Magnetisation

The magnetisation data for TbMnO3 has been previously published [7, 28, 31],

and was repeated as part of this project in order to look for any new features for the single crystal samples grown at the University of Warwick, and to test the reproducibility of the data in advance of work on new multiferroic compounds. The magnetisation of TbMnO3 was measured using a vibrating sample magnetometer

(VSM) along the three principal crystallographic directions (Figure3.7). The data presented below are in very good agreement with those published by Kimura et al. [31].

As with the magnetic susceptibility temperature profiles, the magnetisation as a function of applied magnetic field shows large anisotropy. The a-axis is clearly the “easy” magnetic axis, with a field of approximately 2 T causing a near- saturation of the signal at 2 K and 1.45 K (Figure 3.8(a)). The magnetisation

Chapter 3. Magnetoelectric properties of TbMnO3 and DyMnO3

Figure 3.6: (a) Magnetic DC susceptibility and (b) inverse susceptibility for polycrys- talline TbMnO3, and an average of the data along thea-, b- and c-axes. Measured in

an applied magnetic field of 0.5 T

unit at 10 T for temperatures of 12 K and below. A small amount of hysteresis is seen upon returning the applied field to zero in this direction. Kimura et al. proposed that the saturation with H//a was linked to the Tb moments [31], as discussed further below.

T

Figure 3.7: Magnetisation of a single crystal of TbMnO3 versus applied magnetic field

along the principal crystallographic axes, taken at 1.45 K

The most interesting magnetic behaviour occurs when a magnetic field is ap- plied along the b-axis (Figure 3.8(b)), with 2 distinct metamagnetic transitions seen below 9 K. The metamagnetic transitions forH//aandH//bwere described by Kimura et al. by analogy with TbFeO3 [31]. It was proposed that the Tb

moments lie in along two Ising axes in the a-b plane, as shown in Figure 3.9. The application of a magnetic field parallel to the a-axis causes the moments la- belled 1 and 2 to change direction in a one-step process, resulting in the observed large increase in magnetisation (Figure 3.9(a)). A different situation occurs when a magnetic field is applied parallel to the b-axis, with a two-step spin reversal (Figure3.9(b)). The metamagnetic transition of the Tb moments withH//b∼5 T coincides with a change in the orientation of the Mn moments from ab-ccycloid to

Chapter 3. Magnetoelectric properties of TbMnO3 and DyMnO3

(a)

(b)

(c)

Figure 3.8: Magnetisation of a single crystal of TbMnO3 versus applied magnetic field

along the (a)a-, (b) b-, (c)c-axis.

a b 3 1 2 4 H = 0 a b 2,3 1,4 H_a > 2 T a b 3 1 2 4 H = 0 a b 3 2 1,4 2 T < H_b < 5 T a b 2,3 1,4 H_b > 5 T

(a)

(b)

Figure 3.9: Tb moment configuration in TbMnO3, showing spin reversal under a mag-

netic field applied along (a) the a-axis, and (b) the b-axis. Magnetic field values given correspond to measurements taken at 1.45 K. Adapted from Kimura et al.[31]

thought to order at ∼8 K, which seems to be reflected by the rapid smearing out of the metamagnetic transitions withH//b above this temperature. However, there are still transitions visible in this configuration up to 20 K. It has now been confirmed that the Tb moments also order along the b-axis at the Mn cycloidal transition temperature ∼27 K [40, 41], which is a possible explanation for this behaviour.

From Equation 2.7, the expected saturation magnetisation of the Tb3+ _ions

was calculated as 9 µB. It is known that the behaviour of the Tb moments and the Mn moments are strongly coupled, with Aliouane et al. confirming that the application of a magnetic field parallel to theb-axis results in a change in the orientation of the Mn cycloid from theb-cplane to thea-bplane [36]. It is possible that a similar coupling is found for H//a, and the plateau in the magnetisation is at a value lower than the saturation magnetisation of the Tb3+ _{moments due to}

some antiparallel arrangement of the Mn magnetic sublattice.

The features in the magnetisation with H//b are more pronounced with lower temperature, with the low field transition disappearing above 5 K, and the tran- sition at ∼5 T becoming smeared out and shifted toward higher magnetic field with increasing temperature. Less hysteresis is also seen at higher temperatures.

Chapter 3. Magnetoelectric properties of TbMnO3 and DyMnO3

the additional ordering of the Tb moments at∼7 K. No data appear to have been published confirming the exact nature of the low temperature magnetic order of the Tb moments in TbMnO3, with reports usually focusing on the ferroelectricity-

inducing Mn order.

The c-axis of TbMnO3 is the “hard” magnetic axis, with magnetisation of no

more than 1.2 µB/formula unit found for magnetic fields of 12 T in temperatures

up to 20 K (Figure 3.8(c)). The small magnetisation along this axis agrees with the susceptibility data shown in3.2. A magnetic transition develops at 11 T when the sample temperature is 5 K, with a large amount of hysteresis seen (the width of the loop being greater than 5 T). This behaviour was proposed by Kimura et al. as being due to a magnetic transition of the Mn moments to a canted antiferromagnetic (paraelectric) state [31].