Field-Induced Magnetic Phase Transitions and Rich Phase Diagram of HoMnO₃ Single Crystal

Abstract

An extensive magnetization study in pulsed fields up to 62 T and at temperatures down to ~0.7 K has been performed on the single crystals of hexagonal manganite HoMnO₃. For magnetic fields (H) applied along the c-axis, successive magnetic transitions below 10 T and a step-like transition at ~41 T are observed. The phase diagram for H//c is very complex and new phase boundaries are explored below 6 K. This phase diagram is compared with the early results derived from dielectric constant and neutron scattering measurements. For H//a, two magnetic transitions are found below 3 T dome-shaped and the phase diagram is reported for the first time. The variety of magnetic symmetries of the field-induced magnetic phases is discussed.

1. Introduction

Field-induced magnetic phase transition, characterized as a change in magnetization, is a long-standing issue of magnetic materials [1]. Of particular interest are the highly frustrated hexagonal (h-) manganites RMnO₃ (R = Ho-Lu, Y, Sc), which exhibit phase transitions at low temperature (T) and in the applied magnetic field (H) [2]. Among them, h-HoMnO₃ is the most studied compound due to its multiferroic property and rich H-T phase diagram [2,3,4]. Figure 1a shows the crystallographic structure of h-HoMnO₃ with magnetic ions of Mn³⁺ and Ho³⁺. The Mn³⁺ ions form triangular layers stacked along the c-axis, whereas the Ho³⁺ ions are situated at two different sites 2a and 4b between the layers. As T is lowered, h-HoMnO₃ undergoes three phase transitions at T_N = 76 K, T_SR = 32.8 K, and T_Ho = 5.4 K, respectively [2]. The phase diagram of h-HoMnO₃ for H along the c-axis is extremely complex for H < 8 T. Three magnetic ordered phases (HT1, HT2, and INT) were identified above 5 K, whereas below this temperature more phases and phase boundaries were explored by means of different experimental techniques [5,6,7,8,9,10,11]. Through dielectric constant measurements, Yen et al. observed two dome-shaped phases (LT1, LT2) and additional boundaries in the INT phase [6]. Similar results were obtained by measurements of susceptibility, specific heat, microwave, and ultrasonic velocity [7,8,9]. However, the neutron scattering experiments revealed different phase diagrams in the ranges of 0–5 K and 0–2 T; four boundaries merge into a multicritical point (7 K, 1.4 T) and no LT1 phase was observed [10,11]. On the other hand, the determination of the magnetic structures of these phases is challenging because of the large unit cell and the complexity of this spin system. By optical second harmonic generation (SHG), Fiebig et al. studied the change in symmetry of the Mn³⁺ ions above 5 K [12,13]. However, magnetic symmetries of the LT1, LT2 phases, as well as the magnetic ground state still remain puzzling [2,14]. In addition, the variety of symmetries of the Ho³⁺ ions, which orient along the c-axis, is rarely studied [15]. These controversial results and questions motivate a reinvestigation of the field-induced magnetic transitions and phase diagram of h-HoMnO₃ using other experimental techniques.

Magnetization (M) measurement using a non-destructive pulsed magnet can explore phase transition in a sufficiently high magnetic field. Due to its fast field-sweeping rate (> 1 kT/s) and high-speed (60 MS/s) data collection system, this induction method using a compensated pickup coil is also utilized to detect weak magnetic transition, which is not clearly shown in a steady field. In this work, we measure the magnetization of h-HoMnO₃ in a pulsed-field up to 62 T and explore a new transition at ~41 T for H//c. The pulsed duration is shorter and the sensitivity of the coil is higher. By using a short-pulsed field of ~4 ms and measurement down to ~0.7 K, we reinvestigate the c-axis magnetic transitions and phase diagram below 5 T. Possible magnetic structures and symmetries of the Ho³⁺ ions are proposed for the field-induced magnetic phases. For H//a, two new magnetic transitions are observed below 5 T and the phase diagram is reported.

2. Experimental Details

Single crystals of h-HoMnO₃ were grown by the floating zone method. First, the polycrystalline powder of h-HoMnO₃ was synthesized by the conventional solid-state reaction. Stoichiometric mixtures of Ho₂O₃ and Mn₂O₃ powders were ground and sintered in air at 1120 °C for 24 h. This process was repeated for several times to ensure fully reaction of the starting materials. Then the product was pressed into ~10 cm long rods under a 50 MPa hydrostatic pressure. The rods were sintered at 1120 °C for 20 h and used as feed rod and seed rod. The single crystal growth was then carried out using an optical floating-zone furnace (FZ-T-10000-H, Crystal System Incorporation of Japan). The experimental conditions are almost the same as those in Ref. [16]. The inset of Figure 1b shows the as-grown h-HoMnO₃ single crystal with a diameter of ~7 mm. The crystal was oriented by the X-ray single-crystal diffractometer (XtaLAB mini^TM II, Rigaku, Japan), examined by an X-ray powder diffractometer (XRD, Philips X’pert pro, Japan) as shown in Figure 1b and found to have good quality.

Magnetization measurement was performed in Wuhan National High Magnetic Field Center using a 65 T pulsed magnet. Figure 2a shows the pulsed fields with a discharge voltage of 25 kV driven by different capacitor banks. The pulse duration can be controlled from ~4 ms to 11 ms with peak field changing from 25 to 60 T. In the experiment, two pulse shots with sample-in and sample-out were carried out to subtract the spurious dB/dt signals induced by the pulsed fields. dM/dt signals from the sample were then collected and integrated as a function of magnetic fields. The absolute value of the magnetization was obtained by a comparison with the data measured by a commercial superconducting quantum interference device (SQUID, Quantum Design). He-3 cryogenic system was employed for the measurements down to ~0.7 K.

3. Results and Discussion

Figure 2b shows the magnetization processes of h-HoMnO₃ at 1.4 K and in a pulsed-field up to 5 T. For H//a, the M increases monotonously with a bend in the vicinity of 3 T. From the derivative dM/dH shown in Figure 2d, we distinguish two magnetic transitions at H_c1 = 1 T and H_c2 = 2.5 T. The H_c1 transition was not detected in the previous work [17], probably due to the relatively slow field-sweeping rate. A hysteresis is seen around H_c1, indicating the nature of a first-order transition. For H//c, clear magnetization jumps are seen at ~1 T and ~2.5 T. The dM/dH data in Figure 2e show four successive magnetic transitions at H_c1 = 0.8 T, H_c2 = 1.4 T, H_c3 = 2 T, and H_c4 = 2.4 T, in agreement with the result in Ref. [18]. Because the H_c2 transition is of the first-order type [18], it gives rise to the hysteresis in a pulsed field below 1.5 T. In higher magnetic fields up to 62 T [Figure 2c], the magnetization for H//c shows a change of slope at ~10 T followed by another step-like transition at ~41 T. These two anomalies (H_c5, H_c6) are also visible in dM/dH curves, as shown in Figure 2f. While for H//a, no transition is observed and the magnetization almost saturates above 10 T.

We first study the magnetic transitions for H//a. Figure 3a shows the dM/dH curves from 0.73 to 5 K. It is found that both H_c1 and H_c2 develop well with the temperature and almost disappear at 5 K. The corresponding phase boundaries are shown in the phase diagram of Figure 3b, which was not reported previously. When T is further increased, the two boundaries seem to end at the transition temperature of T_Ho (5.4 K) at H = 0 T because the other two transitions (T_SR and T_N) appear at much higher temperatures of 32.8 and 76 K, respectively. It is known that the Mn³⁺ spins strictly orient in the ab plane, whereas the Ho³⁺ spins are mainly aligned along the c-axis due to a strong uniaxial anisotropy [2,13]. Therefore, we attribute the two transitions in Figure 3a to the magnetic reorientation of the Mn³⁺ spins in applied a-axis fields. As determined by the SHG experiment [13], magnetic symmetries of the two phases above and below T_Ho are P6₃cm (Γ₃) and P6₃cm (Γ₁), respectively. Since no other transition is observed above T_Ho by our magnetization data, the symmetry of the high-field phase should be the same as the high-temperature phase, i.e., P6₃cm. For the middle phase between H_c1 and H_c2, however, the magnetic symmetry is not clear at the moment. Interestingly, we find that the two transition fields are approximate to those of the magnetization jumps for H//c. Whether it is an intermediate phase (P6₃) or not as observed for H//c needs further investigation.

The most important feature of h-HoMnO₃ is the successive magnetic transitions for H//c. We performed comprehensive magnetization measurements at temperatures from 45 down to 0.77 K. The derivative dM/dH data are shown in Figure 4a,b. There is a little difference in the low-temperature region between the data of H-increasing and -decreasing processes. It is ambiguous that the evolutions of H_c1 are opposite and H_c2 is almost invisible in the decreasing field. At temperatures above 6 K, the dM/dH curve shows a plateau, which moves firstly to the high field and then to the low field, as indicated by the dashed lines. From the dM/dH anomalies, we summarize the H-T phase diagram of H//c in Figure 4c. At a first glance, a dome-shaped phase (P6₃cm) below 43 K and an intermediate phase (P6₃) in a higher field are demonstrated, which are consistent with all early results [5,6,7,8,9,10,11,12]. Note that the phase boundary at 5 K and 0–1 T is not observed in this study. The reason is that this boundary is nearly temperature independent and thus insensitive to our measurement. Upon a close inspection on the low-T region, it looks different from those reported in Refs. [6,7,8,9], but similar to the result derived from the neutron scattering experiment [10,11]. Below 5 K, three phases labeled as I, II, and III appear between H_c1 and H_c4. The puzzling LT1 and LT2 phases determined by a dielectric constant are not observed in our data. Besides, the dielectric constant and susceptibility measurements revealed that H_c3 and H_c4 merged into one multicritical point at 1.4 K [2,7]. However, these two transitions, associated with a critical endpoint at 2.05 T and 2.2 K [18], can be distinguished in our data even down to 0.77 K. Another interesting finding in Figure 4c is the evolution of the H_c3 transition. From the neutron scattering data, Vajk et al. proposed a boundary extending H_c3 to a multicritical point at 7 K and 1.4 T [10,11]. However, this transition seems to end at 3.5 K and 2.5 T, where a first-order transition appears and separates phases II and III from the intermediate phase. It is noteworthy that similar hysteresis effect was observed in the same area by the dielectric constant measurement [6].

To understand the H//c phase diagram, the role of the Ho³⁺ spins and their interaction with the Mn³⁺ spins should be considered. In a zero field, the Ho³⁺ spins undergo a change of magnetic symmetry from P6₃cm to P6₃cm (Γ₄→Γ₃) at T_SR and then another change from P6₃cm to P6₃cm (Γ₃→Γ₁) at T_Ho [10,15]. While following neutron experiment did not find a transition at T_Ho arising from the Ho³⁺ orderings [14]. For P6₃cm, all the Ho³⁺ spins are ordered along the c-axis. Due to a strong uniaxial anisotropy, it is hard to align the Ho³⁺ spins along the a-axis by magnetic fields. However, as shown in Figure 2c, the magnetic moment for H//a quickly reaches ~9 μ_B/f.u. at 5 T, much larger than the saturation moment (4.9 μ_B) of the Mn³⁺ spins. In the case of P6₃cm, the Ho³⁺ spins are disordered and may contribute to a rapid increase in the a-axis magnetization, in agreement with our magnetization data. In Figure 2c, the magnetic moment for H//c is smaller than that for H//a. This is because the Mn³⁺ spins lying in the ab plane do not contribute much to the c-axis magnetization. For H//c, the H_c3 and H_c4 transitions are accompanied by a large magnetization jump, see Figure 2b. By extrapolating the magnetization data above H_c4 to zero fields, the magnetic moment at 0 T is ~3.1 μ_B, which is nearly 1/3 of the effective moment of Ho³⁺ (10.4 μ_B). Given the four allowed symmetries (Γ₁–Γ₄) of Ho³⁺, only Γ₂ (P6₃cm) can realize, such a ferrimagnetic phase. This scenario is similar to the 1/3-magnetization plateau phase in the analog h-RMnO₃ (R = Er, Yb) [19]. Based on the above analysis, the variety of Ho³⁺ spin structures in applied fields is proposed in Figure 5. The H_c5 transition is characterized by other techniques, such as thermal conductivity [17]. A flip of the Ho³⁺ 2a spins at H_c6 coincides with a step-like transition at ~41 T. The reorientation of spins around H_c6 is not continuous, while it will be continuous above this transition in a higher field. The magnetic structures of phase I–III in Figure 4c remain unclear, which are likely a result of the rotation of the Mn³⁺ spins triggered by a mutual induction of the Ho³⁺ and Mn³⁺ moments [18].

4. Summary

Large-sized h-HoMnO₃ single crystals were grown by the optical floating zone method. Magnetization measurements up to 62 T show six magnetic transitions for H//c and two magnetic transitions for H//a. By measurements down to ~0.7 K, we construct the phase diagrams of h-HoMnO₃ for H//a and H//c, respectively. The variety of the magnetic symmetry of these field-induced phases is also discussed. The obtained phase diagram for H//c is very complex, which makes new insight into those results reported previously.