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 Ho1-xDyxB2 alloys (x = 0, 0.3, 0.5, 0.7, 1.0). We find that the Curie temperature (TC) gradually increases upon Dy substitution, while the magnitude of the magnetic entropy change |ΔSM| and adiabatic temperature change ΔTad 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.


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][2][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 μ 0 ΔH = 5 T in HoB 2 [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 HoB 2 to a higher temperature is of extreme interest to examine HoB 2 -based materials as possible candidates for refrigeration before the liquefaction stage, especially below temperatures of 77 K. DyB 2 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 μ 0 ΔH = 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-x Dy x B 2 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.

Sample synthesis
Polycrystalline samples of Ho 1-x Dy x B 2 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.

Characterization
Powder X-ray diffraction (XRD) patterns of the arcmelted 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.

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). Zerofield 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.

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 AlB 2 type crystal structure as shown by the red fitting curves. The remaining peaks are assigned as REB 4, unreacted RE or RE 2 O 3 (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.
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/a 0 and c/c 0 ) by the value of x = 0. Both c/c 0 and a/a 0 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-x Dy x B 2 suggest that the substitution of Ho by Dy in the REB 2 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-x Si 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-x Dy x B 2 and HoB 2-x Si x implies that the a-axis and c-axis lengths in HoB 2 -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 rareearth and B-site atoms, while the a-axis length might be more dependent on the B site atom.

Magnetic properties
The ZFC-FC isofield magnetization (M-T) curves for an applied field of µ o H = 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 endmaterial DyB 2 .
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 HoB 2 at T* = 11 K [5] and DyB 2 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.

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: The obtained |ΔS M | for fields up to 5 T is shown in Figure 4(f-j).  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][17][18] and it tends to lead to a high figure of merits. The |ΔS M | for all samples for a field change of μ 0 ΔH = 5 T is shown in Figure 5.
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 ad s 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 µ 0 ΔH = 5 T.
Let us compare the magnetocaloric properties in Ho 1-x Dy x B 2 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:

ΔS 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 liftdependence of TEC in selected materials is shown in Figure 6(e).
In the temperature range of 15-20 K, HoB 2 and Ho 0.7 Dy 0.3 B 2 show superior |ΔS M MAX | and ΔT ad MAX for µ 0 ΔH = 5 T, when compared to compounds with similar T mag such as ErAl 2 [25], TmGa [26], EuS [27], HoN [28,29], DyNi 2 [25] and Ho 2 Au 2 In [30]. For the materials with transition temperatures around 30 K, even though Ho 0.5 Dy 0.5 B 2 shows similar |ΔS M MAX | to Ho 2 Cu 2 Cd [18] and ErGa [31], it has a comparable |ΔT ad MAX | to HoAl 2 [32] and ErCo 2 [33]. Similarly, Ho 0.3 Dy 0.7 B 2 has almost the same |ΔS M MAX | as HoNi [34,35], however with a much larger |ΔT ad MAX |. In the case of DyB 2 , even though it shows almost half of |ΔS M | compared to Gd 3 Ru [36], its |ΔT ad MAX | is higher and comparable to DyAl 2 [37], although both of them are lower than Er 0.53 Ho 0.47 Co 2 [38,39]. Furthermore, the TEC in Ho 1-x Dy x B 2 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-x Dy x B 2 alloys could support a wide temperature span while keeping the figure of merit and indicate that Ho 1-x Dy x B 2 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.

Conclusions
In this work, we have systematically evaluated the effects of Dy substitution on the giant magnetocaloric effect of HoB 2 . 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.