Effect of Dy substitution in the giant magnetocaloric properties of HoB₂

ABSTRACT

Recently, a massive magnetocaloric effect near the liquefaction temperature of hydrogen has been reported in the ferromagnetic material HoB₂. Here we investigate the effects of Dy substitution in the magnetocaloric properties of Ho_1-xDy_xB₂ alloys (x = 0, 0.3, 0.5, 0.7, 1.0). We find that the Curie temperature (T_C) gradually increases upon Dy substitution, while the magnitude of the magnetic entropy change |ΔS_M| and adiabatic temperature change ΔT_ad showed a gradual decrease. On the other hand, due to the presence of successive transitions in these alloys, the peak height of the above magnetocaloric properties tends to be kept in a wide temperature range, leading to a relatively robust figure of merit in a wide temperature span. These alloys could be interesting candidates for magnetic refrigeration in the temperature range of 10–60 K.

Graphical abstract

KEYWORDS:

• Magnetic refrigeration
• magnetocaloric effect
• adiabatic temperature change

CLASSIFICATION:

• 203 Magnetics / Spintronics / Superconductors
• Magnetocaloric Materials

1. Introduction

Magnetic refrigeration is an emerging environmentally friendly technology for refrigeration applications, as it does not require to use of greenhouse gases and does not depend on conventional gas compression cycles [1–3] while having possible higher cycle efficiency [1,4]. It is based on the magnetocaloric effect (MCE), which consists of the adiabatic temperature change (ΔT_ad) a magnetic material will undergo when a magnetic field is applied/removed adiabatically, but it can also be evaluated in terms of the magnetic entropy change (ΔS_M) this magnetic material will undergo for the same field change, where ΔS_M usually peaks at the magnetic transition temperature (T_mag).

Recently, our group has unveiled a giant magnetocaloric effect of |ΔS_M^MAX| = 0.35 J cm⁻³ K⁻¹ (40.1 J kg⁻¹ K⁻¹) in the vicinity of a ferromagnetic transition at the Curie temperature (T_C) of 15 K for a field change of μ₀ΔH = 5 T in HoB₂ [5]. Due to the closeness of its T_C to the liquefaction point of hydrogen (20.3 K), this material became an attractive candidate for use in low-temperature magnetic refrigeration applications focused on the liquefaction stage of hydrogen. Hydrogen is considered to be one of the most promising replacements for hydrocarbon fuels as a clean energy source [6,7] and in particular liquid hydrogen is widely needed in the space industry [8] and its liquid form is one the suitable way for transportation and storage [9]. In this context, the discovery of magnetic materials with a high MCE effect at low temperatures is imperative for the development of such refrigerators working at cryogenic temperatures. Since the magnetocaloric effect peaks at T_mag, tuning the T_C of HoB₂ to a higher temperature is of extreme interest to examine HoB₂-based materials as possible candidates for refrigeration before the liquefaction stage, especially below temperatures of 77 K.

DyB₂ orders ferromagnetically at T_C = 50 K [10,11] and exhibits a |ΔS_M| of 0.16 J cm⁻³ K⁻¹ (17.1 J kg⁻¹ K⁻¹) for μ₀ΔH = 5 T [12]; 9 therefore a partial substitution of Ho by Dy is expected to shift T_C to higher values in the expense of a probable reduction of |ΔS_M|. Also, since both materials exhibit two consecutive transitions, it is interesting to investigate the effect of alloying in the MCE properties of this system. In this work, we study the magnetocaloric properties of Ho_1-xDy_xB₂ alloys (x = 0, 0.3, 0.5, 0.7, 1.0) and compare with other well-known materials working at the same temperature span.

All the magnetocaloric properties of the samples are reported in volumetric units (J cm⁻³ K⁻¹) as this is the adequate unit when comparing materials for application purposes as there is a volume limit when constructing real applications [13,14]. Therefore, herein all comparisons with other materials is done in this unit by converting it using the ideal density of each material when not provided.

2. Experimental section

2.1. Sample synthesis

Polycrystalline samples of Ho_1-xDy_xB₂ were prepared by an arc-melting process in a water-cooled copper hearth arc furnace under Ar atmosphere. Stoichiometric amounts of Ho (99.9% purity), Dy (99.9% purity), and B (99.5% purity) were weighted and then arc melted several times. During the synthesis trials, we found out that annealing under different conditions did not change the X-ray diffraction patterns of the obtained samples, therefore no annealing was carried out in this work.

2.2. Characterization

Powder X-ray diffraction (XRD) patterns of the arc-melted samples were investigated using a MiniFlex 600 (Rigaku, Japan) with Cu Kα radiation. The lattice parameters, the volume of the unit cell, and density were obtained by refining the XRD patterns using the FULLPROF [15] software.

2.3. Magnetization measurements

Magnetization measurements were carried out by a superconducting quantum interference device magnetometer contained in the Magnetic Property Measurement System XL (Quantum Design, US). Zero-field cooling (ZFC) and field cooling (FC) measurement at low fields were taken to evaluate the evolution of T_C as a function of Dy content. For the evaluation of |ΔS_M| the magnetization measurements of the sample under various applied fields ranging from 0.01 to 5 T were performed in ZFC process.

3. Results and discussion

3.1. Crystal structure

Figure 1(a) shows the XRD patterns for the obtained arc melted samples. The main phase peaks can be indexed into a hexagonal P6/mmm AlB₂ type crystal structure as shown by the red fitting curves. The remaining peaks are assigned as REB_4, unreacted RE or RE₂O₃ (RE = Ho, Dy) impurity peaks marked by a black square (■), a black star (★), or a black diamond (♦) respectively. The obtained lattice parameters, the volume of the unit cell, and density are summarized in Table 1.

Table 1. Lattice parameters obtained from XRD patterns for Ho_1-xDy_xB_2.

Nominal Dy (x)	a (Å)	c (Å)	V (Å^3)	ρ (g/cm^3)
0	3.283(3)	3.815(8)	35.62(4)	8.696
0.3	3.285(6)	3.827(1)	35.77(8)	8.626
0.5	3.285(7)	3.832(5)	35.82(9)	8.591
0.7	3.287(8)	3.839(7)	35.94(7)	8.540
1.0	3.292(0)	3.850(6)	36.14(0)	8.461

Figure 1. Powder XRD patterns and lattice constant evolution for Ho_1-xDy_xB₂ alloys. (a) XRD patterns of the obtained alloys. The red lines show the calculated patterns from Rietveld refinement for the REB₂ main phase. The black square (■) marks an REB₄ impurity phase, while the black star (★) marks a RE impurity peak and the black diamond (♦) marks a RE₂O₃ impurity peak (RE = Ho, Dy). (b) The lattice parameters normalized by the value at x = 0, as a function of x. The black dashed line shows a guide based on Vegard’s law, given by $1-x+x\left(\frac{a_1,c_1}{a_0,c_0}\right)$ where (a,c)_0,1 is the lattice constants at x = 0 or 1

As shown in Table 1, Dy substitution in the Ho site seems to strongly affect the c-axis length while the a-axis length weakly changes, illustrated in Figure 1(b) where we plot the normalized lattice parameters (a/a₀ and c/c₀) by the value of x = 0. Both c/c₀ and a/a₀ increase with x, roughly following the so-called Vegard’s law (marked by the dashed black line), but with different rates. The observed changes in the lattice constants in Ho_1-xDy_xB₂ suggest that the substitution of Ho by Dy in the REB₂ main phase was successful, and these partially substituted samples can be in the form of a random alloy. We note that in the case of HoB_2-xSi_x solid solutions [10] where B site is partially substituted, it has been reported that the expansion rate of a-axis length and c-axis length are comparable to each other. This difference in the change of lattice constants between Ho_1-xDy_xB₂ and HoB_2-xSi_x implies that the a-axis and c-axis lengths in HoB₂-based compounds might be closely related to the bonds along axes. Namely, c-axis length seems to be depending on Ho-B bonds and be sensitive to both rare-earth and B-site atoms, while the a-axis length might be more dependent on the B site atom.

3.2. Magnetic properties

The ZFC-FC isofield magnetization (M-T) curves for an applied field of µ_oH = 0.01 T and isothermal magnetization (M-H) curves measured at T = 5 K are shown in Figure 2(a-e, f-g) for each obtained sample, respectively. For the Dy containing samples, the divergence between the ZFC and FC M-T curves becomes more pronounced and a small magnetic hysteresis in the M-H curves is observed, including the end-material DyB₂.

Figure 2. Isofield (M-T) ZFC-FC, Normalized temperature-dependent derivatives of the ZFC curves, and Isothermal (M-H) magnetization curves of Ho_1-xDy_xB₂ alloys. (a-e) ZFC and FC curves for all synthesized alloys for an applied field of µ₀H = 0.01 T. The lower panels show the derivatives of the ZFC curves normalized by the minimum of the derivative value. The two magnetic transitions T_C and T*, are marked by the arrows. (f-g) Isothermal magnetization at T = 5 K

To evaluate the magnetic transition temperatures in this system, the temperature-dependent derivative of the ZFC curves was taken and are shown in the lower panels of Figure 2(a-e). The Curie temperatures that are defined by the peak position in ∂M/∂T curves, are marked by the T_C arrows, showing a systematic increase with Dy content. On the other hand, a second magnetic transition marked by T* that is observed at lower temperatures, which is also observed at HoB₂ at T* = 11 K [5] and DyB₂ at T* = 15 K [12], seems to be almost unchanged by partial substitution of Dy. The origin of T* was attributed to a possible spin-reorientation mechanism [12], however, the nature of this transition is still unknown and its investigation is outside the scope of this work. The Dy doping dependence of both transitions is summarized in Figure 3 showing the monotonic increase of T_C until 50 K, while T* remains almost constant.

Figure 3. Phase diagram between ordering temperature and doping amount (x) for Ho_1-xDy_xB₂. The blue filled circles show the evolution of T_C while the orange triangles show T*. While T_C increases monotonically with x, T* remains almost constant

3.3. Magnetocaloric properties

For evaluating the magnetocaloric effect of the obtained samples, M-T curves in a wide range of applied magnetic fields were measured for all samples, shown in Figure 4(a-e), and |ΔS_M| was calculated using the Maxwell relation:

$\mathrm{\Delta }{S}_M={\mu }_0{\int }_0^H\hspace{0.17em}{\left(\frac{\mathrm{\partial }M}{\mathrm{\partial }T}\right)}_{H}dH\left(1\right)$

Figure 4. M-T curves at a vast range of applied fields and obtained magnetic entropy change for Ho_1-xDy_xB₂ alloys. (a-e) The obtained M-T curves measured by ZFC process from µ₀H = 5 T to 0.01 T. (f-j) Magnetic entropy changes for Ho_1-xDy_xB₂ alloys for µ₀ΔH ranging from 1 to 5 T obtained from the M-T curves of (a-e). (k)-(o) Estimated adiabatic temperature change for Ho_1-xDy_xB₂ alloys for µ₀ΔH ranging from 1 to 5 T [21]. With the increase of Dy content, the maximum value of |ΔS_M| decreases from 0.35 J cm⁻³ K⁻¹ (x = 0) to 0.16 J cm⁻³ K⁻¹ (x = 1.0)

The obtained |ΔS_M| for fields up to 5 T is shown in Figure 4(f-j).

Due to the presence of the two transitions at T* and T_C, two peaks appear at |ΔS_M|. Therefore, here we will define and compare the maximum entropy change |ΔS_M^MAX| as |ΔS_M(T = T_C)|, since T* remains almost unchanged during the whole doping range and is always lower than 15 K while we are interested in the |ΔS_M| peak shifted toward higher temperature by Dy doping. In this way, the obtained values of |ΔS_M^MAX| for µ₀ΔH = 5 T were 0.35, 0.3, 0.18, 0.16 and 0.15 J cm⁻³ K⁻¹ for x = 0, 0.3, 0.5, 0.7 and 1.0, respectively.

In addition to the change in the magnitude of |ΔS_M^MAX|, an interesting characteristic appears in the |ΔS_M| curves of Ho_1-xDy_xB₂. That is, since there are multiple transitions in this series of alloys, even though there is a net loss at |ΔS_M^MAX|, the entropy change curve shows an increase of δT_FWHM, defined as the region in the entropy curve where |ΔS_M| ≥ |ΔS_M^MAX|/2, leading to a gain in maximum entropy change for higher temperature spans. Such a widening of the |ΔS_M| curves due to multiple transitions has been commonly observed in materials that show more than one magnetic transition [16–18] and it tends to lead to a high figure of merits. The |ΔS_M| for all samples for a field change of μ₀ΔH = 5 T is shown in Figure 5.

Figure 5. |ΔS_M| at µ₀ΔH = 5 T for Ho_1-xDy_xB₂ alloys

Another important property in the magnetocaloric performance of materials is the adiabatic temperature change ΔT_ad. Here, we estimated the S(T, H) (shown in Figure S1.) curves by first calculating the zero-field entropy from specific heat data (not shown here) and then we obtain the field-dependent entropy by subtracting the values of |ΔS_M| to the zero-field entropy, in the same manner as Refs. [5,19]. For the x = 0, we used the previously reported data of Ref [5]., and for the x = 1 sample, we used the previously reported zero-field specific heat data of Ref [20]. Then, the ΔT_ads is estimated by taking the horizontal difference between the entropy curves under zero field and final field [21] and the results are shown in Figure 4(k-o). Interestingly, the two-peak structure of |ΔS_M| is also reflected in ΔT_ad and thus these alloys tend to show high ΔT_ad in relatively wide temperature range, that is an important characteristic for practical applications [22]. Here we estimated ΔT_ad^MAX in the same way as |ΔS_M^MAX|, that is, ΔT_ad^MAX = ΔT_ad (T = T_C). The obtained ΔT_ad^MAX is 12 K, 11.5 K, 8.6 K, 8.0 K and 7.2 K for x = 0, 0.3, 0.5, 0.7 and 1.0, respectively for µ₀ΔH = 5 T.

Let us compare the magnetocaloric properties in Ho_1-xDy_xB₂ with those of representative materials that often show prominent magnetocaloric effect with transition temperatures ranging up to 77 K, based on Figure S5 of Ref [5]. Here we consider ΔS_M, ΔT_ad, and Temperature averaged Entropy Curve (TEC) as a practical figure of merit proposed earlier [23]. The last value is defined as:

$TEC\left(\mathrm{\Delta }{T}_{lift}\right)=\frac{1}{\mathrm{\Delta }{T}_{lift}}\underset{T_{mid}}{max}{\int }_{T_{mid}-\frac{\mathrm{\Delta }{T}_{lift}}{2}}^{T_{mid}+\frac{\mathrm{\Delta }{T}_{lift}}{2}}\mathrm{\Delta }{S}_{M}dT$

Where T_mid is chosen to maximize the value of TEC in a given working temperature range of a material (ΔT_lift) (Conventional figure of merits such as refrigerant capacity and relative cooling power are also tabulated in supplementary information).

For this purpose, the values of entropy change of the materials for comparison are converted into volumetric units by using the density contained in the AtomWork [24] database, unless otherwise provided by the authors. Also, the values of TEC (10) and TEC (20) are estimated from the reported entropy curves within the contained references when not reported by the authors. We show the obtained values for |ΔS_M^MAX|, |ΔT_ad^MAX_|, TEC (10), and TEC (20) in Figure 6(a-d). Also, the ΔT_lift-dependence of TEC in selected materials is shown in Figure 6(e).

Figure 6. Maximum entropy and adiabatic temperature change and TEC values for Ho_1-xDy_xB₂ alloys and diverse compounds for µ₀ΔH = 5 T. (a) |ΔS_M^MAX| and (b) |ΔT_ad^MAX| as a function of the magnetic ordering temperature T_mag. (c) Values of TEC for ΔT_lift = 10 K and (d) for ΔT_lift = 20 K. (e) TEC as a function of ΔT_lift for few representative materials with high TEC 10 values. The normal and dashed lines guide for the eyes. The TEC values were obtained by using the reported entropy curves within each material reference

In the temperature range of 15–20 K, HoB₂ and Ho_0.7Dy_0.3B₂ show superior |ΔS_M^MAX| and ΔT_ad^MAX for µ₀ΔH = 5 T, when compared to compounds with similar T_mag such as ErAl₂ [25], TmGa [26], EuS [27], HoN [28,29], DyNi₂ [25] and Ho₂Au₂In [30]. For the materials with transition temperatures around 30 K, even though Ho_0.5Dy_0.5B₂ shows similar |ΔS_M^MAX| to Ho₂Cu₂Cd [18] and ErGa [31], it has a comparable |ΔT_ad^MAX| to HoAl₂ [32] and ErCo₂ [33]. Similarly, Ho_0.3Dy_0.7B₂ has almost the same |ΔS_M^MAX| as HoNi [34,35], however with a much larger |ΔT_ad^MAX|. In the case of DyB₂, even though it shows almost half of |ΔS_M| compared to Gd₃Ru [36], its |ΔT_ad^MAX| is higher and comparable to DyAl₂ [37], although both of them are lower than Er_0.53Ho_0.47Co₂ [38,39]. Furthermore, the TEC in Ho_1-xDy_xB₂ alloys tends to be relatively robust for a higher value of ΔT_lift, due to the multiple transition nature in these materials. This suggests that Ho_1-xDy_xB₂ alloys could support a wide temperature span while keeping the figure of merit and indicate that Ho_1-xDy_xB₂ alloys might be an option for use in magnetic refrigeration ranging from 10 to 60 K as similar materials with T_mag within this range.

4. Conclusions

In this work, we have systematically evaluated the effects of Dy substitution on the giant magnetocaloric effect of HoB₂. Even if there is a net loss in the peak value of the |ΔS_M|, the observed two-peak structure in both the magnetic entropy and adiabatic temperature change might indicate these materials could possibly sustain a large working temperature range based on the figure of merit analysis. Therefore, these alloys could be an option to work as magnetic refrigerants in the temperature range from 10 to 60 K.

Acknowledgments

We acknowledge fruitful discussions with Mohammed Elmassalami and Akiko T. Saito. This work was partly supported by the JST-Mirai Program “Development of advanced hydrogen liquefaction system by using magnetic refrigeration technology”, the JSPS KAKENHI, and the JST-CREST. P.B. Castro acknowledges the scholarship support from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Disclosure statement

The authors declare no conflict of interest.

Supplemental Material

Supplemental data for this article can be accessed here

Additional information

Funding

This work was supported by the JST-Mirai Program (Grant No. JPMJMI18A3), JSPS KAKENHI (Grant Nos. 19H02177, 20K05070), JST CREST (Grant No. JPMJCR20Q4).