Field-dependent AC susceptibility of itinerant ferromagnets

Whereas dc measurements of magnetic susceptibility, χ, fail to distinguish between local and weak itinerant ferromagnets, radio-frequency (rf) measurements of χ in the ferromagnetic state show dramatic differences between the two. We present sensitive tunnel-diode resonator measurements of χ in the weak itinerant ferromagnet ZrZn2 at a frequency of 23 MHz. Below Curie temperature, TC ≈ 26 K, the susceptibility is seen to increase and pass through a broad maximum at approximately 15 K in zero applied dc magnetic field. Application of a magnetic field reduces the amplitude of the maximum and shifts it to lower temperatures. The existence and evolution this maximum with applied field is not predicted by either the Stoner or self-consistent renormalized (SCR) spin fluctuations theories. For temperatures below TC both theories derive a zero-field limit expression for χ. We propose a semi-phenomenological model that considers the effect of the internal field from the polarized fraction of the conduction band on the remaining, unpolarized conduction band electrons. The developed model accurate describes the experimental data. PACS numbers: 75.40.Gb, 75.50.Cc, 75.30.Cr Submitted to: J. Phys.: Condens. Matter Field-dependent AC susceptibility of itinerant ferromagnets 2 DC measurements of magnetic susceptibility fail to distinguish between local and itinerant ferromagnets. A common method of determining χdc is measuring the magnetic moment and then dividing by the applied field, H . However, this is only applicable provided the magnetization is linear in H from H = 0 up to the measurement field. For magnetically soft or small moment ferromagnets, this criterion may not be satisfied. Perhaps a more careful method is to measure M in two slightly different magnetic fields and then calculate ∆M/∆H as shown in Fig. 1. Further, due to limited sensitivity, DC measurements are usually conducted in significant magnetic fields, on the order of 1-10 Oe. In exceptionally soft materials these fields may be sufficient to smear certain zero-field features. In itinerant systems the situation is even more complicated. In order to deduce the size of a magnetic moment per ion, one has to be in a saturation regime by applying a large field. However, this tells nothing about the magnitude of this moment in zero field that, in itinerant systems, is field dependent. Yet, even with a conventional definition, observation of a magnetic moment that is a fraction of a Bohr magneton per ion is not bulletproof evidence for the itinerant nature of magnetism. For example, the localmoment metallic rare-earth compound CeAgSb2 [1] and the insulating titinate YTiO3 [2] both possess a fractional magnetic moment per ion. Possible explanations of such fractional local moments could be a canted antiferromagnetic structure as may occur in YTiO3 [3], or crystalline electric field effects as has been proposed for CeAgSb2 [4]. Unlike dc measurements, ac susceptibility can be measured in much lower magnetic fields. It became a valuable technique in studying magnetic materials. However, interpretation of the results, especially in itinerant systems is complicated. For example, low frequency ac susceptibility measurements on the insulating two dimensional ferromagnet K2CuF4 [5] is strikingly similar to that measured in palladium slightly doped with manganese [6] as well as in an Fe-Ni-B-Si alloy [7]. While it is clear that the insulating compound is a local moment, the nature of the latter two is open to debate. It is suggested in these works that the similarities in the data is due to a combination of demagnetization effects and domain wall motion. In this contribution we report radio frequency temperature dependent ac susceptibility of the well-studied commonly accepted itinerant ferromagnet ZrZn2, and examine its evolution with an applied magnetic field. We then present a semiphenomenological model that describes our data. Low frequency ac susceptibility measurements on ZrZn2 have been reported [8], however, as the focus of that work was not the ferromagnetism of the compound, the only presented data is for T < 2 K. Recently, it has been shown [9] [10] that rf measurements of ac magnetic susceptibility, χac, seem to distinguish between local moment and itinerant ferromagnetism. Further, in Ref. [9] an explanation ruling out the demagnetzation or magnetic domains effects was presented. It is clear from Fig. 2 that the rf susceptibility of the weak itinerant ferromagnet ZrZn2 [11] is distinctly different from that of the 4f local moment CeAgSb2 [1]. The purpose of this work is to present an effective Weiss-type model to describe the data derived from itinerant ferromagnets. Field-dependent AC susceptibility of itinerant ferromagnets 3 The design and operation of a tunnel-diode resonator (TDR) are described in detail elsewhere [12] [13] [14]. The device is built around a tunnel diode, a semiconducting device with a voltage bias region of negative differential resistance. Biasing to this voltage region allows the tunnel diode to drive an LC tank circuit at its natural resonant frequency. In magnetic measurements, a sample is placed in the coil of the tank circuit thereby changing the total inductance, and, hence, the tank circuit’s resonant frequency. It can be shown [15] that the frequency shift of the tank circuit is directly proportional to the magnetic susceptibility, χ, of the sample in the coil as ∆f f0 ≈ − 1 2 Vs Vc 4πχm. (1) Here Vs and Vc are the volumes of the sample and coil, respectively, and χm is the measured susceptibility of the sample. Careful design and construction allows one to resolve changes in resonant frequency induced by the sample on the order of 1-10 mHz. The resulting tuned circuit, operating at 10-20 MHz, gives frequency sensitivity on the order of a few parts per billion. This translates to a typical sensitivity of 10 − 10 change in χ induced by temperature or magnetic field. Due to the operating frequency the measured susceptibility is composed of two parts. The first is due to the magnetic moments in the sample, and may be either paraor diamagnetic depending on the material studied. The second is due to the screening of an rf field via the normal skin effect in metals. This screening is a diamagnetic contribution and is a measure of changes in resistivity [16]. Radio frequency susceptibility data presented herein were collected in a TDR operating at 23 MHz mounted in a He cryostat. The design is similar to that presented in Ref. [9]. The temperature of the sample can be varied from 3 to 100 K and a dc magnetic field up to 2.5 T coaxial with the rf excitation field (∼ 20 mOe) can be applied with a superconducting magnet. The magnet is mounted inside the vacuum can of the cryostat resulting in no trapped magnetic field at the beginning of each run. As the effects studied herein are completely suppressed by fields on the order of 500 Oe, any such trapped magnetic field could affect the data. Single crystal samples were used in this study. The CeAgSb2 sample was prepared as described in Ref. [1], while the ZrZn2 sample was prepared as described in Ref. [17]. Figure 1 compares temperature dependent dc susceptibility for the local moment CeAgSb2 with that for the itinerant ZrZn2 as measured in a Quantum Design MPMS5. Two different techniques were used to determine these susceptibilities. Panel (a) shows the usual χdc where the magnetic moment is measured in a small applied field (H = 20 Oe) andM/H is calculated. While this method is appropriate for temperatures well above TC where magnetization is linearly dependent on field over a fairly large field range, it should be expected to fail in the ferromagnetic state because M is not necessarily linear in H all the way down to H = 0. Bearing this in mind, a delta measurement of χdc was performed (results in panel (b)) as follows. Magnetic moment versus temperature was measured first in a 17 Oe field and then in a 22 Oe field. The difference in the resulting moment was divided by the 5 Oe difference in applied fields to Field-dependent AC susceptibility of itinerant ferromagnets 4