## Fluctuation-Induced First-Order Transition and Tricritical Point in a Cubic Chiral Magnet EuPtSi

#### Sakakibara Group

The cubic chiral compound EuPtSi (space group *P*2_{1}3) helimagneitcally orders at *T*_{N}=4.0 K with the propagation vector *q*_{1}^{*}=(0.2, 0.3, 0.04). There has been growing interest in this compound because a skyrmion lattice phase with a triple-*q* structure emerges in a magnetic field applied along the [111] direction [1,2]. One of the intriguing features of this compound is that the transition at *T*_{N} is of first order [1-3]. We studied the helimagnetic transition on a single crystal of EuPtSi by means of high-precision magnetization measurements, and found that the transition, which is of first order at low fields, becomes of second order at high fields, and there exists a tricritical point (TCP) in the phase diagram [4].

Figure 1 shows the temperature derivative of the magnetization, *dM*/*dT*, in magnetic fields *H* applied along the [110] direction. At *H* = 1.8 kOe, the first-order transition (FOT) is characterized by a sharp peak in *dM*/*dT* at *T* = 4.0 K. By increasing *H*, *T*_{N}(*H*) defined by the peak position in *dM*/*dT* moves to the lower temperature side with a decrease in the peak amplitude. Above *H* = 8.8 kOe, the shape of *dM*/*dT* dramatically changes and excibits a step function like jump at *T*_{N}(*H*), implying that the transition becomes of second order above 8.8 kOe.

In order to construct the phase boundary between the paramagnetic and the ordered states, we show in Fig. 2 the color contour mapping of the *dM*/*dT* data for *H*||[110]. The bright line in the low-field region indicates the FOT boundary, and the dashed line in the high-field region denotes the second-order one. In between there is a TCP as indicated in the figure. A similar crossover of the transition has also been observed for [111] and [100] directions [4].

In systems described by order parameters with *n*>4 components, a usual second-order phase transition is avoided due to interactions among critical fluctuations of the order parameters [5]. FOT then takes place when the correlation length exceeds a certain limit, where a discontinuous phase transition occurs to a state energetically favorable. This fluctuation-induced FOT takes place even for systems in which the mean-field theory predicts second-order phase transitions, and the actual transition temperature is suppressed much below the mean-field transition temperature. In EuPtSi, the lattice-symmetry operations on *q*_{1}^{*} yields 12 distinct propagation vectors, which is large enough in number to drive the transition to be first order. Applying a magnetic field reduces the symmetry of the system, and the number of components of the order parameter is effectively decreased, leading to a second-order phase transition. The presence of TCP in the phase diagram in Fig. 2 supports this scenario of a fluctuation-induced FOT in EuPtSi. This situation is favorable for the occurrence of multi-*q* orders such as the skyrmion lattice phase, since they need to be stabilized against a single-*q* helical (or a conical) phase.

##### References

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*et al*., J. Phys. Soc. Jpn.**88**, 093701 (2019). - [5] P. Bak, S. Krinsky and D. Mukamel, Phys. Rev. Lett.
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