#
Some Magnetic Properties and Magnetocaloric Effects in the High-Temperature Antiferromagnet YbCoC_{2}

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{2}compound, which crystallizes in a base-centered orthorhombic unit cell in the $Amm2$ space group CeNiC

_{2}structure, is unique among Yb-based compounds due to the highest magnetic ordering temperature of ${T}_{N}=27$ K. Magnetization measurements have made it possible to plot the H-T magnetic phase diagram and determine the magnetocaloric effect of this recently discovered high-temperature heavy-fermion compound, YbCoC

_{2}. YbCoC

_{2}undergoes spin transformation to the spin-polarized state through a metamagnetic transition in an external magnetic field. The transition is found to be of the first order. The dependencies of magnetic entropy change $\Delta {S}_{m}\left(T\right)$—have segments with positive and negative magnetocaloric effects for $\Delta H\le 6$ T. For $\Delta H=9$ T, the magnetocaloric effect becomes positive, with a maximum $\Delta {S}_{m}\left(T\right)$ value of 4.1 J (kg K)

^{−1}at ${T}_{N}$ and a refrigerant capacity value of 56.6 J kg

^{−1}.

## 1. Introduction

_{2}, GdNiC

_{2}, NdRhC

_{2}and PrRhC

_{2}are topological Weyl semimetals (TWS) [1]. In these compounds, the inversion symmetry and the time reversal symmetry are violated due to the noncentrosymmetric orthorhombic structure of the CeNiC

_{2}-type and the low-temperature magnetic ordering of these compounds, respectively. The unique properties of magnetic TWS can be extremely useful in the context of information technology (e.g., quantum computing), given that such massless charged particles will carry electric current without Joule heating [2]. The theory provides a clear guide to the implementation of magnetic TWS, but, so far, there are only a few experimentally confirmed examples of TWS with time-reversal symmetry breaking [3,4]. It was shown [5] that the YbCoC compound has special points with linear dispersion in the electronic band structure (see Figure 1). This allows us to consider this compound as a representative member of the class of TWS with a CeNiC

_{2}-type crystal structure.

_{2}compounds with magnetic rare-earth atoms R are ordered ferromagnetically (FM) at low temperatures [6,7,8,9]. It is believed that, in these compounds, Co ions do not have a magnetic moment, and the Ruderman–Kittel–Kasuya–Yosida exchange interaction makes a significant contribution to the stabilization of magnetism [10].

_{2}, ErCoC

_{2}[11] and TbCoC

_{2}[12] and giant reversible MCEs in TWS GdCoC

_{2}[13] have been observed using such measurements.

_{2}($\gamma $ = 190 mJ/mol-K

^{2}) has an antiferromagnetic (AFM) transition at ${T}_{\mathrm{N}}$ = 27 K, which is the highest temperature among the Yb-based magnetic compounds known to date. The magnetic structure of YbCoC

_{2}in a zero magnetic field at T = 1.3–27 K is a sine-modulated incommensurate structure with a wave vector of (0, 0, ${k}_{z}$), where ${k}_{z}$ depends on temperature: ${k}_{z}=0.28$ at ${T}_{\mathrm{N}}$ and locks-in to the value of ${k}_{0}=1/4$ below ${T}_{NC}=9$ K [5]. This simple change in the wave vector with temperature is characteristic of modulated magnetic structures [14]. At $T={T}_{NC}$, there is a rather smooth transition from a commensurate structure to an incommensurable one [5]. The amplitude of the magnetic moment of the Yb ions in a sinusoidal wave is ${\mu}_{\mathrm{Yb}}=1.32$${\mu}_{B}$ at 1.3 K, which is much less than the total magnetic moment of the free ion Yb

^{3+}($gJ=4$ ${\mu}_{B}$). This reduced value can be connected with crystal-field splitting of $j=7/2$ multiplet, Kondo screening of a magnetic moment [5,15] or some covalence in the chemical bonds between Yb and C, which leads to a strong suppression of the effective magnetic moment [16]. We roughly estimate the crystal-field splitting between the ${e}_{g}$ and ${t}_{2g}$ Co bands as occurring at 1.3 eV. The splitting of $4f$ sub-bands can be approximately assessed from the band structure near the $\Gamma $ point (see Figure 1).

_{2}compound in the field range of 0–9 T and temperature range of 2–80 K. Since YbCoC

_{2}has an AFM ground state, we can expect a richer phase diagram than that for the other RCoC

_{2}compounds with simple FM structures. Despite the well-known fact that AFM compounds usually have weak negative MCE, i.e., the material cools when a field is applied, the metamagnetic transition in YbCoC

_{2}leads to a change in the sign of the MCE.

_{2}, for example, to liquefy hydrogen, which is now actively used for various engines [19,20].

## 2. Materials and Methods

_{2}was synthesized using a high pressure–high temperature technique at $P=$ 8 GPa and $T=$ 1500–1700 K in a toroid high-pressure cell by melting the Yb, Co and C components and was characterized in Ref. [5]. The Rietveld analysis of X-ray and neutron diffraction patterns shows that the compound crystallizes in an orthorhombic structure of the CeNiC

_{2}-type (space group $Amm2$, No. 38), similar to other heavy rare-earth carbides, RCoC

_{2}. The impurity of the high-pressure phase of non-magnetic ytterbium oxied (YbO) with a fraction of less than 5 wt % was also found in the sample [5].

_{2}were performed using the WIEN2k package [21], with spin-orbit coupling taken into account. The calculations were made at the experimental lattice parameters measured in Ref. [5], with subsequent relaxation of atomic coordinates. The Yb $4f$ electrons were considered valence electrons. Comparison of our DFT-calculated band structure (Figure 1) and density of states (DOS) with the DMFT results [5] shows consistency between them in the position of bands and corresponding DOS peaks. Therefore, we believe that our DFT results sufficiently reliably describe the details of electronic structure.

## 3. Results and Discussion

#### 3.1. Magnetic Properties

_{2}obtained from the magnetization measurements (see the inset of Figure 3). ${H}_{c1}$ and ${H}_{c2}$ were determined as local maxima in $dM/dH$ vs. T (see right panel of Figure 4) and from $M\left(T\right)$ dependencies. ${H}_{c1}$ was associated with the metamagnetic transition to the intermediate magnetic phase (IM), and ${H}_{c2}$ was probably associated with the transition of YbCoC

_{2}to the FM state induced by the external magnetic field in which the magnetic unit cell has a finite value of magnetization.

^{−1}at T = 2 K, which corresponds to a magnetic moment of about 1.6 ${\mu}_{\mathrm{B}}$/f.u. This value is smaller than the saturation magnetic moment of the Yb

^{3+}ion (${m}_{s}=4.0{\mu}_{\mathrm{B}}$).

_{2}compound at $T=2$ K and at zero magnetic field is sinusoidal (see Figure 5) [5], we note that the average value of the magnetic moment of the Yb atom in, for example, the positive period of this sinusoidal structure containing 4 Yb atoms is $1.32\xb7(1+2\xb7sin(\pi /4\left)\right)$ / 4 = 0.8 ${\mu}_{B}$ / f.u. It is interesting to note that $M\left(H\right)$ for $T=2$ K reaches this value exactly at ${H}_{c1}$. The simplest explanation for this behavior of the magnetization can be the following assumption. Here, when the field is rising H = 0– ${H}_{c1}$, there is a smooth transition from sinusoidal modulation to a spin-polarized magnetic structure, which consists of the rotation of all magnetic moments along the field with the conservation of the average magnetic moment on Yb sites with an increasing field without changing their values (see Figure 5). Such a behavior of the magnetic moments, which is possible in the case of overcoming the magnetocrystalline anisotropy by the magnetic field, will give the observed dependence of the magnetization.

^{3+}(4.54 ${\mu}_{B}$).

_{2}and may be attributed to the small fraction (≈0.3 %) of magnetic impurities. A slight decrease in ${\chi}^{-1}\left(T\right)$ (see Figure 4, left panel) may also be connected with additional magnetism caused by such impurities.

#### 3.2. Magnetocaloric Effect

_{2}in low magnetic fields. The $-\Delta {S}_{m}$ minima shift towards lower temperatures with an increase in $\Delta H$, in accordance with the phase diagram (the inset of Figure 3), and the positive MCE appears at $T<10$ K for $\Delta H\ge $ 0–5 T. For $\Delta H=$ 0–9 T, a strong external magnetic field suppresses the AFM structure, MCE becomes positive in the full temperature range, and $-\Delta {S}_{m}\left(T\right)$ has a typical FM “caret-like” shape [26]. $-\Delta {S}_{m}\left(T\right)$ reaches a maximum of 4.1 J/kg-K at $T\approx 28$ K.

_{2}is rather low in comparison with the other RCoC

_{2}compounds (R = Gd, Tb, Ho, Er). This may be attributed to the lower value of the Yb magnetic moment and high magnetic fields, which are necessary to obtain the metamagnetic transition in YbCoC

_{2}. If we compare the $-\Delta {S}_{m}$ maxima for two TWS, YbCoC

_{2}and GdCoC

_{2}, we find max$(-\Delta {S}_{m})$/$Rln(2J+1)$ = 0.18 and 0.46, respectively.

## 4. Conclusions

_{2}in the range of magnetic fields 0–9 T and the temperature interval 2–30 K. It is shown that, with an increase in the external magnetic field, the metamagnetic transition of YbCoC

_{2}to the IM phase occurs, and with a further increase in the magnetic field, it goes to the FM phase. We have determined that YbCoC

_{2}exhibits a first-order transition at a metamagnetic transition below a magnetic ordering temperature of ${T}_{N}=27$ K. The magnetic structure of the IM and FM phases requires further research by means of neutron diffraction in the external magnetic field and magnetization measurements on a single crystal. The smooth transformation from the sine wave modulation to the spin-polarized magnetic structure for H = 0–${H}_{c1}$ was observed. A further increase in the magnetic field led to an increase in the average magnetic moment Yb and an additional contribution from the magnetic moment Co. No magnetic saturation of the magnetic moment was observed at 9 T and 2.0 K. A small magnetic contribution from the possible Co

^{2+}on the order of 0.3% was found and isolated. The MCE for YbCoC

_{2}has been calculated for $\Delta H$ up to 9 T. Due to the AFM–FM transition, the MCE in YbCoC

_{2}changed sign with the increase in $\Delta H$.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

TWS | topological Weyl semimetals |

FM | ferromagnetic |

MCE | magnetocaloric effect |

AFM | antiferromagnetic |

VSM | vibrating sample magnetometer |

PPMS | physical properties measurement system |

PM | paramagnetic |

IM | intermediate magnetic phase |

DFT | density functional theory |

DOS | density of states |

DMFT | dynamical mean field theory |

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**Figure 1.**The DFT band structure of YbCoC

_{2}. The narrow $4f$-Yb states with $j=7/2$ are present at the Fermi level (${E}_{\mathrm{F}}$). The thickness of the lines depicting the bands is proportional to the contribution of the Co states. The colors of the lines are to help visualization.

**Figure 2.**Isothermal magnetization dependencies $M\left(H\right)$ of YbCoC

_{2}. Inset: Arrot plots (${M}^{2}$ vs. $H/M$) for selected temperatures.

**Figure 3.**Temperature dependencies of $M/H$ measured in various external magnetic fields in field-cooled mode. Inset: Possible magnetic H-T phase diagram of YbCoC

_{2}(where AFM—antiferromagnetic phase (blue area), IM—intermediate magnetic phase corresponding to the metamagnetic phase transition (pink area) and FM—ferromagnetic phase (green area)).

**Figure 4.**Left panel: Black curve is a reciprocal magnetic susceptibility ${\chi}^{-1}$ of YbCoC

_{2}compound measured at H = 100 Oe; open circles are ${\chi}_{9}\left(T\right)$ obtained as a slope of $M\left({\mu}_{0}H\right)$ curves at 9 T at different T; solid line is a Curie–Weiss fit ${\chi}^{-1}=(T-\Theta )/C$, with $\Theta =-7.3$ K and $C=1.84$ emu K/(Oe mol). Insets a) and b): magnetization curves $M\left(H\right)$ of YbCoC

_{2}and the difference $\Delta M=M\left(H\right)-{\chi}_{9}\xb7H$ at 40, 44, 52 and 80 K, shown in the, respectively. The abscissa axes coincide on insets a) and b). Right panel: The first derivative of the original $M({\mu}_{0}H,2)$ (black) and corrected $[M({\mu}_{0}H,2)-\Delta M({\mu}_{0}H,80)]$ (red) magnetization curves at $T=2.0$ K. The vertical arrows indicate the peaks that determine the magnetic fields ${H}_{c1}$ and ${H}_{c2}$ .

**Figure 5.**Possible transformation of YbCoC

_{2}magnetic structure in the external magnetic field: from the antiferromagnetic (AFM) sine wave at zero field to the intermediate spin-polarized (IM) at $H={H}_{c1}$ (generated using the VESTA 3 software [23]). The Yb (cyan circles) and their magnetic moments (red arrows) and Co (blue) and C (brown) ions are shown.

**Figure 6.**Temperature dependencies of the magnetic entropy change $-\Delta {S}_{m}\left(T\right)$ for YbCoC

_{2}for different magnetic field changes (points — experimental data, lines — spline fits ).

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**MDPI and ACS Style**

Salamatin, D.A.; Krasnorussky, V.N.; Magnitskaya, M.V.; Semeno, A.V.; Bokov, A.V.; Velichkov, A.; Surowiec, Z.; Tsvyashchenko, A.V.
Some Magnetic Properties and Magnetocaloric Effects in the High-Temperature Antiferromagnet YbCoC_{2}. *Magnetochemistry* **2023**, *9*, 152.
https://doi.org/10.3390/magnetochemistry9060152

**AMA Style**

Salamatin DA, Krasnorussky VN, Magnitskaya MV, Semeno AV, Bokov AV, Velichkov A, Surowiec Z, Tsvyashchenko AV.
Some Magnetic Properties and Magnetocaloric Effects in the High-Temperature Antiferromagnet YbCoC_{2}. *Magnetochemistry*. 2023; 9(6):152.
https://doi.org/10.3390/magnetochemistry9060152

**Chicago/Turabian Style**

Salamatin, Denis Alexandrovich, Vladimir Nikolaevich Krasnorussky, Mariya Viktorovna Magnitskaya, Alexei Valeryevich Semeno, Alexander Vladimirovich Bokov, Atanas Velichkov, Zbigniew Surowiec, and Anatoly Vasilyevich Tsvyashchenko.
2023. "Some Magnetic Properties and Magnetocaloric Effects in the High-Temperature Antiferromagnet YbCoC_{2}" *Magnetochemistry* 9, no. 6: 152.
https://doi.org/10.3390/magnetochemistry9060152