Single-crystal growth and magnetic phase diagram of the enantiopure crystal of ${\mathrm{NdPt}}_2\mathrm{B}$

We report on the enantiopure single-crystal growth using the Czochralski method and the magnetic properties of the Nd-based monoaxial chiral magnet ${\mathrm{NdPt}}_2\mathrm{B}$ based on electrical resistivity, specific heat, and magnetization measurements. A peak in the magnetic susceptibility and a $\lambda$-type anomaly in the specific heat are observed at $T_{\mathrm{N}1}=19.5\mathrm{K}$. Successively, a first-order magnetic transition at $T_{\mathrm{m}}=9.5\mathrm{K}$ is observed in the electrical resistivity, specific heat, and magnetic susceptibility. In addition, we observed a new magnetic phase transition, which has previously not been reported, at $T_{\mathrm{N}2}=11\mathrm{K}$ between $T_{\mathrm{N}1}$ and $T_{\mathrm{m}}$. We observed multiple plateaus in the low-temperature magnetic phase and constructed a nontrivial magnetic phase diagram, which results from the competitive interactions in this system. Furthermore, we observed an increase and decrease in the in-plane anisotropy in the transverse magnetoresistance, which is related to the change in the magnetic structure.

Figure 1

(a) Unit cell of left-handed (space group: $P{6}_{4}22$) ${\mathrm{NdPt}}_2\mathrm{B}$. Crystal structures were constructed using the vesta [18]. (b) Projection of the crystal structure of ${\mathrm{NdPt}}_2\mathrm{B}$ on the basal plane. The anticlockwise notation in red indicates the chirality of the Nd atoms. (c) Side view of the crystal structure of ${\mathrm{NdPt}}_2\mathrm{B}$. (d) Grown single crystal of ${\mathrm{NdPt}}_2\mathrm{B}$. (e) Cleaved single crystals of ${\mathrm{NdPt}}_2\mathrm{B}$. The arrows indicate the points measured using single-crystal XRD. (f) Laue photograph of ${\mathrm{NdPt}}_2\mathrm{B}$ single crystal.

Figure 2

X-ray diffraction ($\mathrm{Cu}{K}_{\alpha }$) powder pattern of powdered ${\mathrm{NdPt}}_2\mathrm{B}$ single crystals. The blue open circles represent the experimental data, while the red solid line is derived from the Rietveld refinement. The purple solid line shows the intensity difference between the experimental data and Rietveld calculations. The estimated background and Bragg peak positions are indicated by the solid green line and bars. $R_{\mathrm{wp}}$ is the weighted-profile $R$ factor.

Figure 3

(a) Temperature dependence of electrical resistivity $\rho$ of the ${\mathrm{NdPt}}_2\mathrm{B}$ single crystal for $J\parallel a$ (red circles) and $\parallel c$ (blue triangles) below 25 K. The black solid line corresponds to the curve fitted using the expression $\rho \left(T\right)={\rho }_0+A{T}^2$. The red dashed-dotted and green dashed lines are the curves fitted considering magnetic contributions ${\rho }_{\mathrm{FM}}\left(T\right)$ and ${\rho }_{\mathrm{AFM}}\left(T\right)$, respectively (see text for details). The inset shows the $\rho \left(T\right)$ from room temperature to 1.7 K. (b) Field dependence of $\rho$ at $T=0.5$, 0.8, 1.7, and 5.0 K up to ${\mu }_{0}H=2$ T. The anomalies in $\rho \left(H\right)$ are indicated by blue arrows for the data measured at 5 K.

Figure 4

(a) Temperature dependence of specific heat $C$ in a zero field and in constant magnetic fields of ${\mu }_{0}H=0.5$, 1.0, and 1.5 T for $H\parallel a$. The specific heat data are shifted vertically by 10 J/(K mole) for clarity. (b) Field dependence of $C$ measured at various temperatures for $H\parallel a$. The inset shows an enlarged view of $C$ vs. ${\mu }_{0}H$ in the low magnetic field range at $T=4$ and 5 K.

Figure 5

(a) Magnetization curves of ${\mathrm{NdPt}}_2\mathrm{B}$ measured at 2 K for $H\parallel a$ (red), $H\parallel c$ (blue), and the $H\perp ac$ plane (orange). (b) Magnetization curves of ${\mathrm{NdPt}}_2\mathrm{B}$ measured at various temperatures for $H\parallel a$ (left axis). The field derivative of magnetization $dM/d\left({\mu }_{0}H\right)$ is also shown on the right axis as a function of the field at 2 K. (c) Temperature dependence of the magnetic susceptibility $M/H$ of ${\mathrm{NdPt}}_2\mathrm{B}$ measured at 0.05 T for $H\parallel a$ (red circles, left axis) and $H\parallel c$ (blue squares, right axis) in ZFC condition. The inset shows the temperature dependence of the inverse susceptibility $1/\chi$ for $H\parallel a$. The blue solid line represents a least-squares fit obtained with the modified Curie–Weiss law for ${\mathrm{NdPt}}_2\mathrm{B}$ in the paramagnetic region. (d) Magnetic susceptibility $M/H$ of ${\mathrm{NdPt}}_2\mathrm{B}$ in different magnetic fields of 0.05, 0.2, 0.5, 1, and 2 T for $H\parallel a$ as a function of the logarithmic temperature. The magnetic susceptibility data are shifted vertically by 0.6 emu/mole.

Figure 6

Magnetic field-temperature phase diagram of ${\mathrm{NdPt}}_2\mathrm{B}$ (a) for $H\parallel a$ and (b) the $H\perp ac$ plane. PM, AFM, and PPM correspond to the paramagnetic, antiferromagnetic, and polarized paramagnetic states, respectively. The solid line is guide to the eyes. The red line shows the first-order transition at $T_{\mathrm{m}}$ for $H\parallel a$. (c) Schematic sample configuration for the magnetoresistance measurements. [(d)–(h)] Polar plots of the transverse magnetoresistance for the electrical current $J\parallel c$ in the low-temperature MO and PPM states at 1.7 K. The measurement conditions ($T$ and $H$) for the transverse magnetoresistance are indicated by yellow markers in the $H\text{−}T$ phase diagram of the $H\perp ac$ plane.

Figure 7

(a) X-ray diffraction pattern of powdered ${\mathrm{NdPt}}_2\mathrm{B}$ single crystals and the polycrystal. (b) Temperature dependence of the magnetic susceptibility $M/H$ of the ${\mathrm{NdPt}}_2\mathrm{B}$ single crystal ($H\parallel a$) and polycrystal measured at 0.05 T.

Figure 8

Plot of observed squared structure factors ${\langle F_{\mathrm{obs}}\rangle }^2$ of ${\mathrm{NdPt}}_2\mathrm{B}$ single crystal as a function of calculated squared structure factors ${\langle F_{\mathrm{calc}}\rangle }^2$ using logarithmic scale using space groups $P{6}_{2}22$ (red open squares) and $P{6}_{4}22$ (blue closed squares).