Magnetocaloric effect in single crystal GdTiO3

Cryogenics 101 (2019) 58–62

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Research paper

Magnetocaloric effect in single crystal GdTiO3 a

a,⁎

a

T b

b

Hideki Omote , Shota Watanabe , Koichi Matsumoto , Ildar Gilmutdinov , Airat Kiiamov , Dmitrii Tayurskiib a b

Department of Physics, Kanazawa University, Kanazawa 920-1192, Japan Institute of Physics, Kazan Federal University, Kremlevskaya 18, Kazan 420008, Russia

A R T I C LE I N FO

A B S T R A C T

Keywords: Magnetocaloric material Entropy Magnetic refrigeration Hydrogen Liquefaction

We studied the magnetocaloric effect in a single crystal GdTiO3. Single crystal GdTiO3 had a second order phase transition from a paramagnetic to ferrimagnetic state at 33 K. The maximum entropy change of − ΔS = 0.10 J/ cm3 K was observed in a 5 T field at the transition temperature. A small anisotropy was found in the magnetization and specific heat in low magnetic fields. The magnetization showed no hysteresis. Temperature dependencies of entropy, which are important for analyzing the refrigeration cycle, were calculated from the magnetization and specific heat measurements. These results indicate that GdTiO3 has the potential for applications as a magnetic refrigerant for hydrogen liquefaction.

1. Introduction Refrigeration based on the magnetocaloric effect (MCE) has a long history [1,2]. Magnetic refrigeration can achieve a very high thermodynamic efficiency because of the reversibility of entropy changes. Magnetic refrigerators can be environmentally friendly, quiet, and potentially more efficient than conventional gas expansion refrigerators. Magnetic refrigerators can operate over a wide temperature range, from room temperature to microkelvin temperatures with the use of various magnetic materials and thermal cycles. In recent years, magnetic refrigeration research has been expanded, motivated by various potential applications, such as space cryogenics [3], hydrogen liquefaction [4] and room temperature refrigerators [5,6]. Magnetic materials with a large MCE have been extensively studied [7,8]. Hydrogen is one of the cleanest energy resources and is also a useful cryogenic refrigerant for superconducting technologies operating above 20 K. Dense liquid hydrogen has great advantages over gaseous hydrogen in terms of storage and transportation; however, practical applications of liquid hydrogen depend on highly efficient liquefaction methods and adiabatic storage because of its 20.3 K boiling point. One of the authors of this paper developed a hydrogen magnetic refrigeration system that consisted of a Carnot cycle liquefaction stage and an active magnetic regenerator (AMR) cycle for the precooling stages [4]. In the Carnot cycle, a liquefaction efficiency greater than 80% was achieved with the use of Dy-substituted gadolinium aluminum garnet ((DyxGd1 − x )3Al5O12, DGAG) [4,9]. Non-reactivity of the magnetic material with hydrogen is favorable

⁎

for applications to hydrogen magnetic refrigerators because direct heat transfer between the magnetic refrigerant and hydrogen gas is important. We have previously studied garnet materials such as Gd3Al5O12 (GGG), (DyxGd1 − x )3Al5O12 (DGAG)[4,9], and a series of Fe-modified gadolinium gallium garnets (Gd3(Ga1 − x Fex )5O12, GGIG). We demonstrated that GGIGs have a larger entropy change ΔS than that of gadolinium gallium garnet (Gd3Ga5O12, GGG) at 20 K [10,11]. In the present work, we studied the MCE of oxide materials with magnetic transition temperatures higher than 20 K because maximum entropy change is obtained generally at the magnetic transition temperature. RTiO3 (R: rare-earth) is a typical Mott-Hubbard insulator and has various magnetic-orbital ordered states owing to an interplay of charge, spin, and orbital degree of freedom. Structural change is associated with a magnetic phase transition in titanate oxides. GdTiO3 is expected to have a small anisotropy because the 4f electron configuration of Gd3 + ion results in zero total angular momentum and 7/2 spin angular momentum. GdTiO3 has a second order phase transition from a paramagnetic to ferrimagnetic phase at 33 K [12–15]. The MCEs of single crystal DyTiO3[16], HoTiO3[17], TmTiO3[18], and polycrystalline EuTiO3[19] have been reported to date. However, to our knowledge, the MCE of single crystal GdTiO3 has not yet been reported. In this paper, we report the MCE of single crystal GdTiO3. The MCE was evaluated through magnetization and specific heat measurements. A small magnetic anisotropy and no magnetic hysteresis were observed. These results show that GdTiO3 is a good candidate material for hydrogen magnetic refrigeration.

Corresponding author. E-mail address: k.matsu@staff.kanazawa-u.ac.jp (K. Matsumoto).

https://doi.org/10.1016/j.cryogenics.2019.05.008 Received 25 January 2019; Received in revised form 20 May 2019; Accepted 28 May 2019 Available online 30 May 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.

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2. Experimental procedures 2.1. Sample preparation and characterization A single crystal of GdTiO3 was grown by the optical floating zone technique. Stoichiometric amount of Gd2O3 (Alfa Aesar, 99.99%), TiO2 (Alfa Aesar, 99.8%), and Ti (Alfa Aesar, 99.5%) powders were mixed, ground thoroughly. A cylindrical rod was formed using a hydrostatic pressing method, and this rod was used as the ingot for the crystal growth. The single crystal was grown in argon gas with a flow rate of 0.2 l/min at atmospheric pressure using an optical floating zone furnace FZ-T-4000-H-VII-VPO-PC (Crystal Systems Corp., Japan) equipped with four 1 kW halogen lamps. At the beginning the ingot was preheated at a speed of 15 mm/h in argon gas flow. After the preheating procedure heater power was increased, and homogeneous molten zone was obtained. The crystal growth rate was 10 mm/h with counter-rotation of both feed and seed rods at 20–30 rpm. The grown crystal was shiny black, some parts were covered by thin yellow coating. The obtained sigle crystal was cut off to a length of 20 mm. The top and bottom parts of the crystal were ground and characterized with powder X-ray diffraction (Bruker D8 ADVANCE, Cu K α ). X-ray diffraction patterns revealed that the grown crystal was single phase with space group symmetry corresponding to the structure of GdTiO3 and no impurity phase such as Gd2Ti2O7 was detected as shown in Fig. 1. The cell parameters (a = 5.70, b = 7.66, and c = 5.40 Å) were in good agreement with literature data. Crystallographic axes were determined using Laue back diffraction.

2.2. Magnetization and specific heat measurements A small crystal was cut from the large single crystal. We measured magnetization M and specific heat C using the same crystal. M was measured using a commercial SQUID magnetometer (MPMS, Quantum Design) at discrete intervals of the magnetic field between 0.01 and 5 T in three different magnetic field directions with respect to the crystallographic axes. The sample for magnetization measurements was a cuboid whose sides were coincide with crystallographic axes. The length of the a, b, and c-axis were 0.86, 0.80, and 1.46 mm, respectively. The demagnetization coefficients for a, b, and c-axis (Na , Nb , and Nc ) were calculated respectively as 0.40, 0.40, and 0.19 by approximating the cuboid sample as a spheroid. Temperature dependence of the M was obtained in field cooled warming process where sample temperature was increased after the sample was reached 2 K in field cooling. M was also measured during both magnetization and demagnetization processes at 5, 34, and 50 K. Error of magnetization was estimated as several percent. A thermal relaxation method was used to measure the specific heat C as a function of temperature at various magnetic fields from 0 to 5 T using a physical properties measurement system (PPMS, Quantum

Fig. 2. (Upper panel) Temperature dependence of the magnetization of single crystal GdTiO3 along c-axis in magnetic fields of 0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 3, 4, and 5 T. (Lower panel) Magnetization and inverse susceptibility of single crystal GdTiO3 at 0.01 T versus temperature.

Design). The small crystal was fixed to the sapphire platform of the sample holder using a small amount of Apiezon N grease. In order to obtain C of the sample, the C of the sample platform and the grease was measured separately and subtracted from the experimentally obtained C. The experimental error of specific heat usually depends on temperature range. In this study, it was estimated at most 10%. 3. Results 3.1. Magnetization In the upper panel of Fig. 2, the M for single crystal GdTiO3 is shown as a function of temperature in various magnetic fields applied along the c-axis. In any constant field, M decreased with increasing temperature. The lower panel of Fig. 2 shows the M and the inverse susceptibility for a magnetic field of 0.01 T along the c-axis from 2 to 300 K. M demonstrates a paramagnetic to ferrimagnetic transition at TC = 32 K. The inverse magnetic susceptibility (H/M) has a hyperbolic shape, which is typical for two-sublattice ferrimagnets. We fitted the data in the paramagnetic phase to the well-known function,

ξ 1 T−θ = − , χ C T − θ′

(1)

on the basis of the molecular field model [12,15]. From the magnetization measurements along the c-axis, the paramagnetic Curie temperature θ = -30 K and the effective magnetic moment μeff = 7.1 μ B were obtained. The magnetic susceptibility showed little crystalline

Fig. 1. X-ray powder diffraction pattern of the GdTiO3. 59

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Fig. 4. Entropy change − ΔS of GdTiO3 for c-axis in 1, 2, 3, 4, and 5 T calculated from magnetization data. Triangles represent − ΔS in 5 T calculated from specific heat data.

direction agreed within approximately 4% at 5 T. However, the values of − ΔSmax for b-axis was 14% smaller than that for c-axis at 1 T. This behavior corresponds to the suppression of M for b-axis in small fields as shown in the lower panel of Fig. 3. 3.2. Specific heat The specific heat C for the single crystal GdTiO3 in the case of the caxis is shown in Fig. 5. The C in the zero field showed a sharp peak at 34 K against continuously rising background with temperature. The sharp specific heat peak at zero field indicates the high quality of the crystal. On application of a magnetic field, the specific heat peak broadened and shifted to a higher temperature as the magnetic field was increased. In 5 T, the specific heat peak was smeared and showed a shoulder around 50 K. These temperature and magnetic field dependencies are typical for magnetic materials with second order phase transitions. The C (T , H ) curves for other directions were almost identical to that for the c-axis. The C results for a and b-axis had a peak at the same temperature of 33 K in the zero field. However, the specific heat peaks for the a and b-axis were a little broader than that for the caxis under low fields, such as 0.1 T.

Fig. 3. (Upper panel) Isothermal magnetization of single crystal GdTiO3 along the c-axis at 4, 8, 12, 16, 20, 24, 28, 32, 33, 34, 35, 36, 40, 44, 48, 52, 56, and 60 K. (Lower panel) Isothermal magnetization along a, b, and c-axis at 5, 34, and 50 K.

anisotropy. The value of μeff agreed well within 0.2 μ B among the three axes. In the upper panel of Fig. 3, isothermal magnetizations M for single crystal GdTiO3 are shown as functions of magnetic field along the caxis. M was plotted after demagnetization correction. In the ordered state, M increased rapidly in low magnetic fields. M tended to be saturated at approximately 6.0 μ B per formula unit above 1 T at low temperatures. This saturation magnetization agrees well with the results of previous studies [12–15]. This result corresponds to collinear ferrimagnetic ordering of Gd3 + and Ti3 + ions. Isothermal magnetizations M for both the magnetization and demagnetization processes are plotted in Fig. 3. The values of M coincided well with each other and showed no hysteresis. The M results for other directions at 5, 34, and 50 K are shown in the lower panel of Fig. 3. This figure indicates that GdTiO3 has a small magnetic anisotropy. The magnetic entropy change ΔS was calculated from the magnetization using Maxwell’s relation,

ΔS (T , H ) =

∫0

H

⎛ ∂M ⎞ dH , ⎝ ∂T ⎠ H

3.3. Evaluation of entropy The total entropy S was obtained by integrating C / T over temperatures from 0 to T in a constant magnetic field, as

(2)

where H is the applied magnetic field. Fig. 4 shows the obtained − ΔS of GdTiO3 for the c-axis. For a given magnetic field, the entropy change increased with temperature below TC , and showed a peak − ΔSmax at 34 K, before decreasing as temperature was increased further. The form of these results was identical in terms of − ΔS for all directions, and the peak temperatures were the same. The values of − ΔSmax in each

Fig. 5. Specific heat C of GdTiO3 for c-axis in magnetic fields of 0, 1, 3, and 5 T. Solid line shows that of LaGaO3[20]. 60

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Fig. 8. Magnetic entropy Smag of GdTiO3 for c-axis in 0 T.

Fig. 6. Entropy S (T , H ) of GdTiO3 for c-axis in magnetic fields of 0, 1, 3, and 5 T.

S (T , H ) =

∫0

T

⎛ C (T , H ) ⎞ dT , T ⎝ ⎠H

measurement coincides with that from M in the whole temperature range. This means that the calorimetric and magnetic methods give the same results and have consistency. Magnetic contribution to the total entropy was evaluated as below. We evaluated lattice contribution using specific heat of LaGaO3[20] that has same crystal structure, non magnetic elements, and close atomic mass. Specific heat of LaGaO3 has been used to analyze other perovskite materials. LaTiO3 with non magnetic rare earth La isn’t suitable for this purpose because LaTiO3 is antiferromagnetic MottHubbard insulator and Ti spins order at the Neel temperature of 16 K. Then, we calculated magnetic specific heat Cmag by subtraction of that of LaGaO3[20] from that of GdTiO3 in 0 T. Fig. 8 shows magnetic enT tropy determined using the equation Smag = ∫0 (Cmag / T )H dT . The Smag rapidly increases at the transition and almost saturate to the value of Rln(8) + Rln(2) which is theoretically expected total magnetic entropy of Gd3 + (S = 7/2 ) and Ti3 + (S = 1/2 ). This value is reasonable because of the difficulty in evaluating lattice contribution because of magnetic and orbital ordering. In this study, we focus on the MCE of GdTiO3 single crystal. The maximum entropy change − ΔSmax at each field strength and relative cooling power (RCP) are often used to compare the MCE among various materials [21,22]. The parameter RCP is defined as |ΔS| δFWHM , where δFWHM is the full width at half maximum of − ΔSmax in temperature [21,22]. The − ΔSmax values of GdTiO3 are 7.6 and 14.1 J/kg K at 2 and 5 T, respectively. The RCP values of GdTiO3 are 249 and 589 J/kg at 2 and 5 T, respectively. Comparing the − ΔSmax and RCP of GdTiO3 results with those of the intermetallic compound HoAl2, which has a similar magnetic transition temperature of 30 K, the − ΔSmax of GdTiO3 is approximately 60% that of HoAl2. The low magnetization owing to ferrimagnetic ordering gives rise to a small − ΔSmax . However, the RCP of GdTiO3 is the same as that of HoAl2 at 2 T and approximately 80% at 5 T. The large RCP is attributed to the large shoulder of − ΔS in the ordered phase as shown in Fig. 4. Thus, GdTiO3 is suitable for use in an Ericsson cycle and/or AMR cycle. The AMR cycle is considered useful for refrigeration above 20 K; however, numerical simulation is necessary to evaluate the cooling power in the AMR cycle [23–25]. The evaluation of the AMR cycle is beyond the scope of this paper and will be discussed elsewhere. In our previous tests of Carnot cycle magnetic refrigeration, plates of garnet materials were used for hydrogen liquefaction [4]. Here, we will compare the − ΔS of GdTiO3 with those of several oxide materials such as garnet, aluminate perovskite, and rare earth titanate. Owing to the limited available volume in high magnetic field applications, it is useful to compare in terms of the volumetric − ΔS . Fig. 9 represents − ΔS at 5 T for various oxides. GdTiO3 has a larger value of − ΔS in the range from 20 to 45 K than those of GGG, Gd3(Ga 0.5Fe0.5 )5O12 (GGIG(50%)) [11], GdAlO3, DyTiO3[16], HoTiO3[17], TmTiO3[18],

(3)

where C (T , H ) is the specific heat at a constant field H. S (T , H ) of GdTiO3 were calculated from the experimental data using the above equation. Fig. 6 gives the entropy-temperature diagram (S–T) of GdTiO3 for the c-axis. As expected from the magnetization and specific heat measurements, the entropy-temperature diagram for the three orientations of the magnetic field with respect to the crystallographic axes coincided with one another. As shown in Fig. 6, S decreased considerably by magnetic fields over the temperature range from 20 to 45 K, which corresponds to − ΔS in Fig. 4. This result clearly shows that GdTiO3 has potential for applications as a magnetic refrigerant for hydrogen liquefaction magnetic refrigerators.

4. Discussion In order to study magnetic transition of GdTiO3 , M 2 versus H / M curves so called Arrott plots in various temperatures are represented in Fig. 7. This plot shows that the transition temperature is close to 33 K. The positive slope of the Arrott plots around the transition temperature indicates the characteristic feature of second order magnetic transition that is in agreement with continuous decrease in M at the transition as shown in Fig. 2 and λ shape peak of C in 0 T as shown in Fig. 5. On the basis of specific heat data, magnetic entropy change − ΔS of GdTiO3 is able to be calculated using the relation ΔS = S (H , T ) − S (0, T ) , where S (H , T ) is calculated from Eq. 3. The calculated ΔS at 5 T is represented as triangles in Fig. 2. ΔS from C

Fig. 7. Arrott plot of GdTiO3 for c-axis. 61

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Fig. 9. − ΔS of several oxide materials at 5 T. a: Gd3(Ga 0.5Fe0.5 )5O12 (GGIG(50%)), b: GGG, c: GdAlO3, d: EuTiO3, e: HoTiO3, f: DyTiO3, g: TmTiO3.

and EuTiO3[19]. This result highlights the advantages of GdTiO3 over this temperature range. 5. Conclusions Single crystal GdTiO3 was synthesized and the MCE was studied in the vicinity of its ordering temperature. The GdTiO3 had small magnetic anisotropy in MCE. We obtained the S–T diagram of GdTiO3. GdTiO3 has good potential for applications as a magnetic refrigerant for hydrogen liquefaction. Acknowledgments This work was partly supported by JSPS KAKENHI17H03534. The authors from Kazan Federal University are grateful for support from the program of Competitive Growth of Kazan Federal University. The work of I.G. was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (project No. 3.9779.2017/8.9). References [1] Debye P. Einige Bemerkungen zur Magnetisierung bei tiefer Temperatur. Ann Phys 1926;81:1154.

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