#
Giant Rotational Magnetocaloric Effect in Ni(en)(H_{2}O)_{4}·2H_{2}O: Experiment and Theory

^{*}

## Abstract

**:**

_{2}O)

_{4}SO

_{4}∙2H

_{2}O (en = ethylenediamine) single crystal is presented. The study was carried out at temperatures above 2 K and was associated with adiabatic crystal rotation between the easy plane and hard axis in magnetic fields up to 7 T. The magnetocaloric properties of the studied system were investigated by isothermal magnetization measurement. The experimental observations were completed with ab initio calculations of the anisotropy parameters. A large rotational magnetic entropy change ≈12 Jkg

^{−1}K

^{−1}and ≈16.9 Jkg

^{−1}K

^{−1}was achieved in 5 T and 7 T, respectively. The present study suggests a possible application of this material in low-temperature refrigeration since the adiabatic rotation of the single crystal in 7 T led to a cooldown of the sample from the initial temperature of 4.2 K down to 0.34 K. Finally, theoretical calculations show that S = 1 Ni(II)-based systems with easy-plane anisotropy can have better rotational magnetocaloric properties than costly materials containing rare-earth elements in their chemical structures.

## 1. Introduction

_{M}) and the adiabatic temperature change (ΔT

_{ad}) [4,10]. The mentioned parameters are influenced by the magnitude of external magnetic field change. Obviously, the efficient magnetic refrigerants for active MCE should have the given parameters in the relevant temperature and magnetic field ranges as large as possible. Designing materials with a large density of magnetic ions while keeping magnetic coupling weak [11,12] as well as tailoring critical behavior [13] have become conventional approaches in tuning magnetocaloric properties. Alternatively, properties of spin liquids in quantum spin chains [14] and localized excitations in geometrically frustrated magnets proved an enhanced magnetocaloric effect in these systems.

_{R}. A large value of ΔS

_{R}causes a significant temperature change during the rotation of the sample, and therefore the presence of the magnetic anisotropy of the system is a necessary condition for the observation of a large rotational MCE. It is important to note that all investigated systems with large rotational MCE contained rare-earth elements in their chemical structures. However, the single crystal preparation of these materials is money-, time-, and energy-consuming. For this reason, the given materials may not meet the important criteria for selecting appropriate magnetic refrigerants. It should be noted that the magnetocaloric properties of financially affordable S = 1 Ni(II)-based systems have been studied. Their properties can be tuned by magnetic dimensionality, exchange coupling, and single-ion anisotropy [28,29,30]. If the S = 1 Ni(II)-based systems are described within a model of a spin-1 paramagnet in a crystal field with a spin Hamiltonian $H=D{S}_{z}^{2}+E\left({S}_{x}^{2}-{S}_{y}^{2}\right)$, where D and E represent uniaxial and in-plane anisotropy parameters, respectively, an inverse MCE can be observed for the easy-plane anisotropy [31]. Thus, considering the combination of normal and inverse MCE, a large rotational MCE can be expected, comparable to the rotational MCE observed in materials containing rare-earth elements in their chemical structures.

_{2}O)

_{4}SO

_{4}∙2H

_{2}O (en = ethylenediamine) (NEHS) has been identified as a spin-1 paramagnet with the nonmagnetic ground state introduced by the easy-plane anisotropy D/k

_{B}= 11.6 K with E/D = 0.1 and negligible exchange interactions J ≈ 0 [32]. Analysis of the specific heat in zero magnetic field indicated the absence of a phase transition to a magnetically ordered state below 1.8 K as a direct consequence of the dominant influence of the crystal field on the magnetic properties of the studied system.

## 2. Materials and Methods

_{2}O)

_{4}]

^{2+}cations, [SO

_{4}]

^{2−}anions, and two molecules of water. These units are connected by a large number of hydrogen bonds [33]. NEHS single crystals were prepared in the form of blue prisms from an aqueous solution of nickel sulphate and en in stoichiometric amounts.

^{3}was used (Figure 1).

## 3. Results

_{2}O)

_{4}]

^{2+}cation using atom positions as obtained from X-ray diffraction. The SA-CASSCF/NEVPT2 calculations yielded crystal field parameters D/k

_{B}= 11.5 K, E/D = 0.07 with an average g-factor g = 2.22. This result is in excellent agreement with the values obtained from the analysis of the heat capacity in the zero magnetic field [32]. The crystal structure of a [Ni(en)(H

_{2}O)

_{4}]

^{2+}cation with the schematic orientation of the equatorial plane of the octahedron and local anisotropy axes predicted by SA-CASSCF/NEVPT2 calculations is shown in Figure 2. It can be seen that the local anisotropy Z-axis is parallel to the direction of the bond between the nickel ion and oxygen, which corresponds to the axis of the octahedron. On the other hand, the local anisotropy axes X and Y are located within the equatorial plane of the octahedron, with the X-axis passing along the bisector axis of the oxygen–nickel–oxygen angle while the Y-axis is oriented along the bisector axis of the oxygen–nickel–nitrogen angle.

_{i}− B

_{f}, while B

_{f}and B

_{i}stand for the final and initial magnetic fields, respectively. Due to the real conditions of the experiment, relation (1) can be replaced by:

_{j}

_{+1}and M

_{j}are the magnetization values measured in the magnetic field B at temperatures T

_{j}

_{+1}and T

_{j}, respectively. The temperature dependence of the magnetic entropy change (Equation (2)) calculated for several B

_{f}values and B

_{i}= 0 T for the orientations B || Y and B || Z is shown in Figure 4. It can be seen that the normal MCE has been observed for the orientation B || Y in a whole range of temperatures and magnetic fields. The maximum value of –ΔS

_{M}is shifted towards high temperatures with increasing magnetic fields. A large magnetocaloric effect is observed around 6 K (−ΔS

_{max}= 10.9 Jkg

^{−1}K

^{−1}for 7 T). However, an interesting situation is observed in the temperature dependence of –ΔS

_{M}for the orientation B || Z. Approximately below 7 K, an inverse magnetocaloric effect is observed for all magnetic field values, with −ΔS

_{M}decreasing with increasing magnetic field. On the other hand, the temperature dependence of −ΔS

_{M}above 7 K has a similar tendency as the data in the orientation B || Y. Large inverse magnetocaloric effect is observed around 2 K (−ΔS

_{max}= −14.5 Jkg

^{−1}K

^{−1}for 7 T). Further analysis of the experimental data was performed using the model of the S = 1 paramagnet, including single-ion anisotropy with D/k

_{B}= 11.6 K, E/D = 0.1, and g = 2.16 as obtained from the previous analysis of specific heat and susceptibility [32]. Corresponding theoretical prediction of the temperature dependence of −ΔS

_{M}for both field orientations is in excellent agreement with experimental data (Figure 4).

**Figure 4.**Temperature dependence of the isothermal entropy change in NEHS at different magnetic fields for B || Y (

**a**) and B || Z (

**b**). Symbols represent –ΔS

_{M}values obtained from experimental magnetization curves; solid lines represent –ΔS

_{M}values calculated for the S = 1 paramagnet with E/D = 0.1, D/k

_{B}= 11.6 K and g = 2.16.

**Figure 5.**Isothermal entropy changes resulting from the rotation of NEHS single crystal between the Y and Z axes in constant magnetic fields (symbols). Lines represent –ΔS

_{R}values calculated for the S = 1 paramagnet with E/D = 0.1, D/k

_{B}= 11.6 K and g = 2.16. Inset: Field dependence of −ΔS

_{R,max}.

_{R,max}increases with increasing magnetic field and is shifted to lower temperatures. However, high values, −ΔS

_{R}≈ 12 Jkg

^{−1}K

^{−1}and −ΔS

_{R}≈ 16.9 Jkg

^{−1}K

^{−1}, are achieved in 5 T and 7 T, respectively. It should be mentioned again that the temperature dependence of −ΔS

_{R}is in excellent agreement with the theoretical prediction.

_{ad,R}, associated with sample rotation in constant magnetic field from the initial sample position B || Y to the position B || Z under adiabatic conditions. The total entropy in the zero magnetic field was calculated from the experimental specific heat data from Ref. [32]. The temperature dependence of the total entropy in different magnetic fields for both orientations was calculated as the difference between the total entropy of NEHS in zero magnetic field and the absolute values of ΔS

_{M}obtained from experimental magnetization curves (Figure 6). The unavailable experimental d of the total entropy in magnetic fields below 2 K for B || Z were approximated with the model of total entropy for the S = 1 paramagnet with E/D = 0.1, D/k

_{B}= 11.6 K, g = 2.16 with included lattice entropy of NEHS taken from Ref. [32]. It can be seen that the mentioned model perfectly describes the experimental d of the total entropy in magnetic fields for B || Z.

_{ad,R}, calculated from the total entropy, is shown in Figure 7. The maximal value of −ΔT

_{ad,R}is shifted to higher temperatures with an increasing magnetic field. Rotation of the crystal from position B || Y to position B || Z in 5 T and 7 T at the initial temperature of 6.5 K and 8.4 K leads to −ΔT

_{ad,R}≈ 3.55 K and 6.95 K, respectively. If the initial temperature of 4.2 K is considered, the rotation of the crystal in conditions mentioned above in 5 and 7 T leads to cooling of the samples to 1.4 K and 0.34 K, respectively, which suggests the applicability of this material in low-temperature refrigeration. Examples of conventional and rotational magnetocaloric properties of selected magnetic refrigerants compared with the studied system NEHS are given in Table 1. One can conclude that NEHS is not a very suitable material in conventional magnetocaloric applications; however, in rotational MCE it is competitive with expensive materials containing rare-earth metal ions.

_{B}= 11.6 K and E/D = 0.1. For this system, there is a critical value of the magnetic field B

_{c}equal to $\sqrt{\left({D}^{2}-{E}^{2}\right)}/\left(g{\mu}_{B}\right)$ when the energy levels cross, and the character of the ground state changes. For the description of the rotational magnetocaloric effect of the S = 1 paramagnet with easy-plane anisotropy, the temperature dependence of the isothermal entropy change was calculated for magnetic fields applied parallel and perpendicular to the easy plane. For simplicity, only parameter D was considered. It can be seen (Figure 8a) that the normal MCE is observed for orientation B || easy plane in the whole range of temperatures and magnetic fields. The maximum value of −ΔS

_{M}is shifted towards low temperatures with decreasing magnetic field. Different behavior is observed for magnetic fields parallel to the hard axis. For temperatures k

_{B}T/D < 0.5, an inverse magnetocaloric effect is observed for all considered magnetic field values, while the –ΔS

_{M}acquires the maximum value equal to ≈−5.76 Jmol

^{−1}K

^{−1}in the critical magnetic field. However, the magnitude of the inverse magnetocaloric effect begins to decrease with magnetic fields above B

_{c}at temperatures below k

_{B}T/D ≈ 0.5. Normal MCE is observed at temperatures above k

_{B}T/D ≈ 0.5 for all values of the magnetic field, while −ΔS

_{M}is larger with the increasing magnetic field. The resulting isothermal rotational entropy change for the mentioned model is shown in Figure 8b. The largest rotational MCE is observed in the critical magnetic field, −ΔS

_{R}≈ 5.76 Jmol

^{−1}K

^{−1}, at temperatures below k

_{B}T/D ≈ 0.15. In higher magnetic fields exceeding B

_{c}, the isothermal rotational entropy change decreases and the maximum of −ΔS

_{R}is shifted to higher temperatures.

_{c}≈ 7.95 T. The theoretical prediction of the temperature dependence of the adiabatic temperature change −ΔT

_{ad,R}for this magnetic field value was calculated, as depicted in Figure 7. Apparently, in the critical field the −ΔT

_{ad,R}reaches a maximum at T = 9.7 K and −ΔT

_{ad,R}≈ 9.5 K. At liquid helium temperatures (i.e., the initial temperature of 4.2 K), the rotation leads to −ΔT

_{ad,R}≈ 4.18 K, suggesting the applicability of this material in low-temperature cooling at the critical magnetic field.

_{c}. If B

_{c}is equal to 1, 2, 3, 4, 5, or 6 T, the parameter D/k

_{B}must be equal to 1.45, 2.90, 4.35, 5.81, 7.26, and 8.71 K, respectively, to achieve a similar effect for spin-1 systems with easy-plane anisotropy (neglecting in-plane anisotropy parameter E).

**Figure 9.**Theoretical prediction of an adiabatic temperature change as a function of the initial temperature, i.e., cooling of the S = 1 paramagnet with the stated values of single-ion anisotropy and g = 2.16 during the adiabatic rotation from the easy plane to the hard axis in the constant critical magnetic fields. The lattice specific heat of NEHS was considered in the calculations.

_{ad,R}shift to higher temperatures with increasing critical magnetic fields, and the rotation leads to −ΔT

_{ad,R}≈ 4.18 K at an initial temperature of 4.2 K for critical magnetic fields higher than 3 T.

_{R}= 26.7 Jkg

^{−1}K

^{−1}[51]. Theoretical calculations show that the same value of rotational magnetic entropy change in the magnetic field of 5 T has a spin-1 magnet with a nonmagnetic ground state introduced by easy-plane anisotropy with D/k

_{B}= 7.26 K and with a molecular mass of 215.73 g.mol

^{−1}. Such theoretical estimates could help find financially affordable S = 1 Ni(II)-based systems with better magnetocaloric properties than materials containing rare-earth elements in their chemical structures.

## 4. Conclusions

_{2}O)

_{4}SO

_{4}∙2H

_{2}O single crystal at temperatures above 2 K, associated with adiabatic crystal rotation between the easy plane and hard axis in magnetic fields up to 7 T. The magnetocaloric properties of the studied system were investigated by isothermal magnetization measurement. The experimental observations were completed with ab initio calculations of the anisotropy parameters. The calculations enabled determination of the single-ion anisotropy parameters together with the orientations of local anisotropy axes of Ni(II) ions. The calculated values of the single-ion anisotropy parameters are in excellent agreement with the values obtained from previous analysis of heat capacity. A large rotational magnetic entropy change ≈12 Jkg

^{−1}K

^{−1}and ≈16.9 Jkg

^{−1}K

^{−1}was achieved in 5 and 7 T, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A photograph of the NEHS single crystal glued to a quartz holder for the orientation B || Z with a schematic illustration of the direction of the local anisotropy and crystallographic axes.

**Figure 2.**The crystal structure of [Ni(en)(H

_{2}O)

_{4}]

^{2+}cation in NEHS with the schematic orientation of the equatorial plane of the octahedron and local anisotropy axes determined by ORCA calculations.

**Figure 3.**Magnetic-field dependence of the magnetization of NEHS for B || Y (

**a**) and B || Z (

**b**,

**c**), temperature steps ΔT = 0.5 K and 1 K for intervals 2–10 and 11–20 K, respectively.

**Figure 6.**Temperature dependence of the total (i.e., magnetic and lattice) entropy in NEHS at different magnetic fields for B || Y (

**a**) and B || Z (

**b**). Symbols represent the total entropy calculated as the difference between the total entropy of NEHS in zero magnetic field (calculated from the experimental specific heat) and the absolute values of ΔS

_{M}obtained from experimental magnetization curves. Lines represent the total entropy for the S = 1 paramagnet with E/D = 0.1, D/k

_{B}= 11.6 K, g = 2.16 with included lattice entropy of NEHS. Inset: Temperature dependence of specific heat of NEHS in zero magnetic field taken from Ref. [32].

**Figure 7.**Adiabatic temperature change as a function of the initial temperature, i.e., cooling NEHS single crystal during the adiabatic rotation from the position B || Y to the orientation B || Z in the constant magnetic fields (symbols). Lines represent the results of the extrapolation of total entropy data for orientation B || Z below 2 K. The dashed line represents the theoretical prediction of the adiabatic temperature change in the mentioned rotation conditions for NEHS single crystal in the critical magnetic field B

_{c}(see text below).

**Figure 8.**(

**a**)Temperature dependence of the isothermal entropy change for the S = 1 paramagnet with easy-plane anisotropy for B || easy plane (dotted lines) and B || Z (solid lines) at different magnetic fields; (

**b**) isothermal entropy changes resulting from the rotation of S = 1 paramagnet with easy-plane anisotropy between the easy plane and hard axis in constant magnetic fields. The critical magnetic field B

_{c}was calculated using relation B

_{c}= D/(gμ

_{B}).

**Table 1.**Examples of conventional and rotational magnetocaloric properties of selected potential refrigerants.

System | −ΔS_{M}^{max} (Jkg^{−}^{1}K^{−}^{1}) | −ΔS_{M}^{R} (Jkg^{−}^{1}K^{−}^{1}) | References | ||
---|---|---|---|---|---|

B = 5 T | B = 7 T | B = 5 T | B = 7 T | ||

Ni(en)(H_{2}O)_{4}SO_{4}∙2H_{2}O | 7.6, −8 | 10.9, −14.5 | 12 | 16.9 | This work |

HoNiGe_{3} | 13.9 | ≈16 | 12.3 | ≈13 | [23] |

NdGa | - | 21.1 | - | 16.6 | [22] |

Tb_{2}CoMnO_{6} | −7.5 | -17.3 | 20.8 | 20.5 | [21] |

h-ErMnO_{3} | 20.5 | 22.7 | 17 | 20 | [20] |

o-DyMnO_{3} | 14.6 | 17.25 | 14.2 | 16.3 | [19] |

HoMn_{2}O_{5} | 10 | 13.1 | 10 | 12.43 | [18] |

TbMn_{2}O_{5} | 12.35 | 13.35 | ≈12 | 13.14 | [17] |

GdVO_{4} | ≈44 | 56.03 | ≈8 | 10.1 | [16] |

DyScO_{3} | 21.18 | 21.91 | 21.61 | 22.41 | [15] |

TbScO_{3} | 23.71 | 24.71 | 23.63 | 24.58 | [50] |

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**MDPI and ACS Style**

Danylchenko, P.; Tarasenko, R.; Čižmár, E.; Tkáč, V.; Feher, A.; Orendáčová, A.; Orendáč, M.
Giant Rotational Magnetocaloric Effect in Ni(*en*)(H_{2}O)_{4}·2H_{2}O: Experiment and Theory. *Magnetochemistry* **2022**, *8*, 39.
https://doi.org/10.3390/magnetochemistry8040039

**AMA Style**

Danylchenko P, Tarasenko R, Čižmár E, Tkáč V, Feher A, Orendáčová A, Orendáč M.
Giant Rotational Magnetocaloric Effect in Ni(*en*)(H_{2}O)_{4}·2H_{2}O: Experiment and Theory. *Magnetochemistry*. 2022; 8(4):39.
https://doi.org/10.3390/magnetochemistry8040039

**Chicago/Turabian Style**

Danylchenko, Petro, Róbert Tarasenko, Erik Čižmár, Vladimír Tkáč, Alexander Feher, Alžbeta Orendáčová, and Martin Orendáč.
2022. "Giant Rotational Magnetocaloric Effect in Ni(*en*)(H_{2}O)_{4}·2H_{2}O: Experiment and Theory" *Magnetochemistry* 8, no. 4: 39.
https://doi.org/10.3390/magnetochemistry8040039