The effects of high magnetic fields applied perpendicular to the spontaneous ferroelectric polarization on single crystals of BiFeO3 were investigated through magnetization, magnetostriction, and neutron diffraction measurements. The magnetostriction measurements revealed lattice distortion of 2 × 10 −5 , during the reorientation process of the cycloidal spin order by applied magnetic fields. Furthermore, anomalous changes in magnetostriction and electric polarization at a larger field demonstrate an intermediate phase between cycloidal and canted antiferromagnetic states, where a large magnetoelectric effect was observed. Neutron diffraction measurements clarified that incommensurate spin modulation along [110] Recently, multiferroic materials have been widely investigated due to their coupling between magnetic and ferroelectric ordering. BiFeO 3 is perhaps the most extensively studied multiferroic material as it possesses robust multiferroicity at room temperature as well as various possible applications [1][2][3][4][5][6][7][8][9][10]. The effects of magnetic fields on the coupled multiple degrees of freedom behind these phenomena are not fully understood.BiFeO 3 exhibits a cycloidal magnetic order below 640 K [11]. This state is known to exhibit marginal quadratic magnetoelectric (ME) effect at low magnetic fields [12]. High magnetic fields of ∼20 T stabilize the canted antiferromagnetic (CAFM) phase as opposed to the cycloidal phase [13][14][15][16][17]. Although several groups succeeded in realizing the CAFM phase at zero field [18][19][20][21][22][23], the ME effect in this phase has not been clarified. In this study, several features were observed when a magnetic field was applied normal to the trigonal c-axis, and they indicated that a third magnetic phase emerged in bulk BiFeO 3 between the cycloidal and CAFM phases at approximately room temperature.BiFeO 3 has a crystal structure with the polar space group of R3c. A large switchable spontaneous electric polarization emerges along the c-axis of the trigonal cell [24][25][26]. Degeneracy exists in selecting the polarization direction from eight 111 directions in the cubic unit. Hence, depending on synthesis methods, BiFeO 3 crystals can contain multiple ferroelectric domains [27].Magnetic domains can be present even in single ferroelectric domain crystals. The magnetic propagation vector Q points in one of the 110 directions of the trigonal cell [11] in the cycloidal spin ordered state below ∼640 K. The three-fold rotational symmetry around the c-axis (Z direction in this paper) leads to three equivalent Q i (i = 1, 2, 3), as shown in Fig. 1(d). The spins rotated primarily in the Q i -Z plane in a magnetic domain with a given Q i .Recently, Tokunaga et al. indicated the emergence of an electric polarization perpendicular to the Z direction that was controlled by magnetic fields [17]. Theoretical calculations suggested that the cycloidal spin order in BiFeO 3 could involve electric polarization perpendicular to the Q i -Z plane as illustrated as P T in...