]. The rods for intermetallic alloys have beenconventionally shaped by melting the starting materials in an arc furnace or a radio-Inorganics 2023, 11, 20 4 of 15frequency induction-heating furnace. However, these methods may introduce cracks insidethe resultant rods, and the cracks prevent a stable form of the molten zone during thecrystal growth. An alternative advanced method has been reported, consisting of designinga modified radio-frequency induction-heating furnace [36].We prepared a polycrystalline feed rod of NdAlGe by the following process. First, weprepared polycrystalline ingots of NdAlGe with a nominal composition via arc-meltingunder an Ar atmosphere (Techno Search Corp., SE-11399). The button-shaped ingot wasturned over and melted several times to ensure homogeneity. The arc-melted ingots weresubsequently powdered using an agate mortar and pestle. The powder with a typicalweight of 18 g was packed into a tubular rubber balloon for shaping into a cylindricalrod. The powder-filled balloon was pressed under hydrostatic pressure at 40 MPa for5 min. Here, to avoid the contamination from the as-purchased balloon of which surfaceswere coated with a fine powder, we carefully cleaned both the inner and outer surfacesof the balloon before filling the NdAlGe powder, as experienced from the growth ofruthenates [27]. After their removal from the balloon, the uniform-shaped rods weresintered at 1123 K for 24 h in a tube furnace under an Ar gas flowing at 3 L/min. The Argas was regenerated using an oxygen pump made of yttria-stabilized zirconia heated at873 K and circulated under an ultra-low oxygen partial pressure of less than 10−26 atm(Canon Machinery Inc., ULOCE-530) [37]. Finally, the sintered rod with a typical diameterof 6 mm was cut into two unequal parts. The longer part, with a length of 80 mm, wasdesignated as the feed rod and the shorter part, with a length of 30 mm, was used as theseed. High-quality ruthenates were previously grown by a similar procedure [27,38–43].This process obtained homogeneous rods with a minimal contamination risk; consequently,a series of ruthenate crystals was successfully grown under stable conditions, with noaccidental cracks to the rods during irradiation in the furnace [27,39,41–43]. We note thatthe procedure can be applied to that for the growth of intermetallic alloys.2.4. Crystal GrowthBoth the feed and seed rods were set into a laser diode floating-zone furnace equippedwith five 400 W GaAs-based laser heads with a wavelength of 940 nm (L-FZ 2000, QuantumDesign Japan). Here, the bell-shaped distribution profile of the vertical irradiation intensitywas optimized. The feed rod was suspended from a hock (made of platinum) on the uppershaft using molybdenum wire, and the seed rod was set in an alumina holder on the lowershaft. Since the growth area of the furnace was separated by a quartz tube from the outside,we could select the desired atmosphere and pressure of the gas during the crystal growth.For the growth of NdAlGe, we used a gas mixture of Ar (96%) and H2 (4%). As the laserpower was smoothly increased, the bottom end of the rod started to melt. The molten rodwas then connected to the top of the seed rod. The growth started with necking because apolycrystalline rod was used as the seed. Once the necking was complete, the molten zonewas stabilized at both feed and seed speeds of 5 mm/h in the Ar-H2 gas mixture at 0.4 MPaand with a flow rate of 1 L/min. Applying the pressure to 0.4 MPa was in order to attemptthe suppression of the evaporation during the growth. The feed and seed were rotated at10 rpm in opposite directions to homogenize the molten liquid. The molten zone remainedstable until the end of the growth without any cracking or other accidental issues arisingfrom the sintered rods prepared by the above procedure.2.5. CharacterizationThe phase purity of the crushed single crystals was checked using power X-raydiffraction under Cu Kα radiation (MiniFlex600, Rigaku) at room temperature. To cut thegrown crystals along their principle crystallographic axes (the a and c axes), the orientationsof the crystals were checked by a back-scattered X-ray Laue diffraction technique. Thecomposition of the grown crystal was determined using inductively coupled plasma opticalemission spectrometry (ICP-OES).Inorganics 2023, 11, 20 5 of 15The bulk physical properties were measured down to 2 K using the options of thePhysical Property Measurement System (Dynacool, Quantum Design). The temperaturedependence of the magnetic susceptibility was measured in a magnetic field (H) of 0.01 Tunder zero-field-cooled (ZFC) and field-cooled (FC) conditions: that is, by cooling thesample before and after applying a static magnetic field, respectively. The isothermalmagnetization (M) was measured between −9 and 9 T. The temperature dependence ofthe specific heat (CP) was measured by a relaxation method. The thermal expansion wasmeasured by a capacitive-based technique with a temperature sweep of 0.1 K/min. In thethermal expansion measurements, we used a fused quartz dilatometer cell because fusedquartz has the weakest temperature dependence among the known thermally expansivematerials [44]. The magnetic entropy change (∆SM) of H//a and H//c was determinedusing the thermodynamic Maxwell relation, ∆SM =∫ H0∂M∂T dH [45], obtained from thetemperature dependence of the magnetization up to 9 T under the FC process. The magneticsusceptibility, magnetization, specific heat, and thermal expansion measurements weremeasured on the same sample with dimensions of 2.0 mm after cutting and polishingalong the a and c axes. The electrical resistivity was measured by the standard four-probe AC method, after spot-welding electrical contacts on the rectangular-shaped crystals.We also examined measurements of the a-axis resistivity of the crystals in a top-loadeddilution fridge.3. Results and Discussion3.1. Crystal GrowthFigure 2a shows a photo of the crystal growth of NdAlGe. The bell-shaped distribution,created by the five laser diodes, focused on the molten zone with a length of 6 mm. The rodwas not cracked by the laser emission during the growth. As seen in Figure 2b, crystals witha length of 50 mm were grown under stable conditions. Additionally, there were no signson the surface of the grown crystals that the molten liquid was dropped during the growth,suggesting that the growth was performed under stable temperature control. Figure 3displays the powder diffraction pattern of a partially crushed crystal. All peaks were wellindexed to the space group I41md [11] and no impurity phases were detected. The latticeparameters were deduced as a = 0.42245(13) nm, and c = 1.4576(6) nm, consistent withprevious reports on polycrystals [46] and flux-grown crystals [23]. Figure 2c,d show theback-scattered Laue photographs of the grown crystal along the [100] and [001] directions,respectively. Clear and sharp spots from the bulk crystal confirmed that a large singlecrystal was obtained. From the ICP-OES results, the molar ratio of the grown crystalwas determined as Nd: Al: Ge = 1.00: 0.93: 0.98. The ratio was identical along thecrystal rods within the experimental error, suggesting the grown crystal is homogeneous.The aluminum deficiency reflects the evaporation of aluminum during the growth. Theevaporated powder was deposited on the inside surface of the quartz tube.3.2. Bulk Properties of the Grown CrystalThe temperature dependences of the magnetic susceptibility (M/H) were measuredin a field of 0.01 T. The results along the a and c axes are presented in Figure 4a,b, re-spectively. A clear magnetic transition (TM) appears at 13.5 K in both field directions.The transition temperature of our floating-zone crystal exceeded that of the flux-growncrystals [23]. Here, TM defines the temperature at which clear hysteresis occurs betweenthe ZFC and FC processes. Such hysteresis can be attributed to pinning of the magneticdomains below the magnetic ordering temperature. We also observe a large anisotropy ofthe magnetic susceptibility below TM between H//a and H//c, as seen in the flux-grown crys-tal [23]. Figure 4c,d plot the temperature dependence of the inverse magnetic susceptibility(M/H)−1 along the a and c axes, respectively. The black lines in the figures are the fits tothe Curie–Weiss law, MH =NAµ2e f f µ2B3kB(T−θP)+ χ0, where kB, NA, µB are the Boltzmann constant,Avogadro’s number, and the Bohr magneton, respectively. From the fits between 100 and300 K, the effective magnetic moments (µeff) in the paramagnetic region were µeff = 3.57 µBInorganics 2023, 11, 20 6 of 15and 3.66 µB under H//a and H//c, respectively. These values are very close to the theoreticalvalue of the free Nd3+ with a total angular momentum of J = 9/2, which corresponds toµeff = 3.62 µB. The results suggest a well-localized nature of the 4f electrons. The smalltemperature-independent term χ0, which typically represents Pauli paramagnetic andLarmor diamagnetic contributions, was 8.14 × 10−4 (4.82 × 10−4) emu/mol for H//a (H//c).The Weiss temperatures under H//a and H//c were obtained as θP = −4.4 K and +11.4 K,respectively. Here, the negative and positive θP indicate an antiferromagnetic correlationand ferromagnetic coupling, respectively.Inorganics 2022, 10, x FOR PEER REVIEW 6 of 17   Figure 2a shows a photo of the crystal growth of NdAlGe. The bell-shaped distribution, created by the five laser diodes, focused on the molten zone with a length of 6 mm. The rod was not cracked by the laser emission during the growth. As seen in Figure 2b, crystals with a length of 50 mm were grown under stable conditions. Additionally, there were no signs on the surface of the grown crystals that the molten liquid was dropped during the growth, suggesting that the growth was performed under stable temperature control. Figure 3 displays the powder diffraction pattern of a partially crushed crystal. All peaks were well indexed to the space group I41md [11] and no impurity phases were detected. The lattice parameters were deduced as a = 0.42245(13) nm, and c = 1.4576(6) nm, consistent with previous reports on polycrystals [46] and flux-grown crystals [23]. Figure 2c,d show the back-scattered Laue photographs of the grown crystal along the [100] and [001] directions, respectively. Clear and sharp spots from the bulk crystal confirmed that a large single crystal was obtained. From the ICP-OES results, the molar ratio of the grown crystal was determined as Nd: Al: Ge = 1.00: 0.93: 0.98. The ratio was identical along the crystal rods within the experimental error, suggesting the grown crystal is homogeneous. The aluminum deficiency reflects the evaporation of aluminum during the growth. The evaporated powder was deposited on the inside surface of the quartz tube.  Figure 3. Powder X-ray diffraction pattern showing the indices of crushed NdAlGe crystal (Cu Kα radiation at room temperature). 3.2. Bulk Properties of the Grown Crystal The temperature dependences of the magnetic susceptibility (M/H) were measured in a field of 0.01 T. The results along the a and c axes are presented in Figure 4a,b, respectively. A clear magnetic transition (TM) appears at 13.5 K in both field directions. The transition temperature of our floating-zone crystal exceeded that of the flux-grown crystals [23]. Here, TM defines the temperature at which clear hysteresis occurs between the ZFC and FC processes. Such hysteresis can be attributed to pinning of the magnetic domains below the magnetic ordering temperature. We also observe a large anisotropy of the magnetic susceptibility below TM between H//a and H//c, as seen in the flux-grown crystal [23]. Figure 4c,d plot the temperature dependence of the inverse magnetic susceptibility (M/H)−1 along the a and c axes, respectively. The black lines in the figures are the fits to the Curie–Weiss law, = (  ) + 𝜒 , where kB, NA, μB are the Boltzmann constant, Avogadro’s number, and the Bohr magneton, respectively. From the fits between 100 and 300 K, the effective magnetic moments (μeff) in the paramagnetic region were μeff = 3.57 μB and 3.66 μB under H//a and H//c, respectively. These values are very Figure 3. Powder X-ray diffraction pattern showing the indices of crushed NdAlGe crystal (Cu Kαradiation at room temperature).Inorganics 2022, 10, x FOR PEER REVIEW 7 of 17   close to the theoretical value of the free Nd3+ with a total angular momentum of J = 9/2, which corresponds to μeff = 3.62 μB. The results suggest a well-localized nature of the 4f electrons. The small temperature-independent term χ0, which typically represents Pauli paramagnetic and Larmor diamagnetic contributions, was 8.14 × 10−4 (4.82 × 10−4) emu/mol for H//a (H//c). The Weiss temperatures under H//a and H//c were obtained as θP = −4.4 K and +11.4 K, respectively. Here, the negative and positive θP indicate an antiferromagnetic correlation and ferromagnetic coupling, respectively.  Figure 4. Temperature dependences of the magnetic susceptibility of NdAlGe under the field along (a) H//a and (b) H//c. Measurements were performed under zero-field-cooled (open circles) and field-cooled (closed circles) processes at 0.01 T. Inverse magnetic susceptibility as a function of temperature under (c) H//a, and (d) H//c. Solid black lines are fits to the Curie–Weiss law between 100 and 300 K. The anisotropy of the magnetic property was observed by the isothermal magnetization at 2 K under H//a and H//c up to 9 T (Figure 5a). Figure 5b enlarges the low-field region to emphasize the obvious hysteresis under H//c. The overall behavior is similar to that observed in flux-grown crystals, in which measurements were performed up to 30 T [23]. The magnetization under H//c shows a clear hysteresis with a remnant magnetization and a small coercive field of 0.07 T, indicating magnetic order with a spontaneous magnetization. In contrast, the a-axis magnetization shows no clear hysteresis and is nearly 100 times smaller than the c-axis magnetization at 0.3 T. The a-axis magnetization is linear in H up to 2 T and slightly deviates upwards at higher field. The Figure 4. Temperature dependences of the magnetic susceptibility of NdAlGe under the field along(a) H//a and (b) H//c. Measurements were performed under zero-field-cooled (open circles) and field-cooled (closed circles) processes at 0.01 T. Inverse magnetic susceptibility as a function of temperatureunder (c) H//a, and (d) H//c. Solid black lines are fits to the Curie–Weiss law between 100 and 300 K.Inorganics 2023, 11, 20 7 of 15The anisotropy of the magnetic property was observed by the isothermal magnetiza-tion at 2 K under H//a and H//c up to 9 T (Figure 5a). Figure 5b enlarges the low-field regionto emphasize the obvious hysteresis under H//c. The overall behavior is similar to thatobserved in flux-grown crystals, in which measurements were performed up to 30 T [23].The magnetization under H//c shows a clear hysteresis with a remnant magnetization and asmall coercive field of 0.07 T, indicating magnetic order with a spontaneous magnetization.In contrast, the a-axis magnetization shows no clear hysteresis and is nearly 100 timessmaller than the c-axis magnetization at 0.3 T. The a-axis magnetization is linear in H upto 2 T and slightly deviates upwards at higher field. The strong anisotropy suggests thatNdAlGe has an Ising-like magnetism with the c axis being the easy axis.Inorganics 2022, 10, x FOR PEER REVIEW 8 of 17   strong anisotropy suggests that NdAlGe has an Ising-like magnetism with the c axis being the easy axis.  Figure 5. (a) Isothermal magnetization of NdAlGe at 2 K under H//a, and H//c between –9 and +9 T. (b) Zoom-in of the low-field region between –0.6 and +0.6 T to emphasize the hysteresis under H//c. Figure 6a,b plot the isothermal magnetization of NdAlGe under H//a, and H//c, respectively, at several temperatures across the TM. These data were taken after field cooling. Under H//c, the rapid increase in magnetization at low fields was suppressed as the temperature increased. The remnant magnetization disappeared at TM. Under H//a, the upward behavior observed at 2 K was suppressed as the temperature was raised. Figure 5. (a) Isothermal magnetization of NdAlGe at 2 K under H//a, and H//c between –9 and +9 T.(b) Zoom-in of the low-field region between –0.6 and +0.6 T to emphasize the hysteresis under H//c.Figure 6a,b plot the isothermal magnetization of NdAlGe under H//a, and H//c, respec-tively, at several temperatures across the TM. These data were taken after field cooling.Under H//c, the rapid increase in magnetization at low fields was suppressed as the temper-ature increased. The remnant magnetization disappeared at TM. Under H//a, the upwardbehavior observed at 2 K was suppressed as the temperature was raised.Figure 7a shows the temperature dependence of the specific heat (CP) without field. Wecan see a well-defined lambda-type anomaly, as seen in the sister materials RAl(Ge,Si) [14,18].A second-ordered-like transition temperature at 13.5 K, defined as the midpoint of thejump, corresponds accurately to the onset of the magnetic transition at TM observed inthe magnetic susceptibility measurements. Judging from the result, the observed phasetransition in NdAlGe occurs in bulk. We mention that only a single peak with a sharpInorganics 2023, 11, 20 8 of 15transition width of less than 0.4 K is seen; no other transitions were detectable at ourexperimental resolution down to 2 K. Figure 7b plots the temperature dependence of thespecific heat divided by temperature (CP/T). The ∆CP/T jumped by 0.69 J/mol K2 at TM.Inorganics 2022, 10, x FOR PEER REVIEW 9 of 17    Figure 6. Isothermal magnetization curves of NdAlGe under (a) H//a, and (b) H//c at temperatures below and above the transition temperature at 13.5 K. The data were taken under the field-cooled process. Figure 7a shows the temperature dependence of the specific heat (CP) without field. We can see a well-defined lambda-type anomaly, as seen in the sister materials RAl(Ge,Si) [14,18]. A second-ordered-like transition temperature at 13.5 K, defined as the midpoint of the jump, corresponds accurately to the onset of the magnetic transition at TM observed in the magnetic susceptibility measurements. Judging from the result, the observed phase transition in NdAlGe occurs in bulk. We mention that only a single peak with a sharp transition width of less than 0.4 K is seen; no other transitions were detectable at our experimental resolution down to 2 K. Figure 7b plots the temperature dependence of the specific heat divided by temperature (CP/T). The ΔCP/T jumped by 0.69 J/mol K2 at TM. Figure 6. Isothermal magnetization curves of NdAlGe under (a) H//a, and (b) H//c at temperatures belowand above the transition temperature at 13.5 K. The data were taken under the field-cooled process.Thermodynamic phase transitions can be detected through thermal expansion ex-periments, which provide the directional information along the independent crystallo-graphic axes [47]. In contrast, specific heat measurements probe the overall informationon phase transitions, as shown in Figure 7. Figure 8a shows the linear thermal expansions∆LiLi= Li(T)−Li(300 K)Li(300 K) , where the index i refers to the a and c axes, as functions of temper-ature. The inset shows the temperature-dependent ∆LiLiup to 300 K. Both ∆LaLaand ∆LcLcshow a clear kink (not a discontinuous jump) at TM = 13.5 K, suggesting a second-orderedphase transition. Moreover, the results are highly anisotropic: on cooling, the thermalexpansions along the a and c axes increase and decrease below TM, respectively. Thisresult is possibly attributable to the anisotropic magnetic correlations of this material, asdiscussed for NdAlSi [14]. Figure 8b presents the temperature dependence of the linearthermal expansion coefficient αi = 1Li(300 K)d∆Li(T)dT along the a and c axes. Also shownis the volume expansion coefficient αv deduced as 2αa + αc, considering the tetragonalcrystal symmetry of this material. Anomalies in both αa and αc correspond to the magnetictransition temperature at TM, suggesting a strong magnetoelastic coupling in NdAlGe.Inorganics 2023, 11, 20 9 of 15Inorganics 2022, 10, x FOR PEER REVIEW 10 of 17    Figure 7. (a) Temperature dependence of specific heat (CP) of NdAlGe under zero field. (b) Specific heat divided by temperature (CP/T) plotted against temperature. Thermodynamic phase transitions can be detected through thermal expansion experiments, which provide the directional information along the independent crystallographic axes [47]. In contrast, specific heat measurements probe the overall information on phase transitions, as shown in Figure 7. Figure 8a shows the linear thermal expansions ∆ = ( ) (  )(  ) , where the index i refers to the a and c axes, as functions of temperature. The inset shows the temperature-dependent ∆  up to 300 K. Both ∆  and ∆  show a clear kink (not a discontinuous jump) at TM = 13.5 K, suggesting a second-ordered phase transition. Moreover, the results are highly anisotropic: on cooling, the thermal expansions along the a and c axes increase and decrease below TM, respectively. This result is possibly attributable to the anisotropic magnetic correlations of this material, Figure 7. (a) Temperature dependence of specific heat (CP) of NdAlGe under zero field. (b) Specificheat divided by temperature (CP/T) plotted against temperature.For a second-ordered phase transition, the uniaxial and hydrostatic pressure depen-dence of the magnetic transition temperature can be determined by the Ehrenfest rela-tion [47] dTMdPi= Vm∆ai∆(CP/T) , where Vm = 3.92 × 10−5 m3/mol is the molar volume, ∆(CP/T)defines the jump in the specific heat divided by the temperature (CP/T) (Figure 7b), and ∆αiis the jump in the thermal expansion coefficient at TM (Figure 8b). Using our experimentalresults with ∆(CP/T) = 0.69 J/mol K2, ∆αa = −2.2 × 10−6 K−1, and ∆αc = +1.2 × 10−5 K−1,we obtained dTMdPa= −0.13 K/GPa, and dTMdPc= +0.68 K/GPa under the uniaxial pressure alongthe a and c axes, respectively. This result suggests that uniaxial pressure along the c axisstabilizes the magnetic ordered state, whereas that along the a axis suppresses this state.In addition, the hydrostatic pressure dependence of the magnetic transition temperaturedTMdP = 2 dTMdPa+ dTMdPcwas obtained as +0.42 K/GPa. The obtained hydrostatic pressure depen-dence on TM in NdAlGe is close to that in the sister compounds CeAlGe, and CeAlSi withdTMdP = +0.64 K/GPa, and +0.62 K/GPa, respectively, and the signs of all dependencies arepositive although the magnetically easy axis in these Ce-based materials reportedly alignsperpendicular to the c axis. [20,21]. The same trend of dTMdP > 0 was seen in a substitutionstudy of PrAl(Ge1-xSix); specifically, the magnetic ordered tempera ture monotonicallyincreased with shrinkage as Si was substituted for Ge [18].Inorganics 2023, 11, 20 10 of 15Inorganics 2022, 10, x FOR PEER REVIEW 11 of 17   as discussed for NdAlSi [14]. Figure 8b presents the temperature dependence of the linear thermal expansion coefficient 𝛼 = (  ) ∆ ( ) along the a and c axes. Also shown is the volume expansion coefficient αv deduced as 2αa + αc, considering the tetragonal crystal symmetry of this material. Anomalies in both αa and αc correspond to the magnetic transition temperature at TM, suggesting a strong magnetoelastic coupling in NdAlGe.  Figure 8. (a) Temperature dependences of (a) thermal expansion ∆ = ( ) (  )(  )  and (b) linear thermal expansion coefficient 𝛼 = (  ) ∆ ( ) along the a and c axes. Indexed by i. The volume expansion coefficient αv, obtained as 2αa + αc considering the tetragonal crystal symmetry of NdAlGe, is also shown. For a second-ordered phase transition, the uniaxial and hydrostatic pressure dependence of the magnetic transition temperature can be determined by the Ehrenfest Figure 8. (a) Temperature dependences of (a) thermal expansion ∆LiLi=Li(T)−Li(300 K)Li(300 K)and (b) linearthermal expansion coefficient αi =1Li(300 K)d∆Li(T)dT along the a and c axes. Indexed by i. The volumeexpansion coefficient αv, obtained as 2αa + αc considering the tetragonal crystal symmetry of NdAlGe,is also shown.The magnetocaloric effect, which determines the correlation between the orderedmagnetism and entropy, is worth exploring in magnetic materials. The magnetocaloriceffect is a consequence of temperature change (heating or cooling) in a magnetic materialunder adiabatic conditions when an external magnetic field is applied and removed [48].The efficiency of the magnetocaloric effect can be evaluated through the magnetic entropychange ∆SM, defined as the entropy difference between the magnetized material (S(H)) anddemagnetized material (S(0). Formally, ∆SM = S(H)–S(0) [45]. The magnetocaloric effect isusually examined in ferromagnetic materials because such materials should, in principle,gain larger ∆SM through the demagnetized and magnetized process than non-ferromagneticmaterials [49–51]. Although evaluating the ∆SM of NdAlGe with Ising-like magnetizationunder H//c (Figure 5a) is an interesting proposition, the ∆SM of Nd-containing materialsare rarely considered because the magnetic moments of materials containing light rare-earth elements are smaller than those of other magnetocaloric materials containing heavyrare-earth elements such as Ho, Gd or transition metal Fe [49–51].To evaluate the ∆SM of NdAlGe, we first show the temperature dependences ofthe magnetization (M vs. T) of NdAlGe under H//a and H//c (Figure 9a,b, respectively),under various magnetic fields up to 9 T. These measurements were performed underthe FC process. Figure 9c,d present the magnetic entropy changes (∆SM) as functions oftemperature under H//a, and H//c, respectively, for various fields up to 9 T. Here, the ∆SMInorganics 2023, 11, 20 11 of 15was evaluated from the above-mentioned Maxwell relation. Under H//c, the ∆SM showsa single minimum around TM. The negative magnetic entropy change indicates that theentropy was released/gained under magnetization/demagnetization in NdAlGe. Whenthe field was changed from zero to 5 and 9 T, the ∆SM values were −4.2 and −5.7 J/Kmol, respectively. The value at 5 T was comparable to that in a series of ternary systemssummarized in a review article [52], which focused mainly on materials containing heavyrare-earth elements. In contrast, the ∆SM under H//a peaked at low temperatures andbecame negative at higher temperatures. Similar sign-changing behavior is seen in Ni-Mn-Sn alloys [53]. When the field changed to 9 T, the minimum value of ∆SM under H//a was−1.3 J/K mol. The positive and negative behavior of ∆SM under H//a, and the smallervalues than under H//c might reflect the anisotropic magnetic coupling.Inorganics 2022, 10, x FOR PEER REVIEW 13 of 17    Figure 9. Temperature dependence of magnetization of NdAlGe for (a) H//a and (b) H//c under the field-cooled process. The applied magnetic fields are 0.01, 0.05, 0.1, 0.3, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, and 9 T. The magnetic entropy change ΔSM as a function of temperature for (c) H//a, and (d) H//c. The floating-zone technique obtained the large-sized NdAlGe crystals in which we could investigate the directional electrical charge transport properties. Figure 10a presents the temperature dependences of the electrical resistivities ρa and ρc as the current flow along the a and c axes, respectively. Figure 10b enlarges the low temperature region. Both ρa and ρc exhibit metallic behaviors with sublinear temperature dependence at a high temperature. We also mention that the resistive behavior in ρa was identical along the radial direction in the grown crystal, suggesting there were homogeneous crystals in the ingot. The residual resistivity ratios (RRRs) were approximately 1.5 and 1.4, respectively. Comparable RRRs were reported in floating-zone crystals CeAlGe and PrAlGe, in which the materials were almost stoichiometric [11,17]. We also mention that the RRRs in our crystals were lower than those seen in the flux-grown crystals [14,16,18,21]. The resistive anisotropy of NdAlGe (ρc/ρa~2) was almost temperature-independent in the paramagnetic region (above TM), but the behaviors of ρa and ρc contrasted below TM; specifically, ρa and ρc were suppressed and enhanced below TM, respectively. In typical magnetic materials, in general, spin scattering and/or reconstruction of the Brillouin zone can influence the scattering rate of the conducting carriers when the system enters the ordered state [54,55]. Suppression of the scattering rate by spin scattering is frequently seen in the magnetic materials, for example, in the ferromagnetic oxide SrRuO3 [42]. Meanwhile, Brillouin zone reconstruction may enhance the resistivity, as observed in a pressure-induced antiferromagnetic ordered state in FeSe [56]. In NdAlGe, the upturn seen in ρc is possibly Figure 9. Temperature dependence of magnetization of NdAlGe for (a) H//a and (b) H//c under thefield-cooled process. The applied magnetic fields are 0.01, 0.05, 0.1, 0.3, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, and 9 T.The magnetic entropy change ∆SM as a function of temperature for (c) H//a, and (d) H//c.The floating-zone technique obtained the large-sized NdAlGe crystals in which wecould investigate the directional electrical charge transport properties. Figure 10a presentsthe temperature dependences of the electrical resistivities ρa and ρc as the current flow alongthe a and c axes, respectively. Figure 10b enlarges the low temperature region. Both ρa andρc exhibit metallic behaviors with sublinear temperature dependence at a high temperature.We also mention that the resistive behavior in ρa was identical along the radial direction inthe grown crystal, suggesting there were homogeneous crystals in the ingot. The residualresistivity ratios (RRRs) were approximately 1.5 and 1.4, respectively. Comparable RRRswere reported in floating-zone crystals CeAlGe and PrAlGe, in which the materials werealmost stoichiometric [11,17]. We also mention that the RRRs in our crystals were lowerthan those seen in the flux-grown crystals [14,16,18,21]. The resistive anisotropy of NdAlGe(ρc/ρa~2) was almost temperature-independent in the paramagnetic region (above TM),but the behaviors of ρa and ρc contrasted below TM; specifically, ρa and ρc were suppressedand enhanced below TM, respectively. In typical magnetic materials, in general, spinscattering and/or reconstruction of the Brillouin zone can influence the scattering rate ofthe conducting carriers when the system enters the ordered state [54,55]. Suppression of thescattering rate by spin scattering is frequently seen in the magnetic materials, for example,in the ferromagnetic oxide SrRuO3 [42]. Meanwhile, Brillouin zone reconstruction mayInorganics 2023, 11, 20 12 of 15enhance the resistivity, as observed in a pressure-induced antiferromagnetic ordered statein FeSe [56]. In NdAlGe, the upturn seen in ρc is possibly attributable to a reconstructedzone, whereas the downturn in ρa below TM might be dominated by suppression of thespin scattering.Inorganics 2022, 10, x FOR PEER REVIEW 14 of 17   attributable to a reconstructed zone, whereas the downturn in ρa below TM might be dominated by suppression of the spin scattering.  Figure 10. (a) Temperature dependence of electrical resistivities ρa, and ρc under the current flow along the a axis and c axes, respectively. (b) Low temperature resistivities for capturing the anisotropic behavior below the transition temperature. 4. Summary In summary, we successfully grew single crystals of a magnetic Weyl semimetal candidate NdAlGe using the laser diode heated floating-zone technique. Five laser diodes produced a bell-shaped distribution profile of vertical irradiation intensity. After the nominal powder, crushed from an arc-melted ingot, was shaped under hydrostatic pressure, we sintered the feed and seed rods under Ar gas at ultra-low oxygen partial pressure (<10−26 atm). The crystals were grown under the stable conditions of the molten Figure 10. (a) Temperature dependence of electrical resistivities ρa, and ρc under the current flowalong the a axis and c axes, respectively. (b) Low temperature resistivities for capturing the anisotropicbehavior below the transition temperature.4. SummaryIn summary, we successfully grew single crystals of a magnetic Weyl semimetal can-didate NdAlGe using the laser diode heated floating-zone technique. Five laser diodesproduced a bell-shaped distribution profile of vertical irradiation intensity. After the nomi-nal powder, crushed from an arc-melted ingot, was shaped under hydrostatic pressure, wesintered the feed and seed rods under Ar gas at ultra-low oxygen partial pressure (<10−26atm). The crystals were grown under the stable conditions of the molten zone without anycracks on the rods. We finally obtained a large-sized crystal with a length of 50 mm. Whenexamined with bulk-sensitive probes, the grown crystals showed magnetic order at 13.5K. The ordered state presented Ising-like behavior. The magnetic entropy largely changedwhen a magnetic field was applied along the easy axis (the c axis). The linear thermalexpansion also confirmed anisotropic responses at the magnetic transition temperature. Ap-plying the thermodynamic Ehrenfest relation based on our experimental data, we revealedthe anisotropic uniaxial pressure dependence of the magnetic transition temperature. Thehydrostatic pressure dependence on the magnetic transition temperature in NdAlGe wasInorganics 2023, 11, 20 13 of 15positively signed, as observed in sister materials of NdAlGe. Anisotropic charge transportbelow the ordered temperature probably originates from the scattering mechanism.Author Contributions: N.K. and T.T. conceived the project. N.K. grew and characterized the crystals.T.K., M.H. and H.Y. performed the ICP-OES. S.U. joined the discussion and contributed to themanuscript preparation. wrote the manuscript with input from all coauthors. All authors have readand agreed to the published version of the manuscript.Funding: This work is supported by a KAKENHI Grants-in-Aids for Scientific Research (Grant Nos.17H06136, 18K0475, 21H01033, and 22K19093), and a Core-to-Core Program (No. JPJSCCA20170002) fromthe Japan Society for the Promotion of Science (JSPS), and a 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 fruitful advice about the laser floating-zonefurnace, and Takeshi Shimada, Noritaka Kimura, John McArthur, Naohiro Kaga, Yuta Maegawa,Tohru Nagasawa, and Nobuyuki Ochiai for technical support.Conflicts of Interest: The authors declare no conflict of interest.References1. Wang, Z.; Zhang, S.-C. Chiral Anomaly, Charge Density Waves, and Axion Strings from Weyl Semimetals. Phys. Rev. B 2013,87, 161107. [CrossRef]2. Burkov, A.A. Topological Semimetals. Nat. Mater. 2016, 15 1145. [CrossRef] [PubMed]3. Yan, B.; Felser, C. Topological Materials: Weyl Semimetals. Annu. Rev. Condens. Matter Phys. 2017, 8, 337. [CrossRef]4. Armitage, N.P.; Mele, E.J.; Vishwanath, A. Weyl and Dirac Semimetals in Three-Dimensional Solids. Rev. Mod. Phys. 2018,90, 015001. [CrossRef]5. Nagaosa, N.; Morimoto, T.; Tokura, Y. Transport, Magnetic and Optical Properties of Weyl Materials. Nat. Rev. Mater. 2020, 5, 621.[CrossRef]6. Otrokov, M.M.; Klimovskikh, I.I.; Bentmann, H.; Estyunin, D.; Zeugner, A.; Aliev, Z.S.; Gaß, S.; Wolter, A.U.B.; Koroleva, A.V.;Shikin, A.M.; et al. Prediction and Observation of an Antiferromagnetic Topological Insulator. Nature 2019, 576, 416. [CrossRef]7. Rienks, E.D.L.; Wimmer, S.; Sánchez-Barriga, J.; Caha, O.; Mandal, P.S.; Růžička, J.; Ney, A.; Steiner, H.; Volobuev, V.V.;Groiss, H.; et al. Large Magnetic Gap at the Dirac Point in Bi2Te3/MnBi2Te4 Heterostructures. Nature 2019, 576, 423. [CrossRef]8. Bernevig, B.A.; Felser, C.; Beidenkopf, H. Progress and Prospects in Magnetic Topological Materials. Nature 2022, 603, 41.[CrossRef]9. He, Q.L.; Hughes, T.L.; Armitage, N.P.; Tokura, Y.; Wang, K.L. Topological Spintronics and Magnetoelectronics. Nat. Mater. 2022,21, 15. [CrossRef]10. Giustino, F.; Lee, J.H.; Trier, F.; Bibes, M.; Winter, S.M.; Valentí, R.; Son, Y.-W.; Taillefer, L.; Heil, C.; Figueroa, A.I.; et al. The 2021Quantum Materials Roadmap. J. Phys. Mater. 2020, 3, 042006. [CrossRef]11. Puphal, P.; Mielke, C.; Kumar, N.; Soh, Y.; Shang, T.; Medarde, M.; White, J.S.; Pomjakushina, E. Bulk Single-Crystal Growth of theTheoretically Predicted Magnetic Weyl Semimetals RAlGe (R = Pr, Ce). Phys. Rev. Mater. 2019, 3, 024204. [CrossRef]12. Chang, G.; Singh, B.; Xu, S.-Y.; Bian, G.; Huang, S.-M.; Hsu, C.-H.; Belopolski, I.; Alidoust, N.; Sanchez, D.S.; Zheng, H.; et al.Magnetic and Noncentrosymmetric Weyl Fermion Semimetals in the RAlGe Family of Compounds (R = Rare Earth). Phys. Rev. B2018, 97, 041104. [CrossRef]13. Yao, X.; Verma, R.; Graf, D.E.; Yang, H.Y.; Bahrami, F.; Zhang, R.; Aczel, A.A.; Subedi, S.; Torchinsky, D.H.; Sun, J.; et al. TopologicalSpiral Magnetism in the Weyl Semimetal SmAlSi. arXiv 2022, arXiv:2206.05121.14. Gaudet, J.; Yang, H.-Y.; Baidya, S.; Lu, B.; Xu, G.; Zhao, Y.; Rodriguez-Rivera, J.A.; Hoffmann, C.M.; Graf, D.E.; Torchinsky, D.H.; et al.Weyl-Mediated Helical Magnetism in NdAlSi. Nat. Mater. 2021, 20, 1650. [CrossRef]15. Puphal, P.; Pomjakushin, V.; Kanazawa, N.; Ukleev, V.; Gawryluk, D.J.; Ma, J.; Naamneh, M.; Plumb, N.C.; Keller, L.;Cubitt, R.; et al. Topological Magnetic Phase in the Candidate Weyl Semimetal CeAlGe. Phys. Rev. Lett. 2020, 124, 017202.[CrossRef]16. Meng, B.; Wu, H.; Qiu, Y.; Wang, C.; Liu, Y.; Xia, Z.; Yuan, S.; Chang, H.; Tian, Z. Large Anomalous Hall Effect in FerromagneticWeyl Semimetal Candidate PrAlGe. APL Mater. 2019, 7, 051110. [CrossRef]17. Destraz, D.; Das, L.; Tsirkin, S.S.; Xu, Y.; Neupert, T.; Chang, J.; Schilling, A.; Grushin, A.G.; Kohlbrecher, J.; Keller, L.; et al.Magnetism and Anomalous Transport in the Weyl Semimetal PrAlGe: Possible Route to Axial Gauge Fields. NPJ Quantum Mater.2020, 5, 5. [CrossRef]18. Yang, H.-Y.; Singh, B.; Lu, B.; Huang, C.-Y.; Bahrami, F.; Chiu, W.-C.; Graf, D.; Huang, S.-M.; Wang, B.; Lin, H.; et al. Transitionfrom Intrinsic to Extrinsic Anomalous Hall Effect in the Ferromagnetic Weyl Semimetal PrAlGe1-xSix. APL Mater. 2020, 8, 011111.[CrossRef]http://doi.org/10.1103/PhysRevB.87.161107http://doi.org/10.1038/nmat4788http://www.ncbi.nlm.nih.gov/pubmed/27777403http://doi.org/10.1146/annurev-conmatphys-031016-025458http://doi.org/10.1103/RevModPhys.90.015001http://doi.org/10.1038/s41578-020-0208-yhttp://doi.org/10.1038/s41586-019-1840-9http://doi.org/10.1038/s41586-019-1826-7http://doi.org/10.1038/s41586-021-04105-xhttp://doi.org/10.1038/s41563-021-01138-5http://doi.org/10.1088/2515-7639/abb74ehttp://doi.org/10.1103/PhysRevMaterials.3.024204http://doi.org/10.1103/PhysRevB.97.041104http://doi.org/10.1038/s41563-021-01062-8http://doi.org/10.1103/PhysRevLett.124.017202http://doi.org/10.1063/1.5090795http://doi.org/10.1038/s41535-019-0207-7http://doi.org/10.1063/1.5132958Inorganics 2023, 11, 20 14 of 1519. Wang, J.-F.; Dong, Q.X.; Huang, Y.F.; Wang, Z.S.; Guo, Z.P.; Wang, Z.J.; Ren, Z.A.; Li, G.; Sun, P.J.; Dai, X.; et al. Temperature DependentQuantum Oscillations at a Constant Magnetic Field in a Magnetic Weyl Semimetal. arXiv 2022, arXiv:2201.06412, 06412.20. Piva, M.M.; Souza, J.C.; Brousseau-Couture, V.; Pakuszewski, K.R.; John, J.K.; Adriano, C.; Côté, M.; Pagliuso, P.G.; Nicklas, M.Tuning the Nontrivial Topological Properties of the Weyl Semimetal CeAlSi. arXiv 2021, arXiv:2111.05742, 05742.21. He, X.; Li, Y.; Zeng, H.; Zhu, Z.; Cao, C.; Luo, Y. Pressure Tuning Domain-Wall Chirality in Noncentrosymmetric Magnetic WeylSemimetal CeAlGe. arXiv 2022, arXiv:2207.08442.22. Sanchez, D.S.; Chang, G.; Belopolski, I.; Lu, H.; Yin, J.-X.; Alidoust, N.; Xu, X.; Cochran, T.A.; Zhang, X.; Bian, Y.; et al. Observationof Weyl Fermions in a Magnetic Non-centrosymmetric Crystal. Nat. Commun. 2020, 11, 3356. [CrossRef] [PubMed]23. Zhao, J.; Liu, W.; Rahman, A.U.; Meng, F.; Ling, L.; Xi, C.; Tong, W.; Bai, Y.; Tian, Z.; Zhong, Y.; et al. Field-Induced TricriticalPhenomenon and Magnetic Structures in Magnetic Weyl Semimetal Candidate NdAlGe. New J. Phys. 2022, 24, 013010. [CrossRef]24. Schmehr, J.L.; Wilson, S.D. Active Crystal Growth Techniques for Quantum Materials. Annu. Rev. Mater. Res. 2017, 47, 153.[CrossRef]25. Basov, D.N.; Averitt, R.D.; Hsieh, D. Towards Properties on Demand in Quantum Materials. Nat. Mater. 2017, 16, 1077. [CrossRef]26. Samarth, N. Quantum Materials Discovery from a Synthesis Perspective. Nat. Mater. 2017, 16, 1068. [CrossRef]27. 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]28. 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]29. Rey-García, F.; Ibáñez, R.; Angurel, L.A.; Costa, F.M.; de la Fuente, G.F. Laser Floating Zone Growth: Overview, Singular Materials,Broad Applications, and Future Perspectives. Crystals 2020, 11, 38. [CrossRef]30. 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]31. Admasu, A.S.; Vavilapalli, D.S. The Laser-Diode Heated Floating Zone Method for Automated Optimal Synthesis of RefractoryOxides and Alloys. arXiv 2021, arXiv:2103.05587.32. Neubauer, A.; Jonietz, F.; Meven, M.; Georgii, R.; Brandl, G.; Behr, G.; Böni, P.; Pfleiderer, C. Optical Floating Zone Growth ofHigh-Quality Cu2MnAl Single Crystals. Nucl. Instrum. Methods Phys. Res. A 2012, 688, 66. [CrossRef]33. Brunt, D.; Hatnean, M.C.; Petrenko, O.A.; Lees, M.R.; Balakrishnan, G. Single-Crystal Growth of Metallic Rare-Earth Tetraboridesby the Floating-Zone Technique. Crystals 2019, 9, 211. [CrossRef]34. Amigó, M.L.; Maljuk, A.; Manna, K.; Stahl, Q.; Felser, C.; Hess, C.; Wolter, A.U.B.; Geck, J.; Seiro, S.; Büchner, B. Laser-AssistedFloating Zone Growth of BaFe2S3 Large-Sized Ferromagnetic-Impurity-Free Single Crystals. Crystals 2021, 11, 758. [CrossRef]35. Sinha, M.; Vivanco, H.K.; Wan, C.; Siegler, M.A.; Stewart, V.J.; Pogue, E.A.; Pressley, L.A.; Berry, T.; Wang, Z.; Johnson, I.; et al.Twisting of 2D Kagomé Sheets in Layered Intermetallics. ACS Cent. Sci. 2021, 7, 1381. [CrossRef] [PubMed]36. Bauer, A.; Neubauer, A.; Münzer, W.; Regnat, A.; Benka, G.; Meven, M.; Pedersen, B.; Pfleiderer, C. Ultra-High VacuumCompatible Induction-Heated Rod Casting Furnace. Rev. Sci. Instrum. 2016, 87, 063909. [CrossRef]37. 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]38. Mao, Z.Q.; Maeno, Y.; Fukazawa, H. Crystal Growth of Sr2RuO4. Mater. Res. Bull. 2000, 35, 1813. [CrossRef]39. Perry, R.S.; Maeno, Y. Systematic Approach to the Growth of High-Quality Single Crystals of Sr3Ru2O7. J. Cryst. Growth 2004,271, 134. [CrossRef]40. Zhou, M.; Hooper, J.; Fobes, D.; Mao, Z.Q.; Golub, V.; O’Connor, C.J. Electronic and Magnetic Properties of Triple-LayeredRuthenate Sr4Ru3O10 Single Crystals Grown by a Floating-Zone Method. Mater. Res. Bull. 2005, 40, 942. [CrossRef]41. Kikugawa, N.; Balicas, L.; Mackenzie, A.P. Physical Properties of Single-Crystalline CaRuO3 Grown by a Floating-Zone Method.J. Phys. Soc. Jpn. 2009, 78, 014701. [CrossRef]42. Kikugawa, N.; Baumbach, R.; Brooks, J.S.; Terashima, T.; Uji, S.; Maeno, Y. Single-Crystal Growth of a Perovskite RuthenateSrRuO3 by the Floating-Zone Method. Cryst. Growth Des. 2015, 15, 5573. [CrossRef]43. Kikugawa, N.; Sokolov, D.A.; Nagasawa, T.; Mackenzie, A.P. Single-Crystal Growth of Sr2RuO4 by the Floating-Zone MethodUsing an Infrared Image Furnace with Improved Halogen Lamps. Crystals 2021, 11, 392. [CrossRef]44. 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]45. Gschneidner, K.A.; Pecharsky, V.K. Magnetocaloric Materials. Annu. Rev. Mater. Sci. 2000, 30, 387. [CrossRef]46. Wang, T.; Guo, Y.; Wang, C.; Yang, S. Correlation between Non-centrosymmetic Structure and Magnetic Properties in WeylSemimetal NdAlGe. Solid State Commun. 2020, 321, 114041. [CrossRef]47. Barron, T.H.K.; White, G.K. Heat Capacity and Thermal Expansion at Low Temperatures; Kluwer Academic/Plenum: New York, NY,USA, 1999.48. 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. 5035–5041.49. 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]50. Pecharsky, V.K.; Gschneidner, K.A., Jr. Giant Magnetocaloric Effect in Gd5(Si2Ge2). Phys. Rev. Lett. 1997, 78, 4494. [CrossRef]http://doi.org/10.1038/s41467-020-16879-1http://www.ncbi.nlm.nih.gov/pubmed/32620859http://doi.org/10.1088/1367-2630/ac430ahttp://doi.org/10.1146/annurev-matsci-070616-124006http://doi.org/10.1038/nmat5017http://doi.org/10.1038/nmat5010http://doi.org/10.3390/condmat4010006http://doi.org/10.1016/j.jcrysgro.2012.10.059http://doi.org/10.3390/cryst11010038http://doi.org/10.1016/j.jcrysgro.2019.125435http://doi.org/10.1016/j.nima.2012.06.012http://doi.org/10.3390/cryst9040211http://doi.org/10.3390/cryst11070758http://doi.org/10.1021/acscentsci.1c00599http://www.ncbi.nlm.nih.gov/pubmed/34471681http://doi.org/10.1063/1.4954926http://doi.org/10.1063/1.1992671http://doi.org/10.1016/S0025-5408(00)00378-0http://doi.org/10.1016/j.jcrysgro.2004.07.082http://doi.org/10.1016/j.materresbull.2005.03.004http://doi.org/10.1143/JPSJ.78.014701http://doi.org/10.1021/acs.cgd.5b01248http://doi.org/10.3390/cryst11040392http://doi.org/10.1109/TMAG.2018.2866831http://doi.org/10.1146/annurev.matsci.30.1.387http://doi.org/10.1016/j.ssc.2020.114041http://doi.org/10.1088/0953-8984/26/4/046004http://doi.org/10.1103/PhysRevLett.78.4494Inorganics 2023, 11, 20 15 of 1551. Fujieda, S.; Fujita, A.; Fukamichi, K. Large Magnetocaloric Effect in La(FexSi1-x)13 Itinerant-Electron Metamagnetic Compounds.Appl. Phys. Lett. 2002, 81, 1276. [CrossRef]52. Gupta, S.; Suresh, K.G. Review on Magnetic and Related Properties of RTX Compounds. J. Alloys Compd. 2015, 618, 562. [CrossRef]53. Krenke, T.; Duman, E.; Acet, M.; Wassermann, E.F.; Moya, X.; Mañosa, L.; Planes, A. Inverse Magnetocaloric Effect in Ferromag-netic Ni-Mn-Sn Alloys. Nat. Mater. 2005, 4, 450. [CrossRef] [PubMed]54. Van Peski-Tinbergen, T.; Dekker, A.J. Spin-Dependent Scattering and Resistivity of Magnetic Metals and Alloys. Physica 1963,29, 917. [CrossRef]55. Maki, S.; Adachi, K. Antiferromagnetism and Weak Ferromagnetism of Disordered Bcc Cr-Mn Alloys. J. Phys. Soc. Jpn. 1979,46, 1131. [CrossRef]56. Terashima, T.; Kikugawa, N.; Kasahara, S.; Watashige, T.; Shibauchi, T.; Matsuda, Y.; Wolf, T.; Böhmer, A.E.; Hardy, F.; Meingast,C.; et al. Pressure-Induced Antiferromagnetic Transition and Phase Diagram in FeSe. J. Phys. Soc. Jpn. 2015, 84, 063701. [CrossRef]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.http://doi.org/10.1063/1.1498148http://doi.org/10.1016/j.jallcom.2014.08.079http://doi.org/10.1038/nmat1395http://www.ncbi.nlm.nih.gov/pubmed/15895096http://doi.org/10.1016/S0031-8914(63)80182-2http://doi.org/10.1143/JPSJ.46.1131http://doi.org/10.7566/JPSJ.84.063701 Introduction  Materials and Methods  Crystal Growth by the Floating-Zone Method  Laser Floating-Zone Technique  Preparation of Feed and Seed Rods  Crystal Growth  Characterization  Results and Discussion  Crystal Growth  Bulk Properties of the Grown Crystal  Summary  References